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OPTIC A APPLICATA

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EDITOR IN CHIEF

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TOPICAL EDITORS

I<RzYSZTOF ABRAMSKI, Wroclaw University of Technology, Poland

TADEUSZ PUSTELNY, Silesian University of Technology, Gliwice, Poland

TOMASZ SZOPLIK, Warsaw University, Poland

HENRY!< KASPRZAK, Wroclaw University of Technology, Poland

EwA WEJNERT-R.J\CZKA, Szczecin University of Technology, Poland

INTERNATIONAL ADVISORY BOARD

The quarterly of the Institute of Physics Wroclaw University of Technology, Poland

PL lSSN 0078-5466 Index 367729

MIRON GAJ

WACLAW URBANCZYK

AGNIESZKA POPIOLEK-MASAJADA

Fiber ·optics and optical communication, spectroscopy, lasers and their applications

Integrated optics, acoustooptics, microoptics, optical instrumentation, optical measurements, optical sensing

Nanooptics, plasmonics, optical imaging, optical computing, optical data storage and processing

Holography, diffraction and gratings, biooptics, medical optics, optometry, optical imaging, Fourier optics

Nonlinear optics, optical waveguides, photonic crystals

OLEG V. ANGELSKY, Chernivtsy University, Ukraine Y ASUHIKO ARAKA WA, The University of Tokyo , Japan IV AN GLESK, University of Strathclyde, UK CHRJSTOPHE GORECKI, FEMTO-ST, Besan{:on, France EUGENIUSZ JAGOSZEWSKI (Chairman), Wroclaw University of Technology, Poland ROMUALD JOZwiCKI, Warsaw University of Technology, Poland FRANCISZEK KACZMAREK, Adam Mickiewicz University, Poznan, Poland BOLESLA w ~DZIA, Poznan University of Medical Sciences, Poland MALGORZATA KUJA WINSKA, Warsaw University of Technology, Poland NoRBERT LJNDLEIN, University of Erlangen - Niirnberg, Germany MIROSLAV MILER, Institute of Photonics and Electronics of the ASCR, v. v.i., Prague, Czech Republic JAN MISIEWICZ, Wroclaw University of Technology, Poland WWDZIMIERZ NAKWASKI, Technical University ofL6di, Poland WoLFGANG OSTEN, Universitiit Stuttgart, Germany JAN PERJNA, Palack); University, Olomouc, Czech Republic BARBARA PIERSCIONEK, University of Ulster, UK COLIN SHEPPARD, National University of Singapore CoNCITA SIBILIA, Universita di Roma "La Sapienza ", Italy TADEUSZ ST ACEWICZ, University of Warsaw, Poland ToMASZ WOLINSKI, Warsaw University of Technology, Poland JAN WOJCIK, Maria Curie-Skiodowska University in Lublin, Poland PAVEL ZEMANEK, Institute of Scientific Instruments of the ASCR, v. v.i., Brno, Czech Republic

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- KAT ARZYNA SZTYLINSKA

- HALINA MARCINIAK

-Institute ofPhysics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland

- Wroclaw University of Technology, Wybrzeze Wyspiailskiego 27, 50-370 Wroclaw, Poland [email protected] www.if.pwr.wroc.plroptappl tel. 48 71-320-23-93 fax 48 71-328-36-96

Optica App/icata has been published since 1971 in a non-periodical form. Starting from 1973 it is published quarterly.

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Review of matter

Diffraction theory and its application, quantum optics, problems in radiation coherence, light sources, holography and its application, scientific photography, methods of image reconstruction, optical application of Fourier transform, theory of optical systems, criteria of optical image evaluation, optical materials, technology of manufacturing optical elements, aspheric optics, optical properties of solids and thin films, lasers and their application, photo- and radiometry, problems in spectroscopy, nonlinear optics, optical data processing, optical measurements, fibre optics, optical instrumentation, interferometry, microscopy, non-visible optics, automation of optical computing, optoelectronics, colorimetry, optical detectors, ellipsometry and photoelasticity, optical modulation, optics of electron beams, biooptics, optometry.

Article and issue photocopies of this journal are available through University Microfilms International, 300 North Zeeb Road, Ann Arbor, Michigan 48106-1346, USA.

© Copyright by Oficyna Wydawnicza Politechniki WrocJawskiej, WrocJaw 2012

Drukamia Oficyny Wydawniczej Politechniki Wroclawskiej Zam. nr 482/2012.

OPTICA APPLICATA

Contents

Optical measurements

Vol. XLII (2012) No. 1

Multispectral polarized BRDF: design of a highly resolved rejlectometer and development of a data inversion method N. R..iYIERE, R. CEOLATO, L. HESPEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Interference effect in a dual microresonator-coupled Mach- Zehnder interferometer YING L u, XIAOHUI HUANG, XIANGYONG Fu, WuQI WEN, JIANQUAN YAo . . . . . . . . . . • . . . . . 23

An on-line phase measuring projilometry based on modulation Wu YINGCHUN, CAo YIPING, Lu MINGTENG, LI KUN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Novel method to determine laser scanner accuracy for applications in civil engineering H. GONZALEZ-JORGE, M. SOLLA, J. ARMESTO, P . ARJAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Optical amplifiers

Small-signal circuit modeling for a semiconductor optical amplifier monolithically integrated with a sampled grating distributed Bragg reflector laser HUI Lv, ZIQIANG LI, TAo YANG, CHUYUN HuANG. . .... . . ... .. . . ..... ... .. .. .. . .. . . 55

Optical components

Polarization-independent two-port beam splitter grating under second Bragg incidence angle with usual duty cycle B. WANG . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . • . . . . . . . . . . . . . . . . . . • • . . . . . . . . 69

Optical fibers

Near infrared transmission in dual core lead silicate photonic crystal fibres H.T. BOOKEY, R. BUCZYNSK.l, A. WISCHNEWSK.l, D. P YSZ, R. KASZTELANIC, A .J. WADDlE,

R. Sn; PIEN, A.K. KAR, M.R. TAGHIZADEH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Optical focusing

Conditions for tighter focusing and higher focal depth ofradially polarized vector beam X. GAo, Q. WANG, M. YUN, J. Yu, H. Guo, S . ZHUANG ..... .. . . .. ........ ....... .. . 85

Nonlinear optics

The transmission characteristics under the influence of the fifth-order nonlinearity management XIUJUN HE, KANG XJE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 03

4

Integrated optics

A 2-bit polymer waveguide delay device using right-angle X junctions YUNJI Y1 , Q1 W ANG, PENGCH ENG ZHAO, fEI W ANG, DAMI NG ZHA NG

Research and fabrication of integrated optical chip of Mach- Zehnder microinterference accelerometer

Ill

T ANG D ONG-LIN, D AI BING, H E SHAN, X IAO K UN-QlNG, ZHANG L IANG, WANG P ENG . . . . . • . . 12 1

Nonlinear materials

Influence of gamma radiation on the second-order optical susceptibilities and piezoelectricity of the Rb J-xKxTiOPO 4 single ctystals R. MI EDZINSKI, I. FUKS-JANCZAREK, A. MAJCHROWSKI, L.R. JAROSZEWICZ . . . . . • . . . . . . . . • . 129

Image processing

Human optic sensitivity computation based on singular value decomposition S.A. AMIRSHAH I, F . T ORKAMANI-AZAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . • . . . 13 7

Laser processing

Modelling of reproduction process fo r power laser radiation 1. 0WSIK, A.A. LIBERMAN, A.A. K OVALEV, S .A. M OSKALUK

Free space communication

An analytical model of the power spatial distribution for underwater optical wireless communication

147

W EI W EI, ZHANG XIAO-H UI, CHAO YuE-YUN, ZHou XuE- JUN . . . • . . . . . . . . • . . . . . . . . . . • . . 157

Liquid crystals

High birefringence liquid crystal mixtures for electro-optical devices E. NOWINOWSKI-KRUSZELNlCKI, J . K.l;DZIERSKI, Z . RASZEWSKI, L. JAROSZEWJCZ, R. D ABROWSKI,

M . K OJDECKI , W . PIECEK, P . P ERKOWSKI, K . G ARBAT, M . OLIFIERCZUK, M . S UTKOWSKI,

K. O GRODNIK, P . M ORAWIAK, E . MISZCZYK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Thin films

Direct determination of the refraction index normal dispersion for thin fi lms of 3, 4, 9, 10-perylene tetracarboxylic dianhydride (PTCDA) J . CISOWSKI, B. J ARZf\BEK, J . J URUS IK, M . D OMANSK.l . . . . . . . . . . . . . . . . . . . . . . . . • • • . . . . . 181

Waveguides

Theoretical study of slab waveguide optical sensor with left-handed material as a core layer S .A. T AYA, T .M . EL-AGEZ, H .M . KULLAB, M .M . ABADLA, M.M. SHABAT . . . . . . . . . . . . . . . 193

Holography

Pholoinduced anisolropy and polarizalion holography on UV exposure in films of N-benzylideneaniline in PMMA malrix

5

0. I LI EVA, L. N EDELCHEY . . . . . . . . . . . . . . . . . . . . . • . . . . . . . • • . . . . . . . . . . . . . . . . . • . . . 207

Interferometry

Wavele!/ransform me/hod ofphase-slep determinalion Y EU- JENT Hu, JIN- Y1 SHEU, JIUNN-CHYI LEE, YA-FEN Wu

Magnetic resonance imaging

Me/as/ability exchange oplical pumping low field polarizer for lung magnetic resonance imaging G. COLLIER, M . SUCHANEK, A. WOJNA, K . C IESLAR, T. P ALASZ, B. GLOWACZ, Z. O LEJNICZAK,

2 15

T. D OHNALIK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Optica Applicata, Vol. XLII, No. 1, 2012DOI: 10.5277/oa120101

Multispectral polarized BRDF: design of a highly resolved reflectometer and development of a data inversion method

NICOLAS RIVIERE*, ROMAIN CEOLATO, LAURENT HESPEL

Onera – The French Aerospace Lab, F-31055, Toulouse, France

*Corresponding author: [email protected]

Multispectral and polarized light reflectance measurements are very useful to characterizematerials such as paint coatings. This article presents an overview of an automated high-angularresolved, in-plane multispectral polarized reflectometer and its calibration process. A compre-hensive study based on multispectral BRDF and DOLP measurements is conducted on differentcolour and glossy aspects of paint coatings. An original inverse method from in-planemeasurements is used to model the out-of-plane BRDF and to investigate the role of the surfaceand subsurface scattering phenomena in its components.

Keywords: bidirectional reflectance distribution function (BRDF), degree of linear polarization (DOLP),multispectral, polarization, light scattering, paint coatings, inverse method, optimization.

1. IntroductionOptical characterization of materials is particularly needed in different activitiesranging from aerospace or automobile industry (quality control, roughness measure-ments, etc.) to remote-sensing (instrument calibration, target reflectance, etc.)including defence or security applications (laser imaging, guidance, etc.) Bidirectionalreflectance of materials is a useful way to probe physical properties of materials. Mostof them are considered as ideal Lambertian reflectors that scatter light uniformly inspace. However, this approximation does not stand for man-made materials (ceramics,composites, plastic compounds or paint coatings). They require accurate measure-ments of the bidirectional reflectance distribution function (BRDF) to quantify howlight is angularly and spectrally reflected by a material surface. From polarized BRDF,one can also determine degree of linear polarization (DOLP) to quantify and inspecthow surface reflection affect light polarization states. Both BRDF and DOLP givea good insight and a better understanding of the scattering processes involved.

Different instruments are designed to measure the BRDF of samples. Some arededicated only to measure the light backscattered by the media [1–4]. Others are usedto estimate the light reflected and/or transmitted [5, 6]. A few of them are to measure

8 N. RIVIERE et al.

polarized BRDF at fixed wavelength, and they often take into account an angularresolution of the BRDF ranging from 2° to 10° [7–9].

The purpose of this paper is to report the calibration process of a fast and highlyresolved instrument dedicated to measure the in-plane multispectral polarized BRDFand DOLP. An original multispectral method based on the inversion of experimentalin-plane BRDF data was developed to retrieve the full BRDF. Then, we present BRDFand DOLP measurements on paint coatings to illustrate the capacity of our instrumentand our inversion method. Using this approach, we separate the different scatteringprocesses involved from multispectral and polarized measurements and can retrievethe full BRDF from in-plane BRDF measurements.

2. Theoretical framework

2.1. Bidirectional reflectance distribution function (BRDF)Materials reflect light in a certain way according to the incident light direction andviewing angles. A comprehensive way to characterize the reflectance properties ofthe scattering media is to evaluate its full BRDF. It fully characterizes the local lightscattering by the material for every set of angles. Figure 1 shows the geometry usedto define the full BRDF in a three-dimensional standard Cartesian coordinate system.

The BRDF is a non-integrated parameter defined by NICODEMUS [10] as:

[sr–1] (1)

where, for a particular wavelength: dLr (θi, φi; θr, φr; λ) is the differential reflectedradiance in the direction Ωr = (θ r, φ r); dEi(θi, φi; λ) is the differential incidentirradiance from direction Ω i = (θ i, φ i).

Fig. 1. Definition of the BRDF in a three-dimensional Cartesian coordinate system.

E

z

θi

Lr

y

x

θr

φi

φr

→

→

BRDF θi φi θr φr λ;,;,( )dLr θi φi θr φr λ;,;,( )

dEi θi φi λ;,( )-------------------------------------------------------=

Multispectral polarized BRDF... 9

We distinguish the in-plane BRDF as BRDF(θi, φi; θr, φr = φi; λ) from the out-of--plane BRDF defined as BRDF(θi, φi; θr, φr ≠ φi; λ). The Lambert law inducesa cosine factor in radiance measurements. For this reason, we choose to useBRDFcos(θi, φi; θr, φr; λ) = BRDF(θi, φi; θr, φr; λ)cos(θr).

2.2. Directional hemispheric reflectance (DHR)

Directional hemispheric reflectance (DHR) is an integrated parameter calculated asa ratio of the total reflected energy to the total incident energy from a given direction.Also, it can be computed by integrating the BRDF over the half-space [11] as:

(2)

2.3. Degree of linear polarization

BRDF definition can be extended to a polarized-BRDF k, j to determine DOLP fromcross-polarized BRDF k, j:

(3)

(4)

where: is the measured radiance with k, j referring to the polarization states(P: parallel, S: perpendicular, U: unpolarized) of the incident and detected light,respectively.

3. Numerical model and data inversionThe BRDF of materials can be represented by mathematical models. DifferentBRDF semi-empirical models were developed for various applications: deterministic(fully based on electromagnetism without data) [12, 13], physical (data interpolationusing physical parameters) [14–16] and empirical models (data interpolation usingnon-physical parameters) [17]. In this paper, the Li–Torrance model [16] is adaptedto our experimental data for multispectral BRDF inversion.

3.1. Li–Torrance BRDF model

The light scattered from a material can be divided into two parts: surface scatteringreferring to light scattered at the material surface and subsurface scattering referring

DHR θi φi λ;,( ) BRDF θi φi θr φr λ;,;,( ) θr( ) θr( ) dθr dφrsincos0

π 2⁄

∫0

2π

∫=

BRDFk j, θi φi θr φr λ;,;,( )Lr

k j, θi φi θr φr λ;,;,( )

Eik θi φi λ;,( )

-------------------------------------------------------=

DOLP θi φi θr φr λ;,;,( )BRDFP P, θi φi θr φr λ;,;,( ) BRDFP S, θi φi θr φr λ;,;,( )–

BRDFP U, θi φi θr φr λ;,;,( )-----------------------------------------------------------------------------------------------------------------------------------------=

Lrk j,

10 N. RIVIERE et al.

to light scattered within the material (Fig. 2). Both scattering phenomena result fromsingle and multiple scattering. Furthermore, one should consider the complex opticalindex m of the scattering media as m = n + iκ, where n and κ are respectively the realand the imaginary parts of the complex optical index. Absorption phenomena resultin κ ≠ 0.

On the one hand, surface scattering is composed of:– a surface directional (or mirror-like) part due to surface reflection. It is related

to Fresnel coefficients and to the surface roughness;– a surface diffuse (or self-shadowing) part due to multiple scattering by the micro-

facets. On the other hand, subsurface scattering is also composed of:– a subsurface directional part from the base contribution;– a subsurface diffuse part resulting from multiple scattering inside the material.Depending on the type of materials, one needs to quantify the contribution of

light scattering part in order to apply BRDF model such as Li–Torrance model [18].In the following, we applied the Li–Torrance model extended to our multispectralmeasurements to investigate scattering phenomena involved in BRDF. This modelincorporates all of the physical phenomena appearing in the He–Torrance model [13]and is described by only 4 k-parameters:

(5)

where: kdd is related to the Fresnel coefficients and the roughness of the surface. Itcontributes to the directional reflection (mirror-like) component and to the first surfacedirectional-diffuse component. kuds accounts for multiple scattering on rough surfaces(Lambertian component) and contributes to the first surface uniform-diffuse compo-

Absorption

Multiple scattering

Incident light

Surface scattering Subsurface scattering

Surface-diffuse

Surface-directive

Subsurface-directive

Subsurface-diffuse

Base contribution

Fig. 2. Light scattering from material: surface and subsurface contributions.

BRDF θi φi θr φr λ;,;,( ) BRDF kdd kuds kudf kfs, , ,( )=


nent. kudf is related to the directional-hemispherical reflectance of the subsurfaceand to the Fresnel transmission coefficient. It contributes to the subsurface uniform--diffuse component. kfs is an empirical BRDF model based on functional reasoningand data fitting. It contributes to the subsurface forward-scattering component. Thesek-parameters are related to the BRDF directional and diffuse components (Tab. 1).

We extended the Li–Torrance model to a multispectral model for our inversiontechnique. For N different wavelengths, the determination of 4×N k-parameters isrequired to model the multispectral BRDF:

(6)

Thus, a 4×N-matrix KN is defined from the k-parameters as follows:

(7)

where

(8)

3.2. Data inversion method

For many applications [1, 3, 7, 15, 18], collecting the full-BRDF takes a great effort,and as a consequence only the in-plane BRDF is measured. We propose an inversionmethod to retrieve the multispectral full-BRDF from highly resolved in-plane BRDFmeasurements. For a numerically stable data inversion algorithm, high angularresolution is needed for BRDF measurements.

The aim of our method is to retrieve the KN matrix to model the full BRDF.Because an analytical inversion cannot be achieved for solving nonlinear problems,an optimization technique is performed to identify a complete KN matrix. Our method

T a b l e 1. Relations between k-parameters and BRDF components.

BRDF Directional component Diffuse component

Scattering phenomena

Surface--directional

Subsurface--directional

Surface-diffuse (self-shadowing)

Subsurface uniform-diffuse

kdd kfs kudf kuds

BRDF θi φi θr φr λ1…N;,;,( ) BRDF kdd1…N kuds

1…N kudf1…N kfs

1…N λ1…N;, , ,⎝ ⎠⎛ ⎞=

BRDF θi φi θr φr λ1…N;,;,( ) BRDF KN( )=

KN

kdd1 … … kdd

N

kuds1 … … kuds

N

kudf1 … … kudf

N

kfs1 … … kfs

N

=


combines a Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton optimizationtechnique [19] with the multispectral Li–Torrance BRDF model. Figure 3 describesthe optimization schemes.

First, we define an objective function Fj based on various combinations ofk-parameters (Li–Torrance model) for a fixed wavelength λj:

(9)where Ωi = (θi, φi) and Ωr = (θr, φr).

The previous formula is a sum of root mean square differences between measuredand simulated in-plane BRDFs. We also define a general objective function F asthe sum of objective functions Fj defined for each λj (where j ranges from 1 to N ) andfor each scattered angle:

(10)

Then, we minimize F in order to retrieve each k-parameter for each wavelengthconsidered (for an ideal case where the simulated BRDF is equal to the experimentalone, F equals zero). From the retrieved KN matrix, the multispectral full BRDF can becomputed. We applied our data inversion method for various coatings as will be shownin Section 5.

4. Reflectometer design and calibrationThe BRDF of materials can be measured in experimental setups. An automated andaccurate calibration process is needed to measure in-plane multispectral polarized

Initialvalue

Set of N×k parameters k-matrix KNMultispectral

Optimization process

Data comparisonand minimization of

the objective function

Determination of a new setof new k-parameters

BRDF model

Multispectral BRDFmeasurements

Fig. 3. Data inversion method.

Fj Ωi Ωr λj;,( )BRDFsimulated

kddj kuds

j kudfj kfs

j, , ,Ωi Ωr λj;,( ) BRDFmeasurement Ωi Ωr λj;,( )–

BRDFmeasurement Ωi Ωr λj;,( )---------------------------------------------------------------------------------------------------------------------------------------------------------

2

k∑=

F 1N

---------- Fj Ωi Ωr λj;,( )j 1=

N

∑=


BRDF and DOLP of different types of samples. Figure 4 shows a general view of ourinstrument and Fig. 5 describes its optical layout.

The incident lighting system consists of three different laser sources (Nd:Yag laserat 532 nm, He-Ne laser at 633 nm, diode laser at 814 nm) linearly polarized usinga wideband polarizer. The detection system measures the in-plane BRDF with an angu-lar resolution lower than 1°. It provides highly resolved reflectance measurementsneeded for a better data inversion. It is composed of an Si-detector DET-90 (HindsInstruments) mounted on a rotation stage 1 meter apart from the sample coupled witha wideband polarizer and interferential filters. A simple method based on Fresnel

Fig. 4. General view of the instrument.

Sample

Polarizeddetectionsystem

Dataacquisitionsystem

Multispectrallaser sources

Polarizer P-polarized, S-polarized or

Unpolarized

532 nm

633 nm

814 nm

Laser sources Sample

Lighting system Selection of the wavelength

Selection of the incident polarization state

Lock-in and PC

Data processing

Detection system Polarizer (P,S, U state)

and detector

Rotation aroundthe sample

Det

Fig. 5. Optical layout of the instrument.


equations is used to identify polarizer’s axes. A lock-in amplifier is used to increasethe signal-to-noise ratio for noisy signals. Measurements are fully interfaced via GPIBand PCI cards to control step motors and the lock-in amplifier using homemadesoftware.

For experimental use, we express BRDF with ΔΩr = 10–4 sr the reflected solidangle, and the incident and reflected powers,respectively:

(11)

We apply geometric and angular corrections by calculating the instrument func-tion (IF). It is the ratio of the theoretical Lambertian BRDF to a measured Lambertianmaterial BRDF for each angle of incidence

(12)

Figure 6 shows the theoretical and measured in-plane BRDF at 0° lighting at532 nm of a typical Lambertian material. Spectralon® SRS-99 provided by LabSphere(DHR = 0.99) is used to evaluate the instrument function. IF is close to unity for anglesranging from 0° to 85°: the isotropy and uniformity are verified and corrections aresignificant only for large angles.

We used three different reference Lambertian samples with different DHR (0.99,0.70 and 0.50) to process a radiometric calibration. We measured multispectralin-plane BRDF of these samples at 0° light incidence. In these conditions, the in-planeBRDF can be extended to the out-of-plane BRDF to compute the sample’s DHR.Moreover, we compared the computed DHR to DHR measurement results froma spectrophotometer (Perkin Elmer Lambda-950 UV/vis/NIR). These results arepresented in Tab. 2. The average error found is less than 3% and no additionalradiometric calibration is needed for our instrument.

The selection of the incident and detection polarization states is fully automatedand calibrated. A polarization analyzer (Meadowlark Optics D3000) is used tocharacterize polarizers and to align their fast axis. Fresnel equations are also

Pik θi φi λ;,( ) Pi


BRDFk j, θi φi θr φr λ;,;,( )Lr


Eik θi φi λ;,( )

-----------------------------------------------------

Prk j, θi φi θr φr λ;,;,( )

Pik θi φi λ;,( ) θr( )ΔΩrcos

------------------------------------------------------------------

= =

=

IFBRDFLambertian, th θi φi θr φr λ;,;,( )BRDFLambertian, exp θi φi θr φr λ;,;,( )

------------------------------------------------------------------------------------------

DHR θi φi λ;,( ) π⁄BRDFLambertian, exp θi φi θr φr λ;,;,( )

------------------------------------------------------------------------------------------

= =

=


determined from polarized reflection coefficients measured on a germanium waferwith an error less than 2% [18].

Electromagnetic theorems and radiometric analysis are commonly used to demon-strate the BRDF reciprocal property. In other words, if the laser source and the detectorare switched, the field amplitude and power are equal. This fundamental property [20]is still available for multiple scattering. For a set of different angles of incidencefrom 0° to 60°, we verified the reciprocal relation for Lambertian samples withan average error lower than 1%.

100

10–1

10–2

10–3

0 10 20 30 40 50 60 70 80 90

5

4

3

2

1

0

Reflected angle θr

Inst

rum

ent f

unct

ion

BR

DF

cos(

θ r) [

sr–1

] a

b

0 10 20 30 40 50 60 70 80 90

Fig. 6. Geometric calibration results: Spectralon® BRDF (dotted curve) and theoretical LambertianBRDF (continuous curve) at 0° lightning at 532 nm (a) and the associated instrument function (b).

T a b l e 2. Radiometric calibration results.

DHR (LabSpheredata)

DHR (spectrophotometerdata)

DHR (computed from in-planeBRDF data)

Wav

elen

gths

532 nm0.990 0.980 0.9890.660 0.640 0.6530.500 0.506 0.518

633 nm0.990 0.989 0.9890.650 0.630 0.6450.500 0.505 0.520

814 nm0.990 0.989 0.9890.620 0.610 0.6140.500 0.505 0.519


Our instrument is fully calibrated for polarized and multispectral in-plane BRDFmeasurements. In the next section, experimental results are presented and analyzed forvarious paint coatings (from diffuse to directional coatings).

5. Application to paint coatings

As explained above, light scattering of materials is physically described as the resultof surface and subsurface scattering and their BRDFs are decomposed into directionaland diffuse components [8]. This decomposition is commonly used although the ratiobetween the two terms is often arbitrary [18]. We propose to analyze the scatteringphenomena for the directional and the diffuse parts of the BRDF with our multispectralpolarized-measurements.

5.1. Polarized measurements

From a physical viewpoint, one can explain DOLP values from single or multiplescattering within the media. On the one hand, single scattering or mirror-likereflections do not change the incident polarization state: DOLP is very close to 1. Onthe other hand, multiple scattering processes do change the polarization state of light:DOLP decreases and is lower than 1.

From experimental results, the BRDF is often separated into two components:directional and diffuse. Table 1 shows the directional component to be mainly due tosurface directional scattering and to subsurface directional scattering. It also showsthat the diffuse component corresponds to subsurface diffuse scattering and surfacediffuse scattering. It is assumed from physical considerations [8] that the polarizationstate mainly remains almost unchanged for the directional component and is changedfor the diffuse component.

Fig. 7. Angular evolution of the DOLP linked to the light path within the material.

Incident light

Specular directionof the light

DOLP ~ 1

0 < DOLP < 1

DOLP ~ 0

Short optical path Long optical path


Therefore, the maximum value of the DOLP is always measured at the reflectionangle and a lower DOLP is measured apart from the directional component. Also,the DOLP tends to 0 for large angles (Fig. 7) where multiple scattering is dominantfor large optical thickness (i.e., long optical path within the material).

Let us study more complex scattering media. The ratio between the differentscattering parts impacts directly the BRDF components: the shape of the BRDF isthe result of different scattering ratios. Measurements at 532 nm are presented in Fig. 8for various black paint coatings on aluminium plates with different aspects (matte,matte-glossy and glossy). It shows BRDF and DOLP of these samples: the glossierthe paint coating, the more directional the BRDF and the higher the DOLP at reflectionangle. From matte to glossy, surface directional scattering contribution is increasedcompared to subsurface directional scattering: it is measured by higher DOLP valuesfor glossy coatings (Fig. 8).

Polarized measurements are used to separate the different scattering processes inBRDF directional components. DOLP is a useful tool to quantify the ratio betweenthese processes. It tends to 1 when surface directional scattering is high and tends to0 otherwise (Fig. 8). In order to separate the diffuse components, multispectralmeasurements should be considered.

100

10–4

10–2

BRD

F co

s(θ r

) [sr

–1]

DO

LP

Reflected angle θr [deg]

Matte paint Matte-glossy paint Glossy paint

–15 0 30 60 90

1.0

0.5

0.0

θi = 30 degλ = 532 nm

–15 0 30 60 90

θi = 30 degλ = 532 nm

100

10–4

10–2


–15 0 30 60 90

1.0

0.5

0.0

θi = 30 degλ = 532 nm

–15 0 30 60 90

θi = 30 degλ = 532 nm

100

10–4

10–2


–15 0 30 60 90

1.0

0.5

0.0

θi = 30 degλ = 532 nm

–15 0 30 60 90

θi = 30 degλ = 532 nm

Fig. 8. BRDF (upper figures) and DOLP (lower figures) of a black matte paint coating (left), a blackmatte-glossy paint coating (center) and a black glossy paint coating (right) at a 30° angle of incidence at532 nm.


5.2. Multispectral measurementsMultispectral BRDF and DHR of a red glossy paint coating on a polished aluminiumplate are measured. Table 3 shows multispectral DHR measurements of the sample atthree different wavelengths.

Multispectral DHR measurements are carried out to quantify the absorptionphenomena in the subsurface: DHR532 nm << DHR633 nm and DHR532 nm << DHR814 nm.Among the three measured wavelengths, DHR532 nm is the lowest DHR resulting froma strong absorption phenomena at 532 nm.

In addition, multispectral BRDF measurements are carried out on the same sampleto investigate the different scattering phenomena. Figure 9 shows the measured andfitted BRDFs from the Li–Torrance model at the same wavelengths.

Subsurface scattering within the material is spectrally dependent due to differentscattering patterns as well as to pigment absorption (related to the relative imaginaryrefractive index κ ) within the media. Therefore, one can use this spectral dependenceto distinguish the contribution of the subsurface scattering to the BRDF components.

The directional component of the BRDF is also composed of two scattering terms.One of them is weakly spectral dependent since only a small part of it results fromsubsurface directional scattering.

Multispectral measurements are used to distinguish the subsurface contribution inthe diffuse components of the BRDF.

T a b l e 3. Experimental DHR of a red paint coating on an aluminium plate.

Wavelengths 532 nm 633 nm 814 nmDHR (spectrophotometer data) 0.01 0.47 0.48

100

10–4

10–1

BRD

F co

s(θ r

) [s

r–1]

Reflected angle θr [deg]–20 0 20 60 80

λ = 532 nm

10–2

10–3

40

θi = 30 deg

λ = 633 nmλ = 814 nm

Fig. 9. Measured BRDF (dotted curves) and Li–Torrance BRDF models (solid line) of a red glossypaint coating at a 30° light incidence at 532 nm (grey dotted curve 1), 814 nm (white dotted curve 2) and633 nm (black dotted curve 3).

1

2

3


5.3. Measurements inversionIn this section, we bring into play our inversion method of measurements.Experimental in-plane multispectral BRDFs of the red paint coating are introducedinto our inversion method to retrieve the full BRDF. For this typical red paint coating,we rewrite Eq. (8) for N = 3 as:

(13)

The multispectral in-plane and full BRDFs computed from this retrieved KN matrixare presented in Figs. 9–11.

100

10–4

10–1

BR

DF

cos(

θ r)

[sr–1

]

Angle θr [deg]–20 0 20 60 80

10–2

10–3

40–40–60

BRDF model

BRDF models – red paint at 532 nm – θi = 30 deg

100

10–4

10–1

BR

DF

cos(

θ r)

[sr–1

]

Angle θr [deg]–20 0 20 60 80

10–2

10–3

40–40–60

BRDF obtained on Melopee instrumentBRDF model


100

10–4

10–1

BR

DF

cos(

θ r)

[sr–1

]

Angle θr [deg]–20 0 20 60 80

10–2

10–3

40–40–60

BRDF obtained on Melopee instrumentBRDF model


Fig. 10. Multispectral in-plane BRDF of a red paint coating on an aluminium plate (experimental data inblue and model BRDF in red).

BRDF obtained on Melopee instrument

KN

kdd532 kdd

633 kdd814

kuds532 kuds

633 kuds814

kudf532 kudf

633 kudf814

kfs532 kfs

633 kfs814

=


As discussed in the previous sections, the diffuse BRDF component is stronglyspectral dependent. It is governed by subsurface diffuse scattering which is veryspectral dependent. Thus, BRDF diffuse components are quite lower at 532 nm thanthose at 633 nm and 814 nm.

To take these physical considerations into account, the Li–Torrance model inputparameters (such as n, κ and DHR) were optimized giving additional conditions:κ532 nm >> κ633 nm or κ814 nm and DHR532 nm >> DHR633 nm or DHR814 nm. The resultingk-parameters are presented in Tab. 4.

log

BR

DF

cos(

θ r)

[sr–1

]

θr

BRDF model




log

BR

DF

cos(

θ r)

[sr–1

]

log

BR

DF

cos(

θ r)

[sr–1

]

BRDF modelBRDF model 0

–2

–4

–6

BRDF measurements

θr

θr

φr

0

–2

–4

–6

1.5

0.0

–1.5

0

–2

–4

–6

–500

50

–500

50

–500

50

φr

1.5

0.0

–1.5

φr

1.5

0.0

–1.5

Fig. 11. Multispectral full BRDF of a red paint coating on an aluminium plate (experimental data in redand model BRDF in grey).

T a b l e 4. Experimental DHR and Li–Torrance DHR of a red paint coating on an aluminium plate.

Wavelengths 532 nm 633 nm 814 nmLi–Torrance kudf 0.0162 0.0300 0.0001Li–Torrance kuds 0.0028 0.4860 0.4914DHR (inversion method) 0.0190 0.4890 0.4915


From our inversion method, the modelled multispectral full BRDF and the multi-spectral DHR were retrieved with an error lower than 1%.

6. ConclusionsAn instrument for studying the light scattered by materials has been designed at Onera.Our instrument measures in-plane multispectral polarized-BRDF and DOLP witha high angular resolution. Such measurements can be either used for a physical analysisof the optical surface signature or for applications such as laser-imaging simulationcodes using the full BRDF.

Based on our measurements on paint coatings, we discussed how to dissociatesurface and subsurface scattering processes in the BRDF components. Polarized andmultispectral measurements quantify the different scattering ratios from directionaland diffuse BRDF components, respectively. This method was applied to various paintcoatings to illustrate the potential of the method as a surface quality control tool.

We also introduced a data inversion technique. The full BRDF and multispectralDHR are retrieved from multispectral in-plane measurements for different angles ofincidence and for either diffuse or specular media.

References

[1] MYOUNG KOOK SEO, KANG YEON KIM, DUCK BONG KIM, KWAN H. LEE, Efficient representation ofbidirectional reflectance distribution functions for metallic paints considering manufacturingparameters, Optical Engineering 50(1), 2011, article 013603.

[2] VOSS K.J., CHAPIN A., MONTI M., ZHANG H., Instrument to measure the bidirectional reflectancedistribution function of surfaces, Applied Optics 39(33), 2000, pp. 6197–6206.

[3] BRAKKE T.W., Goniometric measurements of light scattered in the principal plane from leaves,Proceedings of Geoscience and Remote Sensing Symposium, IGARSS, 1992.

[4] JAFOLLA J.C., THOMAS D.J., HILGERS J.W., REYNOLDS W.R., BLASBAND C., Theory and measurementof bidirectional reflectance for signature analysis, Proceedings of SPIE 3699, 1999, p. 2.

[5] LELOUP F.B., FORMENT S., DUTRE P., POINTER M.R., HANSELAER P., Design of an instrument formeasuring the spectral bidirectional scatter distribution function, Applied Optics 47(29), 2008,pp. 5454–5467.

[6] CHUNNILALL C.J., CLARKE F.J.J., SMART M.P., HANSSEN L.M., KAPLAN S.G., NIST–NPL comparisonof mid-infrared regular transmittance and reflectance, Metrologia 40(1), 2003, pp. 55–59.

[7] BETTY C.L., FUNG A.K., IRONS J., The measured polarized bidirectional reflectance distributionfunction of a Spectralon calibration target, Proceeding of Geoscience and Remote SensingSymposium, Vol. 4, 1996, pp. 2183–2185.

[8] ELLIS K.K., Polarimetric bidirectional reflectance distribution function of glossy coatings, Journalof the Optical Society of America A 13(8), 1996, pp. 1758–1762.

[9] HANER D.A., MCGUCKIN B.T., BRUEGGE C.J., Polarization characteristics of Spectralon illuminatedby coherent light, Applied Optics 38(30), 1999, pp. 6350–6356.

[10] NICODEMUS F.E., Directional reflectance and emissivity of an opaque surface, Applied Optics 4(7),1965, pp. 767–773.

[11] HANER D.A., MCGUCKIN B.T., MENZIES R.T., BRUEGGE C.J., DUVAL V., Directional-hemisphericalreflectance for Spectralon by integration of its bidirectional reflectance, Applied Optics 37(18),1998, pp. 3996–3999.


[12] BECKMANN P., Shadowing of random rough surfaces, IEEE Transactions on Antennas andPropagation 13(3), 1965, pp. 384–388.

[13] XIAO D. HE, TORRANCE K.E., SILLION F.X., GREENBERG D.P., A comprehensive physical model forlight reflection, ACM SIGGRAPH Computer Graphics 25(4), 1991, pp. 175–186.

[14] TORRANCE K.E., SPARROW E.M., Theory for off-specular reflection from roughened surfaces, Journalof the Optical Society of America 57(9), 1967, pp. 1105–1112.

[15] COOK R.L., TORRANCE K.E., A reflectance model for computer graphics, ACM Transactions onGraphics (TOG) 1(1), 1982, pp. 7–84.

[16] LI H., TORRANCE K.E., A practical, comprehensive light reflection model, Program of ComputerGraphics, Technical Report PCG-05-03, Cornell University, 2005.

[17] PHONG B.T., Illumination for computer generated images, Communications of ACM 18(6), 1975,pp. 311–317.

[18] NOCEDAL J., WRIGHT S.J., Numerical Optimization, 2nd Ed., Springer-Verlag, Berlin, New York,2006.

[19] LI H., TORRANCE K.E., Validation of the Gonioreflectometer, Program of Computer Graphics,Technical Report PCG-03-02, Cornell University, 2003.

[20] SEARS F.W., Optics, Addison-Wesley Press, 1949.

Received May 16, 2011in revised form August 31, 2011


Interference effect in a dual microresonator-coupled Mach–Zehnder interferometer

YING LU*, XIAOHUI HUANG, XIANGYONG FU, WUQI WEN, JIANQUAN YAO

College of Precision Instrument and Opto-electronics Engineering, Tianjin University, Tianjin 300072, P.R. China,

Key Laboratory of Opto-electronics Information Technology, Tianjin University, Ministry of Education, Tianjin 300072, P.R. China


We present a theoretical study of interference effect in a Mach–Zehnder interferometer in whichtwo microresonators are side coupled to both arms of the interferometer. The results show thatsharp asymmetric Fano resonance, coupled resonator induced transparency and absorptioneffects can be created in such a structure. We demonstrate that these effects arise from interferencebetween a resonance mode and a continuing propagating mode with asymmetric phase dif-ference, destructive interference between two overcoupled resonance modes, and constructiveinterference between an overcoupled resonance mode and an undercoupled mode or a continuingpropagating mode with symmetric phase differences, respectively. These effects may offer a betterunderstanding of the analogous effects in atomic medium and also make optical resonatorsa potential device to utilize these effects.

Keywords: microresonator, Mach–Zehnder interferometer, Fano resonance, coupled resonator inducedtransparency and absorption.

1. IntroductionOptical microring, microdisk and microsphere resonators have attracted considerableattention to device applications because of their high Q-factor and small modalvolumes [1–4]. Recently, it has been demonstrated that the effects analogous to Fanoresonance, electromagnetically induced transparency and absorption in atomic systemcan be established in microresonator system [5–17]. Such microresonator inducedeffects, which do not suffer from the specific light wavelength limitations in atomicsystem, have the advantages of improving the optical switching characteristics of micro-resonator-based devices and controlling dispersion and the group velocity of light.

In this paper, we investigate the interference effect in an alternative microresonatorstructure based on a Mach–Zehnder interferometer, as shown in Fig. 1. By interferencebetween the propagating on-resonance (or non-resonance) modes in two arms, Fanoresonance, coupled resonator-induced transparency (CRIT) and absorption (CRIA)

24 YING LU et al.

similar to quantum interference effects in atomic physics can be induced. Our systemis different from the other two microresonator structures reported, as two micro-resonators respectively are coupled to separate arms of the interferometer and Fanoresonance and CRIT can simultaneously appear in the transmission spectrum.Moreover, we show that CRIT arises from the interference between two resonancemodes that have the same phase shifts and different amplitudes.

2. Theoretical analysis Figure 1 shows the configuration of the dual microresonator-coupled Mach–Zehnderinterferometer. We find transfer response in crossing the coupling zone of the upperarm and the lower arm,

(1)

where:

Ei is the complex field amplitude (at the i-th port) normalized such that |Ei |2 = Pi,the power entering or exiting that port, ti is the real amplitude coupling coefficient,

Ein Eout

E1 – in E1 – out

1

2

I1

I2

E2 – in E2 – out

Fig. 1. Schematic diagram of a dual microresonator-coupled Mach–Zehnder interferometer; two micro-resonators are side coupled to both arms, respectively.

Ei out–

Ei in–-------------------- Ei out–

Ei in–-------------------- iΦi( )exp=

Ei out–

Ei in–--------------------

21 ti

2–αiLi

2---------------–

⎝ ⎠⎜ ⎟⎛ ⎞

exp–2

4 1 ti2–

αiLi

2---------------–

⎝ ⎠⎜ ⎟⎛ ⎞

sin2 φi

2---------⎝ ⎠⎜ ⎟⎛ ⎞

exp+

1 1 ti2–

αiLi

2---------------–

⎝ ⎠⎜ ⎟⎛ ⎞

exp–2

4 1 ti2–

αiLi

2---------------–

⎝ ⎠⎜ ⎟⎛ ⎞

sin2 φi

2---------⎝ ⎠⎜ ⎟⎛ ⎞

exp+

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------=

Φi arg1 ti

2– iφiαi Li

2----------------–

⎝ ⎠⎜ ⎟⎛ ⎞

exp–

1 1 ti2– iφi

αi Li

2----------------–

⎝ ⎠⎜ ⎟⎛ ⎞

exp–

----------------------------------------------------------------------------------=

Interference effect in a dual microresonator-coupled Mach–Zehnder interferometer 25

αi represents attenuation coefficient of the microcavity, Li = 2πai , ai is the radius ofthe microcavity and φi is the total phase shift acquired by the light during one roundtrip. |Ei – out /Ei – in | and Φi represent the amplitude and the phase of Ei – out relativeto Ei – in , respectively.

Incident light is equally distributed into two arms at the dividing Y junction andsubsequently recombined at the output by an adding Y junction. Both arms havethe same physical length La. At the combing Y junction the light in the arm couplingwith the microcavity acquires an optical phase Φ1 + βLa (β is propagation constant),while in the other arm the phase accumulated is given by Φ2 + βLa . Therefore,the output transmitted power is determined by

(2)

Fig. 2. Intensity transmission spectra through optical system as shown in Fig. 1, with a1 = a2 = 10 μm,refractive index contrast n = 1.5, t1 = 0.99, α1, 2 = 10–4 μm–1 for t2 = 0 (a), t2 = 0.1 (c), t2 = 0.3 (e).The phase shifts of the transmitted mode passing the coupling zone between the microresonator andthe arm (b, d and f ). The solid curves are the phase shifts of the mode in the upper arm and the dashedcurves are the phase shifts of the mode in the lower arm. The parameters used in b, d and f are same asthose in a, c and e, respectively.

1.560 1.570 1.580

1.0

0.5

0.0

5

0

–51.570 1.571 1.572

Tran

smis

sion

Pha

se s

hift

[rad]

Wavelength [μm]

a b

c d

e f

1.560 1.570 1.580

1.560 1.570 1.580

1.570 1.571 1.572

1.570 1.571 1.572Wavelength [μm]

5

0

–5

5

0

–5

1.0

0.5

0.0

1.0

0.5

0.0

Pha

se s

hift

[rad]

Pha

se s

hift

[rad]

Tran

smis

sion

Tran

smis

sion

Eout

Ein--------------

2 14

------- E1 out–

E1 in–---------------------

22 E1 out–

E1 in–---------------------

E2 out–

E2 in–--------------------- Φ1 Φ2–( )cos E2 out–

E2 in–---------------------

2+ +=

26 YING LU et al.

3. Results and discussion

Figure 2 shows the transmission spectra of the dual microresonator-coupledMach–Zehnder interferometer and the phase shifts of the transmitted mode passingthe coupling zone between the microresonator and the arm in the case where the sizesof microresonators are equal. Figure 2a shows the transmission spectrum for a singlemicroresonator coupled Mach–Zehnder interferometer where the coupling coefficientbetween the second resonator and the arm is t2 = 0. A broad absorption dip appears at

Fig. 3. Intensity transmission spectra through optical system as shown in Fig. 1, with a1 = a2 = 10 μm,refractive index contrast n = 1.5, t1 = 0.1, α1 = 10–6 μm–1, α2 = 10–2 μm–1 for t2 = 0.2 (a), t2 = 0.65 (c),t2 = 0.7 (e), t2 = 0.9 (g). The phase shifts of the transmitted mode passing the coupling zone betweenthe microresonator and the arm (b, d, f and h). The solid curves are the phase shifts of the mode inthe upper arm and the dashed curves are the phase shifts of the mode in the lower arm. The parametersused in b, d, f and h are the same as those in a, c, e and g, respectively.

1.560 1.570 1.580

1.0

0.5

0.0

5

0

–51.570 1.571 1.572

Tran

smis

sion

Pha

se s

hift

[rad]

a b

c d

e f

1.560 1.570 1.580

1.560 1.570 1.580

1.570 1.571 1.572

1.570 1.571 1.572

5

0

–5

5

0

–5

1.0

0.5

0.0

1.0

0.5

0.0

1.0

0.5

0.0

5

0

–5

Wavelength [μm]1.560 1.570 1.580 1.570 1.571 1.572

Wavelength [μm]

g hTran

smis

sion

Tran

smis

sion

Tran

smis

sion

Pha

se s

hift

[rad]

Pha

se s

hift

[rad]

Pha

se s

hift

[rad]


the resonance wavelength. When t2 increases and the second resonator is also coupledinto the arm, a narrow transparent peak appears in the broad absorption dip, whichis similar to the EIT effect in an atomic system. This CRIT peak results fromthe destructive interference between the two on-resonance modes: the mode inthe lower arm has narrower resonance than the one in the upper arm and their phasedifference is around 0, as seen in Fig. 2d. As t2 increases, the transparency peak grows,as shown in Figs. 2c and 2e.

In Figures 3a, 3c, 3e and 3g, we show transmission spectra for the system as wetune the second resonator from undercoupled to overcoupled, showing the progressionfrom CRIA to CRIT. When the first resonator is overcoupled and the second isundercoupled, the phase difference between the guiding modes in the upper and lowerarms is around π at the resonance wavelength, as shown in Fig. 3b and 3d. Twomodes interfere constructively to enhance absorption. The result is that a sharp dropinduced by the mode in the upper arm with narrower resonance appears in a broadabsorption dip induced by the mode in the lower arm, producing CRIA, as shown in

1.56 1.58 1.60

1.0

0.5

0.0

5

0

–5

Tran

smis

sion

Pha

se s

hift

[rad]

a b

c d

e f

Wavelength [μm]

5

0

–5

5

0

–5

1.0

0.5

0.0

1.0

0.5

0.0

1.54 1.56 1.58 1.601.54

1.56 1.58 1.601.54 1.56 1.58 1.601.54

1.56 1.58 1.601.54 1.56 1.58 1.601.54Wavelength [μm]

Fig. 4. Intensity transmission spectra through optical system as shown in Fig. 1, with a1 = 10 μm,refractive index contrast n = 1.5, t1 = 0.2, t2 = 0.9, α1 = 10–6 μm–1, α2 = 10–2 μm–1 for a2 = 10 μm (a),a2 = 5 μm (c) a2 = 1 μm (e). The phase shifts of the transmitted mode passing the coupling zone betweenthe microresonator and the arm (b, d and f ). The solid curves are the phase shifts of the mode in the upperarm and the dashed curves are the phase shifts of the mode in the lower arm. The parameters used in b,d and f are the same as those in a, c and e , respectively.

Phas

e sh

ift [r

ad]

Pha

se s

hift

[rad]

Tran

smis

sion

Tran

smis

sion

28 YING LU et al.

Figs. 3a and 3c. When the second resonator turns to overcoupled, the phase differencebetween two guiding modes is around 0 at the resonance wavelength, as shown inFigs. 3f and 3h. Destructive interference between two modes decreases absorption toproduce a narrow CRIT peak in the broad absorption dip, as shown in Figs. 3e and 3g.

Now, we investigate the transmission spectra in the case when the sizes of twomicroresonators are unequal. For comparison purposes, we present transmissionspectrum for the same system with two resonators of the same size (a1 = a2 = 10 μm)in Fig. 4a, showing three CRIT peaks. When the diameter of the second resonator ischanged as a2 = 1 μm, the second resonator is off-resonance at the first and thirdresonant wavelengths of the first resonator, and on-resonance at the second resonantwavelength. Thus, the sharp asymmetric Fano resonances which result frominterference between the optical resonance mode in the upper arm and the continuingpropagating mode in the lower arm, appear on the left-hand side and the right-side ofthe spectrum, as shown in Fig. 4a. The phase differences between the two modes areopposite in these two regions of the spectrum, hence two Fano resonances areinverted. On the other hand, the destructive interference between two resonant modesin the middle of the spectrum gives CRIT. When the diameter of the second resonatoris changed to a2 = 5 μm, the Fano resonances turn to symmetric CRIA dips whichresult from constructive interference between two optical pathways, as shown inFig. 4c. These symmetric or asymmetric line shapes are due to symmetric or asym-metric phase differences between two modes at the shorter and longer wavelength sidesof the resonance of the first resonator, as shown in Figs. 4b and 4d.

4. Conclusions We have investigated interference effect between propagating modes in two arms ofa Mach–Zehnder interferometer in which two microresonators were side coupled toboth of its arms. The analysis showed that asymmetric Fano resonance, CRIT andCRIA which arise from interference between a resonance mode and a continuingpropagating mode with asymmetric phase difference, destructive interference betweentwo overcoupled resonance modes, and constructive interference between an overcou-pled resonance mode and an undercoupled mode or a continuing propagating modewith symmetric phase differences, can be created. These effects may offer a betterunderstanding of the analogous effects in atomic medium and also make opticalresonators a potential device for utilizing these effects.

Acknowledgements – This work was supported by the National Natural Science Foundation of China(grant number: 10874128 and 60278032).

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[15] DARMAWAN S., LANDOBASA Y.M., CHIN M.K., Nested ring Mach–Zehnder interferometer, OpticsExpress 15(2), 2007, pp. 437–448.

[16] TOMITA M., TOTSUKA K., HANAMURA R., MATSUMOTO T., Tunable Fano interference effect in coupled--microsphere resonator-induced transparency, Journal of the Optical Society of America B 26(4),2009, pp. 813–818.

[17] MIROSHNICHENKO A.E., FLACH S., KIVSHAR Y.S., Fano resonances in nanoscale structures, Reviewsof Modern Physics 82(3), 2010, pp. 2257–2298.

Received June 3, 2011


An on-line phase measuring profilometry based on modulationWU YINGCHUN, CAO YIPING*, LU MINGTENG, LI KUN

Department of Opto-electronics Science and Technology, Sichuan University, Chengdu, P.R. China


An on-line phase measuring profilometry (PMP) based on Stoilov’s algorithm which can be usedfor on-line 3-D shape inspection is proposed in this paper. A stationary sinusoidal grayscale fringepattern is projected onto the object kept on the production line, and an immobile charge-coupleddevice (CCD) is used to capture five deformed patterns equidistantly. The phase distributionis calculated by using Stoilov’s algorithm, and the height distribution of the inspected object isobtained through the relation of phase–height mapping. When inspected object moves, the posi-tions of images in different deformed patterns change, so the pixel matching is implemented toacquire the equivalent phase-shifting which meets the requirement of Stoilov’s algorithm.Modulation which represents the contour of inspected object is used as the template to performthe pixel matching for the first time in this paper. Computer simulation and experiment verifiedthe effectiveness of the method.

Keywords: on-line inspection, phase measuring profilometry (PMP), Stoilov’s algorithm, pixel matching,modulation.

1. IntroductionDue to the advantages of non-contacting operation, higher speed, accuracy, and easierimplementation, optical 3-D shape measurement for deformable and motional objecthas a huge potential for applications in many areas, including industrial manufacturing,on-line inspection, reverse engineering, computer graphics, plastic surgery, securitychecks, etc. With the advanced development of optics, optoelectronics and the comput-er technique, the possibility has increased greatly for 3-D shape measurement to beachieved at a higher speed, higher degree of accuracy, and more handy [1].

A variety of optical 3-D shape measurement methods have been proposed to dealwith dynamic and motional objects [2–8]. As a simple method in fringe projectionprofilometry, Fourier transform profilometry (FTP) has been extensively studied inrecent years [2, 3]. XIANYU SU et al. discussed a 3-D shape measurement method ofdynamical object based on FTP and successfully measured a man’s chest of lowbreathing [4]. He quoted FTP in hydromechanical measurement field to measure anddisplay the process of eddy generation and deepening [5]. The above methods are basedon Fourier spectrum analyzing, which only needs one captured image, so the measure-

32 WU YINGCHUN et al.

ment speed is fast, but at the cost of reducing the accuracy. Using color to codethe patters, LI ZHANG et al. developed a color structured light technique for high-speedscans of moving objects [6]. SONG ZHANG et al. proposed a real-time 3-D shapemeasurement system [7, 8], which can be used for the measurement of dynamicalobjects. He had successfully measured the facial expression changes of a smiling person.

As a common method in three-dimensional sensing, phase measuring profilo-metry (PMP) has a huge potential in on-line inspection for its low cost and highaccuracy. In this method, a stationary sinusoidal grayscale fringe pattern is projectedonto the measured object, and a charge-coupled device (CCD) is used to capturea sequence of deformed patterns. If the object before the CCD is moving, the positionsof object’s image in different patterns obviously change. If the phase-shifting can beproduced by the post-processing of the deformed patterns according to the change ofthe positions of object’s image, the digital phase-shifting can be replaced and the phaseof object can be calculated. However, the post-processing such as images’ pixelmatching of the deformed patterns is difficult, because the contour of the object iscovered by the stripes. If we extract the object’s contour from the deformed patternsby means of some digital image processing technology and use the contour toimplement pixel matching, this will extend the application scope of the traditional PMPto inspect the moving objects.

The modulation of the object can well reflect the contour of the measuredobject [9]. So a novel on-line 3-D shape inspection method for obtaining equivalentphase-shifting step using modulation is discussed in this paper. And a reasonablechoice of improved Stoilov’s algorithm successfully lessens the requirement foraccuracy of phase-shifting step, which makes the PMP more suitable for on-lineinspection in automatic assembly line.

2. Principle

In on-line inspection, the measured object moves with uniform speed. If we can obtainthe phase shifting by means of movement of the object instead of digital phase-shifting,the phase distribution of deformed pattern can be calculated by phase-shiftingalgorithm [10–12]. Figure 1 shows the layout of the inspected system; a computergraphics card sends a stationary sinusoidal grayscale fringe image signal to a digitallight processing (DLP) projector that projects image onto the moving object [13].A CCD is used to capture N frames deformed patterns with a constant frame rate whenthe object is moving. The captured images are then digitized by a frame grabber andtheir intensity In(x, y ) can be described as follows:

n = 1, 2, 3, ..., N (1)

where Rn(x, y ) is the object’s surface reflectivity, A(x, y ) is the ambient light,B(x, y )/A(x, y ) is the fringe contrast, ϕn(x, y ) is the phase of the deformed fringepatterns modulated by the height of the object.

In x y,( ) Rn x y,( ) A x y,( ) B x y,( ) ϕn x y,( )( )cos+ ,=

An on-line phase measuring profilometry based on modulation 33

The motion of the inspected object before CCD results in the change of positionsof the images in different deformed patterns, so the distributions of Rn(x, y ) andϕn(x, y ) in different deformed patterns are different. The subscript n is used todistinguish them. In order to calculate the phase, pixel matching [14] must be carriedout to guarantee that the images of the object in different deformed patterns havethe same pixel position. The pixel matching also converts Δx (the motion of the objectin equal time interval) to the equivalent phase-shifting step. A sequence of equivalentphase-shifting patterns are cut from the original deformed patterns after pixelmatching, and their intensity can be described as follows:

(2)n = 1, 2, 3, ..., N

where ϕ0 is the equivalent phase-shifting step. R(x, y) is the object’s surface reflectiv-ity and ϕ (x, y ) is the phase of the deformed fringe patterns modulated by the heightof inspected object. The pixel coordinate values of the object’s image in different de-formed patterns are uniform because they are adjusted by the process of pixel matching.So, the subscript n in Rn(x, y ) and ϕn(x, y ) in Eq. (1) can be omitted in Eq. (2).

Here, a reasonable choice of improved five-step Stoilov’s algorithm [15, 16] makesthe inspection more convenient to operate. Stoilov’s algorithm is also an equal steplength phase-shifting algorithm, but the value of phase-shifting is arbitrary; in otherwords, the sum of phase-shifting steps does not need to be integer multiple of 2π,which greatly reduces the requirement of control accuracy of measuring instrument.In Stoilov’s algorithm, the value of N is 5 and the phase distribution can be calculatedas follows:

(3)

DLPCCD

Z

X

θ

ν

Computer

Y Fig. 1. On-line 3-D inspection system.

In' x y,( ) R x y,( ) A x y,( ) B x y,( ) ϕ x y,( ) n 1–( )ϕ0+cos+⎩ ⎭⎨ ⎬⎧ ⎫,=

ϕ x y,( )2 I2' x y,( ) I4' x y,( )–

2I3' x y,( ) I1' x y,( )– I5' x y,( )–------------------------------------------------------------------------------- ϕ0( )sin

⎩ ⎭⎪ ⎪⎨ ⎬⎪ ⎪⎧ ⎫

atan=


and the phase-shifting sin(ϕ0) is:

(4)

From Eq. (3), the values of the phase ϕ (x, y ) range from –π to π and isdiscontinuous by an arctangent function. A phase-unwrapping algorithm is used toconvert the sawtooth-like phase-wrapped image into a continuous phase distribu-tion Ψ (x, y ). The height distribution h (x, y ) is restored by mapping the unwrappedphase Ψ (x, y ) into the height [17, 18]:

(5)

where a (x, y), b (x, y) and c (x, y) depend on the parameter of system setup and requireto be calibrated.

3. Pixel matching based on modulationAccording to the process described above, pixel matching is a key procedure, whichdirectly affects the measurement result of 3D on-line inspection. The process of pixelmatching is described in the following subsections.

3.1. Extraction of modulationEquation (1) is Fourier transformed and the Fourier spectrum is described as follows:

(6)n = 1, 2, 3, ..., N

where Gn( fx , fy), Pn( fx , fy), Qn( fx , fy) represent the Fourier spectrum of I (x, y),Rn (x, y) A(x, y) and Rn (x, y) B (x, y), respectively. A suitable band-pass filter is usedto filter only the +1 order term of the Fourier spectrum and then inverse Fouriertransform is carried out to deal with Qn( fx – f1, fy):

(7)

The distributions of modulation Mn(x, y) are defined as the model of gn(x, y):

n = 1, 2, 3, ..., N (8)

ϕ0 x y,( )sin 1I1' x y,( ) I5' x y,( )–

2 I2' x y,( ) I4' x y,( )–-----------------------------------------------------------

⎩ ⎭⎨ ⎬⎧ ⎫

2

–=

1h x y,( )

---------------------- a x y,( ) b x y,( ) 1Ψ x y,( )

------------------------ c x y,( ) 1

Ψ 2 x y,( )---------------------------+ +=

Gn fx fy,( ) Pn fx fy,( ) Qn fx f1– fy,( ) Qn fx f1+ fy,( ),+ +=

gn x y,( ) Qn fx f1– fy,( ) i2π fx x fy y+( ) dfxdfyexp∞–

∞

∫∫12

--------Rn x y,( )B x y,( ) iϕn( )exp

= =

=

Mn x y,( ) abs gn x y,( ) 12

--------Rn x y,( )B x y,( ),= =


Here, the modulation information of deformed fringe patterns includes reflectivitydistribution Rn(x, y) and grating contrast distribution B(x, y). B(x, y) can be regardedas a constant if the projected grating is of good uniformity. The reflectivity of objectand reference plane are different, so the modulation can be used to distinguishthe measured object from the reference plane. When the object is moving beforethe CCD, the images of the object in the deformed patterns change and cannot bedistinguished from the fringes. Therefore, the modulation can act as a template to markthe change of the object positions.

3.2. Pixel matchingAccording to the contour of the object, a particular region C is cut from the firstmodulation pattern M1(x, y) in Eq. (8), which is used as a template. The regions withmaximum degree of correlation are evaluated through the correlation calculationbetween the template and all the modulation patterns; the difference of the coordinatevalues of regions reflects the motion of the object. Here, the bidirectional greatestcorrelative coefficient matching law is used to calculate the relative displacementbetween all the deformed patterns [19].

The function of correlation is as follows [19]:

(9)

where E1( j, k ) denotes the template C, En( j, k ) denotes a part of the n-th modulationMn(x, y) and keeps the same size as template C, j is the abscissa and k is the ordinate,J and K describe the size of the template.

According to the coordinate values of the regions with maximum degree ofcorrelation in each modulation pattern Mn(x, y), a sequence of equivalent phase--shifting fringe patterns with the same size are cut down from the originaldeformed patterns , and the pixel coordinates of measured object’s image in

are identical with each other. This process is regarded as pixel matching. Inthis way, the movement of object is translated to the grating’s phase shifting, andStoilov’s algorithm is used to calculate the phase distribution handily.

4. Numerical simulation and experiment4.1. Numerical simulationTo demonstrate the feasibility of the methods proposed, a numerical simulation isperformed. As shown in Fig. 2, a “cone like” object is used as the moving objectwith a size of 402×417 pixels. Figure 3 shows the pixel matching process diagram.Figure 3a shows five simulative deformed patterns In (x, y), the object is covered by

RL

E1 j k,( ) En j k,( )k 1=

K

∑j 1=

J

∑

E12 j k,( )

k 1=

K

∑j 1=

J

∑ En2 j k,( )

k 1=

K

∑j 1=

J

∑×

-------------------------------------------------------------------------------------------------------------------=

In' x y,( )In x y,( )

In' x y,( )


the fringes. Because of the movement of the object, the pixel coordinates of the imagesof measured object at each deformed pattern change. Figure 3b shows the correspondingmodulation distributions. Figure 3c is a template cut from M1 (x, y). It can be seen thatthe template is unique and can reflect the character of the measured object. Figure 3dshows the equivalent phase-shifting fringe patterns with the same pixelcoordinate of the images, which are cut from Fig. 3a after pixel matching. Figure 4ais the 3-D reconstruction result. Figure 4b is the corresponding error distribution andits root mean square (RMS) value is 0.0149 mm.

4.2. Experiment

In order to verify the effectivity of the proposed method used in on-line 3-D inspection,a series of experiments were carried out. The experimental system is shown inFig. 5. A sinusoidal fringe pattern is generated by a PC and projected onto the plane(used as a flowing-water production line where measured objects lie) by a DLP(CP-HX6500). The plane moves with a uniform speed, which is controlled by a step--motor (SC300-1A). CCD (MTV1881EX) which is controlled by a trigger signalcaptures the deformed fringe patterns with a constant frame rate and sends them tothe PC to process.

One of the experiments is to inspect a “Mickey” moves with the work plane whichis controlled by a step-motor. Figure 6a shows the inspected object; Fig. 6b shows oneof the deformed patterns, Fig. 6c denotes the corresponding modulation. After pixelmatching based on modulations, a sequence of equivalent phase-shifting fringe patternswith the same pixel coordinates of the images of measured object are obtained, andthe calculation of wrapped phase is performed. Through unwrapping the wrappedphase and calculating the height from the unwrapped phase, the height reconstructionof object is completed according to Eq. (5), in which the parameters of the measure-ment setup [20, 21], a (x, y), b (x, y), and c (x, y) are evaluated using a series of cali-bration planes. The reconstructed height distribution is shown in Fig. 6d. Becausethe actual height of the “Mickey” is unknown, the error analysis is not carried out.Under the same measurement setup, the traditional static PMP which is considered as

Fig. 2. Inspected object.

50

40

30

20

10

0500

400300

200100

0

500400

300200

1000

Z [m

m]

Y [pixel]X [pixel]

In' x y,( )


Fig. 3. Process of pixel matching: deformed patterns (a), modulations (b), template (c), and equivalentphase-shifting fringe patterns after pixel matching (d).

Deformed pattern I1 Modulation of I1 I1'

Template

a b c d






Fig. 4. Inspection result: 3-D reconstruction result (a) and error distribution (b).

Fig. 5. The experimental system.

Fig. 6. Demonstration of accuracy: inspected object (a), deformed pattern (b), modulation (c),reconstruction result of the proposed method (d), reconstruction result of traditional static PMP (e) anddeviation distribution (f ).

0.10

0.05

0

–0.05

–0.10

Work plane

PCCCD

Step-motor

DLP

50

40

30

20

10

0500400

300200

1000

5004003002001000

Z [m

m]

Y [pixel] X [pixel]

500400300

200100

0

5004003002001000

Y [pixel] X [pixel]

Erro

r [m

m]

a b

a b c

d e f20

00

200

100

200

100

0

Hei

ght [

mm

]

Y [pixel]X [pixel]

20

00

200

100

200

100

0

Hei

ght [

mm

]

Y [pixel]X [pixel]

0.10

0

200

100

200

100

0

Dev

iatio

n [m

m]

Y [pixel]X [pixel]


a universal measurement method with high accuracy is used to restore the surface shapeof the “Mickey”. The restored result is shown in Fig. 6e. Figure 6f is the deviationdistribution between the two reconstruction results. Its RMS value is 0.0233 andpeak-to-valley (PV) value is 0.2602. It shows that the proposed on-line inspectionmethod can restore the shape of object as the traditional static PMP and the deviationbetween the two measurement results is small. So, the proposed method has an ap-proximate accuracy compared with the traditional static PMP.

In addition, to analyse the accuracy of the proposed approach, a gage plane withthe height of 10 mm is measured using the above method. One of the deformed patternsis shown in Fig. 7a, and its corresponding modulation is shown in Fig. 7b. FromFig. 7a, we can see that the fringe is discontinuous at the edge of the plane due tothe shadow. Therefore, we calculate the phase of the measured plane by using a “mask”to filter the shadow, and the “mask” is obtained through setting a threshold ofmodulation and is shown in Fig. 7c. The reconstruction height distribution of the testedplane is shown in Fig. 7d. The error distribution is shown in Fig. 7e and the RMSvalue is 0.0601 mm. It shows that the accuracy of the proposed method is considerable.

5. Conclusions

A novel on-line 3-D inspection method with PMP based on Stoilov’s algorithm isproposed in this paper, which extends the application scope of the traditional PMP to

Fig. 7. Measurement of a gage plane: deformed pattern (a), modulation (b), mask (c), 3-D reconstructionof height (d) and error distribution (e).

a b c

d e

0

15

0

0

200100

200100

Hei

ght [

mm

]

Y [pixel] X [pixel]

0.1

0

0

200100

200100

0

Erro

r [m

m]

Y [pixel] X [pixel]

300300

0.2

–0.2

–0.1

300300

10

5


inspect the moving objects. In on-line 3-D inspection, the movement of inspectedobject leads to the displacement of images in deformed patterns, so pixel matching isrequired to obtain the equivalent phase-shifting which satisfies Stoilov’s algorithm.Because modulation represents the contour of inspected object, modulation ofthe deformed pattern is originally used as a mark to implement the pixel matching inthis paper. A region cut from the first modulation pattern acts as a template toimplement correlation calculation with all the modulation patterns, and the regionswith maximum degree of correlation in different modulation patterns are found.The difference of the positions of these regions which reflects the motion of objectis converted to the equivalent phase-shifting, and the phase distribution is calculatedwith the equivalent phase-shifting patterns based on Stoilov’s algorithm. Bothnumerical simulation and experiment verify the effectiveness and practicability ofthe proposed method.

References[1] CHEN F., BROWN G.M., MUMIN SONG, Overview of three-demensional shape measurement using

optical methods, Optical Engineering 39(1), 2000, pp. 10–22.[2] LURONG GUO, XIANYU SU, JIAN LI, Improved Fourier transform profilometry for the automatic

measurement of 3D object shapes, Optical Engineering 29(12), 1990, pp. 1439–1444.[3] TAKEDA M., HIDEKI I., KOBOYASHI S., Fourier-transform method of fringe-pattern analysis for

computer-based topography and interferometry, Journal of the Optical Society of America 72(1),1982, pp. 156–160.

[4] CHUNCAI WU, XIANYU SU, Dynamic 3-D shape detected, Optronics Laser 7(5), 1996, pp. 273–278,(in Chinese)

[5] XIANYU SU, WHENJING CHEN, QICAN ZHANG, YIPING CAO, Dynamic3-D shape measurement methodbased on FTP, Optics and Lasers in Engineering 36(1), 2001, pp. 49–64.

[6] LI ZHANG, CURLESS B., SEITZ S.M., Rapid shape acquisition using color structured light andmulti-pass dynamic programming, Proceedings of the First International Symposium on 3D DataProcessing Visualization and Transmission, 2002, pp. 24–36.

[7] SONG ZHANG, PEISEN S. HUANG, High-resolution, real-time three-dimensional shape measurement,Optical Engineering 45(12), 2006, article 123601.

[8] SONG ZHANG, Recent progresses on real-time 3D shape measurement using digital fringe projectiontechniques, Optics and Lasers in Engineering 48(2), 2010, pp. 149–158.

[9] LIKUN SU, XIANYU SU, WANGSONG LI, LIQUN XIANG, Application of mudulation measurementprofilometry to objects with surface holes, Applied Optics 38(7), 1999, pp. 1153–1158.

[10] JIAHUI PAN, PEISEN S. HUANG, FU-PEN CHIANG, Color phase-shifting technique for three-dimen-sional shape measurement, Optical Engineering 45(1), 2006, article 013602.

[11] BERRYMAN F., PYNSENT P., CUBILLO J., A theoretical comparison of three fringe analysis methodsfor determining the three-dimensional shape of an object in the presence of noise, Optics andLasers in Engineering 39(1), 2003, pp. 35–50

[12] FARRELL C.T., PLAYER M.A., Phase step mesaurement and variable step algorithms in phase-shiftinginterferometry, Measurement Science and Technology 3(10), 1992, pp. 953–958.

[13] YONEYAMA S., MORIMOTO Y., FUJIGAKI M., YABE M., Phase-measuring profilometry of moving objectwithout phase-shifting device, Optics and Lasers in Engineering 40(3), 2003, pp. 153–161.

[14] KO-CHEUNG HUI, WAN-CHI SIU, YUI-LAM CHAN, New adaptive partial distortion search usingclustered pixel matching error characteristic, IEEE Transactions on Image Processing 14(5), 2005,pp. 597–607


[15] STOILOV G., DRAGOSTINOV T., Phase-stepping interferometry: Five-frame algorithm with an arbi-trary step, Optics and Lasers in Engineering 28(1), 1997, pp. 61–69.

[16] XINFEN XU, YIPING CAO, An improved Stoilov algorithm based on statistical approach, Acta SinicaSinica 29(3), 2009, pp. 733–737, (in Chinese).

[17] WENSHEN ZHOU, XIANYU SU, A direct mapping algorithm for phase-measurement profilometry,Journal of Modern Optics 41(1), 1994, pp. 89–94.

[18] WANSONG LI, XIANYU SU, ZHOUBAO LIU, Large-scale three-dimensional object measurement:A practical coordinate mapping and image data-patching method, Applied Optics 40(20), 2001,pp. 3326–3333.

[19] JIANNING WU, BAOLONG GUO, ZONGZHE FENG, An image mosaic technique based on interest pointsfeature matching, Journal of Optoelectronics, Laser 17(6), 2006, pp. 733–737, (in Chinese).

[20] TAVARES P.J., VAZ M.A., Linear calibration procedure for the phase-to-height relationship in phasemeasurement profilometry, Optics Communications 274(2), 2007, pp. 307–314.

[21] LEGARDA-SÁENZ R., BOTHE T., JÜPTNER W.P., Accurate procedure for the calibration of a structuredlight system, Optical Engineering 43(2), 2004, pp. 464–471.

Received May 29, 2011in revised form October 7, 2011


Novel method to determine laser scanner accuracy for applications in civil engineering

HIGINIO GONZALEZ-JORGE*, MERCEDES SOLLA, JULIA ARMESTO, PEDRO ARIAS

Close Range Remote Sensing and Photogrammetry Group, Department of Natural Resources and Environmental Engineering, School of Mining Engineering, University of Vigo, 36310 Vigo, Spain


One of the most important aspects of controlling the condition of civil engineering structures isthe deformation monitoring. 3D laser scanners show some advantages related to the controlling ofunexpected deformations which cannot be monitored with total stations or levels. Technicaldatasheets provided by laser manufacturers give the accuracy of single point measurements,although these figures can be improved using fitting algorithms. This paper depicts a noveltechnical procedure used to detect real accuracy that can be achieved using surface fittingtechniques. This technique is based on the displacement of an aluminum plate by means ofa precision actuator. Shift produced in the plate is measured by a laser scanner and a totalstation. Accuracy is evaluated as the difference between the values given by the actuator andthose provided for the geodetic instruments.

The procedure has been tested using a laser scanner RIEGL LMS Z390i and a total stationLeica TCR 1102. The results obtained are very close in both cases and depict values of accuracyless than 1 mm. These results confirm the possibilities of the RIEGL system to detect smalldeformations. It can be concluded that this system can be used in the monitoring of civil engineeringstructures.

On the other hand, the single point measurement exhibits an accuracy around 6 mm andconfirms the data provided by the manufacturer of the laser scanner.

Keywords: laser scanning, deformation monitoring, accuracy, surveying, civil engineering.

1. IntroductionThe number and complexity of the current civil engineering infrastructures makes itnecessary to use accurate, fast and reliable monitoring systems to ensure the safetyboth during construction and operation. One of the most important aspects iscontrolling the deformations in tunnels, bridges, dams, etc. Convergence processes intunnels depend of the re-arrangement of stresses just after the excavation, and hencedescribes the deformation of the surrounding rockmass and of support, independentlyof any stress-focusing models and measurements. Convergence values are typicallyfrom 0.1 mm to 5 mm /day until the tunnel stabilization [1, 2]. Deformation in bridges

44 H. GONZALEZ-JORGE et al.

is important in load tests to evaluate the fatigue resistance and assess the loadcarrying capacity. Values around 20 mm are common in these tests [3–6]. Deformationmonitoring in dams is also a topic of interest. The actual behavior may differ fromthe initial values computed at the design stage for differences between the proposeddesign and built structure, assumptions in structural modeling and analysis, materialfatigue, earthquakes, etc. Deformation values around 20 mm can be measured. Thesedeformations correlate with the water level height of the dam [7, 8]. Other engineeringstructures with important requirements in deformation monitoring are the slopes ofthe roads [9, 10].

Geodetic instrumentation such as precise levels, total stations, global positioningsystems and terrestrial laser scanners can be used for these inspection works. Thesetechniques have become especially useful as inspection tools in civil engineeringapplications, where physical access to the structure is not possible or usually involveshigh risk to operators. The classical topographic methods based on angles and distancesare very common and include instrumentation such as levels and total stations withaccuracies around 0.5–2 mm. The accuracy depends on the working distance andthe technical specifications of the instruments. Contact sensors comprising incli-nometers, dial gauges, extensometers, reflectors and precision bar codes completethe measurement unit. Global Navigation Satellite Systems (GNSS) are used in someapplications such as the monitoring of large dams [11, 12]. However, this techniquehas two main limitations: accuracy is a changeable magnitude which depends onthe number of satellites, geomorphology, density and distribution of vegetation and itcannot be used indoors (tunnel applications). On the other hand, the precision limitsof GNSS are around 1 cm horizontally and 2 cm vertically. The classical topographicmethods operate at a relatively small number of single points. This situation causesthat the resulting models used for geometric analysis have to be strongly simplified.Consequently, full area coverage cannot be provided.

Non-contact techniques for surveying and documenting built-up structures haveevolved significantly in the last decade. 3D laser scanning and close rangephotogrammetry are the main exponents of this evolution: both provide point cloudsof thousands or millions of coordinates with millimeter accuracy. These techniquesovercome some of the disadvantages of traditional geodetic methods in surveyingcivil structures. In this sense, terrestrial laser scanners show simplicity of usage andhigh speed of data acquisition [13]. They allow a complete geometrical model ofthe structure to be obtained and it is not necessary to discretize the object by referencepoints [14, 15]. This fact enables the detection of unexpected deformations.

Single shot accuracy laser scanning is poorer than that obtained with the totalstations. Values around 5–10 mm can be achieved [16]. They are usually consideredas inadequate for the monitoring of structural deformations due to the subtle nature ofsome deformations. However, it should be noted that the average of the precision fromthe object surface improces the results. Some authors report that modeled terrestriallaser scanner data could achieve accuracy up to 20 times as high as that of the singlepoint coordinate precision [17]. This result is close to those obtained for the classical

Novel method to determine laser scanner accuracy... 45

topographic methods and makes the system reliable to be used in the inspection ofdeformations in civil engineering structures. In this situation, technical specificationsof the systems typically include accuracy data that cannot be easily extrapolated tothe accuracy required for measuring a real deformation. The data of the technicalspecifications include single point accuracy. However, deformations must be obtainedfrom the fitting data from the surface. In this work, a laboratory procedure based onthe displacement of a precision electromechanical actuator is proposed to evaluatethe accuracy of deformation measurement, prior to the field data acquisition. The aimof this procedure is to contribute to the evaluation of the instrumentation beforethe final selection. Another application of the procedure is to detect a potential needof recalibration in the systems. This procedure was applied to the accuracy detectionof terrestrial laser scanning system RIEGL LMS Z390i and it was compared withthe results provided by the Leica TCR 1102 total station.

2. Materials and methods

The experimental procedure designed to evaluate the accuracy of laser scanningsystems is based on the three main pillars: a device, data acquisition and processing.A laser scanner and a total station are the instruments used to perform the geometricacquisition. An actuator device causes a precise displacement of a plate to simulatesmall deformations. Measurements are performed at different ranges. Figure 1 showsa scheme of the system.

The device mainly consists of an electromechanical actuator which producesa precise shift of a target plane. The precision actuator is a linear stage PLS-85 (Micos)which is mainly intended for precision applications. Cross-roller bearings guaranteevery high guiding stiffness. It is driven by a recirculating ball screw and equippedwith a DC stepper motor. Two hall sensors limit the travel range to 52 mm.The straightness of the system is 2 μm, pitch 90 μrd, yaw 90 μrd, weight 1.3 kg, andpoint repeatability 1 μm. The system is computer controlled using a Matlab programspecifically developed for this purpose. A right angle precision mounting fromThorlabs is used to fix the plane target (aluminum plate) to the actuator. The aluminumplate can be easily measured by the laser scanning system and the total station.The dimensions of the aluminum plate are 100 mm×100 mm×2 mm. The wholesystem is mounted on a topographic tripod.

Fig. 1. Experimental arrangement.

Total station10 m 25 m 50 m

Terrestrial laser scanning Precision actuator Displacement


Data acquisition and processing must reproduce the measuring conditions ofthe system during real inspection of deformations in a bridge, tunnel, dam, slope, etc.Metrological parameters (laser scanner resolution, range or processing algorithms)must be kept constant to produce comparable results. The test performed in ourlaboratory uses a laser scanning system RIEGL LMS Z-390i and a total station LeicaTCR 1102. Temperature and relative humidity are monitored and introduced intothe control software of the laser scanner to establish the correction related withthe Edlén equation, and the relationship between the refractive index of air andthe speed of light [18]. The control software of the laser scanner makes it possible tointroduce temperature and relative humidity data to correct the range measurement.The only way to introduce it is by the human operator. The procedure we adopt hereuses an environmental sensing unit located in the neighbourhood of the laser scanner.After each displacement of the actuator and the corresponding measurement withthe laser scanner, the environmental conditions are checked and reintroduced inthe RIEGL software to guarantee the quality of measurements. The ranges ofmeasurement of the geodetic equipment evaluated are: 10, 25 and 50 m. Thesedisplacements make it possible to measure lengths of 0.1, 0.3, 0.6, 1.0, 3.0, 6.0, 10.0,20.0 and 30.0 mm. These displacements make it possible to measure displacements of0.1 mm (from 0 to 1 mm), 1 mm (from 1 to 10 mm) and different intervals (from 10to 30 mm), as well as repeated measurements calculated from different combinationsof absolute positions. Finally, the total number of combinations between theseestablished positions gives 42 displacements. This procedure was repeated for the threeranges of measurement. Maximum displacement is limited to 30.0 mm. It is clear thatlarger deformations can be perfectly detected with the RIEGL LMS Z-390i. It appearsmost important to determine the measurement limit for small deformations.

Angular differences between the measurements are very small. If we take intoaccount the distances of 10, 25 and 50 m and the size of the aluminum plate(100 mm×100 mm), the maximum angles of ray incidence are 2.86°, 1.14° and 0.57°,respectively.

The terrestrial laser scanner used in this work, RIEGL LMS Z-390i, classified astime of flight (TOF), is composed of a collimated laser source that emits infrared laserbeam pulses. Part of the signal reflected by the object surface re-enters the laser systemand is collected by the detector diode which generates an electric signal. The periodof time between the emission and reception of the pulsed beam is measured by a quartzclock. The TOF allows the distance between the object and the laser equipment to bemeasured. The velocity of light propagation in air is known for a certain temperature,relative humidity and pressure. The system for distance measurement is combined witha ray deflector which points the beam towards the object surface. The RIEGL configu-ration consists of a rotary mirror which allows vertical scanning and a servomotor thatmakes the mechanism rotate about the optical axis for the horizontal scanning. Atthe same time, the intensity of the reflected signal is stored as an attribute ofthe intensity for each measured point. It collects information about the reflectivity ofan object, and consequently, information about the spectral characteristics of the sur-


face of the object. The RIEGL LMS Z-390i is a long range terrestrial laser scanner,with a range of measurement from 1.5 m to 400 m. The nominal accuracy is 6 mm at50 m range (standard illumination conditions). Beam wavelength is 1540 nm, withan acquisition rate between 8000 and 11000 points per second. The field of view ofthis instrument covers 360 degrees horizontally and 80 degrees vertically. The mini-mum stepwidth is 0.002 degrees horizontally and vertically.

The Leica TCR 1102 total station was used for the purpose of comparison withthe data obtained from the laser scanning system. Each position of the actuator is alsomonitored by means of 16 points taken with the total station. Technical specificationsgive an angular accuracy (horizontal and vertical) of 2" and maximum range ofmeasurement from 3500 m to 80 m, depending on whether the measurement isperformed using a prism or in a reflectorless mode. The accuracy of distancemeasurement according to ISO 17123-4 [19] is 2 mm + 2 ppm (standard measurementmode). Red laser (633 nm wavelength) is used in phase measurement configuration.These instruments modulate the laser beam and measure the phase difference betweenthe emitted and collected signals which is proportional to the range measurements.


3.1. Data acquisitionThree scanner stations were selected. A panoramic point cloud of the laser environmentwas collected. This option only pretends to establish the position of the target objectin space. It takes 713261 points during 89 s, with a step-width of 0.2° for vertical andhorizontal angles and covering all the scanner angular ranges (360° horizontal and80° vertical). Figure 2 shows a scan made with the RIEGL LMS Z390i in “overview”mode (full field of view).

Subsequently, the data acquisition continues with a detailed point cloud fromthe actuator and aluminum plate (Fig. 3). A step-width of 0.004° is selected in allthe cases. The acquisition time and the number of points change from 74 s and around223000 points at 10 m to 29 s and around 38000 points at 50 m.

Fig. 2. Full field point cloud. Fig. 3. High resolution point cloud (actuatorand aluminum plate).


Simultaneously, the total station was positioned sided with the laser scanner. Foreach position, all the shifts of the actuator were registered by means of the measurementof 16 points all over the plate surface.

3.2. Data processing

The data from aluminum plate are segmented from the raw point cloud to be used infurther calculations (Fig. 4a). Octree (Fig. 4b) and raster 2.5D (Fig. 4c) filters are alsoapplied to the images. All this data processing is performed using RiSCAN PROsoftware provided by RIEGL.

Octree filter is based on an octree structure where a cube is divided into 8 equallysized cubes. These cubes are again divided until cubes with minimum size are obtained.The extension of the base cube can be entered by the user. The division into sub-cubesis done on demand by filling the points into the octree, and stopped as soon as a givenminimum cube size is reached. After generation of the octree, the cube contains onepoint which is the center of gravity of the averaged points representing, in general,a larger number of points.

Raster 2.5D filter divides the point cloud in cells whose size is defined by the user.The filter forces each cell to contain only one point. One cell containing more thanone point inside is forced to select from among the higher value, the lower value orthe value given by the gravity center of them. The entire filtering process is developedusing a resolution of 5 mm.

The shift of the actuator is evaluated using two different approaches: first,the distance between planes is determined, and on the other hand, the distance betweena single point and a plane. Matlab algorithms are used for this purpose:

– The raw point cloud of aluminum plate (Fig. 4a) is fitted to a plane using a leastsquare fitting algorithm. The same procedure is applied to the point cloud filtered usingthe Octree (Fig. 4b) and 2.5D raster (Fig. 4c) filters and to the total station data.Displacement LS is evaluated in all the cases as a distance between the parallel planesobtained from the different steps of the actuator. Figure 5a shows the results for

Fig. 4. Point cloud segmented from the aluminum plate. Raw data (a), octree filter (b) and raster 2.5 Dfilter (c).

a b c


the laser scanner (30 mm displacement) and Fig. 5b for the total station (30 mm dis-placement).

– Single point accuracy. A random point from the laser scanning data locatedaround the center area of the plate, as well as another random point of the point cloudmeasured by the total station, is used to calculate the displacement of the actuator.That displacement LS is considered to be a distance between the single point anda plane fitted to the point cloud captured from the initial position of the actuator.Figure 6 shows the results for a 20 mm displacement.

The results depicted in Fig. 7 for the accuracy ΔL are obtained as the differencebetween the values provided by the shift of the actuator LA (standard values) and thoseprovided by the geodetic instruments LS, using the Matlab algorithms shownpreviously:

ΔL = LA – LS (1)

–8.25

–8.30

–8.35

–5.65

–5.70

–5.75–0.3

–0.25

–0.20

110.18

110.16

110.14

110.12

103.00102.95

102.90 101.3

101.4

101.5

z [m

]

y [m]x [m]

z [m

]

y [m]

x [m]

a b

Displacement

Raw dataFitted data

Displacement

Raw dataFitted data

Fig. 5. Distance between planes. Laser scanner (a) and total station (b).

z [m

]

y [m]

x [m]

z [m

]

y [m]x [m]

a b

Displacement

Raw dataFitted data

Displacement

Raw dataFitted dataSingle point

Single point

–8.26

–8.30

–8.34

–5.6

–5.7

–5.8–0.35

–0.25

–0.15

110.19

110.17

110.15

101.50

101.45

101.40

101.35

102.9

103.0

103.1

Fig. 6. Distance between a single point and a plane. Laser scanner (a) and total station (b).


Fig. 7. Accuracy. Ranges of 10 m (a), 25 m (b) and 50 m (c).

Fig. 8. Accuracy per unit of length. Ranges of 10 m (a), 25 m (b) and 50 m (c).

6

4

2

0

–2

–4

–60 5 10 15 20 25 30

Leica TCR1102RIEGL LMS Z390i – octreeLeica TCR1102 – single pointRIEGL LMS Z390i – raw dataRIEGL LMS Z390i – raster 2.5DRIEGL LMS Z390i – single point

Displacement [mm]

Acc

urac

y [m

m]

6

4

2

0

–2

–4

–60 5 10 15 20 25 30

Displacement [mm]

Acc

urac

y [m

m]

6

4

2

0

–2

–4

–60 5 10 15 20 25 30

Displacement [mm]

Acc

urac

y [m

m]

a b

c

5040

20

0

–20

–40–50

0 5 10 15 20 25 30

Leica TCR1102RIEGL LMS Z390i – octreeLeica TCR1102 – single pointRIEGL LMS Z390i – raw dataRIEGL LMS Z390i – raster 2.5 DRIEGL LMS Z390i – single point

Displacement [mm]

Acc

urac

y [%

]

0 5 10 15 20 25 30Displacement [mm]

0 5 10 15 20 25 30Displacement [mm]

a b

c

30

10

–10

–30

5040

20

0

–20

–40–50

Acc

urac

y [%

]

30

10

–10

–30

5040

20

0

–20

–40–50

Acc

urac

y [%

]

30

10

–10

–30


Displacement data obtained from the single point approximation with the laserscanner show a variability of accuracy achieved to be 4–5 mm in many cases andconfirm the nominal accuracy of 6 mm at 50 m range given by the manufacturer.The variability of the values is caused by the random selection of the single point. Onthe other hand, the results of plane fitting and distance evaluation between parallelplanes are clearly improved. The three cases under study for the laser scanner (rawdata, octree and raster 2.5D filters) show accuracy values of less than 1 mm. There arenot any important differences between them. Neither is there a perceptible dependenceas regards the range. The data are also similar to those obtained by the total stationusing plane fitting and distance evaluation. They are better than those obtained forthe total station in single point configuration.

Figure 8 shows the accuracy per unit of length ΔL% and its relationship withdisplacement and range (Eq. (2));

(2)

The displacements over 3 mm show accuracy values lower than 10% for all the data,except those provided by a single point laser scanner which reaches values over 25%.

It must be noted that this procedure could be perfectly adapted to situations wherethe field of view or the requirements about the angle of the incident ray are larger,which affect to the laser scanner accuracy and cannot be compared with these idealcases [20]. In those cases, the aluminum plate could be tilted or moved to extremeangular positions to be useful for this kind of situations.

This procedure shows, in a simple manner, the suitability of the RIEGL LMS Z390ilaser scanner to detect deformations around few millimeters. RIEGL LMS Z390iachieves accuracy close to that typically obtained with the classic topographicmethods. The simplicity of the procedure opens up many possibilities for users of laserscanning systems to verify their metrological characteristics. This procedure can beuseful when purchasing such systems to verify their real possibilities. These charac-teristics are not always included in the technical specifications provided by the manu-facturer. On the other hand, this methodology could be implemented by users of laserscanners in order to verify the metrological drift of the system during its lifetime andits accordance or not with service requirements.

4. ConclusionsLaser scanning systems have been shown as a reliable technology for monitoringdeformations in engineering structures, especially for the accurate and dense pointclouds generated. The behavior of the system before its use in real conditions isevaluated using a laboratory procedure that mainly consists in the precision movementof an aluminum plate.

Displacements of the aluminum plate can be measured by means of the geodeticinstrumentation as a distance between the planes fitted to the sets of point clouds

ΔL%ΔLLA

------------ 100%×=


generated. The procedure is tested using a RIEGL LMS Z390i laser scanner anda Leica TCR1102 total station. In addition, the results appear suitable for deformationmonitoring, with accuracies less than 1 mm. The test is also repeated for single pointmeasurements, using the laser scanner and the total station. The results obtained in thiscase are poor, all of them around the accuracy of data provided by the manufacturer.The present procedure is important in that it allows checking the real technicalspecifications of laser systems for detection of deformations, which are not typicallycollected in the datasheet provided by the manufacturers. This information could beessential to determine whether a system passes the evaluation prior to the purchasingor when the need arises to recalibrate a laser scanner.

Acknowledgements – The authors would like to give thanks to Consellería de Economía e Industria(Xunta de Galicia), Ministerio de Ciencia e Innovación and CDTI (Gobierno de España) for the financialsupport provided; human resources programs (IPP055 – EXP44, FPU AP2006-04663, IDI-20101770)and projects (INCITE09 304 262 PR, BIA2009-08012). All the programs are co-financed by the FondoEuropeo para el Desarrollo Regional (FEDER).

References[1] STIROS S., KONTOGIANNI V., Mean deformation tensor and mean deformation ellipse of an exca-

vated tunnel section, International Journal of Rock Mechanics and Mining Sciences 46(8), 2009,pp. 1306–1314.

[2] NUTTENS T., DE WULF A., BRAL L., DE WIT B., CARLIER L., DE RYCK M., STAL C., CONSTALES D.,DE BACKER H., High resolution terrestrial laser scanning for tunnel deformation measurements,XXIV FIG Congress, Sydney, Australia, April 11–16, 2010, pp. 1–15.

[3] LOVAS T., BARSI A., DETREKOI A., DUNAI L., CSAK Z., POLGAR A., BERENYI A., KIBEDY Z., SZOCS K.,Terrestrial laser scanning deformation measurements of structures, ISPRS – International Archivesof the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXVII, 2008,pp. 527–531.

[4] ZOGG H.-M., INGENSAND H., Terrestrial laser scanning for deformation monitoring – load tests onthe Felsenau viaduct, ISPRS – International Archives of the Photogrammetry, Remote Sensing andSpatial Information Sciences, Vol. XXXVII, 2008, pp. 555–561.

[5] BAO XING ZHOU, JIAN PING YUE, KE YONG JIA, Automatic deformation acquisition using terrestriallaser scanner, Applied Mechanics and Materials 90–93, 2011, pp. 2811–2817.

[6] MING C.C., CHEN C.-S., WU C.-T., WANG E.H., Monitoring of sag deformation in suspension bridgesusing a 3D laser scanner, Materials Evaluation 68(12), 2010, pp. 1368–1378.

[7] ALBA M., FREGONESE L., PRANDI F., SCAIONI M., VALGOI P., Structural monitoring of a large damby terrestrial laser scanning, Proceedings of the ISPRS Commission V Symposium ‘ImageEngineering and Vision Metrology’, Dresden, Germany, September 25–27, 2006, Vol. XXXVI,Part 5.

[8] GONZÁLEZ-AGUILERA D., GÓMEZ-LAHOZ J., SÁNCHEZ J., A new approach for structural monitoringof large dams with a three-dimensional laser scanner, Sensors 8(9), 2008, pp. 5866–5883.

[9] JIA PING ZHANG, HE WU, YU QIN FENG, GUANG YANG, GUO FENG WANG, QI GE, Research on the datacollection method in road slope detection based on 3D laser scanner, Applied Mechanics andMaterials 94–96, 2011, pp. 826–829.

[10] FERRERO A.M., MIGLIAZZA M., RONCELLA R., RABBI E., Rock slopes risk assessment based onadvanced geostructural survey techniques, Landslides 8(2), 2011, pp. 221–231.


[11] HUDNUT K.W., BEHR J.A., Continuous GPS monitoring of structural deformation at Pacoima Dam,California, Seismological Research Letters 69(4), 1998, pp. 299–308.

[12] LOVSE J.W., TESKEY W.F., LACHAPELLE G., CANNON M.E., Dynamic deformation monitoring of tallstructure using GPS technology, Journal of Surveying Engineering 121(1), 1995, pp. 35–41.

[13] SOUDARISSANANE S., LINDENBERGH R., GORTE B., Reducing the error in terrestrial laser scanning byoptimizing the measurement set-up, ISPRS – International Archives of the Photogrammetry, RemoteSensing and Spatial Information Sciences, Vol. XXXVII, 2008, pp. 615–620.

[14] ARMESTO J., ROCA-PARDIÑAS J., LORENZO H., ARIAS P., Modeling masonry arches shape usingterrestrial laser scanning data and nonparametric methods, Engineering Structures 32(2), 2010,pp. 607–615.

[15] LUBOWIECKA I., ARMESTO J., ARIAS P., LORENZO H., Historic bridge modelling using laser scanning,ground penetrating radar and finite element methods in the context of structural dynamics,Engineering Structures 31(11), 2009, pp. 2667–2676.

[16] TSAKIRI M., LICHTI D., PFEIFER N., Terrestrial laser scanning for deformation monitoring,XXIII FIG Congress, Munich, Germany, October 8–13, 2006.

[17] GORDON S.J., LICHTI D.D., Modeling terrestrial laser scanner data for precise structural deformationmeasurement, Journal of Surveying Engineering 133(2), 2007, pp. 72–80.

[18] EDLÉN B., The refractive index of air, Metrologia 2(2), 1966, pp. 71–80.[19] Optics and optical instruments. Field procedures for testing geodetic and surveying instruments.

Part 4. Electro-optical distance meters (EDM instruments), ISO 17123-4, 2001.[20] RIVAS-LÓPEZ M., SERGIYENKO O.YU., TRYSA V.V., HERNANDEZ-PERDOMO W., DEVIA-CRUZ L.F.,

HERNANDEZ-BALBUENA D., BURTSEVA L.P., NIETO-HIPÓLITO J.I., Optoelectronic method for structuralhealth monitoring, Structural Health Monitoring 9(2), 2010, pp. 105–120.

Received June 24, 2011in revised form October 26, 2011


Small-signal circuit modeling for a semiconductor optical amplifier monolithically integrated with a sampled grating distributed Bragg reflector laser

HUI LV1, 2*, ZIQIANG LI1, TAO YANG1, CHUYUN HUANG1

1School of Science, Hubei University of Technology, Wuhan, 430068, China

2Wuhan National Laboratory for Optoelectronics, College of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China


In this paper, a small-signal equivalent circuit model of a semiconductor optical amplifier (SOA)monolithically integrated with a sampled grating distributed Bragg reflector (SGDBR) laser ispresented. To take into account the wavelength dependence of the circuit parameters of our model,the extraction of parameters has been performed by fitting the circuit model including parasiticeffect with measured S-parameters of the integrated device for different operating wavelengths ofthe SGDBR laser. The optical frequency chirp caused by the current modulation of the SOA sectionhas been simulated by the obtained small-signal circuit model.

Keywords: semiconductor optical amplifier, sampled grating distributed Bragg reflector laser, small--signal circuit model, optical frequency chirp.

1. IntroductionSemiconductor optical amplifiers (SOAs) play an important role in optical networksdue to their use in a wealth of applications. With the rapid development of photonicintegrated circuits (PIC) technology, an SOA can be easily monolithically integratedwith a semiconductor tunable laser to achieve highly varied functions [1–3]. For thismultisection device, the SOA can act as an external modulator for the laser by directcurrent modulation of the SOA section, which can overcome the shortages induced bythe direct modulation of the laser, such as the mode hopping. The main drawback ofthis application is the slow modulation response of the SOA section. However, currentmodulation of several GHz has been demonstrated for SOA [4], so the modulationmethod can be used for wavelength-division multiplexing (WDM) networks when noextremely high data rate is required.

56 HUI LV et al.

A detailed theoretical analysis of the modulation response of an SOA has beenpresented in [5] using a direct solution of the photon propagation equation and the car-rier rate equation. This method of analysis requires complex programming and is notsuited to inclusion of electrical parasitics due to the various levels of the packaginghierarchy. TUCKER and POPE [6] proposed a lumped-element circuit modeling approachto analyze semiconductor injection lasers, which is to transform the rate equations ofcarrier and photon density to the microwave small-signal equivalent circuit model,including the intrinsic nonlinear behavior, heterojunction I–V and space-chargecharacteristics, package and substrate parasitics. The small-signal performance ofsemiconductor lasers can be easily obtained from the circuit model by using generalcircuit simulators (such as SPICE). In this paper, we introduce the lumped-elementcircuit modeling approach into the analysis of SOAs. A small-signal equivalent circuitmodel of an SOA monolithically integrated with a sampled grating distributed Braggreflector (SGDBR) laser is proposed based on Tucker’s model. Considering the spatialvariation of the photons inside the cavity of a SOA due to a nonuniform longitudinalfield distribution, some corrections are introduced into the model by use of the photonpropagation equation to relate the photon density at the output facet to the injectedcurrent of an SOA. Due to the wavelength tunability of the integrated SGDBRlaser and the wavelength dependence of the circuit parameters of the SOA model,the parameters are extracted by fitting the circuit model including parasitic effect withthe measured S-parameters of the integrated device for different operating wavelengthsof the SGDBR laser. By using the obtained small-signal equivalent circuit model,the optical frequency chirp caused by the current modulation of the SOA section issimulated. The simulation results agree well with the measured results presented in [1].

2. Small-signal equivalent circuit modelThe rate equations of the carrier and photon density of an SOA can be expressedas [6, 7]

(1)

(2)

where N (t ) is the carrier density, S(t ) is the photon density, Γ is the optical confinementfactor, a is the differential gain constant, Ntr is the carrier density at transparency,τn is the carrier lifetime and τp is the photon lifetime, β is the fraction of spontaneousemission coupled into the signal mode, w, d, and l are the width, thickness, and lengthof the active layer, respectively, rin is the rate of injection of photon density due tothe input signal, q is the electronic charge, and I is the current injected into the activelayer. When using the above rate equations to analyze the performance of an SOA as

dN t( )dt

-------------------- I t( )qVact

----------------- N t( )τn

----------------– Γa N t( ) Ntr–⎝ ⎠⎛ ⎞ S t( )–=

dS t( )dt

------------------- Γa N t( ) Ntr–⎝ ⎠⎛ ⎞ 1

τp---------– S t( ) Γβ N t( )

τn----------------- rin+ +=

Small-signal circuit modeling for a semiconductor optical amplifier... 57

a whole, the spatial variations of carriers and photons inside the cavity are neglected.We use the following equations to relate the variables in Eqs. (1), (2) to the correspondingz-dependent ones

(3)

A classical Shockley relationship can be used to relate the carrier density N (t ) tothe heterojunction voltage Vj(t ) as follows

(4)

where Ne is the equilibrium carrier density, η is the emission coefficient of the diode,k is the Boltzmann constant, and T is the temperature of the active layer in Kelvin scale.

We split the time-varying variables into dc and ac components as follows

(5a)

(5b)

(5c)

(5d)

With Equations (5) substituted in Eqs. (1), (2) and (4), and with the products ofsmall-signal terms neglected, the following equations can be obtained

(6)

(7)

where

(8a)

(8b)

(8c)

S t( ) 1l

-------- S z t,( )dz0

l

∫=

N t( ) NeqVj t( )ηkT

----------------------⎝ ⎠⎜ ⎟⎛ ⎞

exp 1–⎝ ⎠⎜ ⎟⎛ ⎞

=

I t( ) I0 i jω t( )exp+=

Vj t( ) Vj0 vj jω t( )exp+=

N t( ) N0 n jω t( )exp+=

S t( ) S0 s jω t( )exp+=

i vj jω Ct1

R1----------+⎝ ⎠

⎛ ⎞ is+=

vj is jωLs R2 Rin+ +⎝ ⎠⎛ ⎞=

is Γaqwdl N0 Ntr–⎝ ⎠⎛ ⎞ s=

vjη kTqN0

----------------- n=

Rdτnη kT

q2wdlN0

----------------------------=

58 HUI LV et al.

(8d)

(8e)

(8f)

(8g)

(8h)

The photon propagation equation of an SOA can be expressed as [5]

(9)

where α i is the spatially-averaged loss coefficient in the active layer of the amplifier.We neglect the z-dependence of the carrier density, integrate and normalize Eq. (9)on [0, z], and then solve it for the photon density at location z in terms of the photondensity at the input facet of the SOA as

(10)

At the output facet of the SOA, the photon density is

(11)

Substituting Eq. (10) in Eq. (3) gives

(12)

Comparing Eq. (11) with Eq. (12), we can obtain the relationship

(13)

R1Rd

1 aΓ S0τn+-----------------------------------=

Ctτn

Rd------------=

LsRd

Γ 2a N0 Ntr–( ) β aτn S0+( )------------------------------------------------------------------------=

R2Γβ N0

τn S0---------------------Ls=

Rinrin

S0------------Ls=

∂S z t,( )∂z

------------------------ Γa N z t,( ) Ntr–⎝ ⎠⎛ ⎞ αi– S z t,( )=

S z t,( ) S 0 t,( ) Γa N t( ) Ntr–⎝ ⎠⎛ ⎞ αi– z

⎩ ⎭⎨ ⎬⎧ ⎫exp=

S l t,( ) S 0 t,( ) Γa N t( ) Ntr–⎝ ⎠⎛ ⎞ αi– l

⎩ ⎭⎨ ⎬⎧ ⎫exp=

S t( )S 0 t,( ) Γa N t( ) Ntr–⎝ ⎠

⎛ ⎞ αi– l⎩ ⎭⎨ ⎬⎧ ⎫exp 1–

Γa N t( ) Ntr–⎝ ⎠⎛ ⎞ αi– l

----------------------------------------------------------------------------------------------------------------=

S l t,( ) Γa N t( ) Ntr–⎝ ⎠⎛ ⎞ αi– lS t( ) S 0 t,( )+=


We define the output photon density as

(14)

Substituting Eq. (5) and Eq. (14) in Eq. (13) gives

(15)

Defining small-signal voltage vs as

(16)

and then substituting Eqs. (8) and (16) in Eq. (15), we can obtain

(17)

where

(18a)

(18b)

The small-signal equivalent circuit model of the intrinsic part of an SOA is directlyderived from Eqs. (6), (7) and Eq. (17). With the electrical parasitics taken intoaccount, the total circuit model can be obtained, as shown in Fig. 1. For an SOAintegrated with an SGDBR laser, the impact of the SGDBR laser on the SOA sectionis represented by the resistance Rin and the wavelength dependence of the circuitparameters. i is the small-signal current injected into the SOA section. Cp, Lp andRp represent the package parasitics, and Cs and Rs characterize the chip parasitics. Ctis the sum of the space-charge capacitance of the heterojunction Csc and the diffusioncapacitance Cd. The resistances R1, R2 and Rin cause the damping of the electro-opticalresonance. The spatially-averaged small-signal photon storage is modeled by the in-

S l t,( ) S0' s' jω t( )exp+=

s' Γa N0 Ntr–⎝ ⎠⎛ ⎞ αi– ls ΓalS0n+=

vs s'=

vs is jωL R+⎝ ⎠⎛ ⎞=

LΓalS0qN0

ηkT------------------------------ Ls=

RΓa N0 Ntr–( ) αi–Γaqwd N0 Ntr–( )

--------------------------------------------------ΓalS0qN0

ηkT------------------------------ R2 Rin+( )+=

Fig. 1. Small-signal equivalent circuit model of an SOA.

Parasitics Intrinsic SOA

i RpLp

Rs

Cp Cs Pinvj Ct

R2Ls

isRt

Rinis

L

R

vs Pout

60 HUI LV et al.

ductance Ls. The traveling-wave effect in the cavity of the SOA section can berepresented by R and L. The output small-signal photon density is represented by vs.

3. Parameters extraction

All the circuit parameters in Fig. 1 can be extracted by fitting the circuit model withthe measured S-parameters of an SOA integrated with an SGDBR laser. The deviceused under our test has been reported with quasi-continuous wavelength coverage over35 nm and side mode suppression ratio (SMSR) of more than 30 dB for all selectedwavelength channels [8]. The experimental setup for the measurement of the S-param-eters is illustrated in Fig. 2. The gain section and tuning sections of the device aredriven by low noise and high stability current drivers to keep the SGDBR laser workingat a certain wavelength. The SOA section is biased through a wide bandwidth bias tee,while a thermoelectric cooler (TEC) controller is introduced to obtain a precise settingand stabilization of the lasing wavelength. The output modulated optical signal ofthe device is routed to the wide bandwidth optical receiver unit of the networkanalyzer, which can provide both the reflection response S11 (when configured forelectrical measurement) and the IM response S21 (when configured for electro-opticalmeasurement). The optical receiver response can be calibrated before measurement [9].

When the SOA section is biased at high current above transparency, the space--charge capacitance of heterojunction has a small impedance and small junctiondynamic resistance. In this case, the intrinsic part of the SOA section can be modeled

NETWORK ANALYZER

ELECTRICAL

OPTICAL

OUT

OUT

IN

IN

Current

Bias tee

Rear mirror Phase Gain Front mirror SOA

TECSOA-integrated SGDBR laser controller

sourceCurrentsource

Currentsource

Currentsource

Currentsource

Fig. 2. Microwave measurement setup for the SOA section.


by using a short circuit. So, the small-signal equivalent circuit model can be simplifiedas shown in Fig. 3, and the parasitic parameters can be regarded invariable for differentbias currents [10]. For this situation, the microwave reflection coefficient S11 ofthe input port is entirely determined by the parasitic elements and can be related tothe input admittance Y11 by [11]

(19)

where Z0, usually assumed as 50 Ω, is the characteristic impedance of the transmissionline between the network analyzer and the SOA section under test. From Fig. 3, wecan obtain the expression of Y11 as

(20)

The five parasitic parameters are extracted by fitting the S11 converted fromthe complex admittance of the simplified SOA-section circuit model by Eqs. (19)and (20) with the measured data. Since the parasitic parameters are determined by

Fig. 3. Simplified small-signal equivalent circuit model of the SOA section biased above transparency.

Z0 Rp Rs

Y11Cp Cs

Lp

S11Z0Y11 1–Z0Y11 1+

-------------------------------=

Mag

nitu

de S

11 [d

B]

Frequency [GHz]

Measured

Fitted

0

–2

–4

–6

–80 2 4 6 8 10

Fig. 4. Measured and fitted S11 of the SOA section.

Y111 jω RsCs+

Rp Rs ω2RsCs Lp– jω Rp RsCs Lp+( )+ +----------------------------------------------------------------------------------------------------------- jω Cp+=

62 HUI LV et al.

the electrical characteristics of the SOA section, they are independent of the wave-length of the input optical signal. The measured and fitted S11 of the SOA section arepresented in Fig. 4, and the extracted values of the parasitic parameters are given inTable 1.

The IM response S21 of the SOA section is determined by both the photon responseand the effect of the parasitic elements. The expression of S21 is as follows:

(21)

where pi is the transmitted radio frequency (RF) power of the network analyzer andset at –10 dBm during the RF measuring process. po is the small-signal output powerof the SOA section. The coefficient A relates po to the small-signal photon density s'.As described in [10], the small-signal current transformation function is /i can beexpressed as

(22)

where

(23a)

(23b)

(23c)

Substituting Eqs. (22), (23) in Eq. (21) and fitting Eq. (21) with the measured S21,we can extract all the intrinsic circuit parameters. To avoid the numerical overflowproblem that occurs in the general circuit simulator, the output voltage vs is normalizedby the static photon density S'0. From Eqs. (8) and (18), we can see that all the intrinsic

T a b l e 1. Extracted values of the parasitic parameters.

Parameters ValuesCp [pF] 12.58Lp [nH] 0.29Rp [Ω] 0.47Cs [pF] 21.26Rs [Ω] 8.62

S212 po

pi------------

Avs

Z0 i2----------------- A jωL R+

pi Z0

----------------------------is

i---------= = =

is

i---------

Z1 Z3

Rs Z2-----------------

R1

R1 R2 Rin ω2Ls R1Ct jω Ls R1 R2 Rin+( )Ct++–+ +---------------------------------------------------------------------------------------------------------------------------------------------=

Z1Rs

1 jω RsCs+----------------------------------=

Z2 Rp jω Lp Z1+ +=

Z3Z2

1 jω Z2Cp+----------------------------------- Z0+=


circuit parameters are dependent on the dc components of the photon and carrierdensity, which are determined by the static bias current of the SOA section withEqs. (1) and (2). Figure 5 gives the measured and fitted S21 for different bias currentson the SOA section, where the operating wavelength is set at 1541.35 nm. The ex-tracted intrinsic circuit parameters corresponding to Fig. 5 are shown in Tab. 2.

In our model, the optical gain provided by the SOA section is characterized bythe intrinsic circuit parameters. As described in [12], the single-pass gain of the SOAsection is a function of the wavelength of the input signal. This feature will leadto the wavelength dependence of the intrinsic circuit parameters. Furthermore, due tothe nonuniformity of the output optical power for different wavelength channels [8],the wavelength change of the integrated SGDBR laser can also cause the variation

Mag

nitu

de S

21 [d

B]

Frequency [GHz]

Measured at:

Fitted at:–20

–30

–40

–50

–60

–70

–800 2 4 6 8 10

60 mA70 mA80 mA90 mA

100 mA110 mA

60 mA70 mA80 mA90 mA

100 mA110 mA

Fig. 5. Measured and fitted IM response of the SOA section for different bias currents (operatingwavelength of the SGDBR laser is set at 1541.35 nm).

T a b l e 2. Extracted values of the intrinsic parameters for different bias currents of the SOA section.Operating wavelength of the integrated SGDBR laser is set at 1541.35 nm, with the measured parameters:w = 2.2 μm, d = 90 nm, l =600 μm, Γ = 0.1, ng = 3.6 (ng is the group refractive index of the active layer).

ParametersBias currents

60 mA 70 mA 80 mA 90 mA 100 mA 110 mA

S'0 [m–3] 1.8×1022 2.19×1022 2.67×1022 3.01×1022 3.33×1022 3.62×1022

Ct [pF] 26.8 961.19 875.47 997.47 966.47 998.7R1 [Ω] 0.16 3.86 4.67 5.43 5.1 4.55R2 + Rin [Ω] 13.83 11.88 13.68 12.62 12.17 13.55Ls [pH] 704.61 1.49×103 298.76 17.45×10–3 21.26×10–3 73.76L [nH] 0.53 0.9 0.79 0.65 0.52 0.44R [mΩ] 7.13×103 181.68 77.98 30.13 58.29 100.53

64 HUI LV et al.

of the input power of the SOA section, which will have an impact on the intrinsiccircuit parameters by changing the dc components of the photon and carrier densitymentioned above. The wavelength dependence of the intrinsic circuit model can beseen in Fig. 6, which gives the measured and fitted S21 curves for different operatingwavelengths at the bias of 90 mA on the SOA section. The extracted intrinsic circuitparameters corresponding to Fig. 6 are listed in Tab. 3.

4. Optical frequency chirp analysisA phase modulation will take place when the injected current of the SOA sectionis amplitude modulated due to the complex susceptibility of the gain medium inthe SOA [13, 14]. The small-signal circuit model can be used to determine the fre-

Mag

nitu

de S

21 [d

B]

Frequency [GHz]

–20

–30

–40

–50

–60

–70

–800 2 4 6 8 10

Measured at 1532.68 nmMeasured at 1541.35 nmMeasured at 1551.72 nmFitted at 1532.68 nmFitted at 1541.35 nmFitted at 1551.72 nm

Fig. 6. Measured and fitted IM response of the SOA section for different operating wavelengths (dc biascurrent of the SOA section is set at 90 mA).

T a b l e 3. Extracted values of the intrinsic parameters for different operating wavelengths. λ1 == 1532.68 nm, λ2 = 1541.35 nm, λ3 = 1551.72 nm, the SOA section is biased at 90 mA, with the measuredparameters: w = 2.2 μm, d = 90 nm, l = 600 μm, Γ = 0.1, ng = 3.6.

Operating wavelengthsParameters λ1 = 1532.68 nm λ2 = 1541.35 nm λ3 = 1551.72 nm

S'0 [m–3] 2.56×1022 3.01×1022 2.9×1022

Ct [pF] 385.06 997.47 995.78R1 [Ω] 0.71 5.43 2.76R2 + Rin [Ω] 4.73 12.62 7.05Ls [pH] 0.74 17.45×10–3 71.58L [nH] 0.44 0.65 0.89R [mΩ] 307 30.13 139.62


quency modulation (FM) response of the SOA section. The optical frequency shift atthe output facet of the SOA section can be expressed as [15]

(24)

where α is the linewidth enhancement factor and Po (t ) is the output optical power ofthe SOA section and can be obtained by [7]

(25)

where h is the Planck constant, vg is the group velocity at the output facet of the SOAsection, and ν (t) is the optical frequency of the output signal. We split ν (t) into dcand ac components as

(26a)

(26b)

where ν1 is the small-signal FM component at the output facet of the SOA section.With Eq. (14), Eqs. (25), (26) substituted in Eq. (24), and Eq. (24) can be linearized to

(27)

and

(28)

Therefore, the current i1 through the capacitance CFM in the circuit model shownin Fig. 7 can be used as a quantitative analog of the optical frequency chirp term ν1.Since α has a value of approximately 5 in InGaAsP [16], the value of the capaci-tance CFM can be considered to be as about 0.4 F. As described in [1], the opticalfrequency chirp caused by the current modulation of the SOA section is dependent onthe amplifier bias, which can be divided into two cases. The measured P–I curve ofthe SOA section for the signal wavelength of 1541.35 nm is given in Fig. 8. Whenthe bias current is less than 90 mA, the gain saturation of the SOA section can beneglected to assume a simple case. In this case, the strength of the frequencymodulation is greater for higher amplifier bias. This point can be confirmed by

Δν t( ) α4π

------------d Po t( )ln

d t-----------------------------------=

Po t( )vg wdhv t( ) S l t,( )

Γ------------------------------------------------=

ν t( ) ν0 ν1 jω t( )exp+=

Δν t( ) ν1 jω t( )exp=

ν1ν0

S'0----------- jω

4πα

------------ν0 jω–--------------------------------------s'=

ν1ν0

S'0----------- ω

4πα

------------ν0⎝ ⎠⎛ ⎞

2ω 2+

---------------------------------------------- s' α4π

------------ω vs

S'0-----------≈= ω << 4π

α------------ν0⎝ ⎠

⎛ ⎞

66 HUI LV et al.

the calculated results from our small-signal circuit model, as shown in Fig. 9. Differentfrom the IM response in Fig. 6, which has the conventional low-pass shape witha resonance peak, the FM response is depressed sharply below a low-frequency turnpoint. It has a resonance peak at approximately the same frequency as the IM response.As shown in Fig. 8, when the amplifier bias is higher than 90 mA, the gain saturationbecomes serious and cannot be neglected. According to the measured results providedin [1], the occurrence of the amplifier gain saturation will depress frequencymodulation, which is consistent with our simulation results shown in Fig. 9. To clearlydemonstrate the chirp characteristics, a repeated 2-bit patterned sequence ‘10’ of

8

6

4

2

00 20 40 60 80 100

Out

put p

ower

[mW

]

ISOA [mA]

vs/S'0

+

–

i1

CFM = α /4π

Fig. 7. Small-signal equivalent circuit model for FM of the SOA section.

Fig. 8. Measured P–I curve of the SOA section (operating wavelength of the integrated SGDBR laser isset at 1541.35 nm).

Frequency [GHz]0 2 4 6 8 10

Fig. 9. Calculated FM responses for different bias currents of the SOA section (operating wavelengthof the integrated SGDBR laser is set at 1541.35 nm).

–10

–30

–50

–70

–90

–110

60 mA90 mA

110 mA

20lo

g(10

–12

i 1/i)

[dB

]


3 Gbit/s has been used to simulate the current modulation of the SOA section.The peak–peak current of 20 mA is selected to avoid the deviation from our small--signal model. The simulation results of the output frequency chirp in time domain aregiven in Fig. 10, where the maximum chirp of several GHz can be observed, which iscomparable to the measured results for the direct modulation of the SGDBR laser [17].

5. Conclusions

In this paper, we have proposed a small-signal equivalent circuit model for an SOA,which is monolithically integrated with an SGDBR laser. In this model, the interactionbetween the photon density and injected current of the SOA section, includingthe traveling-wave effect in the SOA, is taken into account. The parasitic circuitparameters are extracted separately from the intrinsic part with some simplifications.All the circuit parameters are obtained by fitting the circuit model with the experimen-tally measured microwave S-parameters of the total device. The intrinsic parametersof our circuit model are dependent on the static bias current of the SOA section andthe operating wavelength of the integrated SGDBR laser. The extraction of parametershas been performed on different conditions and all the fitted results agree well withthe measured data. The optical frequency chirp caused by the current modulation ofthe amplifier has been analyzed with our small-signal circuit model and the simulationresults are consistent with those measured earlier.

Acknowledgements – This work has been supported in part by the National Natural Science Foundationof China under Grant No. 61106046, and in part by the China Postdoctoral Science Foundation underGrant No. 20110491142. Additionally the authors wish to thank for the device supports from Dr. RuikangZhang and Mr. Lei Dong, with Accelink Technologies Co., Ltd.

6

4

2

0

–2

–4

–60.0 0.2 0.4 0.6 0.8 1.0

60 mA90 mA

110 mA

Time [ns]

Chi

rp [G

Hz]

Fig. 10. Simulated output chirp for different bias currents of the SOA section in time domain (operatingwavelength of the integrated SGDBR laser is set at 1541.35 nm).

68 HUI LV et al.

References[1] SAN-LIANG LEE, HEIMBUCH M.E., COHEN D.A., COLDREN L.A., DENBAARS S.P., Integration of

semiconductor laser amplifiers with sampled grating tunable lasers for WDM applications,IEEE Journal of Selected Topics in Quantum Electronics 3(2), 1997, pp. 615–627.

[2] WARD A.J., ROBBINS D.J., BUSICO G., BARTON E., PONNAMPALAM L., DUCK J.P., WHITBREAD N.D.,WILLIAMS P.J., REID D.C.J., CARTER A.C., WALE M.J., Widely tunable DS-DBR laser withmonolithically integrated SOA: Design and performance, IEEE Journal of Selected Topics inQuantum Electronics 11(1), 2005, pp. 149–156.

[3] NIELSEN M.L., SUDO S., MIZUTANI K., OKAMOTO T., TSURUOKA K., SATO K., KUDO K., Integration offunctional SOA on the gain chip of an external cavity wavelength tunable laser using etched mirrortechnology, IEEE Journal of Selected Topics in Quantum Electronics 13(5), 2007, pp. 1104–1111.

[4] HANSEN P.B., RAYBON G., WIESENFELD J.M., BURRUS C.A., LOGAN R.A., TANBUN-EK T., TEMKIN H.,Optical demultiplexing at 6 Gb/s using a semiconductor laser amplifier as an optical gate,IEEE Photonics Technology Letters 3(11), 1991, pp. 1018–1020.

[5] MORK J., MECOZZI A., EISENSTEIN G., The modulation response of a semiconductor laser amplifier,IEEE Journal of Selected Topics in Quantum Electronics 5(3), 1999, pp. 851–860.

[6] TUCKER R.S., POPE D.J., Microwave circuit models of semiconductor injection lasers, IEEETransactions on Microwave Theory and Techniques 31(3), 1983, pp. 289–294.

[7] CHU C.Y.J., GHAFOURI-SHIRAZ H., Analysis of gain and saturation characteristics of a semiconductorlaser optical amplifier using transfer matrices, Journal of Lightwave Technology 12 (8), 1994,pp. 1378–1386.

[8] HUI LV, TAN SHU, YONGLIN YU, DEXIU HUANG, LEI DONG, RUIKANG ZHANG, Fast power control andwavelength switching in a tunable SOA-Integrated SGDBR laser, in 14th OptoElectronics andCommunications Conference (OECC 2009), 2009, paper ThPD4.

[9] HALE P.D., WILLIAMS D.F., Calibrated measurement of optoelectronic frequency response, IEEETransactions on Microwave Theory and Techniques 51(4), 2003, pp. 1422–1429.

[10] JIANJUN GAO, XIUPING LI, FLUCKE J., BOECK G., Direct parameter-extraction method for laser dioderate-equation model, Journal of Lightwave Technology 22(6), 2004, pp. 1604–1609.

[11] YIKAI SU, SIMSARIAN J.E., LIMING ZHANG, Improving the switching performance of a wavelength--tunable laser transmitter using a simple and effective driver circuit, IEEE Photonics TechnologyLetters 16(9), 2004, pp. 2132–2134.

[12] DURHUUS T., MIKKELSEN B., STUBKJAER K.E., Detailed dynamic model for semiconductor opticalamplifiers and their crosstalk and intermodulation distortion, Journal of Lightwave Technology 10(8),1992, pp. 1056–1065.

[13] HARDER C., VAHALA K., YARIV A., Measurement of the linewidth enhancement factor α ofsemconductor lasers, Applied Physics Letters 42(4), 1983, pp. 328–330.

[14] ARAKAWA Y., YARIV A., Fermi energy dependence of linewidth enhancement factor of GaAlAsburied heterostructure lasers, Applied Physics Letters 47(9), 1985, pp. 905–907.

[15] COLDREN L.A., CORZINE S.W., Diode Lasers and Photonic Integrated Circuits, Wiley, 1995.[16] TUCKER R., High-speed modulation of semiconductor lasers, Journal of Lightwave Technology 3(6),

1985, pp. 1180–1192.[17] MAHER R., KAI SHI, ANANDARAJAH P.M., KASZUBOWSKA A., BARRY L.P., YONGLIN YU, Novel

frequency chirp compensation scheme for directly modulated SG DBR tunable lasers, IEEEPhotonics Technology Letters 21(5), 2009, pp. 340–342.

Received April 25, 2011


Polarization-independent two-port beam splitter grating under second Bragg incidence angle with usual duty cycle

BO WANG

School of Physics and Optoelectronic Engineering, Guangdong University of Technology, Guangzhou 510006, China; e-mail: [email protected]

Based on the total internal reflection (TIR) under second Bragg incidence angle, polarization--independent two-port beam splitter grating etched in fused silica is described for the usual dutycycle of 0.5. There are three diffraction orders in the reflection: –2nd order, –1st order, and0th order. The grating depth and period are optimized using the rigorous coupled-waveanalysis (RCWA) in order to separate the incident wave into the –2nd and 0th orders with gooduniformity and high efficiency for the TE and TM polarization wavelength of 800 nm. The dif-fraction properties for operation have been investigated for the incident wavelength and angle,indicating that good tolerance of incidence angle can be obtained for the designed beam splittergrating. Most importantly, the advantages of usual duty cycle of 0.5 and much shallower-etcheddepth will facilitate effective fabrication the reported beam splitter, which is of great significancefor the practical use in numerous optical systems.

Keywords: second Bragg angle, total internal reflection, beam splitter.

1. Introduction

High-density deep-etched gratings have attracted a great deal of attention due to theirnovel optical properties and promising use in micro-optical elements [1–3]. Andrefinements in photolithography and inductively coupled plasma dry etching methodmake it possible to fabricate the designed and optimized grating-based diffractiveoptical elements for low cost mass production [4]. Such grating elements haveadvantages of the simple structure, high efficiency, and small feature size overconventional optical devices [5].

A series of works presented optimized high-density deep-etched gratings asthe high-efficiency element [6, 7], polarizing beam splitter [8, 9], and two-port beamsplitter [10, 11]. Compared with a beam splitter based on multilayer coatings, beamsplitter gratings can achieve high efficiency without multiple refractions and reflec-tions. A transmission wideband two-port beam splitter can be realized with a binaryfused-silica phase grating for not only TE or TM polarization but also for both TE

70 B. WANG

and TM polarizations, where the optimized polarization-independent two-port beamsplitter is with special duty cycle of 0.643 [12]. In order to improve the efficiency,a two-port beam splitter of total internal reflection (TIR) grating [13] was introduced.Such a beam splitter grating can show polarization-independent property with specialduty cycle of 0.35 [14]. For easy fabrication in practice, it is desirable for a polarization--independent beam splitter with usual duty cycle of 0.5. Although a transmissionpolarization-independent beam splitter was designed and fabricated with optimizedperiod of 891 nm, depth of 2.873 μm, and usual duty cycle of 0.5. The aspect ratio ofgrating depth to ridge width is about 6.45 [10], which may be much higher forfabrication of a transmission grating. To the best of our knowledge, no one haspresented polarization-independent two-port beam splitter grating under the secondBragg incidence angle with usual duty cycle.

In this paper, we describe a polarization-independent two-port beam splitter basedon TIR grating with usual duty cycle, where energies under second Bragg incidenceangle are reflected in the –2nd and 0th orders. Grating period and depth are optimizedusing rigorous coupled-wave analysis (RCWA) [15]. The diffraction properties ofwavelength range and angular bandwidth are investigated for the diffracted –2nd,–1st, and 0th orders.

2. Polarization-independent two-port beam splitterAs shown in Fig. 1, the two-port beam splitter with period d and depth h is etched infused silica with refractive indices n1 and n2 = 1 for air, which is illuminated by a planewave with wavelength λ under second Bragg angle of θi = sin–1(λ /(n1d )). The polar-ization-independent beam splitter can separate both TE- and TM-polarized incidentwaves into the –2nd and 0th orders equally. The grating duty cycle f is the ratio ofthe ridge width to the period. Generally speaking, grating pattern can be generated bylaser direct writing, electron beam, and holographic interference. For high-densitydeep-etched grating, small variation of duty cycle can greatly affect the diffraction

d

h

n2

n1

θi

θ–2nd

θ0th

Fig. 1. Schematic of a polarization-independent two-port beam splitter based on TIR grating undersecond Bragg incidence angle (n1 and n2 refractive indices of fused silica and air, respectively, d period,h depth, θi incidence angle, θ0th and θ–2nd diffraction angles of the 0th and –2nd reflection orders in fusedsilica, respectively).

Polarization-independent two-port beam splitter grating... 71

efficiency and property. For fabrication purposes, it is interesting for a grating withusual duty cycle of 0.5 to realize desirable optical functions.

In the design, the TIR together with the second Bragg incidence angle are takeninto account. The entire incident wave can be reflected without transmission to achievehigh efficiency by TIR, where the period should satisfy the inequality

(1)

There are three diffracted orders: –2nd order, –1st order, and 0th order. Accordingto the grating equation, the period should vary as follows

(2)

For an incident wavelength of 800 nm, the refractive index is 1.45332 for fusedsilica. With TIR and second Bragg incidence conditions, a range of 551–800 nm isconsidered in the design. The diffraction property can be widely investigated withdifferent grating parameters. Figure 2 is the contour of the efficiency ratio betweenthe –2nd order and 0th order versus grating period and depth for the incident wave-length of 800 nm with usual duty cycle of 0.5 under the second Bragg incidence angle.In Fig. 2, the efficiency ratio can be unity for not only TE but also TM polarizationwith optimized grating depth of 0.62 μm and period of 663 nm. With deviations ofdepth and period from the optimized results, the efficiency ratio of the –2nd to 0thorder may not be equal to unity. In Fig. 2, efficiency ratios within the range of0.8–1.25 can still be tolerated with the depth of 0.604–0.631 μm and period of

λn1

---------- d λn2

----------< <

λn1

---------- d 2λn1

------------< <

0.65

0.62

0.60

0.55650 655 660 663 665 670 675 680

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

Dep

th [μ

m]

Period [nm]

a b

650 655 660 663 665 670 675 680Period [nm]

Fig. 2. The contour of the efficiency ratio between the –2nd order and 0th order versus grating period anddepth for the incident wavelength of 800 nm with usual duty cycle of 0.5 under second Bragg incidenceangle: TE polarization (a); TM polarization (b).

72 B. WANG

662–664 nm. Figure 3 shows the efficiency versus the grating depth under secondBragg incidence angle for the incident wavelength of 800 nm with period of 663 nmand usual duty cycle of 0.5. In Fig. 3, efficiencies of the –2nd and 0th orders for TEand TM polarizations are = 46.38%, = 46.14%, = 46.81%, and

= 46.36%. This indicates that with optimized grating period and depth, the TIRgrating can separate both TE and TM polarizations into different orders withuniformity under second Bragg incidence angle for the usual duty cycle of 0.5.

3. Properties for operationFigure 4 shows the diffraction efficiency and efficiency ratio versus the incidentwavelength near the 800 nm with the optimized grating parameters under second Bragg

η 2nd–TE η0th

TE η 2nd–TM

η0thTM

Fig. 3. The efficiency versus the grating depth under second Bragg incidence angle for the incidentwavelength of 800 nm with a period of 663 nm and usual duty cycle of 0.5.

100

80

60

40

20

00 0.2 0.4 0.6 0.8 1.0

TE(0th)TE(–1st)TE(–2nd)TM(0th)TM(–1st)TM(–2nd)

Depth [μm]

Ref

lect

ion

effic

ienc

y η

[%]

Fig. 4. Reflection efficiency (a) and efficiency ratio (b) versus the incident wavelength near the 800 nmwith the optimized grating parameters under second Bragg incidence angle for the usual duty cycle of 0.5.

100

80

60

40

20

0750 800 850


Wavelength λ [nm]

Ref

lect

ion

effic

ienc

y η

[%]

3.0

750 800 850

TETM

Wavelength λ [nm]

Effic

ienc

y ra

tio η

–2nd

/η0t

h 2.5

2.0

1.5

1.0

0.5

0

a b

Polarization-independent two-port beam splitter grating... 73

incidence angle for the usual duty cycle of 0.5. Equal efficiency between the –2nd and0th orders can be achieved with the wavelength of 800 nm, which will not be so uniformwith deviations of wavelength. In Fig. 4, efficiency ratios of 0.8–1.25 can still beachieved within the range of 798–802 nm for both TE and TM polarizations.

Figure 5 shows the diffraction efficiency and efficiency ratio versus the incidenceangle near the second Bragg incidence angle with the optimized results and the incidentwavelength of 800 nm for the usual duty cycle of 0.5. It indicates that with the secondBragg incidence angle, the TIR grating can work as a polarization-independenttwo-port beam splitter with good uniformity. Efficiency differences between twoorders may increase with incidence angle deviating from the given mounting. In Fig. 5,efficiency ratios of the –2nd to 0th orders are in the range of 0.8–1.25 with the incidenceangle of 53.29°-57.95° for both TE- and TM-polarized waves. This indicates thatthe polarization-independent two-port beam splitter can tolerate a wide range ofincidence angle.

4. ConclusionsBased on TIR under second Bragg incidence angle, a polarization-independenttwo-port beam splitter has been presented for the usual duty cycle of 0.5. Withoptimized depth of 0.62 μm and a period of 663 nm, good uniformity and highefficiency can be achieved, and the designed beam splitter can separate the incidentwave into the –2nd and 0th orders for not only TE but also TM polarization. The beamsplitter is designed with novel structure of TIR etched in fused silica together withthe second Bragg incidence angle. Compared with reported beam splitter, the advan-tages of usual duty cycle and shallower-etched depth will facilitate effective fabrication.

Fig. 5. Reflection efficiency (a) and efficiency ratio (b) versus the incidence angle near the secondBragg incidence angle with the optimized results and the incident wavelength of 800 nm for the usualduty cycle of 0.5.

100

80

60

40

20

050 54 60


Incidence angle θi [deg]

Ref

lect

ion

effic

ienc

y η

[%]

1.4

TETM

Incidence angle θi [deg]

Effic

ienc

y ra

tio η

–2nd

/η0t

h 1.2

1.0

0.8

0.6

0.4

0

a b52 56 58 50 54 6052 56 58

0.2

74 B. WANG

The presented TIR fused-silica grating under second Bragg incidence angle should beuseful polarization-independent beam splitter for various optical applications.

Acknowledgements – This work is supported by the National Natural Science Foundation (11147183) ofChina and the Foundation (LYM09065) for Distinguished Young Talents in Higher Education ofGuangdong Province.

References[1] DELBEKE D., BAETS R., MUYS P., Polarization-selective beam splitter based on a highly efficient

simple binary diffraction grating, Applied Optics 43(33), 2004, pp. 6157–6165.[2] NÉAUPORT J., JOURNOT E., GABORIT G., BOUCHUT P., Design, optical characterization, and operation

of large transmission gratings for the laser integration line and laser megajoule facilities, AppliedOptics 44(16), 2005, pp. 3143–3152.

[3] CLAUSNITZER T., KÄMPFE T., KLEY E.-B., TÜNNERMANN A., TISHCHENKO A. V., PARRIAUX O.,Investigation of the polarization-dependent diffraction of deep dielectric rectangular transmissiongratings illuminated in Littrow mounting, Applied Optics 46(6), 2007, pp. 819–826.

[4] WANG S., ZHOU C., RU H., ZHANG Y., Optimized condition for etching fused-silica phase gratingswith inductively coupled plasma technology, Applied Optics 44(21), 2005, pp. 4429–4434.

[5] PETERS D.W., BOYE R.R., WENDT J.R., KELLOGG R.A., KEMME S.A., CARTER T.R., SAMORA S.,Demonstration of polarization-independent resonant subwavelength grating filter arrays, OpticsLetters 35(19), 2010, pp. 3201–3203.

[6] KONTIO J.M., SIMONEN J., LEINONEN K., KUITTINEN M., NIEMI T., Broadband infrared mirror usingguided-mode resonance in a subwavelength germanium grating, Optics Letters 35(15), 2010,pp. 2564–2566.

[7] KARAGODSKY V., SEDGWICK F.G., CHANG-HASNAIN C.J., Theoretical analysis of subwavelength highcontrast grating reflectors, Optics Express 18(16), 2010, pp. 16973–16988.

[8] WANG B., ZHOU C., WANG S., FENG J., Polarizing beam splitter of a deep-etched fused-silica grating,Optics Letters 32(10), 2007, pp. 1299–1301.

[9] ZHENG J., ZHOU C., FENG J., WANG B., Polarizing beam splitter of deep-etched triangular-groovefused-silica gratings, Optics Letters 33(14), 2008, pp. 1554–1556.

[10] FENG J., ZHOU C., ZHENG J., CAO H., LV P., Design and fabrication of a polarization-independenttwo-port beam splitter, Applied Optics 48(29), 2009, pp. 5636–5641.

[11] ZHENG J., ZHOU C., WANG B., FENG J., Beam splitting of low-contrast binary gratings under secondBragg angle incidence, Journal of the Optics Society of America A 25(5), 2008, pp. 1075–1083.

[12] WANG B., ZHOU C., FENG J., RU H., ZHENG J., Wideband two-port beam splitter of a binaryfused-silica phase grating, Applied Optics 47(22), 2008, pp. 4004–4008.

[13] MARCIANTE J.R., HIRSH J.I., RAGUIN D.H., PRINCE E.T., Polarization-insensitive high-dispersiontotal internal reflection diffraction gratings, Journal of the Optics Society of America A 22(2),2005, pp. 299–305.

[14] WANG B., High-efficiency two-port beam splitter of total internal reflection fused-silica grating,Journal of Physics B: Atomic, Molecular and Optical Physics 44(6), 2011, article 065402.

[15] MOHARAM M.G., GRANN E.B., POMMET D.A., GAYLORD T.K., Formulation for stable and efficientimplementation of the rigorous coupled- wave analysis of binary gratings, Journal of the OpticalSociety of America A 12(5), 1995, pp. 1068–1076.

Received May 23, 2011


Near infrared transmission in dual core lead silicate photonic crystal fibres

HENRY T. BOOKEY1, RYSZARD BUCZYŃSKI1, 2*, ANDREW WISCHNEWSKI1, DARIUSZ PYSZ3, RAFAŁ KASZTELANIC2, ANDREW J. WADDIE1, RYSZARD STĘPIEŃ3, AJOY K. KAR1, MOHAMMAD R. TAGHIZADEH1

1Heriot-Watt University, School of Engineering and Physical Sciences, Edinburgh EH14 4AS, Scotland, UK

2University of Warsaw, Faculty of Physics, Pasteura 7, 02-093 Warsaw, Poland

3Institute of Electronic Materials Technology, Wólczyńska 133, 01-919 Warsaw, Poland


Photonic crystal fibres (PCF) can provide the high confinement needed to enable nonlinear opticalprocesses to be studied in silicate fibre over short lengths without the need for large pulse ener-gies. Additionally, the capillary stacking technique for PCF fabrication lends itself to the designof multiple core fibres and this capability has triggered much work into the properties of dualcore PCF. In this paper, the effect of the dual core interaction on the nonlinear wavelengthconversion is studied using a femtosecond oscillator in the near IR range. Effective supercontinuumgeneration in the range 1300–1700 nm is achieved in the anomalous dispersion regime.

Keywords: photonic crystal fibres, supercontinuum generation, soft glass.

1. Introduction

Photonic crystal fibres (PCF) are well known to provide the high confinement neededto enable nonlinear optical processes to be studied in silicate fibre over short lengthswithout the need for large pulse energies [1].

Pure silica based PCFs offer low attenuation over a large wavelength range andhave been shown to be the perfect medium for various fibre sensors [2, 3] and activeoptoelectronic devices based on liquid crystals [4] as well as a very good medium forthe study of nonlinear supercontinuum effects due to their very high confinement andlong interaction length [5].

PCFs made of soft glasses cannot compete with pure silica PCFs in terms of opticalattenuation, but they offer a much broader transmission window in the infrared [6],a higher refractive index and a much higher nonlinear refractive index [7]. As a conse-

76 H.T. BOOKEY et al.

quence, mid-IR supercontinuum generation is possible in PCFs made of tellurite, heavymetal oxide and chalcogenide glasses [8–10].

The stack and draw technique for PCF fabrication lends itself to the design ofcomplex structures such as fibres with nanostructured cores [11] as well as multiplecore fibres [12–15]. This capability has triggered much work into the properties ofdual core PCF for applications in nonlinear switching, frequency conversion and gainflattening [12, 13].

Multi-frequency generation in dual core fibres was initially described in [12] andthe first prediction of the distinct advantages of multi-core PCF over single core inthe context of nonlinear frequency conversion was given by BUGAR et al. [14] andfurther developed in [15]. The observed nonlinear properties were due to the complexnonlinear intermixing processes taking place in the dual core PCFs leading to an en-hancement in the spectral content of the generated supercontinuum and opening newways to control supercontinuum generation (SG). A drawback of this solution isthe lower beam quality, which could potentially be an issue when coupling to standardsingle mode fibres.

In this paper, we study the effect of the dual core interaction on the nonlinearwavelength conversion using a femtosecond oscillator operating at 800 nm andan femtosecond OPA system operating at 1300 nm. The effects of core coupling andpolarisation are investigated. This paper is a complementary study of the fibrepresented previously in [15], where we focused on operation within the visible andnear infrared ranges up to 1200 nm.

2. Modelling and development of dual core photonic crystal fibre

A two glass dual core PCF was fabricated using the stack and draw technique.The photonic structure of the cladding was made of the borosilicate soft glass NC21,developed in-house at ITME, whereas the cores were made from the commerciallyavailable F2 glass from Schott Corp. The fibre consists of three rings of holes arrangedaround the dual core. The material properties of NC21 glass are: refractive indexnD = 1.518, density ρ = 2.50 g/cm3, coefficient of thermal expansion α20–300 == 82×10–7 K–1, glass transition temperature Tg = 500 °C and dilatometric softeningpoint DTM = 545 °C. The oxide composition, transmission and viscosity propertiesof NC21 glass are shown in [14]. The nonlinear refractive index of the silicate glassNC21 is very close to that of pure silica [7]. The main advantage of NC21 is its excellentrheological properties and very good performance at low temperatures that allowsthe preparation of complex fibre structures. Since it is thermally matched to the highindex F2 glass, dual glass fibres can be successfully developed with greatly reducedinternal stresses.

As can be seen in the SEM images (Fig. 1), the core shapes are non-circular andof different sizes. The major and minor axes of the cores are 3.04 μm and 1.92 μm forthe small core, and 2.42 μm and 1.78 μm for large core. The central air hole betweenthe cores has a diameter of 1.69 μm. The cores were fabricated with different sizes to

Near infrared transmission... 77

create dissimilar dispersion curves for four components of the fundamental mode.The lattice pitch Λ in the fibre was 2.29 μm while the filling factor d /Λ in the photoniccladding equalled 0.91. The overall diameter of the photonic structure was 21.33 μm.

The modal and dispersion properties as well as the effective mode areas of the fibrewere calculated with a finite difference method based on the real structure taking intoaccount the dispersion of the bulk glass by means of Sellmeier coefficients.

The fundamental mode of the dual core PCF is composed of four components thatdiffer in electrical field symmetry (even and odd) and in polarization (along main axis).

The calculated phase birefringence is B = 0.2×10–3 and B = 0.7×10–3 for both pairsof components with a similar type of symmetry in the electrical field. The calculatedeffective mode area for every component of fundamental mode was 6.3 μm2. The zerodispersion wavelength (ZDW) was calculated to be 1.22, 1.37, 1.38 and 1.51 μm forthe four components of the fundamental mode (Fig. 2). The obtained dispersion doesnot allow the use of a femtosecond Ti:sapphire oscillator in the range of 750–900 nmto pump in the anomalous dispersion region as was shown in our previous paper [15].

Fig. 1. SEM micrographs of the dual core photonic crystal fibre: photonic structure of the fibre (a); corearea of the fibre (b). Light grey indicates area made of F2 lead-silicate glass, while dark grey area indicatesan area made of low index NC21 borosilicate glass. Cores are intentionally different in size.

a b

Fig. 2. Dispersion characteristics for the four components of the fundamental mode of the dual corephotonic crystal fibre.

50

0

–50

–100

–150

–2000.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

D [p

s/km

nm]

λ [μm]


3. Near infrared transmission propertiesThe linear transmission properties of the fibre were studied in the third telecommu-nication window. An amplified spontaneous emission (ASE) source based on erbiumdoped fibre was used as a broadband source in the spectrum range 1550–1580 nm.The following schematic (Fig. 3) depicts the setup used. A small core silica fibre(Sumitomo HNLF Φ 3.5 μm) was used to butt-couple to the test fibre. A set of twomicropositioners with submicrometer precision allowed highly efficient coupling intothe test fibre cores and selective collection of the signal from the core area withoutscattered light in the fibre cladding. A test sample 50 cm long of the dual core PCFwas used for tests.

The output modes for different launch conditions are shown in Fig. 4. The innercladding tube in which the capillaries are stacked during fabrication can be seen inFigs. 4a and 4b as these structures guide the cladding modes and can act as multimodewaveguides when the input fibre is offset from the core region. When input light isproperly aligned against the test PCF all of the incident light can be effectively coupledinto both cores as shown in Fig. 4c. Energy transfer into cladding was not observed inthis case.

The transmission spectrum for both the ASE source and the light transmittedthrough the PCF fibre were recorded and shown in Fig. 5. This spectrum was observed

ASE sourceSplice

Small core fibre

Micro-positioners

Dual core PCF

OSA

Small core fibre

Fig. 3. Schematic of setup used to study near IR transmission.

Fig. 4. Near field images of the photonic crystal fibre output under different coupling conditions at1550 nm: light is coupled into fibre cladding (a), light is coupled into inner cladding tube in whichthe capillaries are stacked during fabrication (b), light is coupled into both cores (c).

a b c


for the case where the output from one core is collected for a single core excitation.The spectral modulation results from a combination of the inter core and polarizationmode coupling.

Attenuation of 6.7 dB/m for the PCF was measured using cut back technique at1550 nm. This is typical attenuation possible to achieve in PCF made of silicate glass.It limits practical use of this type fibre up to a few tens of centimeters and determinesits application to some specific purposes as nonlinear medium.

4. Propagation of femtosecond pulses in dual core PCF

A schematic of the system used to study femtosecond pulse propagation in the dualcore fibre is given in Fig. 6. Microscope objectives with high numerical aperture(NA = 0.65) were used to generate the spot sizes required to excite each coreseparately. The linear polarisation of the optical parametric amplifier (OPA) sourcewas adjusted using a half-wave plate and the output spectra were recorded usinga multimode silica fibre coupled to a USB spectrometer.

The signal output from the OPA was tuned to 1330 nm and the transmittedspectra were recorded for a 500 nJ incident pulse energy for a 18 cm section of

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.01550 1555 1560 1565 1570 1575 1580

TransmittedInputN

orm

alis

ed s

igna

l

Wavelength [nm]

Loss

[dB

]

Wavelength [nm]

–35

–36

–37

–38

–39

–401570 1571 1572 1573 1574 1575

a b

Fig. 5. Normalised ASE transmission before and after the dual core fibre (a). The modulation from intercore coupling is shown in (b).

Fig. 6. Experimental arrangement for femtosecond pulse propagation measurements.

Fibre under test USBspectrometer

×40, 0.65 NA

600 μm core patch cord

×40, 0.65 NA

P λ/2

Femtosecond OPA system:Δt = 100 fs, λsignal = (1.1–1.6) μm,

Epulse = 50 μJ


the dual core PCF. The coupling efficiency was estimated to be 40%. The amount ofbroadening observed was optimised by rotating the half-wave plate, since the PCF isbirefringent and the polarization components of fundamental mode possess differentdispersion characteristics. Spectra are shown for the wave plate angle producingthe largest extent of continuum and also the polarisation orthogonal to this (Fig. 7).The dependence was found to be greater in the larger core and corresponds to the higherbirefringence present in this core.

The collated spectra are shown on a log scale in Fig. 8. At this energy and fibrelength, there appears to be little improvement in the extent of the continuum whencoupling to either the large or both cores simultaneously whereas coupling to the smallcore produces significantly less broadening. This is thought to be due to a decrease inthe coupling efficiency to this smaller core in a manner similar to that observedpreviously when the dual core fibre was excited at 806 nm [15]. In this case, however,the general character of spectrum is different. We can identify several separatepeaks and a very asymmetric spectrum with respect to the pump wavelength shiftedinto the longer wavelength regime. This is typical of the spectrum that might beobserved during soliton generation when the fibre is pumped in the anomalousdispersion regime [5].

The generated spectrum had a bandwidth of 400 nm red shifted with respect tothe pump wavelength. However, further simulations have shown that the registered

1.2

0.8

0.4

0.01200 1300 1400 1500 1600 1700

0 deg45 deg

Nor

mal

ised

sig

nal [

a. u

.]

Wavelength [nm]

a b

c1.2

0.8

0.4

0.01200 1300 1400 1500 1600 1700

0 deg45 deg

Nor

mal

ised

sig

nal [

a. u

.]

Wavelength [nm]

1.2

0.8

0.4

0.01200 1300 1400 1500 1600 1700

0 deg45 deg

Nor

mal

ised

sig

nal [

a. u

.]

Wavelength [nm]

90 deg

Fig. 7. Nonlinear spectral broadening and wavelength generation in dual core fibre for different anglesof the half-wave plate for coupling to the small (a), large (b) and both (c) cores.


spectrum is limited to 1700 nm due to the sensitivity limit of the USB spectrometer,not the generated spectrum (Fig. 9).

To confirm the solitonic origin of the spectral broadening we numericallyinvestigated SG in the dual core PCF by solving numerically a nonlinear Schroedingerequation (NLSE) with the split step Fourier method implemented by TRAVERS et al. [16].For this set of simulations we considered all four components of the fundamental mode

0

1200 1300 1400 1500 1600 1700

Input (dB)

Nor

mal

ised

sig

nal [

a. u

.]

Wavelength [nm]

–4

–8

–12

–16

–20

Dual core couplingLarge core (45 deg)Small core (45 deg)

Fig. 8. Normalised output spectra for three launch conditions with input spectrum shown for comparison.

0.18

0.12

0.06

0.00800 1000 1200 1400 1600 1800

40

20

0

–20

–40

Dis

tanc

e [m

]In

tens

ity [d

B]

Wavelength [nm]

Wavelength [nm]

a

b

800 1000 1200 1400 1600 1800

Fig. 9. Propagation of 100 fs pulse in 18 cm long dual core fibre (a), spectrum broadening at the distanceof 18 cm (b).


and introduced an optical pulse with a pump wavelength of 1330 nm, a pulse lengthof 100 fs and total pulse energy 200 nJ. Three of four components of the fundamentalmode have normal dispersion at pump wavelength (Fig. 2). The obtained broadeningis symmetric and narrow since self phase modulation is the dominant nonlinearmechanism in this case. These components are responsible for the symmetric broad-ening of the peak related to the pump wavelength at 1330 nm. The fourth componentof the fundamental mode with ZDW = 1220 nm is responsible for the large non-sym-metric broadening. Simulation results for this component allow the identification ofthe generation of two solitons. We observe a red shift of their intensity peaks duringpropagation in the fibre (Fig. 9a) and have calculated that the two main peaks lie at1566 nm and above 1900 nm. Similar results were observed in the experimental resultswhen the large core was excited (Fig. 8), although the soliton peak was at 1620 nm inthis case.

The agreement between simulation and experiment is not perfect for severalreasons. Firstly, the numerical solution of the nonlinear Schroedinger equation isperformed for a single dispersion characteristic, while in the experiment all fourcomponents with different dispersion characteristics contribute to the spectrumgeneration [16]. Moreover, some additional errors are introduced by the estimation ofthe nonlinear coefficient and the attenuation of the fibre as well as the peak powerof the pulse coupled into fibre’s core. The simulations do provide a qualitativeexplanation of the origin of the observed spectral broadening and allow an approximateprediction of the generated spectral bandwidth.

5. ConclusionsThe transmission properties of a dual core photonic crystal fibre fabricated with a leadsilicate glass have been studied in the near infrared range. The inter core coupling hasbeen confirmed by observing the transmission of a broadband source. Supercontinuumgeneration in the anomalous dispersion regime is observed under illumination witha 100 fs pulse at 1330 nm. The effects of incident polarisation on the nonlinear spectralbroadening have been introduced.

Acknowledgements – This work was supported by the Polish Ministry of Science and Higher Educationresearch grants R0204302 and NN515523738. HTB is supported by a Royal Society of Edinburgh ScottishGovernment Personal Research Fellowship.

References[1] BJARKLEV A., BROENG J., BJARKLEV A.S., Photonic Crystal Fibres, Principles of Optics, 1st Edition,

Kluwer Academic, Dordrecht, 2003.[2] SZCZUROWSKI M.K., MARTYNKIEN T., STATKIEWICZ-BARABACH G., URBANCZYK W., WEBB D.J., Mea-

surements of polarimetric sensitivity to hydrostatic pressure, strain and temperature in birefringentdual-core microstructured polymer fiber, Optics Express 18(12), 2010, pp. 12076–12087.

[3] SKOROBOGATIY M., Microstructured and Photonic Bandgap fibers for applications in the resonantbio- and chemical sensors, Journal of Sensors 2009, article 524237.


[4] WOLINSKI T.R., ERTMAN S., CZAPLA A., LESIAK P., NOWECKA K., DOMANSKI A.W., NOWINOWSKI--KRUSZELNICKI E., DABROWSKI R., WOJCIK J., Polarization effects in photonic liquid crystal fibers,Measurement Science and Technology 18(10), 2007, pp. 3061–3069.

[5] DUDLEY J.M., GENTY G., COEN S., Supercontinuum generation in photonic crystal fiber, Reviews ofModern Physics 78(4), 2006, pp. 1135–1184.

[6] STEPIEN R., BUCZYNSKI R., PYSZ D., KUJAWA I., FILIPKOWSKI A., MIRKOWSKA M., DIDUSZKO R.,Development of thermally stable tellurite glasses designed for fabrication of microstructured opticalfibers, Journal of Non-Crystalline Solids 357(3), 2011, pp. 873–883.

[7] LORENC D., ARANYOSIOVA M., BUCZYNSKI R., STEPIEN R., BUGAR I., VINCZE A., VELIC D., Nonlinearrefractive index of multicomponent glasses designed for fabrication of photonic crystal fibers,Applied Physics B 93(2–3), 2008, pp. 531–538.

[8] DOMACHUK P., WOLCHOVER N.A., CRONIN-GOLOMB M., WANG A., GEORGE A.K., CORDEIRO C.M.B.,KNIGHT J.C., OMENETTO F.G., Over 4000 nm bandwidth of mid-IR supercontinuum generationin sub-centimeter segments of highly nonlinear tellurite PCFs, Optics Express 16(10), 2008,pp. 7161–7168.

[9] BUCZYNSKI R, BOOKEY H.T., PYSZ D., STEPIEN R., KUJAWA I., MCCARTHY J.E., WADDIE A.J.,KAR A.K., TAGHIZADEH M.R., Supercontinuum generation up to 2.5 μm in photonic crystal fibermade of lead-bismuth-gallate glass, Laser Physics Letters 7(9), 2010, pp. 666–672.

[10] FATOME J., KIBLER B., EL-AMRAOUI M., JULES J.-C., GADRET G., DESEVEDAVY F., SMEKTALA F.,Mid-infrared extension of supercontinuum in chalcogenide suspended core fibre through solitongas pumping, Electronics Letters 47(6), 2011, pp. 398–400.

[11] BUCZYNSKI R., PYSZ D., STEPIEN R., KASZTELANIC R., KUJAWA I., FRANCZYK M., FILIPKOWSKI A.,WADDIE A.J., TAGHIZADEH M.R., Dispersion management in nonlinear photonic crystal fibreswith nanostructured core, Journal of the European Optical Society – Rapid Publications 6, 2011,article 11038.

[12] BETLEJ A., SUNTSOV S., MAKRIS K.G., JANKOVIC L., CHRISTODOULIDES D.N., STEGEMAN G.I., FINI J.,BISE R.T., DIGIOVANNI D.J., All-optical switching and multifrequency generation in a dual-corephotonic crystal fiber, Optics Letters 31(10), 2006, pp. 1480–1482.

[13] KHAN K.R., WU T.X., CHRISTODOULIDES D.N., STEGEMAN G.I., Soliton switching and multi-fre-quency generation in a nonlinear photonic crystal fiber coupler, Optics Express 16(13), 2008,pp. 9417–9428.

[14] BUGAR I., FEDOTOV I.V., FEDOTOV A.B., KOYS M., BUCZYNSKI R., PYSZ D., CHLPIK J., UHEREK F.,ZHELTIKOV A.M., Polarization-controlled dispersive wave redirection in dual-core photonic crystalfiber, Laser Physics 18(12), 2008, pp. 1420–1428.

[15] BUCZYNSKI R., PYSZ D., MARTYNKIEN T., LORENC D., KUJAWA I., NASILOWSKI T., BERGHMANS F.,THIENPONT H., STEPIEN R., Ultra flat supercontinuum generation in silicate dual coremicrostructured fiber, Laser Physics Letters 6(8), 2009, pp. 575–581.

[16] TRAVERS J.C., FROSZ M.H., DUDLEY J.M., Nonlinear fibre optics overview, [In] SupercontinuumGeneration in Optical Fibers, [Eds.] Dudley J.M., Taylor J.R., 1st Edition, Cambridge UniversityPress, 2010.

Received September 28, 2011in revised form December 1, 2011


Conditions for tighter focusing and higher focal depth of radially polarized vector beam

XIUMIN GAO1*, QI WANG2, MAOJIN YUN3, JIANCHENG YU1, HANMING GUO2, SONGLIN ZHUANG2

1Electronics and Information College, Hangzhou Dianzi University, Hangzhou 310018, China

2University of shanghai for Science and Technology, Shanghai 200093, China

3College of Physics Science, Qingdao University, Qingdao 266071, China


The radially polarized vector beam has attracted much attention recently and was also used toobtain a smaller focal spot. In this paper, highly focusing properties of radially polarized vectorbeam are investigated by comparing them with those of linearly polarized beam. A condition wasfound for tighter focusing of radially polarized vector beam. The focal spot of radially polarizedvector beam is not always smaller than that of linearly polarized beam. Even if only a longitudinalfield component is considered, in fact, the condition for tighter focusing of radially polarized vectorbeam is very complicated. Therefore, more attention should be paid to the smaller focal spotgeneration by means of radially polarized vector beam in practical use. In addition, the focaldepth of radially polarized beam decreases on increasing numerical aperture under condition ofsmall radius ratio, and increases on increasing radius ratio. The focal depth difference betweenthese two kinds of beams shrinks upon increasing radius ratio and numerical aperture.

Keywords: radially polarized vector beam, focusing properties, vector diffraction theory.

1. IntroductionAs a kind of the cylindrical vector beam, radially polarized beam (RPB) has recentlygained much interest and attention due to its novel properties and wide applications,such as particle-trapping, optical data storage, laser machining and lithography [1–7].Especially, the focusing properties of RPB are investigated inventively [8–12].KOZAWA and SATO investigated the strong focusing of higher transverse modes ofradially polarized beams [13], which illustrates that the strong longitudinal componentforms a sharper spot at the focal point under a high-NA focusing condition. Inaddition, focusing properties of higher radial modes were also studied systemically byRASHID et al. [14]. It was demonstrated both theoretically and experimentally thatthe introduction of RPB illumination combined with an annular beam illuminationexhibits advantages in two aspects [9]. Firstly, it corrects the focus elongation and

86 X. GAO et al.

splitting in a focused evanescent field associated with a linearly polarized beam, andsecondly, it also improves significantly the lateral localization to approximatelya quarter of the illumination wavelength, which is less than half of the size thatis achievable under linearly polarized beam (LPB) illumination. The effect ofapodization on spot size under tight focusing conditions was also studied [15].

In this paper, highly focusing properties of RPB and LPB are studied to investigatethe smaller focal spot generation effect of the RPB beam in detail. It has been foundthat the condition for tighter focusing of RPB is complicated in fact. On the other hand,focal depth is also a very important parameter in many optical systems and can be usedto enhance the performance [16–20]. For example, in high-density optical data storagesystem, large focal depth makes it easy for the servo system to track. It was found inour investigation that the focal spot of RPB is not always smaller than that of LPB,and the focal depth difference between these two kinds of beams shrinks on increasingnumerical aperture. Focusing principle is given in Section 2. Section 3 showsthe simulation results and discussion. In addition, comparisons under high-order radialmodes are given. The conclusions are summarized in Section 4.

2. Focusing principle of RPB and LPB In the focusing system, we investigated the incident beam convergence throughan objective lens. The focusing principle of RPB has been analyzed recently, andthe electric field in the focal region in cylindrical coordinates can be written inthe form [12, 21],

(1)

where er and ez are the unit vectors in the radial and propagating directions,respectively. ECR and ECZ are amplitudes of the two orthogonal components, whichcan be expressed as

(2)

(3)

where r and z are the radial and longitudinal coordinates of observation point in focalregion, respectively. Parameter A is a constant, and k is the wave number. Parameterθj ( j = 1, 2) represents the polar angle corresponding to the optical aperture, namely,θ2 = asin(NA), and θ1 = a tan[R tan(θ2)], R is the normalized inner radius of the opticalaperture by outer radius of the optical aperture, and if R = 0 the optical aperture isa circle aperture, else it is an annular aperture. P(θ ) is the pupil function that describesthe amplitude of the field in the pupil of the lens which is assumed to be a function

EC r ϕ z, ,( ) ECR er ECZ ez+=

ECR r z,( ) A P θ( ) θ( )cos 2θ( ) J1 kr θ( )sin⎝ ⎠⎛ ⎞ ikz θ( )cos⎝ ⎠

⎛ ⎞ dθexpsinθ 1

θ 2

∫=

ECZ r z,( ) 2iA P θ( ) θ( )cos sin2 θ( ) J0 kr θ( )sin⎝ ⎠⎛ ⎞ ikz θ( )cos⎝ ⎠

⎛ ⎞ dθexpθ 1

θ 2

∫=

Conditions for tighter focusing and higher focal depth... 87

of θ only [12, 14]. The optical intensity of RPB in focal region can be obtained bycalculating the square modulus of Eq. (1). It can be seen that the focal pattern of RPBis cylindrical symmetric.

The electric field in the focal region of LPB is expressed in Cartesian coordinates,and if the incident polarization is in x direction, the electric field is in the form [22, 23],

(4)

where x, y, and z are the unit vectors in the x, y, and z directions, respectively. E0 isa constant. It is clear that the incident Gaussian beam is depolarized and has threecomponents (ELX , ELY and ELZ ). Variables r, φ, and z are the cylindrical coordinatesof an observation point in focal region. Variables I0, I1, and I2 are [22, 23],

(5)

(6)

(7)

where k is also the wave number. J0(x), J1(x), J2(x) and are the zero-order, the first--order, and the second-order Bessel functions of the first kind, respectively. In orderto make a comparison simple, parameter θj ( j = 1, 2) represents the same polarangle corresponding to the optical aperture, θ2 = asin(NA) and θ1 = a tan[R tan(θ2)].P(θ ) in Eqs. (5)–(7) has the same meaning as that in Eqs. (2) and (3). Focusing prop-erties of RPB and LPB can be obtained numerically by calculating Eqs. (1) and (4),respectively.

3. Numerical results and discussion3.1. Transverse focal size comparison between RPB and LPB

Here, the focusing property comparison between RPB and LPB is discussed. Withoutloss of validity and generality, the pupil function is taken as P(θ ) = 1. It should benoted that the size of focal spot is shown as the full width at half maximum (FWHM)in the focal plane, and its unit is k–1, k is the wave number and equals 2π /λ, whereλ is the wavelength of incident beam. And all the distance units in the tables andfigures of this article are also k–1. Table 1 shows the transverse FWHM of focal spot

EL r φ z, ,( ) ELX x ELY y ELZ z+ +

π E0iλ

----------------- I0 2φ( )I2cos+ x 2φ( )sin I2 y 2i φ( )I1zcos+ +⎩ ⎭⎨ ⎬⎧ ⎫

= =

=

I0 P θ( ) θ( )cos sin θ( ) 1 θ( )cos+⎝ ⎠⎛ ⎞ J0 kr θ( )sin⎝ ⎠

⎛ ⎞ i– kz θ( )cos⎝ ⎠⎛ ⎞ dθexp

θ 1

θ 2

∫=

I1 P θ( ) θ( )cos sin2 θ( ) J1 kr θ( )sin⎝ ⎠⎛ ⎞ i– kz θ( )cos⎝ ⎠

⎛ ⎞ dθexpθ 1

θ 2

∫=

I2 P θ( ) θ( )cos sin θ( ) 1 θ( )cos–⎝ ⎠⎛ ⎞ J2 kr θ( )sin⎝ ⎠

⎛ ⎞ i– kz θ( )cos⎝ ⎠⎛ ⎞ dθexp

θ 1

θ 2

∫=

88 X. GAO et al.

of focusing LPB and RPB. ELY and ELX indicate the transverse FWHM in x and ycoordinate directions in focal region of LPB, respectively. EC and ECZ give the FWHMof the total field and longitudinal field in focal region of RPB, respectively. It can beseen that the focal spot symmetry of LPB is considerably better determined undercondition of higher numerical aperture and larger R. For instance, the FWHM ratio ofELX to ELY is about 2.6 (= 5.30/2.02) for the case of NA = 0.99 and R = 0.4. The widthof the focal spot is smaller in the direction perpendicular to the initial direction of

T a b l e 1. Transverse FWHM of focal spot of focusing LPB and RPB.

NA 0.75 0.80 0.85 0.90 0.93 0.96 0.99

R = 0

ELY 4.16 3.88 3.62 3.38 3.24 3.10 2.96ELX 4.96 4.78 4.66 4.60 4.58 4.60 4.68EC 9.12 7.60 6.04 4.80 4.26 3.80 3.42ECZ 3.86 3.60 3.38 3.18 3.06 2.96 2.84

R = 0.1

ELY 4.12 3.82 3.56 3.30 3.14 2.94 2.54ELX 4.92 4.74 4.62 4.54 4.54 4.56 4.84EC 9.10 7.54 5.98 4.74 4.16 3.68 3.00ECZ 3.84 3.60 3.38 3.16 3.04 2.90 2.66

R = 0.2

ELY 3.98 3.68 3.38 3.10 2.90 2.66 2.22ELX 4.82 4.64 4.52 4.48 4.50 4.66 5.24EC 8.78 7.16 5.58 4.36 3.80 3.26 2.60ECZ 3.82 3.56 3.32 3.08 2.94 2.76 2.46

R = 0.3

ELY 3.80 3.48 3.20 2.88 2.68 2.44 2.10ELX 4.68 4.52 4.44 4.46 4.60 4.90 5.30EC 8.16 6.44 4.96 3.90 3.40 2.92 2.44ECZ 3.74 3.46 3.22 2.96 2.80 2.62 2.38

R = 0.4

ELY 3.62 3.30 3.02 2.72 2.52 2.32 2.02ELX 4.56 4.44 4.40 4.54 4.76 5.10 5.30EC 7.32 5.66 4.38 3.52 3.10 2.74 2.38ECZ 3.62 3.36 3.10 2.84 2.70 2.52 2.34

R = 0.5

ELY 3.44 3.14 2.86 2.58 2.42 2.22 2.00ELX 4.46 4.38 4.44 4.68 4.92 5.22 5.30EC 6.46 4.98 3.98 3.24 2.90 2.62 2.34ECZ 3.50 3.24 2.98 2.74 2.60 2.46 2.32

R = 0.6

ELY 3.28 3.00 2.74 2.48 2.34 2.16 1.96ELX 4.40 4.38 4.50 4.80 5.06 5.26 5.30EC 5.70 4.46 3.64 3.06 2.78 2.54 2.32ECZ 3.38 3.12 2.88 2.68 2.54 2.42 2.30

R = 0.7

ELY 3.14 2.88 2.64 2.42 2.28 2.14 1.96ELX 4.36 4.40 4.58 4.92 5.14 5.28 5.30EC 5.10 4.08 3.40 2.92 2.70 2.50 2.32ECZ 3.26 3.02 2.80 2.60 2.50 2.40 2.30


polarization than that in x direction. And the transverse FWHM in y direction de-creases more sharply on increasing NA. The FWHM in x direction decreases moreslowly, and then increases back on increasing NA under condition of smaller R. How-ever, for larger R, the FWHM in x direction increases continually on increasing NA.The focal spot of RPB has cylindrical symmetry. And under condition of small R,the dependence of FWHM difference between EC and ECZ on R is not linear, in addition,the dependence of this FWHM difference on NA is also not linea. This article paysmore attention to tighter focal spot generation of RPB by comparison with LPB. FromTable 1, we can see that the focal spot of RPB is not always smaller than that of LPB,even if only a longitudinal field component ECZ is considered. And for certain case,the FWHM of LPB in y direction may be smaller than that of ECZ even for highernumerical aperture.

For the purpose of presenting the information in a more friendly manner, someimportant parts of this data table are given graphically. Figure 1a illustrates the trans-verse FWHMs of fields ELY , ELX , EC , and ECZ for NA = 0.75. It can be seen thatthe FWHMs of fields ELX and EC are relatively big, and are smaller for fields ELYand ECZ. When considering the total optical focal spot, in fact, the focusing of RPBdoes not give a smaller focal spot than LPB, namely, tighter focusing does not appearas usual. Even if only the FWHM of ELY and ECZ is considered, sharper focusing forRPB does not always occur. For small R, FWHM of ECZ is smaller than that of ELY .When R approaches a big value, the FWHM of ECZ is bigger than that of ELY .The FWHMs of fields ELY , ELX , EC, and ECZ for NA = 0.80 are also given accordingto Tab. 1. We can see that the condition for sharper focusing of RPB is verycomplicated even if only ELY and ECZ are considered, because the FWHM ratio ofELY to ECZ fluctuates near 1 on increasing R, and there are three cross points forELY to ECZ FWHM curves. The FWHM curve of EC also crosses with that of ELY .

The FWHMs of fields ELY , ELX , EC, and ECZ under condition of NA = 0.90 are alsoillustrated in Fig. 2a. From this figure, we can see that the FWHM curve cross point

EC

ECZ ELYELX

9

8

7

6

5

4

0 0.1 0.2 0.3 0.4 0.5 0.6

FWH

M

R

EC

ECZ ELY

ELX

7

6

5

4

0 0.1 0.2 0.3 0.4 0.5 0.6

FWH

M

R

3

a b

Fig. 1. Transverse FWHM of fields ELY , ELX , EC , and ECZ under condition of NA = 0.75 (a), andNA = 0.80 (b).

90 X. GAO et al.

of ELY and ECZ shifts towards smaller R, comparing Fig. 2a and Fig. 1a, whichmeans that for larger R, the focal spot of ECZ is actually bigger than that of ELY .Therefore, under condition of higher NA, this critical R value decreases. The range ofpossibilities of generating smaller focal spot using RPB shrinks if only consideringELY and ECZ . Figure 2b shows focusing properties for NA = 0.99. From this figure,we can see that the focal pattern of LPB becomes very asymmetric, and the FWHMdifference between ELY and ELX is very significant. The FWHM of ELY is usuallysmaller than that of EC and ECZ , and the FWHM difference of EC and ECZ is not veryremarkable.

In order to understand the effect of NA on FWHM, the curves representingthe FWHM values upon increasing NA are illustrated in Figs. 3 and 4. We can seefrom Fig. 3 that the FWHM of ELY is always smaller than that of ECZ under conditionof R = 0. And for case of R = 0.1, two FWHM curves of ELY and ECZ cross each otherfor certain value of NA, which indicates that the focal size of longitudinal field

EC

ECZ

ELY

ELX

4.5

4.0

3.5

3.0

2.50 0.1 0.2 0.3 0.4 0.5 0.6

FWH

M

R

EC

ECZ

ELY

ELX

0 0.1 0.2 0.3 0.4 0.5 0.6R

a b4.5

4.0

3.5

3.0

2.5

FWH

M

5.0

2.0

Fig. 2. Transverse FWHM of fields ELY , ELX , EC , and ECZ under condition of NA = 0.90 (a), andNA = 0.99 (b).

EC

ECZ

ELYELX

9

8

7

6

5

0.75 0.80 0.85 0.90 0.95

FWH

M

NA

EC

ECZ

ELY

ELX

a b

4

3

9

8

7

6

5

FWH

M

4

3

0.75 0.80 0.85 0.90 0.95NA

Fig. 3. Transverse FWHM of fields ELY , ELX , EC , and ECZ under condition of R = 0.0 (a), and R = 0.1 (b).


component RPB is not always smaller than that of y-axis component of LPB. And forsmaller NA, the FWHM of EC is bigger than that of ELX . However, because the decreasespeed of FWHM of EC is very sharp, the FWHM of EC becomes smaller than that ofELX for higher NA.

For larger R, the FWHM curves of fields ELY , ELX , EC , and ECZ on increasing NAare also given in Fig. 4. We can see that the cross point position of FWHM curves ofELX and EC shifts continuously in decreasing NA direction. And the cross point positionof FWHM curves of ELX and ECZ also shifts in decreasing NA direction. When R valueranges from 0.5 to 0.7, the focal spot size of ECZ is actually bigger than that of ELYfor the case of changing NA from 0.75 to 0.99, as shown in Figs. 4b and 4c. Therefore,the effect of NA on the focal size difference between RPB and LPB is very remarkable.The focal spot of RPB is not always smaller than that of LPB. Even if only longitudinalfield component is considered, in fact, the condition for tighter focusing of RPB isvery complicated.

Some intensity distributions of the polarization components of the focused beamswere added. Figure 4 illustrates the intensity distributions of LPB under condition of

EC

ECZ

ELY

ELX

8

7

6

5

0.75 0.80 0.85 0.90 0.95

FWH

M

NA

EC

ECZELY

ELX

a b

4

3

0.75 0.80 0.85 0.90 0.95NA

5.0

4.5

4.0

3.5FWH

M

3.0

2.5

2.00.75 0.80 0.85 0.90 0.95

NA

EC

ECZ

ELY

ELX c

5.0

4.5

4.0

3.5

FWH

M

3.0

2.5

5.5

6.0

Fig. 4. Transverse FWHM of fields ELY , ELX , EC , and ECZ under condition of R = 0.3 (a), R = 0.5 (b),and R = 0.7 (c).

92 X. GAO et al.

R = 0.2 and NA = 0.75. And Ex , Ey , and Ez indicate the three polarization componentsin x, y, z direction, respectively. It can be seen that the total intensity distribution isvery similar to that of polarization component of Ex . On increasing NA, the intensityof polarization component of Ez increases considerably, which leads to the extensionof the total intensity distribution in x direction, as shown in Fig. 5. Therefore, forcertain small R, the circle focal spot extends in x direction for higher NA, which resultsin the big FWHM of ELX , so the FWHM of ELX decreases, and then increases onincreasing NA for small R, and when R becomes big, the FWHM of ELX increasescontinuously on increasing NA.

Some intensity distributions of the polarization components under condition oflarger R are given. It can be seen that the intensity of polarization component of Ezincreases considerably on increasing R, comparing Figs. 7 and 8 with Figs. 5 and 6,respectively. And for larger R, the total intensity distribution extends in x directionvery remarkably under condition of higher NA, which leads to the focal splits inx direction, as shown in Fig. 8a.

All three mutually orthogonal field components occur in the focal region offocusing LPB. Because the intensity distribution shapes the evolution of ELX , onincreasing NA, the cross point position of FWHM curves of ELX and EC shiftscontinuously in decreasing NA direction. The intensity distribution of the longitu-dinally polarized component in an axis direction is not rotationally symmetric, whichcauses the asymmetric deformation of the focal spot. And when annular aperture is

Fig. 5. Intensity distributions of LPB for E (a), Ex (b), Ey (c), and Ez (d) under condition of R = 0.2and NA = 0.75.

1.0

0.8

0.6

0.4

0.2

50

–5 –50

5

Inte

nsity

Vx Vy

a b

c d

0.8

0.6

0.4

0.2

50

–5 –50

5

Inte

nsity

Vx Vy

5

10

15

50

–5 –50

5

Inte

nsity

Vx Vy

×10–4

0.10

0.06

0.02

50

–5 –50

5

Inte

nsity

Vx Vy




1.0

0.8

0.6

0.4

0.2

5

0

–5 –50

5

Inte

nsity

Vx Vy

a b

c d

0.8

0.6

0.4

0.2

5

0

–5 –50

5

Inte

nsity

Vx Vy

0.01

0.03

0.04

5

0

–5 –50

5

Inte

nsity

Vx Vy

0.5

0.3

0.1

5

0

–5 –50

5

Inte

nsity

Vx Vy

0.02

1.0

0.8

0.6

0.4

0.2

50

–5 –50

5

Inte

nsity

Vx Vy

a b

c d

0.80.6

0.4

0.2

50

–5 –50

5

Inte

nsity

Vx Vy

2

4

6

50

–5 –50

5

Inte

nsity

Vx Vy

×10–3

0.20

0.10

0.05

50

–5 –50

5

Inte

nsity

Vx Vy

0.15

94 X. GAO et al.


Fig. 9. Intensity distributions of RPB for E (a), Er (b), and Ez (c) under condition of R = 0.2 and NA = 0.75.

1.0

0.8

0.6

0.4

0.2

50

–5 –50

5

Inte

nsity

Vx Vy

a b

c d

0.6

0.4

0.2

50

–5 –50

5

Inte

nsity

Vx Vy

50

–5 –50

5Vx Vy

50

–5 –50

5Vx Vy

0.6

0.4

0.2Inte

nsity

0.08

0.06

0.04

0.02

Inte

nsity

1.0

0.8

0.6

0.4

0.2

5

0

–5 –100

10

Inte

nsity

Vr Vz

a

0.6

0.4

0.2

5

0

–5 –100

10

Inte

nsity

Vr Vz

b

0.8

0.6

0.4

0.2

5

0

–5 –100

10

Inte

nsity

Vr Vz

c


used, the relative contribution of the longitudinal component is increased and the asym-metry becomes more considerable. The focal spot splits in transverse direction undercondition of larger R. When focal splitting occurs, there are two intensity peaks infocal plane, as shown in Fig. 8. In order to avoid the effect of focal splitting on FWHMof the whole intensity distribution, the maximum value of R is chosen as 0.7.

The intensity distributions of the polarization components of RPB under conditionof R = 0.2 and NA = 0.75 are also illustrated in Fig. 9. We can see that the transversesize of Ez is smaller than that of the total optical intensity, which leads to the smallerFWHM of field ECZ . And we also know that, in fact, the RPB is often used to obtainsmaller focal spot by means of its polarization components in z direction. On increasingNA and R, the polarization component of field ECZ becomes stronger and stronger,which accelerates the focal size decrease of total intensity of RPB.

Therefore, the focal spot evolution of RPB and LPB is different. For the case offocusing of LPB, the focal shape change due to polarization component of ELX is veryconsiderable, even results in focal splitting. While, for the case of focusing of RPB,the field ECZ plays an important role in focusing properties, especially in higher NAand R focusing systems.

3.2. Focal depth comparison between RPB and LPB

Now, we investigate the focal depth of RPB by comparing it with LPB. It should benoted that focal depth is defined as the distance between the two axial points betweenwhich the intensity is not smaller than 50% of the intensity peak maximum on opticalaxis. And by calculating on-axis intensity distributions of RPB and LPB numerically,

T a b l e 2. Focal depth comparison of RPB and LPB under condition of different NA and R.

NA 0.75 0.80 0.85 0.90 0.93 0.96 0.99

R = 0EL 16.40 13.94 11.84 10.02 9.02 8.06 7.02EC 17.88 15.12 12.76 10.70 9.54 8.42 7.16

R = 0.1EL 16.72 14.24 12.16 10.38 9.46 8.66 8.72EC 18.00 15.22 12.88 10.86 9.76 8.76 8.54

R = 0.2EL 17.68 15.20 13.16 11.52 10.78 10.48 13.14EC 18.58 15.84 13.58 11.72 10.86 10.40 12.90

R = 0.3EL 19.42 16.90 14.92 13.52 13.10 13.54 19.68EC 20.00 17.10 15.14 13.58 13.08 13.42 19.48

R = 0.4EL 22.20 19.64 17.74 16.64 16.66 18.12 28.82EC 22.56 19.86 17.82 16.62 16.60 18.00 28.66

R = 0.5EL 26.52 23.86 20.04 21.38 22.02 24.88 41.86EC 26.74 23.98 20.08 21.34 21.96 24.76 41.74

R = 0.6EL 33.40 30.56 28.86 28.82 30.36 35.26 61.58EC 33.52 30.64 28.86 28.76 30.30 35.18 61.48

R = 0.7EL 45.30 40.14 40.58 41.52 44.54 52.84 94.62EC 45.36 40.16 40.58 41.50 44.50 52.78 94.56

96 X. GAO et al.

the focal depth values under condition of different R and NA are shown in Tab. 2.And EC and EL mark RPB and LPB in this table, respectively. The foal depth unitis k–1, where k is the wave number of incident beam.

From this table, it can be seen that the focal depth of RPB also decreases onincreasing NA as that of LPB under condition of small R. And focal depth of RPBincreases on increasing R, which is also similar to that of LPB. In practice, it is wellknown that this focal evolution principle is common to LPB, now it is also applicableto focusing RPB. In addition, the focal depth difference between these two kinds ofbeams also shrinks on increasing NA, and larger R can also result in smaller focaldepth difference.

In order to understand the information contained in Tab. 2 more clearly and deeply,the focal depth curves of RPB and LPB on increasing R under condition of differenttypical NA are illustrated in Fig. 10. We can see from this figure that on increasing R,

45

40

35

30

25

20

15

0 0.1 0.2 0.3 0.4 0.5 0.6

NA = 0.75 for RPBNA = 0.75 for LPBNA = 0.85 for RPBNA = 0.85 for LPB

Foca

l dep

th

R

NA = 0.93 for RPBNA = 0.93 for LPBNA = 0.99 for RPBNA = 0.99 for LPB

90

80

70

60

50

40

30

20

10

Foca

l dep

th

0 0.1 0.2 0.3 0.4 0.5 0.6R

Fig. 10. Focal depth curves of RPB and LPB on increasing R under condition of NA = 0.75,NA = 0.85 (a), and NA = 0.93, NA = 0.99 (b).

a b

Fig. 11. Focal depth curves of RPB and LPB on increasing NA under condition of different R.

20

0.75 0.80 0.85 0.90 0.95

R = 0.0 for RPBR = 0.0 for LPBR = 0.3 for RPBR = 0.3 for LPB

NA

Foca

l dep

th

18

16

14

12

10

8


the focal depth increases, while the focal depth difference decreases under conditionof NA being the same. And for higher NA, the focal depth difference becomes veryslight.

Figure 11 shows focal depth curves of RPB and LPB on increasing NA undercondition of two different R. The focal depth decreases on increasing NA forsmaller R. However, when R increases, the focal depth decreases firstly for small NA,and then increases sharply when NA is bigger than 0.93. The whole focal evolutionprocess of RPB is similar that of LPB. Here is one sharp increase of focal depth forhigher NA and larger R.

Figure 12 illustrates the intensity distributions in focal region of the focusing RPB,which shows that the transverse size of longitudinal component is smaller than that oftransverse component, while the axial size of longitudinal component is bigger thanthat of transverse component. Therefore, when the contribution of longitudinalcomponent becomes considerable under condition of larger R and higher NA, the focaldepth also increases simultaneously.

Extension of the focal depth on increasing R may also be explained ifthe interference of the outermost and innermost rays of the beam axis in the regionaround the focal point is considered [24]. As KITAMURA and coworkers have shown inreference [24], when the original radially polarized beam is focused, the incident angles

Fig. 12. Intensity distributions of RPB for R = 0.3 under condition of NA = 0.75 (a), NA = 0.90 (b),and NA = 0.99 (c).

a5

0

–5–10 0 10

Vr

Vz

b

c

5–5–15 15

5

0

–5–10 0 10

Vr

Vz5–5–15 15

5

0

–5–10 0 10

Vr

Vz5–5–15 15

98 X. GAO et al.

of the two rays are significantly different. Constructive interference takes place onlyat the focal plane on the beam axis because the two rays are in phase only at this point.Therefore, strong intensity appears only in close vicinity to the focal plane.

However, the two corresponding rays for the narrow annular incident beaminterfere constructively on the beam axis even away from the focal plane, becausethe phases of the rays match well due to almost identical incident angles. So, the nar-rower annular incident beam possesses longer focal depth, which is the same cause offocal depth extension for incident LPB and RPB, as shown in Fig. 10. When R is verysmall or approaches zero, the effect of NA on focal depth is more remarkable than thatof annular aperture, so the focal depth decreases on increasing NA, as is well knownthat the focal depth decreases on increasing NA for clear aperture, for instance, WANGand GAN show that the focal depth is proportional to 1/NA2 [25]. However, when Rgets larger, the effect of annular aperture becomes more considerable than that of NA,so the focal depth extends sharply on increasing NA, as shown in Fig. 11.

3.3. Comparison under high-order radial modes

In the case of a single radially polarized doughnut beam, a Bessel–Gaussian beam maybe employed, while it was found that the higher-order radially polarized beams arerepresented by Laguerre–Gaussian distribution [12, 14, 26–28]. In this section, inorder to investigate the effect of high-order radial modes on results of Section 3.1, wealso choose Laguerre–Gaussian distribution as the amplitude shape of higher-orderbeams; the distribution can be written as [14, 29],

(8)

where C is constant, r is radial coordinate, and ω0 is the waist radius. representsan associated Laguerre polynomial, and l is the topological charge, q is the radialindex. By a similar viable transformation method presented in references [30, 31],the amplitude distribution can be rewritten in the form

(9)

where w is the radius ratio of waist radius to the radius of optical aperture. NA isthe numerical aperture. By substituting Eq. (9) into the Eqs. (2), (3) and Eqs. (5)–(7),the effect of radial variation amplitude on the results presented in Section 3.1 can beinvestigated numerically.

Figure 13 illustrates the transverse intensity distributions under condition ofNA = 0.75, w = 1, l = 1, and q = 4. The horizontal dashed line indicates the half valueof the maximum intensity. It can be seen from this figure that the transverse focus sizeincreases on decreasing R. And when the value of R approaches zero, the transverse

P r( ) C r2

ω02

-----------–⎝ ⎠⎜ ⎟⎛ ⎞

2 r2

ω02

------------⎝ ⎠⎜ ⎟⎛ ⎞ l 2⁄

Lql 2r2

ω02

-------------⎝ ⎠⎜ ⎟⎛ ⎞

exp=

Lql

P θ( ) C sin2 θ( )

w2 NA2-----------------------–

⎝ ⎠⎜ ⎟⎛ ⎞

2 sin2 θ( )

w2 NA2-----------------------

⎝ ⎠⎜ ⎟⎛ ⎞

l 2⁄

Lql 2sin2 θ( )

w2 NA2---------------------------

⎝ ⎠⎜ ⎟⎛ ⎞

exp=


focal intensity difference becomes very considerable. There is a more pronouncedeffect of radial variation amplitude for larger apertures (namely, under condition ofsmaller R). Therefore, we should pay attention to the radial variation amplitudedistribution when results in this paper will be used in practical applications.

4. ConclusionsWe have investigated tightened focusing of radially polarized beam by comparing itwith linearly polarized beam. Numerical results show that the focal spot of radiallypolarized beam is not always smaller than that of linearly polarized beam. Even it onlya longitudinal field component is considered, the condition for tighter focusing ofradially polarized vector beam is very complicated. Therefore, more attention shouldbe paid to use of radially polarized beam in practice use for sharper focus accordingto numerical aperture and the beam shape. The focal depth of focusing annularradially polarized beam is also investigated by comparison with linearly polarizedbeam. The focal depth of radially polarized beam decreases on increasing numericalaperture like that of linearly polarized beam under condition of small radius ratio, and

Fig. 13. Transverse intensity distributions under condition of NA = 0.75, w = 1, l = 1, q = 4 andR = 0.7 (a), R = 0.3 (b), and R = 0.2 (c).

1.0

0.8

0.6

0.4

0.2

0.0–10 –5 0 5 10

ELX

EC

ECZELY

R = 0.7

Inte

nsity

Radial distance

a b

c

ELX

ECECZ

ELY

ELX

EC ECZ

ELY

1.0

0.8

0.6

0.4

0.2

0.0–10 –5 0 5 10

R = 0.3

Inte

nsity

Radial distance

1.0

0.8

0.6

0.4

0.2

0.0–10 –5 0 5 10

R = 0.2

Inte

nsity

Radial distance

100 X. GAO et al.

increases on increasing radius ratio. Focal depth difference between these two kindsof beams shrinks on increasing numerical aperture. And the larger the radius ratio,the lower the focal depth difference. The above results let us get a deeper insight intothe focusing properties of radially polarized beam, and Tabs. 1 and 2 may serve asreference in practice for choosing parameters when radially polarized beam is used infocusing optical systems.

Acknowledgement – This work was supported by the National Natural Science Foundation of China(60708002, 10904080).

References[1] SALAMIN Y.I., Direct acceleration by two interfering radially polarized laser beams, Physics

Letters A 375(3), 2011, pp. 795–799.[2] YOUYI ZHUANG, YAOJU ZHANG, BIAOFENG DING, TAIKEI SUYAMA, Trapping Rayleigh particles using

highly focused higher-order radially polarized beams, Optics Communications 284(7), 2011,pp. 1734–1739.

[3] HAYAZAWA N., SAITO Y., KAWATA S., Detection and characterization of longitudinal field fortip-enhanced Raman spectroscopy, Applied Physics Letters 85(25), 2004, pp. 6239–6241.

[4] TANG W.T., YEW E.Y.S., SHEPPARD C.J.R., Polarization conversion in confocal microscopy withradially polarized illumination, Optics Letters 34(14), 2009, pp. 2147–2149.

[5] BAOHUA JIA, HONG KANG, JIAFANG LI, MIN GU, Use of radially polarized beams in three-dimensionalphotonic crystal fabrication with the two-photon polymerization method, Optics Letters 34(13),2009, pp. 1918–1920.

[6] KUMAR A., GUPTA M.C., Laser machining of micro-notches for fatigue life, Optics and Lasers inEngineering 48(6), 2010, pp. 690–697.

[7] XIANGPING LI, YAOYU CAO, MIN GU, Superresolution-focal-volume induced 3.0 Tbytes/disk capacityby focusing a radially polarized beam, Optics Letters 36(13), 2011, pp. 2510–2512.

[8] DORN R., QUABIS S., LEUCHS G., Sharper focus for a radially polarized light beam, Physical ReviewLetters 91(23), 2003, article 233901.

[9] BAOHUA JIA, XIAOSONG GAN, MIN GU, Direct measurement of a radially polarized focusedevanescent field facilitated by a single LCD, Optics Express 13(18), 2005, pp. 6821–6827.

[10] XIUMIN GAO, MINGYU GAO, SONG HU, HANMING GUO, JIAN WANG, SONGLIN ZHUANG, Highly focusingof radially polarized Bessel-modulated Gaussian beam, Optica Applicata 40(4), 2010, pp. 965–974.

[11] XIUMIN GAO, MINGYU GAO, QIUFANG ZHAN, JINSONG LI, HANMING GUO, JIAN WANG, SONGLIN ZHUANG,Focal shift in radially polarized hollow Gaussian beam, Optik – International Journal for Light andElectron Optics 122(8), 2011, pp. 671–676.

[12] YOUNGWORTH K., BROWN T., Focusing of high numerical aperture cylindrical-vector beams, OpticsExpress 7(2), 2000, pp. 77–87.

[13] KOZAWA Y., SATO S., Sharper focal spot formed by higher-order radially polarized laser beams,Journal of the Optical Society of America A 24(6), 2007, pp. 1793–1798.

[14] RASHID M., MARAGO O.M., JONES P.H., Focusing of high-order cylindrical vector beams, Journal ofOptics A: Pure and Applied Optics 11(6), 2009, article 065204.

[15] LERMAN G.M., LEVY U., Effect on radial polarization and apodization on spot size under tightfocusing conditions, Optics Express 16(7), 2008, pp. 4567–4581.

[16] INDEBETOUW G., BAI H., Imaging with Fresnel zone pupil masks: extended depth of field, AppliedOptics 23(23), 1984, pp. 4299–4302.

[17] OJEDA-CASTANEDA J., LANDGRAVE J.E.A., ESCAMILLA H.M., Annular phase-only mask for high focaldepth, Optics Letters 30(13), 2005, pp. 1647–1649.


[18] MIKUŁA G., JAROSZEWICZ Z., KOLODZIEJCZYK A., PETELCZYC K., SYPEK M., Imaging with extendedfocal depth by means of lenses with radial and angular modulation, Optics Express 15(15), 2007,pp. 9184–9193.

[19] SAUCEDA A., OJEDA-CASTAÑEDA J., High focal depth with fractional-power wave fronts, OpticsLetters 29(6), 2004, pp. 560–562.

[20] JIE LIN, KE YIN, YUDA LI, JIUBIN TAN, Achievement of longitudinally polarized focusing with longfocal depth by amplitude modulation, Optics Letters 36(7), 2011, pp. 1185–1187.

[21] QIWEN ZHAN, LEGER J., Focus shaping using cylindrical vector beams, Optics Express 10(7), 2002,pp. 324–331.

[22] GU M., Advanced Optical Imaging Theory, Springer, Heidelberg, 2000.[23] RICHARDS B., WOLF E., Electromagnetic Diffraction in optical systems. II. Structure of the image

field, aplanatic system, Proceedings of the Royal Society A 253(1274), 1959, pp. 358–379.[24] KITAMURA K., SAKAI K., NODA S., Sub-wavelength focal spot with long depth of focus generated by

radially polarized, narrow-width annular beam, Optics Express 18(5), 2010, pp. 4518–4525.[25] HAIFENG WANG, FUXI GAN, High focal depth with a pure-phase apodizer, Applied Optics 40(31),

2001, pp. 5658–5662.[26] KOZAWA Y., SATO S., Focusing property of a double-ring-shaped radially polarized beam, Optics

Letters 31(6), 2006, pp. 820–822.[27] TOVAR A.A., Production and propagation of cylindrically polarized Laguerre–Gaussian laser

beams, Journal of the Optical Society of America A 15(10), 1998, pp. 2705–2711.[28] TOVAR A.A., CLARK G.H., Concentric-circle-grating, surface-emitting laser beam propagation in

complex optical systems, Journal of the Optical Society of America A 14(12), 1997, pp. 3333–3340.[29] ARTL J., DHOLAKIA K., ALLEN L., PADGETT M.J., The production of multiringed Laguerre–Gaussian

modes by computer-generated holograms, Journal of Modern Optics 45(6), 1998, pp. 1231–1237.[30] XIUMIN GAO, Focusing properties of the hyperbolic-cosine-Gaussian beam induced by phase plate,

Physics Letters A 360(2), 2006, pp. 330–335. [31] XIUMIN GAO, JINSONG LI, Focal shift of apodized truncated hyperbolic-cosine-Gaussian beam, Optics

Communications 273(1), 2007, pp. 21–27.

Received January 24, 2011in revised form August 12, 2011


The transmission characteristics under the influence of the fifth-order nonlinearity management

XIUJUN HE1, 2, KANG XIE1

1School of Optoelectronic Information, University of Electronics Science and Technology of China,Chengdu, 610054, China

2Chengdu University of Information Technology of China, Chengdu 610225, China

Starting with the nonlinear Schrödinger (NLS) equation, we have derived the evolution equationsfor the parameters of soliton pulse with propagation distance in optical fibers, taking intoconsideration the combined effect of second-order dispersion and the fifth-order nonlinearity bymeans of variation method. According to nonlinear evolution equations, the evolution of the pulsewidth with propagation distance is obtained under the influence of the different fifth-ordernonlinearity. The results show that the pulse width fluctuates periodically under the influenceof the different fifth-order nonlinearity. In the cycle, the negative fifth-order nonlinearity makesthe pulse-width greater than the initial value while the positive fifth-order nonlinearity makesthe pulse width less than the initial value. However, under the positive and negative fifth-ordernonlinearity management, compared to the impact of positive or negative fifth-order nonlinearityonly, the fluctuations of the solitons width are greatly reduced, even disappear. In other words,the width maintains almost steady. Therefore, it is possible that the pulse width is to be transmittedwithout any deformation.

Keywords: fifth-order nonlinearity management, soliton, nonlinear Schrödinger equation, variationmethod.

1. IntroductionThe optical pulse compression and soliton transmission mode have been widelycosidered by researchers [1–3]. At present, under a third-order nonlinearity, the trans-mission of optical pulse has been intensively investigated, but with the development ofhigh-nonlinear fiber (such as semiconductor doped fiber, organic polymer fiber, etc.),fifth-order or higher order nonlinearity can occur in the medium power of light [4].Therefore, researches began to study the self-phase-modulation, the modulationinstability [5], the solitary wave transmission, the bistable behavior [6], ground-statesoliton, the propagation properties of the Gaussian pulse in the case of the fifth-ordernonlinearity [7]. However, it is still a new field for research on transmission of higher

104 XIUJUN HE, KANG XIE

order soliton. With the use of variation method and from the extended nonlinearSchrödinger (NLS) equation of the fifth-order nonlinearity, this paper introducesevolution equations of soliton parameters depending on the propagation distance undersecond-order dispersions and cubic-quintic nonlinearity, simulates the evolution ofsoliton width on the propagation distance. Nowadays, researchers make greater effortsto apply nonlinearity management to control the transmission of soliton, as with thedispersion-managed soliton propagation [8, 9]. The authors of the present paper focuson effects of the fifth-order nonlinearity management on the width of soliton and theirachievements so far appear to be very helpful when investigating the transmission ofsoliton.

2. Theoretical analysis

Let us start with the nonlinear Schrödinger (NLS) equation with the fifth-ordernonlinearity [5]:

(1)

where i = (–1)1/2 and A(z, T ) is the slowly varying envelope of the optical pulse andT the temporal coordinate frame that moves at the group velocity νg of the pulse,and z the spatial coordinate representing the transmission distance, β2 representsthe second-order dispersion parameter, γ and γ ' are respectively the nonlinear Kerreffect coefficient and the fifth-order nonlinearity coefficient.

We proceed to the normalization of Eq. (1) in the following way:

(2)

Here, u = A / , ξ = z/LD, s = –sgn(β2), τ = T /T0, g1 = LD /LNL1, and g2 = LD /LNL2,while LD = / |β2 |, LNL1 = 1/(γ P0) and LNL2 = 1/(γ 'P0).

Variational method was used to solve Eq. (2) and the Lagrangian density isobtained from Eq. (2),

(3)

The following generic ansatz for the stationary solution of Eq. (2) shall beconsidered

(4)

i ∂A z t,( )∂z

-------------------------β2

2----------- ∂2A z t,( )

∂T 2----------------------------– γ A z t,( ) 2 A z t,( ) γ ' A z t,( ) 4 A z t,( )+ + 0=

i ∂u∂ξ

------------- s2

-------- ∂ 2u

∂τ 2--------------- g1 u 2u g2 u 4u+ + + 0=

P01 2⁄

T02

L i2

-------- uuξ* u*uξ–⎝ ⎠

⎛ ⎞– s2

------- uτ2–

g1

2---------- u 4 g2

3----------- u 6+ +=

u asech r t q–( ) iϕ ic t q–( )2 iω t q–( )–+exp=

The transmission characteristics... 105

where a, r, q, ϕ, c and ω represent the pulse amplitude, width inversion, centralposition, the phase, chirp and frequency shift, which are all real functions of ξ

(5)

is the average Lagrange density function, that is,

(6)

From Equation (5), the parameter variation equation can be obtained

(7)

where yi represents parameters a, r, q, ϕ, c and ω. Parameter evolution equations canbe derived by applying Eqs. (6) and (7)

(8)

(9)

(10)

(11)

(12)

(13)

δ L⟨ ⟩dξ∫ 0=

L⟨ ⟩

L⟨ ⟩ Ldτ∞–

+∞

∫a2

r3---------- 1

6-------- π2 dc

dξ-----------– 1

3-------- π2c2– r2ω2– 2r2ω dq

dξ------------– 1

3---------r4–

23

--------- g1r2a2 1645

------------ g2r2a4 2r2 dϕdξ

-------------–

+

+ +

⎝

⎠

⎜

⎟

⎛

⎞

= =

=

d L⟨ ⟩dyi

------------------ 0=

dadξ

-------------- asc–=

drdξ

-------------- 2rsc–=

dqdξ

-------------- sω–=

dωdξ

-------------- 0=

dcdξ

-------------- 2sc2– 1

π2------------ 2r4s 2g1r2a2– 32

15------------ g2r2a4–⎝ ⎠

⎛ ⎞+=

dϕdξ

-------------- 13

--------r2s 56

--------g1a2– 3245

------------g2a4– 12

--------ω2s–=


3. Computational results and analyses3.1. Soliton propagation in different fifth-order nonlinearity situations

Using the above evolution equations of soliton parameters, the change of soliton widthis as shown in Fig. 1. So, here g1 = 1, s = 1 and initial values of solitons, a0 = 1, r0 = 1,c0 = 0. When g2 < 0, the pulse width changes in a periodic and fluctuating way and itis greater than the fluctuation of initial width, that is to say, when the initial pulse widthstarts to increase gradually, eventually increasing to the soliton width peak, it beginsto gradually diminish, eventually reducing to the initial pulse width and starts toincrease again. Then, these changes continue to repeat. The larger the |g2 | is, the longerit lasts, and the more times it is repeated, the larger its fluctuation is. When g2 > 0,the pulse width also changes in a periodic and fluctuating way and it is smaller thanthe fluctuation of initial width, that is to say, when the initial pulse width starts todecrease gradually, eventually decreasing to the lowest value of the width, it beginsto gradually increase, eventually increasing to the initial pulse width and starts todecrease again. Then, these changes continue to repeat. The larger the |g2 | is,the shorter it lasts, and the more times it is repeated, the larger its fluctuation is.As for the equivalent positive and negative fifth-order nonlinearity, the negative fifth--order nonlinearity of influence on the pulse width is much bigger than the positivefifth-order nonlinearity.

3.2. Soliton propagation under the fifth-order nonlinearity managementWe know that the dispersion management lowers mean dispersion of the wholetransmission line through configuring properly the fibers with opposite dispersion

5

4

3

2

1

0

Puls

e w

idth

[ps]

g2 = 0.2 g2 = 0.4 g2 = 0.6

g2 = –0.2 g2 = –0.4 g2 = –0.6

0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50

5

4

3

2

1

0

Pul

se w

idth

[ps]

ξ ξ ξ

Fig. 1. The evolution of the pulse width with propagation distance under the influence of the differentfifth-order nonlinearity.


properties in order to improve transmission performance of solitons. As to the disper-sion management principles, nonlinear coefficient is also a function of ξ, which showsperiodic change along the fiber length. In a cycle, one situation of nonlinear coefficientis that absolute values are identical but opposite in sign, the other situation is thatabsolute values ranges and the opposite is the sign, which is called nonlinearitymanagement. As for the fifth-order nonlinearity management g2(ξ ) should satisfythe following equation, that is,

n = 1, 2, ... (14)

Here, g+ > 0, g– > 0, and L = l1 + l2 are the cycle lengths of the nonlinear management;l1 and l2 are the interaction lengths of the positive and negative nonlinearity. Obviously,the positive nonlinearity makes the pulse width decrease and the negative nonlinearitymakes it increase. Therefore, using the positive and negative nonlinearity management,their functions can cancel out, which improves drastically the fluctuation of width.

At first, when g+ = g– , l1 = l2, the soliton transmission in the fifth-order nonlinearitymanagement is shown in Figs. 2 and 3. Comparing to Fig. 1, the fluctuations ofthe soliton width reduce greatly after applying the fifth-order nonlinearity manage-ment. The negative fifth-order nonlinearity develops the soliton width above and

g+ = g– = 0.2 g+ = g– = 0.4 g+ = g– = 0.6

0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50

5

4

3

2

1

0

Pul

se w

idth

[ps]

ξ ξ ξ

Fig. 2. The evolution of the pulse width with propagation distance under the influence of the fifth-ordernonlinearity management (L =l1 + l2 = LD).

g2 ξ( )g+ nL ξ l1 nL+<≤

g– l1 nL+ ξ n 1+( )L≤ ≤,

⎩⎨⎧=

Fig. 3. The evolution of the pulse width with propagation distance under the influence of the fifth-ordernonlinearity management.

g+ = g– = 0.2 g+ = g– = 0.4 g+ = g– = 0.6

0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50

5

4

3

2

1

0

Puls

e w

idth

[ps]

ξ ξ ξ


beyond its initial value fluctuation, while the positive fifth-order nonlinearity developsthe soliton width to be less than its initial value fluctuation and they can be cancelled,which decreases drastically the fluctuation. Better results are achieved by usinga smaller cycle.

In Figure 4, due to dissymmetry of the function of positive and negative fifth-ordernonlinearity, an effect of the fifth-order nonlinearity management is not good enoughwhen the fifth-order nonlinear coefficient is bigger under the condition of g+ = g– andl1 = l2. According to the function of equal negative fifth-order nonlinearity above and

g+ = g– = 0.8 g+ = g– = 0.8

g+ = 0.8

0 10 20 30 40 50 0 10 20 30 40 50

0 10 20 30 40 50

5

4

3

2

1

0

Pul

se w

idth

[ps]

ξ ξ

ξ

I1 = I2 = LD I1 = LDI2 = 0.7LD

g– = 0.41I1 = I2 = LD

Fig. 4. The evolution of the pulse width with propagation distance under the influence of the fifth-ordernonlinearity management.

5

4

3

2

1

0

Pul

se w

idth

[ps]

15

10

5

0

50

40

30

20

10

0–5 0 5

g2 = 0

Dis

tanc

e

Time–5 0 5 –5 0 5

Time Time

g2 = –0.6 g2 = 0.6

Fig. 5. The evolution of the soliton with propagation distance under the influence of the differentfifth-order nonlinearity.


beyond the positive fifth-order nonlinearity and under the condition of g+ > g– andl1 > l2, choosing a suitable ratio we can get a good performance through the fifth-ordernonlinearity management.

Finally, the soliton transmission as a function of the fifth-order nonlinearity iscalculated by applying numerical methods. The results are consistent with those oftheoretical calculations, see in Figs. 5 and 6.

4. ConclusionsThis paper applies the variation method to research effect of the fifth-order nonlinearityon the soliton transmission. The result shows that pulse width of soliton has a cyclicalfluctuation under the influence of the fifth-order nonlinearity. The negative fifth-ordernonlinearity develops the soliton width above and beyond its initial value fluctuationwhile the positive fifth-order nonlinearity develops the soliton width to be less thanits initial value fluctuation in a cycle, and the bigger the absolute value of the nonlinearcoefficient, the greater the fluctuation. On this basis, the influence of the fifth-ordernonlinearity management is further researched to find out that the fluctuation ofsoliton width is greatly reduced under such conditions, and the soliton width is almostnot changed, which can make pulses realize transmission of original shape underthe function of the fifth-order nonlinearity.

References[1] AGRAWAL G.P., Nonlinear Fiber Optics, Fourth Edition, Academic Press, US, 2007. [2] HASEGAWA A., KODAMA Y., Solitons in Optical Communications, Clarendon Press, Oxford,1995. [3] HASEGAWA A., Theory of information transfer in optical fibers: A tutorial review, Optical Fiber

Technology 10(2), 2004, pp. 150–170. [4] MOUSSA SMADI, DERRADJI BAHLOUL, A compact split step Padé scheme for higher-order nonlinear

Schrödinger equation (HNLS) with power law nonlinearity and fourth order dispersion, ComputerPhysics Communications 182(2), 2011, pp. 366–371.

50

40

30

20

10

0–5 0 5

g+ = g– = 0.2D

ista

nce

Time–5 0 5 –5 0 5

Time Time

g+ = g– = 0.4 g+ = g– = 0.6

Fig. 6. The evolution of the soliton with propagation distance under the influence of the fifth-ordernonlinearity management.


[5] WOO-PYO HONG, Modulation instability of optical waves in the high dispersive cubic–quinticnonlinear Schrödinger equation, Optics Communications 213(1–3), 2002, pp. 173–182.

[6] TANEV S., PUSHKAROV D.I., Solitary wave propagation and bistability in the normal dispersionregion of highly nonlinear optical fibers and waveguides, Optics Communications 141(5–6), 1997,pp. 322–328.

[7] SONESON J., PELEG A., Effect of quintic nonlinearity on soliton collisions in fibers, Physica D:Nonlinear Phenomena 195(1–2), 2004, pp. 123–140.

[8] KONAR S., MANOJ MISHRA, JANA S., The effect of quintic nonlinearity on the propagationcharacteristics of dispersion managed optical solitons, Chaos, Solitons and Fractals 29(4), 2006,pp. 823–828.

[9] ILDAY F.Ö., WISE F.W., Nonlinearity management: A route to high-energy soliton fiber lasers,Journal of the Optical Society of America B 19(3), 2002, pp. 470–476

Received April 3, 2011in revised form July 19, 2011


A 2-bit polymer waveguide delay device using right-angle X junctions

YUNJI YI, QI WANG, PENGCHENG ZHAO, FEI WANG*, DAMING ZHANG

State Key Laboratory on Integrated Optoelectronics, Jilin University Region, Qianjin Street 2699, Changchun 130012, China


A 2-bit polymer waveguide delay device composed of right-angle junctions, Mach–Zehnderthermo-optic switches and bending polymer waveguides is demonstrated. The four path deviceand Mach–Zehnder thermo-optic switch are fabricated using direct ultraviolet photolithog-raphy process. The fabrication procedures are demonstrated. The loss of bending waveguides,right-angle X junctions and Mach–Zehnder thermo-optic switches is calculated and analyzed.The near-infrared field guided-mode patterns of the device are obtained. Time delays of the 2-bitdevice are measured to be 0, 121.1, 242.3, and 365.7 ps.

Keywords: optical true time delay (OTTD), phased array radar, photonic integrated circuit (PIC),waveguide junctions.

1. IntroductionOptical true time delay (OTTD) technology is a promising technology in ultra-widebandwidth phased array antenna (PAA) systems. With this technology, the beamsquint effect can be eliminated, for the beam-steering direction of the phased arrayantennas is determined only by the time delay between the different optical elements.Because the RF signals are transmitted via the optical fiber or the waveguide, the noisedue to the external electromagnetic interference can be greatly reduced. Several OTTDtechnologies have been proposed and demonstrated, including acousto-optic (AO)integrated circuit technique [1–3], Fourier optical technique [4–6], bulky optics tech-niques [7–12], slow light approach [13, 14], and substrate guided wave techniques[15–17]. A great deal of materials have been used to fabricate OTTD devices [18–21].Polymer is considered as promising material, which has adjustable refractive indices,generally higher thermo-optic coefficients and lower thermal conductivities. Polymercan be coated on most of the substrates, which can reduce manufacturing costs andopen the possibility of integrating a single chip with active PAA components.

An OTTD is typically composed of a series of optical delay lines with differentoptical paths, and a set of optical switches to select optical paths for a specific time

112 YUNJI YI et al.

delay. A 2-bit polymer OTTD device with delays up to 199.2 ps has been reported withan insertion loss 9.81 dB [19]. In this paper, we report a 2-bit OTTD device with delaysup to 366 ps. In order to achieve a large time delay between adjacent waveguides infinite space, a cross spiral waveguide array is introduced. Four Mach–Zehnder (MZ)thermo-optic switches were involved in the design. SU-8, a negative tone photoresistfrom MicroChem, is selected to be the channel waveguide core material. The upperand under cladding layers are made of a UV-cured resin, Norland Optical Adhesive 61(NOA-61). The refractive indices of the core, lower cladding and upper claddingmaterials are 1.571, 1.547 and 1.547, respectively.

2. Design, fabrication, experiment resultFigure 1 shows the design of the OTTD device. Figure 1a shows schematic of a 1×4OTTD device in a rectangular chip with dimensions of 1.5 cm×1.8 cm. Numbers 1and 4 stand for the input and output numbers. The 1×4 OTTD contains a 1×4 splitter.The spacing between the output waveguide array of the splitter is 40 μm. The angle

Fig. 1. Design of the OTTD devices: schematic of a 1×4 optical delay device (a) and schematic ofa 2-bit optical delay device (b).

a

b

A 2-bit polymer waveguide delay device... 113

of the Y-branch is less than 1°. There are four paths in our design. Path 1 is a straightwaveguide. The other paths are composed of a bend waveguide and straight wave-guide. The bend radius of each path is fixed. The bend radii from inner to outer pathsare 1.5, 3 and 4.5 mm. The lengths of straight connection waveguides from the innerto outer paths are 2.2, 4.4 and 6.6 mm (the corresponding length l is 2.2 mm in Fig. 1a).We made a design to introduce four MZ thermo-optic switches between two 1×4 OTTDelements to form a 2-bit optical delay device, as shown in Fig. 1b. The thermo-opticswitch using SU-8 was reported before [22]. The integrated device which overcomesthe topographical constraint can provide 0, 122, 244 and 366 ps time delays ina 1.5 cm×4 cm rectangular chip.

For OTTD device, the total insertion loss will be the sum of the coupling loss(including fiber to waveguide and waveguide to fiber) (ICL), the input and outputreflection losses (IRL), the loss from the X junctions (IJL), the bending loss (IBL) fromthe waveguide delay lines, the mismatching losses (IML) between bend waveguidesand straight waveguides and the total path propagation loss (IPL). We demonstratedthese losses separately below. The losses of each channel in a 1×4 OTTD are given as:

(1)

(2)

(3)

(4)

Each of the channels 2, 3 and 4 has 4 connections of straight waveguide and bendingwaveguides. And the light passes through 7 X-junctions in the propagation in eachchannel. The bending loss is also introduced in these channels. So, the optical outputpower of the delay channel waveguide is attenuated gradually as the lengths increase.

2.1. Structure of waveguide

In order to reduce polarization sensitivity, the width and thickness of the waveguidecore are selected to be equal. The dimension of the waveguide determines the quantityof modes in the waveguide and the coupling loss between the single mode fiber (SMF)and the waveguide. We simulate the coupling loss of the fiber to waveguide versusthe waveguide dimension by beam propagation method (BPM). The coupling loss isshown in Fig. 2.

The core width and thickness are selected to be both 4 μm to keep single mode,and the coupling loss is 1.52 dB. The thickness of the upper cladding layer is importantto the loss of the waveguide. We simulate the optical field distribution of the waveguide

Iloss1 ICL 2IRL 3IJL IPL1+ + +=

Iloss2 ICL 2IRL 7IJL IBL2 4IML IPL2+ + + + +=



114 YUNJI YI et al.

profile by BPM. In order to decrease the loss of the waveguide, we should ensurethat the waveguide dimension is larger than the optical field distribution region. So,the upper cladding layer thickness is selected to be 4 μm.

2.2. Right-angle X junctionRight-angle X-junction with two identical waveguides intersecting at 90° helpovercome the topographical constraint in the design of long-length waveguide devicewithin a confined area. The structure is shown in Fig. 3; nco is the refractive index ofthe core, and ncl is the refractive index of the cladding. The waveguide width is selectedto be 2a.

The transmission coefficient for the fraction of incident power leaving port 2 isfound to be 99.8% in a 4×4 μm2 waveguide using the beam propagation method (BPM)and a physical model reported before. The loss of the right junction is approximately0.07 dB. When the angle is larger than 75°, the loss is below 0.13. The total loss ofthe X-junctions is 0.91 dB theoretically in the longest channel.

2.3. Bend waveguideCurved waveguides are widely used in OTTD. The small radius bends are essential toachieve a higher packaging density of optical component in PICs to improve their

Fig. 2. Coupling loss vs. different waveguide dimensions.

3

2

1

03 4 5 6 7 8

Cou

plin

g lo

ss [d

B]

Waveguide width (width = height) [μm]

nco

ncl

1 2 2a

x

z

2a

Fig. 3. The structure of the right-angle junction.


functionality and reliability. The method of Marcuse is used to calculate pure bendingloss. It can be seen from Fig. 4 that for R = 100 μm, the pure bending loss can be 0.1 dBper 90° turn. Comparing with the propagation loss, the bending loss is small enoughwhen the bending radius is larger than 500 μm.

The bend loss is experimentally confirmed to be small. Different radius S-bendcomposed of two 90° circular waveguides were fabricated. Figure 5a shows schematicof the device. The radii from inner to outer paths were 500, 750, 1000, 1250, 1500 μm.We obtained a near-infrared field of the device in Fig. 5b, with 0.4 mW input powerand in a 2 cm long sample. The losses were all below 10 dB. The result demonstratedthat we can fabricate a device with the bend radius larger than 500 μm.

2.4. Propagation loss

Because of the low junction loss and low bend loss, the variation in insertion lossbetween adjacent paths is mainly caused by the different lengths of the waveguide. Inthe parameters given above, the propagation loss which is shown in Fig. 6 has been

10–1

10–11

10–21

10–31

10–41

10–51

100 200 300 400 500Bending radius [μm]

Ben

ding

loss

[dB

]

Fig. 4. Bending loss of the 4 μm×4 μm waveguide/90°.

Fig. 5. Device of S-bend composed of two 90° waveguides (a); near-infrared field of the device ofS-bend (b).

a

b

116 YUNJI YI et al.

calculated experimentally. Propagation loss of straight waveguide is 2 dB/cm. Thoughthe propagation loss is a bit large, the material is cheap and easy to obtain. Byusing new highly fluorinated polymers, the propagation loss can be reduced to0.07 dB/cm [23]. Then the total loss of the device can be dramatically reduced.

The fabrication process is listed below. An 8 μm thick film (NOA-61) was spin--coated (spin speed 4000 rpm, time ~20 s) on silicon substrate. The exposure wasperformed at 365-nm wavelength and 300-W Hg lamp power (100 mW/cm2) for 7 min.A 4 μm thick core film was spin-coated on it (spin speed 3500 rpm, time ~20 s),prebaked at 60 °C for 10 min and at 90 °C for 20 min to remove any traces of solventbefore exposure. The pattern exposure was performed at 365-nm wavelength and350-mW Hg lamp power (10 mW/cm2) for 3 min, then a post exposure baking wasperformed at 65 °C for 10 min and at 95 °C for 10 min to crosslink the polymer.The resist is developed in propyleneglygol monomethylether acetate (PGMEA)for 40 s, rinsed in isopropyl alcohol followed by deionised water, and blown dry toform the channel waveguides. After that, it is very important to cure the wafer bybaking it at 150 °C for 30 min so that the adhesion between polymeric waveguideand the buffer layer can be well enhanced and the glass transition temperature Tg canbe increased. To protect the waveguide and accidental scratches, it is necessary to

0 1 2 3 4 54

8

12

16

Straight waveguide length [cm]

Opt

ical

loss

[dB

]

Fig. 6. Propagation loss of the waveguide with cladding.

Fig. 7. The SEM of the SU-8 waveguide core.


spin-coat a 8 μm thick film (NOA-61) as upper cladding. The square waveguidesidewall roughness value scanned by the AFM was about 0.44 nm [24]. The SEMpicture of the waveguide arrays is shown in Fig. 7.

The near-infrared field patterns of the 1×4 OTTD device are shown in Fig. 8.The optical output power of the delay channel waveguide is attenuated gradually asthe lengths increase with the input power 2 mW. The extinction ratio of the MZ switchwas –21 dB and the driving power was 10 mW. The switching property of the devicewas tested with DC bias. The rise time and the fall time of the switch were 0.9 msand 0.6 ms. The loss of the switches is larger than that required in real-life systems,so they have not been integrated in the 2-bit OTTD system. To test the loss andtime delay of the 2-bit OTTO device, a 1×4 OTTD element and a 4×4 OTTD element(the same structure without a 1×4 splitter) are integrated. A schematic photograph ofthe fabricated OTTD device is shown in Fig. 9. The insert losses of the 2-bit OTTDdevice are measured by the AQ8203 optical power meters. The total losses are 7.4,15.11, 21.15, 27.74 dB.

Exact time delay values between adjacent channels were measured. A continuous--wave laser, operating at 1.55 μm, was modulated by a modulator fed by a networkanalyzer (HP37269C), which was used as the probe signal. The probe signal wasinput to the delay device. A photodetector covering the band frequency range wasused to convert the modulated optical signal to an electrical signal that was fed backto the network analyzer.

Fig. 8. Near-infrared field of the 1×4 OTTD.

4 3 2 1

1.5 mm

Fig. 9. Schematic photograph of 2-bitOTTD.

4

3

21

3 mm

118 YUNJI YI et al.

The delays between adjacent paths were given by the difference of each path.Figure 10 shows the measured microwave phase versus the frequency sampled from0 to 6 GHz. The measured time delays of the 2-bit OTTD were 0, 121.1, 242.3, and365.7 ps at 1550 nm. The experimental uncertainty in the delay measurement is 3 psdue to the jitter in the network analyzer’s measurement of the phase.

3. Discussion and conclusionsA 2-bit true-time delay line using right-angle X junctions has been designed, fabricatedand evaluated. This true-time delay line is compact, accurate, and easy to fabricatewhile providing a wide instantaneous bandwidth. The power consumption of the deviceis low. However, the insertion losses of the polymer delay device are currently largerthan those required for actual PAA systems. These losses could be compensated byintegrating with a polymer waveguide amplifier. Future work will include increasingthe number of bits of the device while at the same time reducing the device size andinsertion loss.

Acknowledgements – This work was supported by the National Natural Science Foundation of China(Nos. 61077041, 60807029), the Science Foundation for Young Scientists of Jilin Province, China(No. 20100174), Program for Special Funds of Basic Science and Technology of Jilin University(Nos. 200810028, 200905005) and the Opened Fund of State Key Laboratory on IntegratedOptoelectronics (No. IOSKL-KFKT-11).

References[1] GESELL L.H., FEINLEIB R.E., LAFUSE J.L., TURPIN T.M., Acousto-optic control of time delays for array

beam steering, Proceedings of SPIE 2155, 1994, pp. 194–204.[2] MAAK P., FRIGYES I., JAKAB L., HABERMAYER I., GYUKICS M., RICHTER P., Realization of true-time delay

lines based on acoustooptics, IEEE Journal of Lightwave Technology 20(4), 2002, pp. 730–739.

800

600

400

200

00 1 2 3 4 5 6

Pha

se s

hift

[deg

]

Frequency [GHz]

Fig. 10. Measurement results for each channel.


[3] RIZA N.A., Acousto-optic liquid-crystal analog beam former for phased-array antennas, AppliedOptics 33(17), 1994, pp. 3712–3724.

[4] KOEPF G.A., Optical processor for phased-array antenna beam formation, Proceedings of SPIE 477,1984, pp. 75–81.

[5] ANDERSON L., BOLDISSAR F., KUNATH R., Antenna beamforming using optical processor, Antennasand Propagation Society International Symposium, Vol. 25, 1987, pp. 431–434.

[6] KONISHI Y., CHUJO W., FUJISE M., Carrier-to-noise ratio and sidelobe level in a two-laser modeloptically controlled array antenna using Fourier optics, IEEE Transactions on Antennas andPropagation 40(12), 1992, pp. 1459–1465.

[7] RIZA N.A., Liquid crystal-based optical time-delay control system for wideband phased arrays,Proceedings of SPIE 1790, 1993, p. 171.

[8] FETTERMAN H.R., CHANG Y., SCOTT D.C., FORREST S.R., ESPIAU F.M., WU M., PLANT D.V., KELLY J.R.,MATHER A., STEIER W.H., OSGOOD R.M. JR., HAUS H.A., SIMONIS G.J., Optically controlled phasedarray radar receiver using SLM switched real time delays, IEEE Microwave and Guided WaveLetters 5(11), 1995, pp. 414–416.

[9] YAO X.S., MALEKI L., A novel 2-D programmable photonic time-delay device for millimeter--wave signal processing applications, IEEE Photonics Technology Letters 6(12), 1994,pp. 1463–1465.

[10] FRIGYES I., SEEDS A.J., Optically generated true-time delay in phased array antennas, IEEETransactions on Microwave Theory and Techniques 43(9), 1995, pp. 2378–2386.

[11] FU J., SCHAMSCHULA M., CAULFIELD H.J., Modular solid optic time delay system, OpticsCommunications 121(1–3), 1995, pp. 8–12.

[12] DOLFI D., JOFFRE P., ANTOINE J., HUIGNARD J.-P., PHILIPPET D., GRANGER P., Experimental demon-stration of a phased-array antenna optically controlled with phase and time delays, AppliedOptics 35(26), 1996, pp. 5293–5300.

[13] BOYD R.W., GAUTHIER D.J., GAETA A.L., WILLNER A.E., Maximum time delay achievable onpropagation through a slow-light medium, Physical Review A 71(2), 2005, article 023801.

[14] GUANSHI QIN, SOTOBAYASHI H., TSUCHIYA M., ATSUSHI MORI, SUZUKI T., OHISHI Y., StimulatedBrillouin scattering in a single-mode tellurite fiber for amplification, lasing, and slow lightgeneration, IEEE Journal of Lightwave Technology 26(5), 2008, pp. 492–498.

[15] YIHONG CHEN, XUPING ZHANG, RAY T. CHEN, Substrate-guided-wave hologram-based continuouslyvariable true-time-delay module for microwave phased-array antennas, Proceedings of SPIE 4652,2002, p. 249.

[16] CHEN Y.H., CHEN R.T., A fully packaged true time delay module for a K-band phasedarray antenna system demonstration, IEEE Photonics Technology Letters 14(8), 2002,pp. 1175–1177.

[17] CHEN Y.H., CHEN R.T., K-band phased-array antenna system demonstration using substrate guidedwave true-time delay, Optical Engineering 42(7), 2003, pp. 2000–2005.

[18] YEGNANARAYANAN S., TRINH P.D., COPPINGER F., JALALI B., Compact silicon-based integrated optictime delays, IEEE Photonics Technology Letters 9(5), 1997, pp. 634–635.

[19] HOWLEY B., YIHONG CHEN, XIAOLONG WANG, QINGJUN ZHOU, ZHONG SHI, YONGQIANG JIANG,CHEN R.T., 2-bit reconfigurable true time delay line using 2×2 polymer waveguide switches,IEEE Photonics Technology Letters 17(9), 2005, pp. 1944–1946.

[20] HOWLEY B., WANG X.L., CHEN M., CHEN R.T., Reconfigurable delay time polymer planar light-wave circuit for an X-band phased-array antenna demonstration, IEEE Journal of LightwaveTechnology 25(3), 2007, pp. 883–890.

[21] CHANGMING CHEN, YUNJI YI, FEI WANG, YUNFEI YAN, XIAOQIANG SUN, DAMING ZHANG, Ultra longcompact optical polymeric array waveguide true-time-delay line devices, IEEE Journal ofQuantum Electronics 46(5), 2010, pp. 754–761.

120 YUNJI YI et al.

[22] LEI GAO, JIE SUN, XIAOQIANG SUN, CAIPING KANG, YUNFEI YAN, DAMING ZHANG, Low switchingpower 2×2 thermo-optic switch using direct ultraviolet photolithography process, OpticsCommunications 282(20), 2009, pp. 4091–4094.

[23] YENIAY A., RENYUAN GAO, TAKAYAMA K., RENFENG GAO, GARITO A.F., Ultra-low-loss polymerwaveguides, IEEE Journal of Lightwave Technology 22(1), 2004, pp. 154–158.

[24] TUNG K.K., WONG W.H., PUN E.Y.B., Polymeric optical waveguides using direct ultravioletphotolithography process, Applied Physics A: Materials Science and Processing 80(3), 2005,pp. 621–626.

Received April 12, 2011in revised form July 18, 2011


Research and fabrication of integrated optical chip of Mach–Zehnder microinterference accelerometer

TANG DONG-LIN*, DAI BING, HE SHAN, XIAO KUN-QING, ZHANG LIANG, WANG PENG

Key Laboratory for Petroleum-gas Equipment of EMC, Southwest Petroleum University, Chengdu 610500, China


A novel hybrid-integrated optical accelerometer, based on Mach–Zehnder interference, isdescribed. The integrated Mach–Zehnder microinterferometer chip is investigated theoreticallyand experimentally. On the LiNbO3 substrate with the dimensions of 38 mm×6 mm×2 mm,MMI optical power splitter, Y-branching guide, phase modulator and polarizers are integratedto constitute the Mach–Zehnder microinterference chip. The performance of a prototype ofthe accelerometer is characterised. The measured frequency spectrum is in good agreement withthe theoretical prediction.

Keywords: integrated optics, Mach–Zehnder microinterference chip, accelerometer, Ti:LiNbO3waveguide.

1. Introduction

Integrated (hybrid-integrated) optical accelerometers (IOA) are interest growinginterest in a variety of application fields. Their reduced dimensions and weight to-gether with the possibility of low-cost mass production make them ideal in a wide fieldrange: automation technology, earth and sky observation, till safety and security [1–3].In the previous papers, several fiber-optic accelerometers have been demonstrated, inwhich single-mode all-fiber Mach–Zehnder [4], Fabry–Pérot [5], and Michelsoninterferometers [6] were employed to detect the phase changes induced by the exter-nally applied acceleration. Those sensing systems tend to occupy a relatively largearea and to require precise alignment of the optical components. A solution to theseproblems is the integration of the optical components for the sensing onto a substrate.This integrated optic sensor has several advantages such as compactness, lightness,alignment-free configuration and potentially efficient interaction between the light-wave and the measurand. There have been several proposals of integrated opticalaccelerometers. For example, GORECKI had realized a silicon-based microinter-ferometer with significant SAW phase modulation, performed by deposition of a ZnO

122 TANG DONG-LIN et al.

thin film transducer [7], LLOBERA et al. designed an optical accelerometer based onantiresonant waveguides, which has an optical sensitivity of 4.6 dB/g [8].

In this paper, based on our previous work on Mach–Zehnder fiber-opticalaccelerometer for seismic prospecting [9], we present a novel high-performancehybrid-integrated fiber-optic accelerometer employing an integrated optical Mach––Zehnder interferometer using single-mode Ti:LiNbO3 waveguides. Three polarizersand two phase modulators are integrated with the Mach–Zehnder interferometerfabricated by integrated optics technology on the same LiNbO3 substrate. The acceler-ometer with the resonant frequency of 3416 Hz and sensitivity of 3.22×10–3 rad/m/s2

(a = 0.2g (1.96 m/s2)) is demonstrated to work well in the range of 100–3000 Hz. Itcan be employed to monitor or accurately measure vibrations in various areas such asseismic measurements in geophysical survey, etc.

2. Principle of accelerometer operationFigure 1 shows a hybrid-integrated fiber-optic accelerometer, which consists of fourparts: the input elements (laser, fiber and V-grooves), the Mach–Zehnder microinter-ferometer (MZI) chip (polarizer, MMI optical power splitter, mass, Y-branch wave-guide, phase modulator, polarizers), the output elements (fiber, V-grooves and twoPIN photodiodes) and the signal processing system.

A light beam of intensity I, coupled from the fiber to the V-grooves, is split bythe MMI optical power splitter into four beams of equal intensities which propagatein the arms of the MZI chip. After traversing the arms of the MZI chip, the beamsmerge at the output Y-junction and produce interference fringes based on the appliedacceleration which is observed at the output port. Two PIN photodiodes are employedto convert interferometric optical intensity into electric signal, which is subsequentlyproceeded by the signal processing system.

Laser

Fiber

V-grooves

Polarizer

II/4

Mass

PIN photodiodes

a

b

Ia

Ib

Signal processing system

Phase modulators

Fiber

Polarizers

V-grooves

I/4I/4

I/4

MMI opticalpower splitter Y-branch

waveguide

Fig. 1. Sketch of the hybrid-integrated fiber-optic accelerometer.

Research and fabrication of integrated optical chip... 123

3. Mach–Zehnder microinterferometer (MZI) chip

A schematic of the Mach–Zehnder microinterferometer (MZI) chip, the key elementof the accelerometer, is shown in Fig. 2.

A light beam, which is polarized perpendicular to the stress direction caused bythe acceleration forces on proof mass, is split by MMI splitter forming four separatebeams traveling in waveguides 1, 2, 3, and 4, each with the intensity of I/4. Whenthe proof mass attached to waveguides 1 and 4 is accelerated with acceleration forcesin the direction of ΔF, it will stress one waveguide in tension and the other incompression. This changes the index of refraction of these photoelastic waveguides.The phase shift following the variation of the index will be adjusted by externalacceleration. The light passing through waveguides 2 and 3, which are not stressed,passes through 90° phase modulators. The light which is modulated by externalacceleration and the phase modulator will pass through polarizers after being coupledby the Y-branching waveguide. The polarizers are employed to realize and maintainthe polarization state of the output lightwaves, and also to filter the optical signals outof detection directions. The light signals are converted to electrical signals by photo-detectors. Acceleration is achieved by feeding the electrical signal into a signalprocessor unit.

Having obtained the change of refractive index of the waveguide, we can obtainthe phase shift caused by the applied acceleration:

(1)

where, Δφ is the phase shift, Δn is the change of refractive index, m is the proofmass, Δa is the change in acceleration, B is the photoelastic constant of LiNbO3,B = 5.78×10–12 m2/N, w is the width of waveguide.

Polarizer

Mass

Y-branchingwaveguide

Polarizer

x

yz

Phase modulator

MMI splitter

I

1 2 3 4Waveguides

a

Acceleration

Mass

Fig. 2. Schematic of the Mach–Zehnder microinterferometer (MZI) chip. Top view of the chip (a) andenlarged view of region I (b).

a b

Δφ 2πλ

-----------Δn l 2π BmΔawλ

-----------------------------= =


Since there is a 90° phase lag between beams, the equation for beam intensity atthe PIN photodiode is:

(2)

where I is the input laser intensity. The signal input to signal processor from PINphotodiode (a ) may be

(3)

and the signal input from PIN photodiode (b ) may be

(4)

with the acceleration ΔF in one direction. For acceleration forces in the oppositedirection only the signs (+ or –) will change.

If the two signals are normalized, the difference of output signal from the signalprocessor is:

(5)

which is proportional to the input acceleration. The sensitivity S is:

(6)

In our design, a typical example may be: light axis n0 = 2.219, ne = 2.145.When the wavelength of polarized light (λ ) is 1.3 μm, the waveguide geometry sizesof the sensors are: L = 10 mm, w = 6.5 μm, h = 2.5 μm, the proof mass m = 100 g, andthe sensitivity of the sensor is 3.22×10–7 rad/m/s2.

4. Fabrication and experimental results

The high-quality Mach–Zehnder microinterferometer chip was prepared on LiNbO3substrates with the use of Ti in-diffusion techniques [10].

In order to minimize the loss, an MMI coupler is selected as the power splitter.The MMI width (W ) is chosen as 116.33 μm to ensure easy separation betweenthe four output ports. The first mirrored-image position of TE polarizations can befound at 68.52 μm according to the BPM results. After properly choosing the param-

IoutI2

-------- 1 Δφ 90°–( )cos+ I2

-------- 1 Δφ( )sin+= =

IaI2

-------- 1 Δφ( )sin+=

IbI2

-------- 1 Δφ( )sin–=

Ia Ib–Ia Ib+

---------------------- Δφ( )sin=

S ΔφΔa

------------- 2π Bmwλ

---------------------= =


eters of the MMI coupler, the simulation shows that the propagation loss decreases toonly 0.3 dB.

It is important in the interferometry to keep the polarization state of the twointerfering beams the same [11], so three Al-shielded polarizers with the length of5 mm, prior to the SiO2 buffer layer with the thickness of 50 nm, are designed onthe microinterferometer to realize and maintain TE mode polarized lights.

Considering the hybrid-integrated optical accelerometer response and fabricatingcraft, we adopt the lumped waveguide phase modulator [12] shown in Fig. 3, which isintegrated on the X-cut and Y-propagation Ti:LiNbO3 substrate, in which TE mode istransmitted and the maximal electro-optic coefficient γ33 is obtained.

According to theoretical analysis and the-state-of-the-art, the structure has beendesigned as follows: electrode voltage V = 2.5000 V, electrode length l = 7.9910 mm,guides width w = 5.8312 μm, electrode interval G = 18.5000 μm, electrode thicknesst = 0.4000 μm, electrode capacitance per unit length C0 = 2.0769 pF/cm, electrodecapacitance 1.6596 pF, electrode bandwidth Δ f = 3.8359 GHz.

It was not possible to provide an accurate characterization of the MZI, since it wasuncertain whether the measured losses were due to the seismic mass displacementand/or not to the misalignment between the input/output optical fiber and the device.Placing the optical fiber in V-groove made of silicon solved this problem [8].An unavoidable coupling loss of 2 dB obtained from the coupling light betweenthe optical fiber and the waveguides.

Light of wavelength 1.3 μm was passed through the waveguides fabricated in MZIto check the quality of the waveguides. Figure 4 gives the diffraction image capturedusing an infrared video camera. So, it is obvious that the quality of the waveguides isexcellent.

Fig. 3. Lumped waveguide phase modulator.

L

W Gx

y

z

x

z

Electrode

Electrode

Waveguide

E| |

+ –


In a further experiment, we tested the performance of the MZI for seismicacceleration detection. The frequency response of the accelerometer was determinedusing an electrodynamic shaker (GS1020 vibration tester). The accelerometer wasbonded to a standard piezoelectric accelerometer; the combination was mounted ontop of the shaker with the sensitivity axes of the accelerometers aligned with the direc-tion of motion. The shaker was driven with sinusoidal inputs having frequenciesranging from zero to 8 kHz. The outputs from the accelerometers were recorded usinga dual-trace oscilloscope. The transfer function for the accelerometer was calculatedfrom these data. It is plotted in Fig. 5.

Fig. 4. Diffraction image of output light withwavelength 1.3 μm.

1.000.80

0.60

0.40

0.200.180.160.140.120.100.08

0.06

0.04

0.02100 400 1000 2000 3000 4000

Frequency [Hz]

Out

put [

V]

a

Fig. 5. Frequency response curve of the accelerometer.


In Figure 5, the measured frequency spectra are shown for a = 0.2g. The frequencyspectrum curve for a = 0.2g is flat in the range of about 100–3000 Hz, which isthe useful frequency band for seismic exploration.

5. Conclusions

A hybrid-integrated chip for optical fiber seismic accelerometer with low propagationloss has been designed in this paper. The Mach–Zehnder interferometer (MZI) isdesigned by analyzing its elements, such as MMI coupler, phase modulator andpolarizer, etc. The frequency response characteristics of the accelerometer have beenmeasured. It can be seen that the accelerometer has good linear frequency respondingcharacteristic when the frequency is below 3000 Hz, which is in accordance withthe operating frequency in high-accuracy seismic exploration.

Acknowledgements – This work was supported by the National Natural Science Foundation of China(No. 40774067) and China Postdoctoral Science Foundation (No. 20100471658).

References[1] JAKSIC Z., RADULOVIC K., TANASKOVIC D., MEMS accelerometer with all-optical readout based on

twin-defect photonic crystal waveguide, 24th International Conference on Microelectronics,May 16–19, 2004, Vol. 1, pp. 231–234.

[2] MÜLLER J., MEMS on silicon for integrated optic metrology and communication systems,Microsystem Technologies 9(5), 2003, pp. 308–315.

[3] KALENIK J., PAJĄK R., A cantilever optical-fiber accelerometer, Sensors and Actuators A 68(1–3),1998, pp. 350–355.

[4] JIA NIAN CAO, YA BIN ZHANG, WEI XIN WANG, TAO HAI, Research and design of a large-phaseshift-fringe-count interferometric fiber-optic accelerometer, Proceedings of SPIE 5634, 2004,pp. 315–322.

[5] KE TAO, ZHU TAO, RAO YUNJIANG, XU MIN, SHI CUIHUA, Accelerometer based on all-fiberFabry–Perot interferometer formed by hollow-core photonic crystal fiber, Chinese Journal ofLasers 37(1), 2010, pp. 171–175.

[6] ZENG N., SHI C.Z., ZHANG M., WANG L.W., LIAO Y.B., LAI S.R., A 3-component fiber-opticaccelerometer for well logging, Optics Communications 234(1–6), 2004, pp. 153–162.

[7] GORECKI C., Preparation of oxinitride optical waveguides with piezoelectric modulation fabricatedby silicon micromachining, Proceedings of SPIE 3825, 1999, pp. 47–52.

[8] LLOBERA A., PLAZA J.A., SALINAS I., BERGANZO J., GARCIA J., ESTEVE J., DOMINGUEZ C., Technolog-ical aspects on the fabrication of silicon-based optical accelerometer with ARROW structures,Sensors and Actuators A 110(1–3), 2004, pp. 395–400.

[9] TANG DONG-LIN, CHEN CAI-HE, CUI YU-MING, DING GUI-LAN, WANG JIN-HAI, XIE JIAN-ZHI,Spring system of three-component photoelastic fiber optic accelerometer, Journal of TianjinUniversity 38(1), 2005, pp. 61–64.

[10] HU H., RICKEN R., SOHLER W., Low-loss ridge waveguides on lithium niobate fabricated by localdiffusion doping with titanium, Applied Physics B 98(4), 2010, pp. 677–679.


[11] HE JUN, XIAO HAO, FENG LEI, LI FANG, ZHANG SONGWEI, LIU YULIANG, Analysis of phasecharacteristics of fiber michelson interferometer based on a 3×3 coupler, Acta Optica Sinica 28(10),2008, pp. 1867–1873.

[12] MARCUSE D., Optimal electrode design for integrated optics modulators, IEEE Journal of QuantumElectronics 18(3), 1982, pp. 393–398.

Received March 3, 2011in revised form July 26, 2011


Influence of gamma radiation on the second-order optical susceptibilities and piezoelectricity of the Rb1–xKxTiOPO4 single crystals

RAFAL MIEDZINSKI1, IZABELA FUKS-JANCZAREK1, ANDRZEJ MAJCHROWSKI2, LESZEK R. JAROSZEWICZ2

1Institute of Physics, Jan Długosz University in Częstochowa, Armii Krajowej 13/15, Częstochowa, Poland

2Institute of Applied Physics, Military University of Technology, Kaliskiego 2, 00-908 Warszawa, Poland

We have performed nonlinear optical and piezoelectric studies of the Rb1–xKxTiOPO4 (RKTP)(with x = 0.01 and 0.002) single crystals irradiated by γ -quanta at power 1.23 Gy. We havefound that for non-irradiated samples with x = 0.01 the effective second-order susceptibilitiesdetermined from the powder-like micrometer samples were less than for x = 0.02 and the effectivevalues of the second-order susceptibilities for 1064 nm were equal to 3.12 pm/V (x = 0.002) and2.56 pm/V (x = 0.01). After the gamma irradiation the corresponding values were equalto 2.45 pm/V and 2.78 pm/V, respectively. Moreover, for the samples with x = 0.01 one canobserve the occurrence of the damage at laser energy density equal to about several J/cm2.Such effect is absent for the pure KTP crystals and may be a consequence of substantial role ofthe intrinsic defects caused by insertion of potassium ions in the positions of the rubidium cations.At the same time the piezoelectrical constants show an opposite behavior with respect to the SHG.

Keywords: nonlinear optical crystal, flux growth, gamma irradiation, second-order susceptibility.

1. Introduction

It is well known that crystals of KTiOPO4 (KTP) family demonstrate excellent second--order optical susceptibilities and first of all are NLO materials for second-harmonicgeneration applications [1, 2].

KTP is a widely used material for frequency-doubling Nd:YAG lasers and otherNd3+-doped laser systems emitting near 1064 nm. Although a few specific character-istics of other materials are better, KTP has a combination of properties that make itunique for second-order nonlinear-optical applications and second-harmonic gener-ation (SHG) of Nd3+ lasers in particular. Its large nonlinear coefficients are phase

130 R. MIEDZINSKI et al.

matched, resulting in a high figure of merit. This property, combined with lowabsorption and a wide matched angle, makes it the preferred doubling crystal whenthe available peak power is limited.

Potassium titanyl phosphate (KTP) is a relatively new material that has been shownto have superior properties for several nonlinear-optical applications and, in particular,for frequency doubling for the 1.06 μm radiation of Nd3+ lasers. Because KTP belongsto the space group Pna21, ferroelectric domains can be present, which decreasenonlinear optical conversion efficiencies. Even though the effective nonlinear coeffi-cient of periodically-poled KTP (PPKTP) crystals is lower than periodically-poledLiNbO3 (PPLN), KTP has still the advantage of being able to operate at room tem-perature without causing photorefractive damage. Efficient frequency-doubling wasdemonstrated in PPKTP crystals pumped by high-power pulsed Nd:YAG lasers [3, 4].KUKLEWICZ et al. have utilized a single PPKTP crystal with a single-beam output thatcan be post-selected by a 50–50 beam splitter to produce a high flux source ofpolarization-entangled photons [5]. FIORENTINO et al. overcome this restriction byusing a bidirectional pumping scheme with a single PPKTP crystal that has producedan ultra-bright source of polarization entanglement at the expense of phase locking ofthe interferometric arrangement [6, 7]. The KTP structure was determined byTORDJMAN et al. in 1974 [8]. KTP belongs to the family of compounds that possessthe formula unit MTiOXO4, where M are K, Rb, Tl, NH4, or Cs (partially) and X areP or As. Solid-state solutions exist among the various members of this family, withonly slight changes in lattice parameters. All members are orthorhombic and belong

Fig. 1. Projection of the KTP crystal structure: red – oxygen, blue – potassium, green – titanium,violet – phosphorus. The crystallographic axis c corresponds to the polar direction. The two positionsof the Ti are indicated by 1 and 2 (a). The position of the RKTP crystal with respect to the measurementset-up (b).

a

b

Influence of gamma radiation on the second-order optical susceptibilities... 131

to the noncentrosymmetric point group mm (space group Pna21). For KTP the latticeconstants are a = 12.814 Å, b = 6.404 Å, and c = 10.616 Å, and each unit cell containseight formula units. The structure is characterized by chains of TiO6 octahedra, whichare linked at two corners, and the chains are separated by PO4 tetrahedra. There aretwo different types of octahedra. For the first type TiO6 contains a short Ti–O bond(of approximate length 1.7 Å) and a long Ti–O bond (approximately 2.1 Å) [8], forthe second group a short Ti–O bond (of approximate length 1.65 Å) and a longTi–O bond (approximately 2.21 Å) [9]. The difference in bond length makes the TiO6highly distorted. It has been suggested that alternating the long and the short Ti–Obonds will result in a net polarization along the polar axis which is the major contributorto the nonlinear optic coefficient for KTP [9–11]. Figure 1a shows KTP crystalstructure.

Figure 1b presents a photo of the crystal and its positions in the experimentalset-up. The RbxK1–xTiOPO4 (RKTP) single crystals [1, 12] may be particularlyinteresting due to the better possibility for poling of such crystals. During last decades,many attempts have been made to improve the properties of KTP family crystals andto develop new applications of KTP for waveguide [13], electrooptic devices [14],periodic poling [15, 16], etc. At present, most commercial KTP crystals are grownwith the flux method instead of the hydrothermal method. Typical flux-grown KTPcrystals are obtained at a temperature around 900 °C, depending on the initialcomposition. The ionic conductivity of flux-grown KTP is equal to 10–6 S/cm rangealong the polar axis.

KTP doped with Rb is an interesting candidate for periodic poling as we know thatboth KTP and RKTP can be poled with good results. The reduction of the ionicconductivity for RKTP is a result of the higher activation energy for Rb+ (0.45 eV)with respect to K (0.33 eV) in the crystal lattice [16]. This is caused by the fact thatRb+ has a larger atomic radius than K+ [12].

2. Crystal growth

Incongruently melting RKTP single crystals were grown by spontaneous crystallizationfrom high-temperature solutions in Rb6P4O13 solvent. The composition of starting meltwas 6:10 (Rb1–xKxTiOPO4/Rb6P4O13) in mass ratio. The crystallization was carriedout in a platinum crucible covered with a platinum lid, which was placed in a lowtemperature gradient two-zone resistance furnace. The temperature of the heatingzones was stabilized independently by two 906S Eurotherm controllers. To assure fulldissolution of the components the melt was soaked for 24 hours at 950 °C and thenrelatively quickly cooled to 900°C, when crystallization started. From that pointthe temperature was lowered at a rate of 1 K/h. The crystallization took two weeksand after that time the furnace was cooled to room temperature at a rate of 20 K/h.The as-grown RKTP single crystals were extracted from the solidified melt withthe use of hot water.


3. Gamma-quanta irradiationIrradiation of the crystals by the γ -quanta was performed by the 60Co source withaverage energy about 1.25 MeV to the absorbed dose 102–107 Gy. Irradiation bythe electrons with the average energy 1.25 MeV was carried out by electron transformerwithout the forced cooling to the absorption dose 103–5×107 Gy. To avoid the sample’sheating the irradiation was done by the 0.5 s cycles with the next interval of 30 s.The temperature of the samples during the irradiation did not exceed 330 K.

4. Results and discussionA simplified diagram of the SHG experiment is shown in Fig. 2. The diagram does notshow the optical lenses, fibers and other additional elements used during the exper-iment. Pulsed Nd:YAG laser with 1064 nm wavelength and 5 ns duration timegenerated the higher harmonic in the RKTP crystals placed on the motorized precisionrotation stage. Each sample was studied within the angle range from –35 °C to +35 °Cwith respect to the incident light. The filter at a wavelength of 532 nm with spectralrange 10 nm cut-off the high energy fundamental laser beam thereby protectedthe sensitive CCD detector of the spectrometer. All experiment was controlled byLabVIEW program.

The detection of the light was performed for the output polarization along the sameaxes. Varying the angle between the direction of the propagation and the direction ofthe optical axis we obtain the system of equations which allow us to obtain the valuesof the d33.

As we can see from Fig. 3 maximum SHG signal for the Rb99.8%K0.2%TP (crystal 1)is 5% for 14° of the angle of incidence. The Rb99.0%K1.0%TP (crystal 2) shows betterconversion efficiency. For the angle 12° the conversion efficiency is 8% with respectto the BiB3O6 (BiBO) single crystal. We have found that for non-irradiated sampleswith x = 0.01 the effective second-order susceptibilities determined from the powder--like micrometer samples were less than for the x = 0.02 and effective values ofthe second-order susceptibilities for 1064 nm were equal to 3.12 pm/V (x = 0.002) and

Fig. 2. Experimental set-up for the measurement of SHG.


2.56 pm/V (x = 0.01), respectively. After the gamma irradiation the correspondingvalues were equal to 2.45 pm/V and 2.78 pm/V. Moreover, for the samples withx = 0.01 one can observe damage occurring at the laser energy power about sever-al J/cm2. Such effect is absent for the pure KTP crystals and may be a consequence ofsubstantial role of the intrinsic defects caused by insertion of the potassium ions inthe positions of the rubidium ions.

To understand the origin of the effects it is necessary to take into account thatduring the cationic substitution of the stoichiometric KTP or RTP crystals there occursome differences in the cationic radii. The latter lead to changes of the effective cationiccharges which are extremely sensitive to the external environment [17]. The externalgamma irradiation causes an occurrence of defect centers, which may enhance localpolarizabilities [18]. Figure 4 presents dependence of d33 on the irradiation time at1.23 Gy produced by 60Co source.

Fig. 3. Rb99.8%K0.2%TP (crystal 1) and Rb99.0%K1.0%TP (crystal 2).

10

8

6

4

2

0

–30 –20 –10 0 10 20 30

Sample destruction

SG

H s

igna

l

Angle [deg]

Rb99.8%K0.2%TP (crystal 1)Rb99.0%K1.0%TP (crystal 2)

(ref

eren

ce to

BiB

O c

ryst

al)

[%]

Fig. 4. Dependence of piezoelectric coefficients on the time of gamma irradiation treatment.

0.010.0021.8

1.6

1.4

1.2

1.0

0.80 100 200 300 400 500 600 700 800

t [s]

d 33

[pm

/V]


Following Fig. 4 one can see that the principal piezoelectric tensor component d33for the RKTP crystals with x = 0.01 d33 increases with increasing gamma irradiationtime and for x = 0.002 the corresponding SHG dependence shows an opposite behaviorwith respect to the SHG. So, generally, the sensitivity to the gamma irradiation hasan inverse behavior with respect to the optical SHG. This fact may indicate thatthe defects stimulated by the gamma irradiation have different influence on occurrenceof the local noncentrosymmetry causing the SHG and for the formation of the localelectrostatic electric field responsible for the piezoelectric effects.

The data presented in Ref. [14] of the KTP show that there were not substantialchanges of elastic constants. So the changes of the piezoelectric properties may becaused by the radiation stimulated charged defects.

Such process may be caused by different contribution of the charged defects tothe polarizablity of the oxide ligand clusters [19] through the formation of the photoin-duced piezooptical effects [20], optically induced electron–phonon interaction [21–23].

5. ConclusionsWe have found that for non-irradiated samples of RKTP (with x = 0.01) the effectivesecond-order susceptibilities determined from the powder-like micrometer-sizedsamples were less than for the x = 0.02 and the effective values of the second-ordersusceptibilities for the 1064 nm were equal to 3.12 pm/V (x = 0.002) and 2.56 pm/V(x = 0.01), respectively. After the γ -irradiation the corresponding values were equalto 2.45 pm/V and 2.78 pm/V. Moreover, for the RKTP samples with x = 0.01 one canobserve the occurrence of the damage at the laser power energy about several J/cm2.Such effect is absent for the pure KTP crystals and may be a consequence of intrinsicdefects.

Acknowledgements – This work was partially supported by the Polish Ministry of Sciences and HigherEducation, Key Project POIG. 01.03.01-14-016/08 “New Photonic Materials and their AdvancedApplications”.

References[1] ZUMSTEG F.C., BIERLEIN J.D., GIER T.E., KxRb1–xTiOPO4: A new nonlinear optical material, Journal

of Applied Physics 47(11), 1976, pp. 4980–4985.[2] LIU Y.S., DRAFALL L., DENTZ D., BELT R., Nonlinear Optical Phase Matching Properties of KTiOPO4

(KTP) (l982), General Electric Technical Report No. 82 (RD) 016, General Electric Company,Schenectady, NY, USA.

[3] ENGLANDER A., LAVI R., KATZ M., ORON M., EGER D., LEBIUSH E., ROSENMAN G., SKLIAR A., Highlyefficient doubling of a high-repetition-rate diode-pumped laser with bulk periodically poled KTP,Optics Letters 22(21), 1997, pp. 1598–1599.

[4] PASISKEVICIUS V., WANG S., TELLEFSEN J.A., LAURELL F., KARLSSON H., Efficient Nd:YAG laserfrequency doubling with periodically poled KTP, Applied Optics 37(30), 1998, pp. 7116–7119.

[5] KUKLEWICZ C.E., FIORENTINO M., MESSIN G., WONG F.N.C., SHAPIRO J.H., High-flux source ofpolarization-entangled photons from a periodically poled KTiOPO4 parametric down-converter,Physical Review A 69(1), 2004, article 013807.


[6] FIORENTINO M., MESSIN G., KUKLEWICZ C.E., WONG F.N.C., SHAPIRO J.H., Generation of ultrabrighttunable polarization entanglement without spatial, spectral, or temporal constraints, PhysicalReview A 69(4), 2004, article 041801(R).

[7] RESHAK A.H., KITYK I.V., AULUCK S., Investigation of the linear and nonlinear optical suscepti-bilities of KTiOPO4 single crystals: Theory and experiment, Journal of Physical Chemistry B114(50), 2010, pp. 16705–16712.

[8] TORDJMAN I., MASSE R., GUITEL J.C., Crystal structure of potassium titanium monophosphate[KTiPO5], Zeitschrift für Kristallographie 139, 1974, p. 103.

[9] DOVGII YA.O., KITYK I.V., On the calculation of dielectric and optical properties of wide band gapsemiconductors, Physics of the Solid State 33, 1991, p. 238.

[10] STUCKY G.D., PHILLIPS M.L.F., GIER T.E., The potassium titanyl phosphate structure field: A modelfor new nonlinear optical materials, Chemistry of Materials 1(5), 1989, pp. 492–509.

[11] BIERLEIN J.D., VANHERZEELE H., Potassium titanyl phosphate: Properties and new applications,Journal of the Optical Society of America B 6(4), 1989, pp. 622–633.

[12] WANG S., PASISKEVICIUS V., LAURELL F., High efficiency frequency converters with periodically--poled Rb-doped KTiOPO4, Optical Materials 30(4), 2007, pp. 594–599.

[13] FURUSAWA S., HAYASI H., ISHIBASHI Y., MIYAMOTO A., SASAKI T., Ionic conductivity of quasi-one--dimensional superionic conductor KTiOPO4 (KTP) single crystal, Journal of the Physical Societyof Japan 62(1), 1993, pp. 183–195.

[14] CHENG L.K., BIERLEIN J.D., Ferroelectrics, fine mechanisms of polarization switching in KTiOPO4,Ferroelectric Crystals 268, 2002, pp. 77–82.

[15] KARLSSON H., LAURELL F., Electric field poling of flux grown KTiOPO4, Applied PhysicsLetters 71(24), 1997, pp. 3474–3476.

[16] PIERROU M., LAURELL F., KARLSSON H., KELLNER T., CZERANOWSKY C., HUBER G., Generation of740 mW of blue light by intracavity frequency doubling with a first-order quasi-phase-matchedKTiOPO4 crystal, Optics Letters 24(4), 1999, pp. 205–207.

[17] FAUGEROUX O., MAJCHROWSKI A., RUTKOWSKI J., KLOSOWICZ S., CAUSSANEL M., TKACZYK S., Mani-festation of second-order nonlinear optical effects in KTP and RTP nanocrystallites incorporatedinto polymer matrices, Physica E: Low-dimensional Systems and Nanostructures 41(1), 2008,pp. 6–8.

[18] HERNÁNDEZ-MEDINA A., NEGRÓN-MENDOZA A., RAMOS-BERNAL S., SÁNCHEZ-MEJORADA G., Behaviorunder gamma irradiation of single crystals of NaCl doped with divalent cations, Journal ofRadioanalytical and Nuclear Chemistry 286(3), 2010, pp. 643–648.

[19] MATKOVSKII A.O., SUGAK D.Y., UBIZSKII S.B., KITYK I.V., Mechanisms of radiation damagesformation in gadolinium gallium garnet (GGG) single crystals, Radiation Effects and Defectsin Solids 133(2), 1995, pp. 153–159.

[20] WILLIAMS T.M., HUNTER D., PRADHAN A.K., KITYK I.V., Photoinduced piezo-optical effect in Erdoped ZnO films, Applied Physics Letters 89(4), 2006, article 043116.

[21] ADAMIV V.T., BURAK YA.V., KITYK I.V., KASPERCZYK J., SMOK R., CZERWIŃSKI M., Nonlinear opticalproperties of Li2B4O7 single crystals doped with potassium and silver, Optical Materials 8(3), 1997,pp. 207–213.

[22] PLUCINSKI K.J., MAKOWSKA-JANUSIK M., MEFLEH A., KITYK I.V., YUSHANIN V.G., SiON filmsdeposited on Si(111) substrates – new promising materials for nonlinear optics, Materials Scienceand Engineering B64(2), 1999, pp. 88–98.

[23] KITYK I.V., Specific features of band structure in large-sized Si2–xCx (1.04 < x < 1.10) nanocrys-tallites, Semiconductor Science Technology 18(12), 2003, pp. 1001–1009.

Received May 6, 2011in revised form August 7, 2011


Human optic sensitivity computation based on singular value decomposition

SEYED ALI AMIRSHAHI1, FARAH TORKAMANI-AZAR2*

1Chair of Computer Vision, Friedrich Schiller University, Jena, Germany

2Cognitive Telecommunication Research Group, Faculty of Electrical and Computer Engineering, Shahid Beheshti University, G.C., Tehran, Iran


In this paper, a new definition for images named as the sensitivity parameter (SP) is introduced.SP is based on the decreasing rate of singular values in an image. It could be used in compressingimages in a lower bit rate or in distinguishing robust image parts against watermarking. SP couldalso be used when we would want to make changes in pixel values but keep the quality ofthe image as it is.

Keywords: image processing, image complexity, singular value decomposition, sensitivity parameter.

1. Introduction

The aim of this paper is to present a new parameter named as the sensitivity param-eter (SP). SP is only based on information obtained from human evaluation to locallydetermine the amount of complexity or spatial activity in an image structure. Basedon human evaluation, even if different structure parts have the same frequency or samebrightness they do not seem equal. This is because human observers are not able toequally focus on image details. An important factor of SP is its ability to separate pixelswith respect to their structural and sensitivity of observation. For this reason, SP couldbe used in applications such as finding the best bit rate in compression withoutdecreasing the image quality, finding the most suitable part to embed watermarks,determining the most important parts to enhance in noisy images, etc. Some researchis reported to be done on image complexity using statistical information such asentropy, variance, edge position and other statistical methods [1–3]. Also, in videocoding, the spatial activity of macro blocks should be detected. These blocks wouldbe more robust against intra-prediction models. A drawback of statistical methodsis that they treat pixel values individually without considering their situation andthe neighboring pixels. Another approach taken consists in using the fuzzy theory to

138 S.A. AMIRSHAHI, F. TORKAMANI-AZAR

distinguish image complexity in three classes [4]. In this study, we propose a newapproach to face this issue. The proposed method is based on singular valuedecomposition (SVD) theorem. The SVD is a method for identifying and orderingthe dimension along the data points which exhibit the greatest variation. SVD is basedon a theorem from linear algebra which says that a rectangular matrix A can be brokendown into the product of three matrices, an orthogonal matrix U, a diagonal matrix Λ,and the transpose of an orthogonal matrix V. The theorem is usually presented asfollows:

(1)

where UTU = I and VTV = I; (I is the identity matrix). The columns of U == {U1, U2, ..., Um} are orthonormal eigenvectors of AAT, the columns of V == {V1, V2, ..., Vn} are orthonormal eigenvectors of ATA, and Λ is a diagonal matrixcontaining singular values, λi , in descending order. If we consider m < n, only mnonzero singular values are computed and indicate the vector . In fact,SVD uses statistical properties while considering their distribution as well.

In Section 2, the proposed approach is introduced, Section 3 is dedicated to the ex-perimental results and a conclusion of the work is given in Section 4.

2. Approach proposedIt should be noted that the mean value and standard deviation (SD) in each matrix arenot related to how pixels are set in the block. Consider the three blocks in Fig. 1 whichhave the same pixel values in different distributions. Although their variance and mean

Am n× Um m× Λm n× Vn n×T⋅ ⋅=

Γ λi{ }i 1=m=

A

B

C

105

104

103

102

101

100

10–10 5 10 15 20

A B C

Sin

gula

r val

ue

No singular value

Fig. 1. Three blocks with the same histogram and different distributions and a plot of their singular values.

Human optic sensitivity computation... 139

values are equal, but as seen in Fig. 1 their singular values are completely different.This is due to the fact of the different frequency definition being embedded in the SVDtheorem. The first singular values show the effects of low frequency components whichare effective in constructing the structure of image and the last ones define the highfrequency components which have an effect on constructing the details in the image.In other words, in complex areas, all singular values are important and we would haveapproximately a uniform distribution. Table 1 shows the ratio of second, third andfourth singular values to the first one for the three blocks shown in Fig. 1.

According to Weber’s ratio, the ability of the eye to discriminate between changesin light intensity is related to background brightness. So, when the value of brightnessarea is high, to distinguish objects, a large percentage change in intensity is required.However, in dark areas, a small percentage in intensity could be enough [5]. Therefore,we would face a decrease in the quality of a redundant object when a brightness withlarge difference value from the background’s intensity is inserted in bright areas ofthe image. This happens in dark areas with a small difference value in brightness. Thisis why considering the mean value of the block is necessary to distinguish bright areasas well. In addition, consider the blocks shown in Fig. 1, the change of a pixel valuein block C is not recognized, it is also not important for the observer as it is in otherblocks. For this reason, image complexity or sensitivity to value changes afterwatermarking or denoising should be considered differently in different blocks. Thisinformation could also be used in the case of block compression. If we need to increaseSNR, the blocks like block C could be compressed with high bit rate. However, in thecase of increasing requirement of quality, or storing bit rate, the blocks like block Ccould be compressed with a fewer bit rate, although its reconstruction error would belarge, it would not be detectable for observers. To compute sensitivity we have toconsider all parameters. As a result, the bright areas with a low decreasing rate insingular values would have less sensitivity to brightness mutation. For this reason wewill give each pixel of the original image, f, a value of sensitivity as follows:

1. Consider a sliding block with a size of n×n (odd n) surrounding the pixel (i, j )which is denoted wij . However, we consider i and j as (for an M×N image):

Since n << M and also n << N, this be to convenient and not affect the procedure results.

T a b l e 1. The statistical parameters of the blocks shown in Fig. 1.

Block Mean of blocks SD of blocks s2/s1 s3/s1 s4 /s1

A 55.87 8.5 0.16 0.11 0.050B 55.87 8.5 0.05 0.01 0.005C 55.87 8.5 0.18 0.17 0.150

n 1+2

------------------ i M n 1–2

-----------------–≤ ≤

n 1+2

------------------ j N n 1–2

-----------------–≤ ≤


2. Compute singular values of each block wij as via the singularvalue theorem.

3. Compute the decreasing rate as:

(2)

Since, in all different image structures, the rate of the second singular value to the firstone has a large value, we decided to consider the decreasing rate as Eq. (2). However,the ratio of the reminder singular values is the same. Because of decreasing complexityin computation, we restricted ourselves to this equation only.

4. Compute the ratio of mean brightness value of block wij as μ (i, j ) with respectto the mean pixel brightness of the original image f:

(3)

5. Compute the effects of brightness value and singular values decreasing rate:

(4)

6. Compute the following equation as a sensitivity parameter that is limitedbetween zero and one:

(5)

In Equation (4), we recognize the areas which are bright and also have a decreasingpattern in the first singular values. In the final step, parameter a (i, j ) should benormalized to the maximum values of a’s. Equation (5) is bounded by zero forthe least sensitive area and one for the most sensitive area. Our aim is to recognizethe irregular chaotic areas as the less sensitive ones. In this case, to have the observablebrightness change, it is necessary to change the brightness of pixels with large values.So, the area with a less sensitive value could be compressed with a low bit rate.

3. Experimental resultsIn the first step, we calculate the sensitivity values of all the pixels for three differentimages from the LIVE database [6, 7]. The images are selected at different complexitylevels and different types of smooth areas and edges. Although the size of the slidingblock could be different, it seems that if n is considered as 3, each pixel is comparedonly with its nearest neighboring pixels. On the other hand, if we consider n as a largevalue, it could be confused for small objects. To observe different situations 3 differentvalues of n (n = 3, 5 and 7) were tested on all images. It was seen that n = 5 could bea suitable value for all images with different levels of complexity. Their sensitivity

Γij λγ{ }γ 1=n=

k1 i j,( )λ3

λ1----------

λ4

λ1----------+=

k2 i j,( ) μ i j,( )f

----------------------=

a i j,( ) k1 i j,( )k2 i j,( )=

SP i j,( ) 1 a i j,( )max

i j,a i j,( ){ }

----------------------------------------–=


maps are computed using a window of the size of 5×5. Figure 2 shows three originalimages from the LIVE database and their sensitivity maps. In addition, as an examplebinary maps of the sensitivity map using a threshold level of 0.5 are shown in the thirdrow.

As seen in Fig. 2, the areas which are covered by the plants (seen in the bottomcorners of the Building 2 image) are identified as a less sensitive area; note that theyhave different brightness values. In the case of the Caps image, we are facing an imagewith a low complexity which contains large smooth areas (hence few changes in pixelvalues could be observable). As can be seen, sensitivity values are large in texturedareas, and small in the spaces between the caps on the board.

To use this idea in image compression, we first simulated a test image of ocean.As seen in the binary image of the sensitivity map of ocean in Fig. 2, the top halfpart of the image (part 1) has approximately a sensitivity value larger than 0.5, whilethe sensitivity value of the bottom part (part 2) is smaller than 0.5. We partitionedthis image in two equal parts and compressed each part with a bit rate different fromthe other part. Compressions are done using the jpeg compression command inMATLAB as seen in Tab. 2. These images after reconstruction are shown in Fig. 3.

Fig. 2. First row: original images, second row: sensitivity maps, third row: binary images of the secondrow used with a threshold level of 0.5.


As seen, however, images have been compressed at different bit rates, afterreconstruction, their appearances look fine. As can be seen in Tab. 2, if we compressparts of the image that are less sensitive with a higher compression rate, we willstill have an image with the same quality. This is due to the complexity of the regiondistortions being invisible. On the other hand, these changes decrease the SNRsignificantly; SNR is computed for reconstructed image as g and original image as f:

. This is why changing the bit rate

in the lower region which is also the region with a lower sensitivity would havean effect on the SNR. The first row of Tab. 2 shows the change in bit rates forthe region with lower sensitivity.

To generalize the idea of image compression, we decided to use all referenceimages in the LIVE database. We will first divide the images in parts of 32×32 pixels.In the next step, we will compute the mean sensitivity of each segment and use differentquality jpeg compression degrees for compressing each segment as follows:

– If the mean sensitivity values of block are smaller than 0.25; jpeg quality degreeis set to 25%;

– If the mean sensitivity values of block are between 0.25 and 0.5; jpeg qualitydegree is fixed to 50%;

– If the mean sensitivity values of block are larger than 0.5; jpeg quality degreeis set to 75%.

Since, in this case, we used the mean of sensitivity parameters, removing the effectof the border pixels, which was discussed in step a of the algorithm in the previoussection, would not be lead to any important error.

T a b l e 2. SNR of Ocean image using different compression quality degrees.

Part 2 75% 50% 25%

Part

1 75% 39.66 dB 37.92 dB 36.39 dB50% 39.98 dB 37.45 dB 36.06 dB25% 38.15 dB 36.85 dB 35.61 dB

10 f m n,( )2

f m n,( ) g m n,( )–2

m n,∑⁄

m n,∑

⎩ ⎭⎨ ⎬⎧ ⎫log

Fig. 3. Ocean image with different quality jpeg compression degrees: part 1 – 75%, part 2 – 75% (a),part 1 – 75%, part 2 – 25% (b), part 1 – 25%, part 2 – 75% (c).

a b c


The images with different jpeg quality degrees after reconstruction are denotedby g. In addition, the whole image was compressed with a jpeg quality degree of 75%and was denoted as f.

To evaluate the effect of the proposed sensitivity idea, three parameters werecalculated (see Tab. 3) as follows:

– The percentage of the reduction in storage memory:

(6)

– The percentage of low sensitivity areas to the whole image:

(7)

where N0.25 and N are the number of blocks with a mean of sensitivity parametersmaller than 0.25 and the number of all blocks, sequentially,

(8)

where SSIMf and SSIMg are the structural similarity index (SSIM) for f and g images,respectively. In other words, SSIM is the quality value of f and g, respectively [8].

As seen in Tab. 3, using the sensitivity idea would lead us to a decrease inthe compression bit rate by 8% on average, while the observation quality issimultaneously preserved. In addition, the maximum and minimum difference of P2belongs to Flowerson and Manfishing. The results of applying two compression

T a b l e 3. Results of 29 images of LIVE database and three measured parameters.

Name P1 P2 P3 Name P1 P2 P3

Bikes 3.3333 5.4688 0.0248 Ocean 7.6923 17.7083 0.0409Building 2 5.102 9.6875 0.0268 Painted 8.2192 16.6667 0.0347Buildings 4.3011 5.2083 0.0210 Parrots 8.8235 8.0729 0.0158Caps 12.5 18.2292 0.0332 Plane 12.5 9.6354 0.0275Carnivaldolls 10.869 23.1579 0.0361 Rapids 5.3333 11.7188 0.0351Cemetery 7.9365 23.5088 0.0409 Sailing 1 7.3529 20.3125 0.0409Churchand 9.2593 29.8246 0.0427 Sailing 2 10.8108 16.9697 0.0248Coinsinfout 7.8125 13.4375 0.0328 Sailing 3 9.5238 11.2121 0.0233Dancers 4.918 13.1579 0.0296 Sailing 4 9.6774 16.6667 0.0434Flowerson 9.5238 31.5625 0.0425 Statue 10.8696 19.0909 0.0348House 8.4746 16.6667 0.0401 Stream 9.434 21.0938 0.0582Lighthouse 11.5385 27.8788 0.0472 Students 6.4935 20.7018 0.0308Lighthouse 2 10.1695 25.5208 0.0350 Woman 7.8125 15.4545 0.0356Manfishing 2.2727 2.4291 0.0175 Womanhat 6.8182 8.787 0.0268Monarch 6.5217 13.2813 0.0144 Average 8.1343 16.3142 0.033

P1requirement storage of grequirement storage of f

----------------------------------------------------------------- 100%×=

P2N0.25

N----------------- 100%×=

P3 SSIMf SSIMg–=


methods in the two images are shown in Fig. 4. As seen in the case of the Flowersonimage, using different jpeg compression rates leads to a decrease in the bit rate of upto 9.5%, while the SSIM quality value has a reduction of only 0.04 and observers arenot able to distinguish this difference.

To see the SP effect in image quality, we consider the two images shown in Fig. 4,in five cases of different distortion in the LIVE database. Table 4 shows the comparisonresults. In each distortion type, we consider the lowest and highest distorted imagesand the difference of their quality degrees from the LIVE database which has beencalled the difference mean opinion score (DMOS) value.

As seen in Table 4, the decreasing rate of quality in the case of Flowerson whichhas a larger P2 in comparison to the Manfishing image is smaller, except in the caseof blurring. Other distortions caused a small decrease in the quality rate when smallbit rates were used in compressing the Flowerson image. In the case of regionswhich have a low SP, since these areas have high frequencies, the blurring affectsthe observer’s estimation of the quality. On the other hand, in regions with high

Fig. 4. Reconstructed images Flowerson and Manfishing after: compression with different quality degreesSSIM = 0.9273 (a), compression with one quality degree, SSIM = 0.9698 (b), compression with differentquality degrees SSIM = 0.9442 (c), compression with one quality degree, SSIM = 0.9617 (d).

a b

c d


sensitivity, we will have uniform regions in which blurring would not have a hugeeffect on the quality of the region. In summary, images with large P2 are more robustwith respect to noise and compression compared to images with small P2 values.

4. Conclusions

In this paper, we introduced a new parameter which helps compute the sensitivity ofimages with respect to the changes in pixel values. The parameter can be used whenwatermarking an image and/or using different bit rates to compress an image. Thisparameter considers the rate of decreasing singular values in masks surroundingthe pixel. In smooth areas, the second and third singular values fall too abruptly. Inthe case of a high spatial activity, the second and third singular values are largecompared to the first singular value and so could play an effective role in the imagestructure. The idea is supported by some practical applications and the experimentsshow that the sensitivity parameter could be used to control the required bit rate tocompress images. Experiments have shown that by using different quality jpegcompression in the non-overlapping parts of an image, we could save a storage memoryof up to 12.5%.

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T a b l e 4. The decreasing rate of DMOS values for the five types of the lowest and the highest distortion.

ImageFlowerson Manfishing

Dis

torti

on ty

pe Additive noise 46 50Gaussian blur 44.4 37.5Fast fading 22.1 30Jpeg compression 34.5 50.1JP2k compression 45 48


[7] SHEIHK H.R., BOVIK A.C., DE VECIANA G., An information fidelity criterion for image qualityassessment using natural scene statistics, IEEE Transactions on Image Processing 14(12), 2005,pp. 2117–2128.

[8] ZHOU WANG, BOVIK A.C., A universal image quality index, IEEE Signal Processing Letters 9(3), 2002,pp. 81–84.

Received March 3, 2011in revised form September 13, 2011


Modelling of reproduction process for power laser radiation

J. OWSIK1*, A.A. LIBERMAN2, A.A. KOVALEV2, S.A. MOSKALUK2

1Institute of Optoelectronics, Military University of Technology, 2 Kaliskiego St., 00-908 Warsaw, Poland

2All-Russian Research Institute for Optical and Physical Measurements (VNIIOFI), 46 Ozernaya St., 119361 Moscow, Russia


The model and algorithms for analysis of the laser photoinduced processes were developed usingnumerical simulations. A statistics of the process was carried out by averaging over a hundredlaser pulses. A special correction algorithm was created. A standard uncertainty of the results fromthe output laser signals without any correction was equal to 0.003527, while for the expected valuewas equal to about 1.000510. After correction procedure standard uncertainty of results was0.000479 for the expected value equal to 0.999955. Due to the applied correction methodology oflaser signal analysis, the uncertainty can decrease by one order of magnitude. The proposedapproach may be used for describing photoinduced nonlinear optical processes with time durationfrom nanosecond to microsecond.

Keywords: reproduction process, transfer process, average power of laser radiation.

1. Introduction

Standards in detection of average laser radiation powers are necessary for correctmetrological measurements and transformation of laser pulses [1, 2]. The mostimportant parameter of a standard is uncertainty for reproduction and transfer of a unitportion of laser power. The uncertainty concerns all the elements of a standard system.These elements include standard measuring converter (SMC), control converter (CC),analogue-to-digital converters (A/D) of electric signals, and the laser as a source ofradiation. To design a standard system for determination of uncertainty uw , analysisof uncertainty for particular elements is needed. Thus, in the present work we willdevelop a mathematical model describing corresponding basic operation. To createa complete mathematical algorithm, appropriate synthesis of basic structural elementsshould be carried out.

148 J. OWSIK et al.

The control of the laser parameters is very crucial during studies of the photo-induced optical and nonlinear optical properties [3, 4]. The principal requirement ofsuch kinds of experiments is reliable reproduction of optical parameters [5, 6].

Section 2 of this paper describes a mathematical model of reproduction and transferprocesses of average power of laser radiation. The basic algorithms are given inSection 3.

2. Mathematical model of reproduction and transfer processes for single pulses of laser radiation

Let us consider measurements in an SMC-A/D converter system devoted to measure-ment of an average power of laser radiation for different variants of standards [7–10].

It is assumed that incident laser radiation is constant P0 and does not change withtime. The output signal of the measuring converter is described as

(1)

where is the unit pulse power weight function

for the measuring converter with time constant τ ' ~ 0.1τ, P(t ) = P0.Conversion of a signal in the measuring converter and its measurement with

A/D converter is carried out with the known value of the standard uncertainty uc . Forthe given value uc , for each of the measuring centres, a function of density distributionfor error probabilities is formulated.

Traditionally three types of probability distribution functions are assumed: evendistribution, triangular distribution or a normal one. During measurements, the func-tion of error distribution of measuring converter includes a drift to the high values withconstant velocity γ.

Calculation of a standard uncertainty for a measuring system is made throughthe generation of the Fj random numbers, according to the given probability distri-bution function for each instrument in a system. Nonlinear processing of the conversionfunction to the given h(x) distribution function is used. For a subjected function ofa measuring converter, the Fj numbers are randomly generated. A basis for generationof Fj numbers is a random y value with an even distribution in the interval (0, 1)which is obtained using the generator of pseudorandom numbers. The set searched forthe random Fj values, with a probability determined by the h(x) density distributionfunction, is found by solving the equation yj = G(Fj), where is

a probability of finding the Fj < F number; . The obtained values areshown in a histogram. Signal average value and a standard uncertainty are alsodetermined.

F t( ) d t' P t'( )g t t'–( )0

t

∫=

g t( ) 1τ τ '–--------------- 1

τ----–⎝ ⎠

⎛ ⎞exp 1τ '-------–⎝ ⎠

⎛ ⎞exp–=

G F( ) dxh x( )∞–

F∫=

lim G F( )[ ]F ∞→

1=

Modelling of reproduction process for power laser radiation 149

It was stated that a form of the distribution function for measuring system errorsis defined using a distribution function of measuring converter errors. Thus, the samemathematical form for error distribution function is taken into consideration incalculations for both instruments.

It is also assumed that for the required total value of uncertainty for the measuringsystem, the parameters of measuring procedure and of the instruments used can beevaluated. At least five most important parameters should be considered: up, uA/D,the uncertainty of the measuring converter and A/D converter, respectively, the numberof N readouts, the measurement time Δt, and a drift velocity γ.

In order to find the values of these parameters, the uc(γ = 0) relationship forthe value τ should be formulated and the uc(γ = 0) = relationship shouldbe used. Because the basic element of the system is the measuring converter, first itsmetrological characteristics should be determined, and next the required conversionuncertainty for A/D converter.

Let us consider the influence of instability of laser radiation power on the result ofreproduction of the unit average power of laser radiation and its value transfer.The instability in laser radiation power is determined from the dependence which isa superposition of power jump, fluctuation, and drift [11–14]

(2)

where A is the relative value of a jumping amplitude, t0 is the time of jump occurrence,t1 = t0 + Δt, Δ t is the jump duration, Θ (t) = 0 for t < 0, for Θ (t) = 1 for t ≥ 0;α = A' /Smax, A' is the maximum relative amplitude for laser radiation fluctuation,Smax is the maximum value of a component of development of the S (t ) function,and γL is the velocity of laser radiation drift.

The output signal of the measuring converter is described by Eq. (1). The processof thermal balance stability should be assumed to last at least about 10τ. Afterwards,

up2 uA/D

2+( )1/2

1.005

1.010

1.015

1.020

1.025

1.030

240 720400 560

2

3

1

0.001

0.003

0.005

0.007

0.009

1

2

3

240 720400 560

P(t)

t0 [s]

uca b

t0 [s]

Fig. 1. Average value of the system signal (a) and system standard deviation (b) vs. the time of jumpoccurrence t0, Δ t = 30 s (curve 1), Δ t = 90 s (curve 2), and Δ t = 120 s (curve 3).

P t( ) P0 1 AΘ t t0–( )Θ t t1–( ) α S t( ) γLt–+ +=

150 J. OWSIK et al.

within the time of 2τ, the signal at the output of the measuring converter is measuredmany times and at equal time intervals by A/D converter.

Figure 1 shows dependences of an average value of the system’s output signalas a function of the t0 time during a jump occurrence. A chart of standard uncertaintyof the system as a function of jump occurrence time is shown in Fig. 1b.

The results obtained from investigations demonstrated that when a jump occursdirectly before the measurements start, the signal at the measuring converter outputcarries information concerning the jump and its influence on the whole measuringprocess.

3. Algorithm for measurement data analysisTwo methods were developed to minimise uncertainty during reproduction of the unitof average power of laser radiation, with regard to power jump of laser radiation.

The first method is as follows: for the given value of the ur deviation of an averagevalue of the power of laser radiation, when the measuring signal is without laserradiation, a series of curves for the various values of the jump duration 0.1τ ≤ Δt ≤ 10τare drawn (Fig. 2). For each time, the jump amplitude is taken in such a way as to fulfilthe inequality

(3)

The maximum value of a jump amplitude is searched for with a constant stepwithin the range of 0 < A ≤ Amax. If the ratio is / > 1 + ur , the previous value ofjump amplitude is taken as the maximum one and the next one is recorded. A set ofthe maximum values of the amplitude is shown in Fig. 3, viewed in 3D.

P

P P0

4

6

8

10

12

14

240 720400 560

3

1

2

2

t0 [s]

A

Fig. 2. Maximum jump amplitude vs. the time of its occurrence t0 for the constant deviation value ur,Δ t = 30 s, ur = 0.01 (curve 1), ur = 0.03 (curve 2), and ur = 0.1 (curve 3).

PP0

------------ 1 ur+≤

P P0


Data handling is performed according to the following scheme:– The point A(Δt, t0), the coordinates of which are closest to the experimental

values Δt and t0, is found at the surface of Fig. 3;– A plane parallel to the plane (Δt, t0) is drawn through this point;– The plane crossing the axis A determines the possible maximum value of a jump

amplitude.If the experimental value of the jump amplitude is lower than the maximum value

found, i.e., the found point is inside the volume limited by the surface from Fig. 3,the measurement result is the proper one. Due to the methodology presented here,errors of a measuring process can be detected and be avoided when the final result isbeing determined.

In the second method, uncertainty of reproduction of the unit of power of laserradiation can be minimised by taking into account the influence of a jump (the timeof jump occurrence, its length and amplitude) on the conditions of operation ofSMC-A/D converter system.

Using this method for the real Pexp values of the power, the corrected P'exp valueis calculated using the expression

(4)

where Pexp is the average experimental value of the power with the jump.The concept of this method is similar to the one described above for the first

method. A data set for various ur values is formed. The deviation ur value is chosenfrom the (urmin, urmax) range with a constant step. Adequate ur value corresponds toeach set of parameters of the power jump. Among the calculated data, the values t0,Δt, and A are the same as the experimental ones. The value ur which corresponds tothe data with the jump parameters is introduced into Eq. (4) and next the P'exp powervalue is calculated.

Amax = 0.05

10τ

A

Δt

t0

Fig. 3. A chart of the maximum values of power jump found for ur = 0.0005.

P'expPexp

1 ur+---------------------=

152 J. OWSIK et al.

It has been determined that using the mathematical model, the spread of the powervalues is higher when some fluctuations decrease. Figure 4 shows the dependence ofrelative standard uncertainty for the system as a function of fluctuation frequency. Itis obvious, from the results obtained, that for the system with the time constant ofthe measuring converter τ = 60 s, low frequency fluctuations significantly affectthe measured results.

Figure 5 shows the permissible fluctuation frequency ωmin as a function of the timeconstant τ of the measuring converter urmax = 0.03.

It has been determined that a drift of laser radiation significantly affects the spreadof values for the system’s output laser signal. A drift of laser radiation, togetherwith a drift of the measuring converter signal, can enhance the measurement errors fordrifts of the same directions, i.e., if the order of the drift values is not 10γL >> γP orγP >> 10γL or decreases the measurement errors if 10γL ~ γP.

For thermal converters, mathematical descriptions of this operation and controlreceiver operation are identical.

0.12

0.080.01 1.00

uc

ωc

Fig. 4. Dependence of the relative standard deviation of the system uc on fluctuation frequency ωc.

16

14

12

10

8

6

4

2

00.6 60

ωmin

τ

Fig. 5. Permissible fluctuation frequency ωmin as a function of the time constant of the measuringconverter urmax = 0.03.


The integrand g (t ) from Eq. (1) sufficiently smoothes the signal jumps caused byinstabilities. Thus, to obtain the required information on instabilities of laser radiation,a fast control receiver is needed. A measurement process of the output signal fora control receiver starts at the time 2τ, before the start of measurement process ofstandard measuring converter. This is indispensable for the complete description ofinstability appearing, especially in the case when a power jump of laser radiationappears just before the start of the measurement process. After time 2τ, the measure-ment process of the output signal of a control receiver proceeds simultaneously.

As a filter of the noise resulting from statistical character of the signal, at the outputof the control receiver–A/D converter system, a discrete filter is used with the charac-teristic expressed as

(5)

where F' is the filtered signal, Fn is the signal including noise, Cn is the filter coeffi-cient, nL is the lower limit of the filter cut-off, and nR is the upper limit of the filter.

The method relies on the division of the output signal into blocks of determinedvalues in which a signal is approximated with the polynomial of the given order,according to a criterion of root-mean-square error.

To obtain, from the filtered signal, the signal originating from laser radiation,the component which is responsible for the receiver drift γP (the drift velocity γP isgiven in the device characteristic) is calculated. Next, the first order Walter integralequation with known nucleus g (t ) is solved. This equation can be transformed intoa convenient form of the second-order Walter equation. Finally, the followingexpression is obtained

(6)

The value of radiation power at each step is calculated from Eq. (6) usingthe method of successive approximations

(7a)

(7b)

where n is the step number.To properly analyse the signal, using this method, application of a control receiver

is necessary. This receiver should be characterized by a low level of uncertainty. Thus,

F' t( ) Cn Fnn n– L=

nR

∑=

P t( ) d t'gt'' t t'–( )

g't 0( )----------------------------- P t'( )

t0

t

∫+ F'' t( )g't 0( )

-------------------=

P 0( ) ti( )F'' t i( )g' 0( )

---------------------=

P n( ) ti( )F'' t i( )g' 0( )

---------------------g'' ti tj–( )

g' 0( )------------------------------ P n 1–( ) tj( )

j t1=

ti

∑+=

154 J. OWSIK et al.

calculations of uncertainty uw of the measurement as a function of uk were performed.The corresponding calculation results are shown in Fig. 6.

Examples of results of calculations for a measuring system providing reproductionof a signal shape with the uncertainty not lower than 0.005 are depicted in Fig. 7.The presented laser radiation power signals correspond to the control receiver ofuk = 0.01. Figure 7a shows the input power signal of laser radiation on the controlreceiver, Fig. 7b a signal at the system’s output. Figure 7c presents laser radiationpower signal reproduced using the methodology developed.

Such an approach is exceptionally powerful for analysis of the photoinduced laserprocesses with pulse duration within 1 ns–100 ms. This is caused by the fact that during

0.008

0.006

0.004

0.0020.0005 0.0300uk

uw

Fig. 6. Dependence between uw and uk.

P

P

P

t

t

t

a b

c

Fig. 7. Laser radiation power signals.


such processes the photoinduced phonons with similar realization times begin to playthe principal role [15–17].

The consecutive stage is the correction of the reproduction result for the averagepower of laser radiation and of its value transfer using the correction algorithm.The corrected value of the average power of radiation is obtained from

(8)

where is the average value of power at the output of SMC in one measurementprocess and corrected considering a measuring converter drift. The coefficient m, forlow values of the corrections, can be given in the form

(9)

where is the average power of a laser radiation calculated using control receiver(when the fluctuations and power jumps of laser radiation are excluded), isthe average power observed experimentally with power jump during the measuringprocess using the control receiver.

4. ConclusionsThe formulated model and algorithms for analysis of results were verified by a numericaltest. When determining the average power of laser radiation, one hundred measurementruns selected at random were analysed by means of the presented algorithms andcompared with the hitherto obtained results, without a correction process. A standarduncertainty of the results from the output signals of SMC, with no correction, was0.003527 whereas the expected value was 1.000510. Next, a standard uncertainty ofthe corrected results was 0.000479 whereas the expected value was 0.999955. It isobvious from the results obtained that for the system with the time constant ofthe measuring converter τ = 60 s, low frequency fluctuations significantly affectthe measured results. Due to the applied methodology of signal analysis for a converterof laser radiation, the result uncertainty of reproduction of transfer of the unit ofaverage power of laser radiation can decrease by one order of magnitude. The proposedmethod may be used for analysis for the photoinduced nonlinear optical processeswithin the nanosecond and microsecond time durations.

References[1] OWSIK J., A basis for metrological protection of energy lasermetry, Journal of Technical Physics 38,

1997, pp. 99–109.[2] OWSIK J., SKRZECZANOWSKI W., DŁUGASZEK A., JANUCKI J., NOWAKOWSKI M., PIETRZYKOWSKI J.,

Calibration of power and energy meters of laser radiation, Journal of Technical Physics 44, 2003,pp. 277–287.

Pcorr

PcorrP

1 m+--------------------=

P

m P P'corr–P'exp

---------------------------=

P'corrP'exp

156 J. OWSIK et al.

[3] MIERCZYK Z., MAJCHROWSKI A., KITYK I.V., GRUHN W., ZnSe:Co2+ – nonlinear optical absorber forgiant-pulse eye-safe lasers, Optics and Lasers Technology 35(3), 2003, pp. 169–172.

[4] EBOTHE J., KITYK I.V., BENET S., CLAUDET B., PLUCINSKI K.J., OZGA K., Photoinduced effects inZnO films deposited on MgO substrates, Optics Communications 268(2), 2006, pp. 269–272.

[5] GHOTBI M., SUN Z., MAJCHROWSKI A., MICHALSKI E., KITYK I.V., EBRAHIM-ZADEH M., Efficient thirdharmonic generation of microjoule picosecond pulses at 355 nm in BiB3O6 , Applied PhysicsLetters 89(17), 2006, article 173124.

[6] KITYK I.V., MAJCHROWSKI A., Second-order non-linear optical effects in BiB3O6 glass fibers, OpticalMaterials 25(1), 2004, pp. 33–37.

[7] ZOLOTAREVSKI JU.M., KOVALEV A.A., KOSTIN A.A., KOTYUK A.F., LIBERMAN A.A., MOJSEJEV S.V.,Computer modelling optical radiometer, Measuring Technique 2, 2003, pp. 12–16, (in Russian).

[8] KOVALEV A.A., LIBERMAN A.A., MOSKALUK S.A., Mathematical modelling of instability radiationand manner of taking into consideration at reproduction process of the unit of power of laserradiation and transfer of its value, Measuring Technique 7, 2004, p. 17, (in Russian).

[9] KOVALEV A.A., LIBERMAN A.A., MOSKALUK S.A., Methods of taking into consideration of influenceof instability radiation on result of a reproduction process of the unit of power of laser radiationand transfer of its value, Measuring Technique 8, 2004, p. 55, (in Russian).

[10] OWSIK J., SKRZECZANOWSKI W., DŁUGASZEK A., JANUCKI J., NOWAKOWSKI M., ZARWALSKA A.,Portable standard for unit of power of laser radiation, Proc. Optoelectronics Symp., Warsaw, 2001,pp. 189–191, (in Polish).

[11] MOSKALUK S.A., Influence of a drift of laser radiation power on final result of reproduction of theunit and its transfer, Metrology 12, 2003, pp. 17–21, (in Russian).

[12] KOVALEV A.A., LIBERMAN A.A., MOSKALUK S.A., Influence of jump of power of laser radiation onresult of measurement, Measuring Technique 6, 2003, pp. 34–36, (in Russian).

[13] KOVALEV A.A., LIBERMAN A.A., MOSKALUK S.A., Methods of taking into consideration of influenceof jump of power on result of a reproduction process of the unit of power of laser radiation,Measuring Technique 9, 2003, pp. 26–28, (in Russian).

[14] MOSKALUK S.A., Influence of fluctuation of laser radiation power on final result of reproduction ofthe unit, Metrology 11, 2003, pp. 3–11, (in Russian).

[15] PLUCINSKI K.J., MAKOWSKA-JANUSIK M., MEFLEH A., KITYK I.V., YUSHANIN V.G., SiON filmsdeposited on Si(111) substrates – new promising materials for nonlinear optics, Materials Scienceand Engineering B 64(2), 1999, pp. 88–98.

[16] KITYK I.V., Photoinduced non-linear optical diagnostic of SiNxOy /Si<111> interfaces, Opticsand Lasers in Engineering 35(4), 2001, pp. 239–250.

[17] KITYK I.V., Photoinduced second-harmonic generation of YBa2Cu3O7–delta single crystals, Journalof Physics: Condensed Matter 6(22), 1994, pp. 4119–4128.

Received June 12, 2011in revised form September 2, 2011


An analytical model of the power spatial distribution for underwater optical wireless communication

WEI WEI*, ZHANG XIAO-HUI, CHAO YUE-YUN, ZHOU XUE-JUN

Department of Weaponry Engineering, Naval University of Engineering, No 717, Jiefang Avenue, Wuhan 430033, China


Employing optical propagation theory in Hankel transform, an analytical model of the opticalpower spatial distribution is derived for the ideal point optical source and the Gaussian laser,respectively. Experimental measurements of the spatial distribution of a Gaussian laser arepresented. The expected results of our analytical model are in good agreement with experimentaldata.

Keywords: spatial distribution, optical wireless communication (OWC), Hankel transform, free-spaceoptical (FSO) communication, underwater.

1. IntroductionUnderwater vehicle to ship or buoy links enable the data to be transferred to a storagesystem for later analysis or to be transferred to shore or satellite by radio. In both cases,current acoustic technologies available in the commercial sector limit the channelbandwidth to a few tens of kilobits per second [1]. An optical link would allow largeamounts of data to be transferred quickly and reliably between the surface and aquaticenvironment. Mobile networks of AUVs would also be possible with these links.A high bandwidth link (the recent published transfer rate has approached 1 Gbit/s [2])of these networks would allow for sophisticated collaborative path planning andobservation. Such a system could be employed for military uses, such as locating anddisarming underwater mines or finding enemy submarines.

In short-range underwater applications, intensity modulation with direct detection(IM/DD) is mainly a practical transmission technique. The signal-to-noise ratio (SNR)of a direct-detection receiver is proportional to the square of the received optical power,implying that underwater links are susceptible to the optical power distribution [3].Although volumetric Monte Carlo simulations have been used to provide uncom-promised solutions to the distribution [4], it is difficult to simulate every scenario,since variables of the system should be accurately defined. The radiative transfertheory has been used to investigate the light propagation in random scattering media

158 WEI WEI et al.

accurately [5–9]. However, theoretical solutions to the radiative transfer equations (RTE)have been found to be difficult and excessively robust. Moreover, the underwaterenvironment can be much more complex than the atmosphere due to the turbulence,subaquatic plants, the plankton, fishes, and the undulant seabed. So, having a modelthat would facilitate the evaluation of results would find wide application in practicalscenarios. In previous works [10–13], exponential attenuation model was usually usedas a simple approximation and model for practical scenarios, which describes theattenuation coefficient of water as the sum of absorption and scattering. But thisapproach is insufficient. JAGDISHLAL [14] experimentally proved that this model tendsto magnify the attenuation of water scattering. As the development in fast Hankeltransform (FHT) algorithms, employing optical propagation theory in Hankel trans-form would facilitate examination of the spatial domain effects of scattering on lightunderwater propagation and provide an analytical model.

To investigate the underwater optical power distribution, we start with a basicanalysis of underwater optical propagation theory in Hankel transform. Then,an analytical model is provided for the ideal optical point source with simpleapproximations. A spatial distribution model for a Gaussian laser source is discussednext and experimental measurements of the spatial dispersion of the Gaussian lasersource are finally presented.

2. Optical transfer theory in Hankel transform

For the line-of-sight underwater optical wireless communications applications, the ge-ometry description of spatial power distribution is shown in Fig. 1, where an opticalsource is located at a distance z = 0. We are interested in computing the opticalpower distribution of this source on some plane perpendicular to the beam axis zwhere an optical receiver is located at a position r away from the beam axis. This power

Fig. 1. Geometrical system in receiver plane.

Tran

smitt

er

Receiver

θ

Z

X

Y

r

O

An analytical model of the power spatial distribution... 159

distribution could also be obtained through the point spread function (PSF). Althoughcomputation of PSF requires solving a complex RTE, a small angle approxima-tion (SAA) can be used so that the RTE can be solved analytically. The assumptionsof the SAA include a forward-peaked scattering phase function (SPF), an axialsymmetry on the plane of incidence, and no contribution from back-scattered light atdistances > z [15].

WELLS [16] convert the volume scattering function (VSF) to an image modulationtransfer function so that the scattering properties can be calculated. MCLEAN [17, 18]and COCHENOUR et al. [19] simplified it by using the Hankel transform because of axialsymmetry on the plane of incidence and introduced it into underwater OWC. It wasgiven as [15–19]

(1)

where a is the absorption coefficient, b is the scattering coefficient, zr is the propagationdistance, S is the spatial domain frequency, P(S ) is the Hankel transform of the for-ward-peaked scattering phase function p(θ ),

(2)

where J0(θS ) is the Bessel function of the first kind. Thus, the PSF Fw(S, zr) describesthe effects of the water on the spatial domain properties of the propagating opticalsignal. If f0(r, zr) is the optical power distribution of the transmitted light in free--space whose Hankel transform is F0(S, zr), the optical power distribution in water isthen given by [16]

(3)

This is a general expression for all light sources. For long range, underwaterenvironment is more complicated and shows varied scattering character such as the ab-sorption coefficient, scattering coefficient, current velocity, temperature and the salinityof water. The long-range water could be divided into several short-range waters, andthe corresponding PSF of each water column is labelled as Fw1(S, zr), Fw2(S, zr),Fw3(S, zr), ... Then the optical power distribution in water would be:

(4)

Fw S zr,( ) a b bP S zr z–( )⎝ ⎠⎛ ⎞–+ dz

0

zr

∫–

⎩ ⎭⎪ ⎪⎨ ⎬⎪ ⎪⎧ ⎫

exp=

P S( ) p θ( ) J0 θ S( )2πθ dθ0

π

∫=

f r zr,( ) 12π

------------ F0 S zr,( )Fw S zr,( ) J0 Sr( )S dS0

∞

∫=

f r zr,( ) 12π

------------ F0 S zr,( )J0 Sr( )S Fw1 S zr,( )Fw2 S zr,( )Fw3 S zr,( )…dS0

∞

∫=

160 WEI WEI et al.

3. Spatial distribution for ideal point optical sourceThe spatial distribution for an ideal point optical source is the optical impulse responseof water column in spatial domain. It describes the spatial domain effects from waterscattering on light propagation. If the laser source f0(r, zr) is an ideal point opticalsource, we have its Hankel transform

(5)

For small S, we can expand J0(θS ) in a Taylor series:

(6)

Substituting it into Eq. (2),

(7)

This allows arbitrary SPFs, only the quadratic term in S is retained in the smallangle diffusion approximation. represents the expected value, and

In these limits we have the Hankel transform from Eq. (1)

(8)

Substituting it and Eq. (5) into Eq. (3), the spatial distribution of an ideal pointoptical source in water is given as

(9)

In this case, fideal(r, zr) is a Gaussian probability density function for r with zeromeans and variances /6. In Equation (9), exp(–azr) is the absorption com-ponent, and the remaining is the scattered component. The analytical model suggeststhat it is a product of an exponential absorbing model and a scattering modifiedfunction which is Gaussian distribution. The pulse response is linked with the inherentoptical properties a, b and p (θ ) through Eq. (9). The mathematical simplicity ofthe model and the clarity with which inherent optical properties enter should appealto theorists.

F0 S zr,( ) 1=

J0 θ S( ) 1 14

------- θ S( )2– 164

----------- θ S( )4+ …=

P S( ) 1 14

------- θ 2⟨ ⟩S2–≈

⟨ ⟩ θ 2⟨ ⟩ =2π θ 2p θ( )θ dθ .

0

π∫=

Fw S zr,( ) azr–( )bzr

3

12------------- θ 2⟨ ⟩S 2–

⎝ ⎠⎜ ⎟⎛ ⎞

expexp≈

fideal r zr,( )azr–( )exp

bzr3π

3----------------- θ 2⟨ ⟩

------------------------------ r2

bzr3

3------------- θ 2⟨ ⟩

--------------------------------–

⎝ ⎠⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎛ ⎞

exp=

bzr3 θ 2⟨ ⟩


4. Spatial distribution for Gaussian laser source In many practical underwater optical communication applications, laser sources areusually Gaussian distributed in free-space, whose optical power distribution in free--space at z with initial power P0 is given by

(10)

whose Hankel transform is given as

(11)

where V0(z) is the variance of the Gaussian source in free-space, here ω is the far field half-angle of divergence for Gaussian light source in free-space.

From among several SPFs, we choose the Gaussian SPF for its high accuracy [20]:

(12)

where is a normalized factor, and θ0 isa characteristic scattering angle which has been experimentally tested by PETZOLD [21].So, from Eqs. (2) and (12), we have

(13)

Substituting P(S ) in Eq. (1) by Eq. (13) and after integration, it becomes

(14)

where

f0 r zr,( )P0

2πV0 zr( )---------------------------- r2

2V0 zr( )------------------------–

⎩ ⎭⎨ ⎬⎧ ⎫exp=

F0 S zr,( ) P0V0 zr( )S 2

2----------------------------–exp=

V0 zr( ) zr ω( )π,tan=

p θ( ) 1

Aπθ02

--------------------- θ 2

θ 02

------------–⎝ ⎠⎜ ⎟⎛ ⎞

exp=

A 2π 1 πθ 02⁄ θ 2– θ 0

2⁄( ) θ( )dθsinexp0

π∫=

P S( ) 2A

--------- 12

------θ0S⎝ ⎠⎜ ⎟⎛ ⎞

2

–exp=

Fw S zr,( ) azr–( ) bzr–( )expexp2b erf 1

2------θ0Szr⎝ ⎠⎜ ⎟⎛ ⎞

Aθ0S------------------------------------------------- πexp=

erf x( ) 2π

---------- t2–( )dexp t.0

x∫=

162 WEI WEI et al.

Then, from Eqs. (3), (11) and (14), the optical power spatial distribution in watercan be obtained,

(15)

In Equation (15), exp(–azr) is the absorption component, and

is determined by the scat-

tering coefficient b and the far field half-angle ω of divergence for Gaussian lightsource. Though Eq. (15) is not formally simple and cannot be evaluated explicitly,the FHT makes it much less time-consuming than methods mentioned in the firstsection and it is easy to predict various ranges and water environments. In the followingsection, this model will be experimentally verified as the light source used in ourexperiments is a Gaussian laser source.

5. Experiments design and results

Based on experimental results and in situ measurements, we can extract the basicfeature of underwater scattering. The experimental setup is placed in a 20 m×5 m×1.2 mwater pond, shown in Fig. 2. On one end, a continuous laser source (diode pumpedsolid state, Gaussian source in free-space, drive current 2 A, output power 200 mW,532 nm, 3.5 mrad for far-field half-angle) was placed. At the opposite end an opticalreceiver, a Hamamatsu S5973 PIN was placed (photosensitive area 0.12 mm2, photo-sensitive area diameter 0.4 mm, spectral response 0.28 AW–1 at 532 nm, dark current

f Gaussian r zr,( )P0 azr–( )exp

2π-------------------------------------

bzr– 12

-------b erf θ0πSzr( )

Aθ0S π----------------------------------------- S2

zr ω( )tan π2

---------------------------------------––

⎩ ⎭⎪ ⎪⎨ ⎬⎪ ⎪⎧ ⎫

J0exp Sr( )S dS0

∞

∫×

×=

bzr– 12

-------b erf θ0πSzr( )

Aθ0S π----------------------------------------- S2

zr ω( )tan π2

---------------------------------------––

⎩ ⎭⎪ ⎪⎨ ⎬⎪ ⎪⎧ ⎫

exp

Active stage

Receiver PIN Water

Water pool

Gaussian laser source

Laser beam

Fig. 2. Experimental setup in indoor pool (20 m×5 m×1.2 m).


maximum 0.1 nA). In an attempt to match the receiving characteristics imposed bythe theoretical assumptions in the previous section, the PIN was placed on a motorizedtranslation stage, maintaining an FOV that was as wide as possible (95°, full angle).A narrowband interference optical filter (Zolex JSL-25, central wavelength 540 nm,full width at half-maximum 15 nm, peak transmissivity ≥30%) was placed in front ofthe PIN, filtering ambient light.

A chlorophyll-based model given by HALTRIN [22] was employed by COCHENOUR etal. [19] and CHANCEY [11] to approach the scattering coefficient. However, thismodel, depending on the concentration of the scattering agents, is impractical ina 20 m×5 m×1.2 m pool. Based on the well-known formula with the dependence onvolume scattering function, the scattering coefficient could be obtained by integratingscattering angle from 0 to π. This formula reproduces the experimental measurementsof PETZOLD [21], who developed a general angular scattering meter to measurethe volume scattering function of ocean water. From his data, the single scatter albedos(the rate of scattering efficiency to total attenuation b/c) were generally consistent forthe same type of water, whose attenuation coefficients c vary just in a small span.Commercial environmental characterization optics (ECO) devices are available onInternet to survey VSF, but they are too expensive for us. In our case, we filled inthe pond with artificial seawater, tap water mixed with industrial salt (sodium nitrite)of certain concentration. As our optical wireless communicating prototype wasdesigned for offshore applications, we took Petzold’s offshore experimental results asreference to carefully adjust the optical attenuation coefficient of the artificialseawater. When the attenuation coefficient was measured approximately 0.4 m–1 inthe pool (which is 0.398 m–1 in Petzold’s data), the single scatter albedo was assumedthe same (0.551 m–1 in Petzold’s data) and the scattering coefficient was 0.219 m–1.Considering the single scatter albedo is determined by the scattering particles in nature,this is a big assumption and it is possible that the differences between our model andexperiment are due to this incomplete characterization of the experimental conditions.But it is also extremely simple, and thus a convenient estimate.

The results in Fig. 3 have been normalized to the intensity received at z = 2 m whenit is precisely aligned with the transmitted beam (position r = 0 mm). A generalagreement is observed between experimental and theoretical results. Both results showthat spatial dispersion increases with the increase of distance z. In contrast with largedistances (z > 14 m), the optical spatial distributions for short distances (z < 14 m)retain much of the directionality that initial transmitted beam holds. When the trans-mitter (TX) and receiver (RX) are nearly aligned, the light is collected and the opticalintensity attenuation is approximately 0.5 dB between 2 m and 3 m and also between3 m and 4 m. As the RX deviates from the aiming axis, the optical power decreasesrapidly while the optical intensities approach each other for different distances. Forlarge distances (z > 14 m), the spatial dispersion of optical power is phanerous. The oncehighly directional characteristic of the transmitted laser light is lost. The opticalintensity attenuation is approximately 0.2 dB between 5 m and 6 m and 0.1 dB between6 m and 8 m when the receiver is accurately positioned. Furthermore, the optical

164 WEI WEI et al.

power fades tardily when the alignment deflection increases. This may be attributedto the dominance of multiple-scattering and diffused photos at large distances.The theory and experimental data are also presented as the intensity versus TX/RXpointing angle. From Figure 4, optical intensity presents distinct forward scatteringcharacters for various distances. For a given TX/RX pointing angle, the intensitydecreases when the distance increases. And the larger the distance becomes the slowerthe intensity decays. This gives us an insight into the beam dispersion in the spatialdistribution of the light in water. The results could explained how the water volumescattering effects optical communication applications. When the distance is relativelyshort (z < 14 m), the RX and TX should be accurately aligned because a slightdeviation from the aiming axis would induce a significant reduction in received optical

Nor

mal

ized

inte

nsity

[dB]

r [m]

0.5

0.0

–0.5

–1.0

–1.5

–2.0

–2.5

TheoryExperiment

0.00 0.01 0.02 0.03 0.04 0.05 0.06

TheoryExperiment

0.00 0.01 0.02 0.03r [m]

–1.3

–1.4

–1.5

–1.6

–1.7

–1.8

–1.9

–2.0

–2.1

Fig. 3. Symmetry distribution for optical power at diverse (r, z), θ0 = 0.13 mrad [21], as far-fieldhalf-angle is 3.5 mrad, V0 = tan(0.0035)zπ: distances of 2, 3 and 4 m (a), distances of 5, 6 and 8 m (b).

a b

2 m3 m

4 m

5 m

6 m

8 m

Nor

mal

ized

inte

nsity

[dB

]

Transmitter/receiver pointing angle [mrad]

0.5

0.0

–0.5

–1.0

–1.5

–2.0

–2.5

TheoryExperiment

0 5 10 15 20 25 30

a

2 m

3 m

4 m

Transmitter/receiver pointing angle [mrad]0 5 10 15 20 25 30

TheoryExperiment

–1.2

–1.4

–1.6

–1.8

–2.0

–2.2

–2.4

–2.6

–2.8

–3.0

5 m

6 m

8 m

b

Fig. 4. The normalized intensity vs. TX/RX pointing angle: distances of 2, 3 and 4 m (a), distances of 5,6 and 8 m (b).


power and lead to a link-break in the communication. When the distance is relativelylong, there is a deviation tolerance for the RX /TX position and the alignment is lesscritical because the loss of power is relatively small for a mild excursion, but thistolerance costs a higher overall loss in optical power. Those results inspire us that ifthe distribution of light source could be adjusted by a controllable optical system, thedistribution of optical power in water would be rebuilt according to the TX/RX positionand the communication link should be more robust in complicated underwaterenvironments.

6. Summary In this paper, we investigate the characteristics of spatial optical power distributionfor underwater light propagation which strongly affects power budget in underwaterwireless optical communication. An analytic spatial domain response function modelfor an ideal optical impulse is deduced, which is suggested to be a Gaussiandistribution. The mathematical simplicity of the model and the clarity of its inherentoptical properties makes it an attractive analytical tool for general problems inthe spatial domain effects of multiple scattering in water. A computer analytic modelfor Gaussian laser source was also developed using Hankel transform of PSF simplifiedwith SAA. The expectation of this model overall agrees with laboratory experimentaldata. The validation between model and experiment confirms that the directionality ofthe laser beam is lost as particulates in the environment broaden the intensitydistribution faster than the divergence of the laser source itself. In our earlierpaper [3], considering the geometrical wastage induced by receiver size, spatialposition and receiving angle, the receiving optical power was obtained based onthe distribution, and we implemented an experimentation in a pool which verified thatour method achieved a better agreement with experimental data than the exponentialattenuation model.

References[1] AKYILDIZ I.F., POMPILI D., MELODIA T., Underwater acoustic sensor networks: Research challenges,

Ad Hoc Networks 3(3), 2005, pp. 257–279.[2] HANSON F., RADIC S., High bandwidth underwater optical communication, Applied Optics 47(2),

2008, pp. 277–283.[3] WEI W., ZHANG X.H., RAO J.H., Study on computing the receiving optical power in underwater optical

wireless communication, Chinese Journal of Lasers 38, 2011, article 0905002.[4] JAFFE J.S., Monte Carlo modeling of underwater-image formation: Validity of the linear and

small-angle approximations, Applied Optics 34(24), 1995, pp. 5413–5421.[5] WEI WEI, XIAOHUI ZHANG, JIONGHUI RAO, WENBO WANG, Time domain dispersion of underwater

optical wireless communication, Chinese Optics Letters 9(3), 2011, article 030101.[6] JARUWATANADILOK S., Underwater wireless optical communication channel modeling and

performance evaluation using vector radiative transfer theory, IEEE Journal on Selected Areas inCommunications 26(9), 2008 , pp. 1620–1627.

166 WEI WEI et al.

[7] SWANSON N.L., GEHMAN V.M., BILLARD B.D., GENNARO T.L., Limits of the small-angle approxi-mation to the radiative transport equation, Journal of the Optical Society of America A 18(2), 2001,pp. 385–391.

[8] ISHIMARU A., KUGA Y., CHEUNG R.L.-T., SHIMIZU K., Scattering and diffusion of a beam wave inrandomly distributed scatterers, Journal of the Optical Society of America 73(2), 1983, pp. 131–136.

[9] SANCHEZ R., MCCORMICK N.J., Analytic beam spread function for ocean optics applications, AppliedOptics 41(30), 2002, pp. 6276–6288.

[10] JIANQI SHEN, HAITAO YU, JINDENG LU, Light propagation and reflection-refraction event in absorbingmedia, Chinese Optics Letters 8(1), 2010, pp. 111–114.

[11] CHANCEY M.A., Short Range Underwater Optical Communication Links, Master Thesis, NorthCarolina State University, 2005, pp. 30–31.

[12] VASILESCU, Data Collection, Storage, and Retrieval with an Underwater Sensor Network,Proceedings of ACM, SenSys’05, November 2–4, 2005, San Diego, California, USA, p. 154.

[13] ARNON S., Underwater optical wireless communication network, Optical Engineering 49(1), 2010,article 015001.

[14] JAGDISHLAL G.Y., Underwater Free Space Optics, Master Thesis, North Carolina State University,2006, pp. 41–57.

[15] MULLEN L., Optical propagation in the underwater environment, Proceedings of SPIE 7324, 2009,article 732409.

[16] WELLS W.H., Loss of resolution in water as a result of multiple small-angle scattering, Journal ofthe Optical Society of America 59(6), 1969, pp. 686–691.

[17] MCLEAN J.W., VOSS K.J., Point spread function in ocean water: Comparison between theory andexperiment, Applied Optics 30(15), 1991, pp. 2027–2030.

[18] MCLEAN J.W., FREEMAN J.D., WALKER R.E., Beam spread function with time dispersion, AppliedOptics 37(21), 1998, pp. 4701–4711.

[19] COCHENOUR B.M., MULLEN L.J., LAUX A.E., Characterization of the beam-spread function forunderwater wireless optical communications links, IEEE Journal of Oceanic Engineering 33(4),2008, pp. 513–521.

[20] MOORADIAN G.C., GELLER M., STOTTS L.B., STEPHENS D.H., KRAUTWALD R.A., Blue-green pulsedpropagation through fog, Applied Optics 18(4), 1979, pp. 429–441.

[21] PETZOLD T.J., Volume Scattering Functions for Selected Ocean Waters, SIO Ref. 72-78, ScrippsInstitution of Oceanography, California, San Diego, 1972, pp. 36, 46.

[22] HALTRIN V.I., Chlorophyll-based model of seawater optical properties, Applied Optics 38(33),1999, pp. 6826–6832 .

Received August 2, 2011in revised form October 27, 2011


High birefringence liquid crystal mixtures for electro-optical devices

EDWARD NOWINOWSKI-KRUSZELNICKI1*, JERZY KĘDZIERSKI1, ZBIGNIEW RASZEWSKI1, LESZEK JAROSZEWICZ1, ROMAN DĄBROWSKI1, MAREK KOJDECKI1, WIKTOR PIECEK1, PAWEŁ PERKOWSKI1, KATARZYNA GARBAT1, MAREK OLIFIERCZUK1, MAREK SUTKOWSKI2, KAROLINA OGRODNIK1, PRZEMYSŁAW MORAWIAK1, EMILIA MISZCZYK3

1Military University of Technology, ul. gen. S. Kaliskiego 2, 00-908 Warsaw, Poland

2Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland

3Radom University of Technology, ul. Malczewskiego 29, 26-600 Radom, Poland


High-birefringence nematic liquid crystals recently developed in the Military University ofTechnology (Poland) are examined for selected physical properties. In particular, for six liquidcrystal mixtures there were determined: two components of dielectric permittivity for voltagefrequencies in the range from 10 Hz to 10 MHz; rotational viscosity; splay, twist and bend elasticconstants; ordinary and extraordinary refractive indices for light wavelengths in the range from0.3 μm to 1.6 μm. The properties are discussed in terms of applicability of the new liquid crystalsto electro-optical devices.

Keywords: liquid crystal, birefringence, physical properties.

1. Introduction

Despite the considerable research progress in the last years in the development ofnematic liquid crystals, one should also know that there are several tradeoffs, such aslimited view angle, brightness, contrast and switching times and that these parameterscan be improved further. Liquid crystal materials containing unsubstituted cyclohexyl-benzene and bicyclohexyl benzene isothiocyanates, biphenyl-, fluoro-substitutedterphenyl-, tolane- and phenyl-tolane isothiocyanates liquid crystalline compoundsfeature high-birefringence, high polarity and low viscosity [1–5]. By combiningseveral components one can control the properties of resulting liquid crystallinemixtures, such as birefringence, viscosity, refractivity indices, dielectric permit-tivity and elastic constants in accordance with requirements for various display andnon-display applications. Further, the following material parameters of six different

168 E. NOWINOWSKI-KRUSZELNICKI et al.

recently produced medium- or high-birefringence liquid crystalline mixtures(HBLCM) are presented and discussed:

– W1898 (composed of two and three ring alkylcyclohexylbenzene andalkylbicyclohexylbenzene isothiocyanates),

– W1820 (composed of fluoro-substituted alkylbiphenyl- and alkylterphenylisothiocyanates),

– W1852 (composed of fluoro-substituted alkylbiphenyl- and alkylcyclohexylbi-phenyl- and alkylbicyclohexylbiphenyl isothiocyanates),

– W1825 and W1791 (composed on fluoro-substituted alkyltolane- andalkylphenyltolane isothiocyanates),

– W1865 (composed of fluoro-substituted alkylphenyl- and alkylbiphenyltolaneisothiocyanates).

2. Experimental methodsThe results of measurements and computations are collected in Table 1. Basic phasetransition temperatures [°C] from crystal (or smectic A) to nematic (Cr–N) and fromnematic to isotropic phase (N–I) for all mixtures were determined using the BIOLARPI microscope equipped with the LINKAM 600 hot stage, controlled by the TMS 91unit. Liquid (or bulk) viscosity Γ was defined at temperature T by using Ostwaldcapillary viscometer. Refractive indices of HBLCMs were measured with Abberefractometer and when the values were higher than 1.87 or in the near infrared (NIR)region up to λ = 1.060 μm, the interference methods with the wedge-shaped cells were

T a b l e 1. Material parameters of HBLCM mixtures at 25 °C.

Note: for W1865 the temperature of SmA–N transition instead of Cr–N one is given.

LC mixtureW1898 W1820 W1852 W1825 W1791 W1865

T [°C] (N–I) 83.5 71.1 152.6 136.0 127.5 170.1T [°C] (Cr–N) –20 10 –10 –12 –20 10no at λ = 0.589 μm 1.51 1.52 1.53 1.54 1.54 1.54Δn at λ = 0.589 μm 0.17 0.32 0.33 0.42 0.44 0.47no at λ = 1.064 μm 1.50 1.51 1.52 1.53 1.53 1.53Δn at λ = 1.064 μm 0.14 0.25 0.29 0.37 0.40 0.41ε⊥ at f = 1.5 kHz 3.5 5.5 4.1 4.7 4.5 5.0Δε at f = 1.5 kHz 8.1 19.5 15.3 17.0 16.4 18.2K11 [pN] 12.0 13.5 11.2 12.5 21.2 10.5K22 [pN] 7.5 8.2 7.7 7.4 8.3 7.8K33 [pN] 24.1 33.0 31.0 32.1 25.2 29.4KTN [pN] 16.4 19.7 26.9 16.8 28.9 23.4Γ [mPa s] 10 18 – 31 31 –γ [mPa s] 97 180 320 284 213 595

High birefringence liquid crystal mixtures... 169

applied. Dielectric measurements were performed using the Hewlett–Packard type4192A low frequency impedance analyzer for frequencies from 10 Hz to 10 MHz.

2.1. Measuring cells

In order to determine dielectric, electro-optic and some spectral characteristics ofHBLCM samples, measurement cells of three types, with planar-homogeneous (or,HG), homeotropic (HT) and twisted nematic (TN) structure, were manufactured in ourlaboratory under WAT1 standard. The layout of such a cell is shown in Fig. 1.

The bottom and top covers were prepared of high-quality float glass plates withthickness of 0.7 mm. The patterns of active areas (5.08 mm×5.08 mm) in all cells wereetched in indium tin oxide (ITO) transparent layers deposited on glass substrates, withsheet resistances of 10, 70, and 500 Ω/sq, respectively. In the case of dispersivedielectric measurements the golden (Au) electrodes with sheet resistance smaller than0.01 Ω/sq were applied. Rubbed polyimides SE 130 and SE 1211 were applied asorienting coatings to obtain proper HG and TN (90° twist) or HT cells, respectively.The adhesive sealing material used in the manufacturing of these cells was rated to180 °C. In order to achieve a proper thickness d of the cells, spacers of 1.6, 2.5, 3.0,5.0, 6.0, 7.0, 8.0 and 10.0 μm in thickness were added to the sealing material andsprayed at the active regions. Thickness and uniformity of the cells gap were measuredby means of PREMA SPM 9001 spectrometer with the accuracy of ±0.1 μm. The labelof the cell contains the thickness of the cell, orientation of LC texture and sheetresistance of the electrode layers. For example, 1.6HG10 indicates a cell gap of 1.6 µm,planar-homogeneous orientation and ITO electrodes with sheet resistance of 10 Ω/sqand 8.4HTAu indicates an 8.4 μm thick cell with homeotropic alignment and goldenelectrodes.

2.2. Dielectric permittivities

The temperature characteristics of real and imaginary parts of the isotropic εI (T ),perpendicular ε⊥(T ) and parallel ε | | (T ) components of the permittivity tensors ε of

A-A

A-A

5.08

5.08

15.0

20.025.0 0.

7 Fig. 1. Layout of a cell manufactured under WAT1 standard(one active area).


HBLCMs were measured in nematic and isotropic phases. The temperature was stableto within 0.2 °C [6–8]. The results of dielectric and optical measurements for HBLCMsare further presented in figures and gathered in Tab. 1.

Typical temperature characteristics of real parts of ε⊥' (T ) and ε | |' (T ) found forW1898 are shown in Fig. 2a. The results of dispersive measurements in the range from100 Hz to 10 MHz for real ε | |' and imaginary ε | |'' parts of ε | | for the same mixture at25 °C are presented in Fig. 2b.

2.3. Refractive indices

Temperature characteristics of isotropic ni(T ), ordinary no(T ) and extraordinary ne(T )refractive indices (up to n = 1.87) of HBLCMs were measured in nematic and isotropicphases (up to 130 °C) by an Abbe refractometer using light waves λ of 0.5007, 0.5400,

5 15 25 35 45 55 65 75 85 95 0.1 1 10 100 1000 10000

14

12

10

8

6

4

2

0

W1898

TC = 83.5 °C

ε⊥

ε | |

ε | |''

T [°C] f [kHz]

ε εW189814

12

10

8

6

4

2

0

ε | |'a b

Fig. 2. Temperature dependences of real parts ε | |' (T ) and ε⊥'(T ) for W1898 LC: at 25 °C and f = 1 kHzmeasured using: 5.4HGAu and 5.2HTAu cells, respectively (a) and 5.2HTAu cell (b).

5 15 25 35 45 55 65 75 85 95

TC = 83.5 °C

T [°C]

W18981.68

1.64

1.60

1.56

1.52

1.48

n ne

no

ni

Fig. 3. Temperature dependence of no(T ), ne (T ) and ni (T ), for W1898 at yellow sodium lineλ = 0.5893 μm measured at 25 °C using Abbe refractometer.


0.5893, 0.6328, 0.6563 and 0.6731 μm. The measurement temperature in each stepwas stable to within 0.2 °C [9, 10]. The characteristics recorded for W1898 are shownin Fig. 3.

The measurements involving the interference method (Fig. 4) were performed bymeans of the JASCO V670 spectrometer. The magnitudes of refractive indicesdetermined for HBLCMs under study are gathered in Table 1. When the measuredrefractive indices of HBLCMs were higher than 1.87 or in the near infrared (NIR)region up to λ = 1.060 μm, the interference methods with the wedge-shaped cells were

W1898

100

80

60

40

20

00.4 0.6 0.8

λ [nm]1.0 1.2 1.4

k = 3 k = 2 k = 1

d = 7.9 μmλ3 = 0.55 μm

λ2 = 0.78 μm

T [%]

Δn λ3( )dK3

----------------- 52--= Δn λ2( )d

λ2----------------- 2k 1–

2---------------- 3

2--= =

Fig. 4. Transmittance of W1898 at 25 °C in 7.9HG500 cell placed between crossed polarizers. The order kof a birefringent peak (maximum) at λk relates Δn(λk) and cell thickness d [6, 11]; Δn(λk) =(2k – 1)λk /2d.

Fig. 5. Formation of interference fringes in a wedge cell for λ = 0.6328 μm at 25 °C: a – in the emptycell (n = 1, the distance of adjacent interference fringes A = 0.0597 mm is measured); b – in the cellfilled with W1898 when direction of light polarization coincides with molecular director (then n = ne,the distance between adjacent fringes E = 0.0357 mm is measured and ne = A /E = 1.672 is calcu-lated [10]); c – in the cell filled with W1898 when direction of light polarization is perpendicular tomolecular director (then n = no and the distance between adjacent interference fringes O = 0.0396 mmis measured and no = A /O = 1.508 is calculated); d – the cell placed between crossed polarizers(the molecular director of the layer forms angles of 45° with transmission axes), (the distance of adjacentinterference fringes B = 0.7067 mm is measured and Δn = 2A/B = 0.169 is calculated).

a

b

c

d


applied [11, 12] (with wedge apex angle of order of a few milliradians). Interferencefringes in wedge cells in visible (VIS) and NIR regions were recorded by CCD camerawithout NIR filter. The results of measurements and calculations of no, ne and Δn ofW1898 for λ = 0.6328 μm at 25 °C are illustrated in Fig. 5.

2.4. Elastic constantsThe measurements of elastic constants K11, K22 and K33 (corresponding to pure splay,twist and bend deformations) are usually based on determining critical magnitudes ofelectric (E1C, E3C, E5C, E7C) and magnetic (H2C, H3C) fields for different types ofFréedericksz transitions in proper HG, HT (see Figs. 6 and 7) or TN cells. Additionally,the reduced TN elastic constant KTN (describing elasticity of LC layer in the transitionfrom the twisted to homeotropic configuration) can be measured in the same wayas K11 by using TN instead of HG cell. When dielectric (Δε > 0) and diamagnetic(Δχ > 0) anisotropies of LCs are known, elastic constants can be calculated fromthe equation Kii = π–2Fii , with factors Fii corresponding to suitable configurationsdefined in Fig. 8. Magnetic field is necessary in some cases. Since diamagnetic(Δχ > 0) anisotropies of mixtures under investigation are still unknown now, all elasticconstants of HBLCMs were measured by exploiting only electric fields [12]. Figure 7presents measurement geometries used for determining elastic constants when onlyelectric fields are applied. To establish E5C and E7C (parallel to the boundary surfaces)in HG cell for twist and in HT cell for bend deformations, the interdigital electrodesare applied. Electric fields inside cells are formed using ITO in-plane switchingtype (IPS) electrodes in the form of rectangular stripes of width b = 10 μm separated

d

E1C

Δε > 0

HG cell

Spla

yTw

ist

Ben

d

H2C

H3C

F11 = Δεε0E1C2 d2

F22 = Δχμ0H2C2 d2

HG cell

HT cellF33 = Δχμ0H3C

2 d2

d

E3C

Δε > 0

HG cell

Spl

ayTw

ist

Ben

d

E5C

E7C



IPSHG cell

IPSHT cellF33 = Δεε0E7C

2 d2

Fig. 6. Measurement geometries used for determining elastic constants Kii when electric (E ) andmagnetic (H ) fields are used (ε0 and μ0 are the electric and magnetic permittivity of free space).

Fig. 7. Measurement geometries used for determining elastic constants Kii when only electric fields Eare used.


by etched stripes of width l = 20 μm in IPSHG or IPSHT cell of thickness aroundd = 5 μm. In the middle between the electrode stripes nearly homogeneous electricfield E5C ≈ Uth / l or E7C ≈ Uth / l is induced by applying voltage Uth to interdigitalelectrodes [12]. Examples of determining elastic constants are given below. The con-stant magnitudes are gathered in Table 1.

2.4.1. Splay elastic constant

Figures 9 and 10 illustrate the Fréedericksz transition in HG cells filled with W1898under voltage U at f = 1 kHz and 25 °C, monitored by dielectric and optical trans-mission measurements of the cell, respectively. In the case of optical measurementthe cell was placed between crossed polarizers. The plane of polarization of incident

W1898

0.4 0.6 0.8λ [nm]

1.0 1.2 1.4

0.20

0.18

0.16

0.14

0.12

Δn

Fig. 8. Dispersion of optical anisotropy Δn (λ ) for W1898 at 25 °C. The selected points on the curveΔn (λ) in VIS and NIR regions follow from values of ne(λ ) and no(λ) determined by combined methods,applying both appropriately prepared Abbe refractometer and interference wedges and being supportedby interference methods [12].

14

12

10

8

6

4

2

00 2 4 6 8 10 12 14

W1898

Δε = 8.1

Uth = 1.3 V

ε

U [V]

K11

Δεε0π2

-----------Uth2 12.2 [pN]= =

Fig. 9. Splay deformation of W1898 in 5.4HGAu cell. Effective dielectric permittivity was monitoredby dielectric measurements.


0.010

00 0.5 1.0 1.5 2.0 2.5 3.0 3.5

W1898

Δε = 8.1

Uth = 1.3 V

U [V]

K11

Δεε0π2

-----------Uth2

12.2 [pN]

= =

=

4.0

I [a.

u.]

0.008

0.006

0.004

0.002

Fig. 10. Splay deformation in 5.4HG70 cell. Fréedericksz transition was monitored by light transmissionmeasurements.

14

12

10

8

6

4

2

00 2 4 6 8 10 12 14

W1898

Δε = 8.1

Uth = 1.5 V

ε

U [V]

KTN

Δεε0π2

-----------UTN2 16.4 [pN]= =

Fig. 11. Determination of KTN reduced elastic constant from electric permittivity measurement in3.1TN70 cell.

0.16

00 1 2 3 4 5 6 7

W1898

Δε = 8.1

UTN = 1.5 V

U [V]8

I [a.

u.]

0.12

0.08

0.04d = 3.1 μm

9

KTN

Δεε0π2

-----------UTN2 16.4 [pN]= =

Fig. 12. Intensity I of light transmitted normally through 3.1TN70 cell.


light formed the angle of α = π /4 with director n of HG LC layer. For both experi-ments the threshold voltages (Uth = 1.3 V) are the same; hence F11 = Δεε0Uth

2 andK11 = π–2F11.

2.4.2. Reduced elastic constant

Figures 11 and 12 illustrate the transition from twisted to homeotropic configurationin 3.1TN70 cell filled with W1898, controlled by voltage U and monitored by dielectricand optical transmission (λ = 0.675 μm) measurements in crossed polarizers, respec-tively. In both experiments the threshold voltages (Uth = 1.5 V) are the same resultingin the same value of FTN = Δεε0Uth

2 and KTN = π–2FTN.

2.4.3. Twist elastic constant

Twist deformation of W1898 layer in IPSHG cell (with thickness d = 5.1 μm) wasmonitored by optical measurements. Figure 13 shows the intensity I of the light

0.22

0 5 10 15

W1898

Δε = 8.1

Uth = 4.0 V

U [V]

I [a.

u.]

0.20

0.18

0.16

d = 5.1 μm

20

K22

Δεε0π2

-----------Uth2

I2------d2 7.5 pN= =

0.14

l = 20 μm

Fig. 13. Twist deformation of W1898 in a IPSHG cell of thickness d = 5.1 μm (intensity I of light withλ = 656.3 nm transmitted normally through the cell versus voltage U applied to the interdigital electrodes).

0.008

0 2 4 6 8 10 12 14

W1898

Δε = 8.1

Uth = 5.8 V

U [V]16

I [a.

u.] 0.006

0.004

0.002

d = 6.3 μm

18

K33

Δεε0π2

-----------Uth2

I2------d2 24.1 pN= =

0

l = 20 μm

20

Fig. 14. Bend deformation of W1898 in an IPSHG cell of thickness d = 6.3 μm, determined from light(λ = 0.589 μm) transmitted through the cell placed between crossed polarizers.


transmitted through the cell versus voltage U applied to the interdigital electrodes.The cell was placed between crossed polarizers and the plane of polarization ofincident light formed the angle of α = π /4 with director n of HG layer. Knowingthe thickness d of IPSHG cell and the distance between the stripes of electrodesl = 20 μm, the twist elastic constant can be determined using the formula K22 == Δεεoπ–2 Uth

2 l–2d2.

2.4.4. Bend K33 elastic constant

Bend deformation of W1898 layer was monitored by optical measurements. Figure 14shows the intensity I of light transmitted through an IPSHT cell of thicknessd = 6.3 μm versus voltage U applied to interdigital electrodes. The cell was placedbetween crossed polarizers. Given thickness d of the cell and the distance betweenthe stripes of electrodes l, the bend elastic constant can be estimated as K33 == Δεεoπ–2 Uth

2 l –2d2.

2.5. Switching-on time and rotational viscosity

Rotational viscosity γ was estimated from measurements of the switching-on timeτON ≈ τ0-90 (see Fig. 15) of TN cells with a twist angle of 90° after applyingan alternative voltage driving pulse of square shape. The rotational viscosity iscalculated from Eq. (1) and Eq. (2) derived by TARUMI et al. [13]:

(1)

where d is the cell gap, U is the amplitude of driving voltage applied to the cell andKTN is the reduced elastic constant for the transition from twisted to homeotropic

1.0

0.8

0.6

0.4

0.2

0 1 2 3 4

W1898

d = 3.4 μmτON = 2.55 msU = 2.9 V

I [a.

u.]

t [ms]

τON

Fig. 15. Fréedericksz transition versus time in 3.4TN70 cell filled with W1898 mixture.

γτONε0ΔεU2 π2KTN–

d2--------------------------------------------- 97 m Pas= =

γτON εo ε U 2Δ π 2 KTN–( )

d 2------------------------------------------------------------------=


configuration in TN cell. These results were verified by study of the switching-offtimes τOFF ≈ τ100-10.

(2)

where K11 is the elastic constant for splay deformation.The values of the rotational viscosity γ obtained from the last formula applied for

HG cell filled with W1898 mixture were consistent with the former ones. The maximaldiscrepancy between the results obtained using the two methods was below 10%.

3. Results for other mixturesUsing the procedures described in the previous sections the following results fortemperature dependences of permittivity and dispersion of optical anisotropy wereobtained for other mixtures. As was mentioned above, temperature dependences ofreal parts (parallel and perpendicular to director) of permittivity were measured ata frequency of 1 kHz using HG and HT cells with low resistivity electrodes.The characteristics of dielectric permittivity versus frequency for all the mixtures

γτOFFπ2 K11

d 2--------------------------------=

Fig. 16. To be continued on the next page.

25

20

15

10

5

015 30 45 60 75

ε

T [°C]

20

16

12

8

4

05 35 65 95 125 155

ε

T [°C]

ε

W1820 W1852

TC = 71.1 °CTC = 152.6 °C

ε⊥

ε | |

ε⊥

ε | |

25

20

15

10

5

05 45 85 125 145

ε

T [°C]

24

18

15

9

6

30 20 60 100 120 140

εI

T [°C]

W1825 W1791

TC = 136 °C TC = 127.5 °C

ε⊥

ε | |

ε⊥

ε | |

25 65 105

12

21

40 80

a b

c d


investigated were very similar to those shown in Figs. 2a and 2b for the W1898mixture. Curves for dispersion of optical anisotropy were obtained by combiningthe results from Abbe refractometer, wedge-cell and spectroscopic measurementat 25 °C. The results are shown in Fig. 16.

4. SummaryThe results of measurements characterising dielectric, refractive, elastic and viscousproperties of the HBLCMs studied are gathered in Table 1. Due to the high optical and

25

20

15

10

5

015 75 135 165

ε

T [°C]

W1865

TC = 170.1 °C

ε⊥

ε | |

45 105

e W18200.50

0.45

0.40

0.35

0.30

0.25

0.200.4 0.6 0.8 1.0 1.2 1.4

Δn

λ [μm]

f

W18520.47

0.42

0.37

0.32

0.270.4 0.6 0.8 1.0 1.2 1.4

Δn

λ [μm]

g

1.6

W18250.9

0.8

0.7

0.6

0.5

0.4

0.30.3 0.5 0.7 1.1 1.3 1.5

Δn

λ [μm]

h

0.9

Δn = 0.37 for λ = 1.064 μm

W17910.65

0.55

0.350.4 0.6 0.8 1.0 1.2 1.4

Δn

λ [μm]

i

1.6

0.45

W1865

0.65

0.55

0.350.4 0.6 0.8 1.0 1.2 1.4

Δn

λ [μm]

j

1.6

0.45

0.75

Fig. 16. Temperature dependences of permittivity (a–e) and dispersion of optical anisotropy (f–j) forW1820, W1852, W1825, W1791 and W1865 mixtures, respectively.


dielectric anisotropies and relatively low rotational viscosities of these mixtures, theycan be applied in different kinds of liquid crystal electro-optical devices with lowresponse times, operating in visible and near infrared regions. For example:

– The W1825 LC with Δn = 0.37 at λ = 1.064 μm can be exploited in producingliquid crystal cell (LCC) to be applied in space-borne laser rangefinder for spacemissions. Such LCC may operate in the positive TN mode tuned to first TN maximum(d = 31/2λ/(2Δn) = 2.5 μm), switching the polarization plane of laser beam with workwavelength of 1.064 μm and the energy density not smaller than 0.15 J/cm2 at the pulseduration about 8 ns. Transmission of LCC should be not smaller than 85% (see Fig. 12)at the working aperture not less than 15 mm. The switching on and switching off timesin a 2.5 μm thick LCC driven by voltage of 10 V are not longer than 0.7 ms and 7 ms,respectively, in operating temperature range from 20 °C to 60 °C [14].

– The W1791 LC with Δn > 0.40 up to λ = 1.5 μm can be exploited in electricallytunable liquid crystal filters (ETLCF). Due to relatively high and electrically controlledoptical anisotropies Δn (U ) and thin cell gaps d (1 μm, 3 μm and 5 μm) applied inETLCF with W1791, one can select the required wavelength λ (U ) from visible up tonear infrared spectrum range [15]. The ETLCF can achieve the response time shorterthan 1 ms in temperature range from 20 °C to 60 °C.

– The W1898 LC with Δn = 0.17 at λ = 0.589 μm can be used for producing liquidcrystal light valve (LCLV). Such LCLV may operate in electrically controlled bire-fringence mode, tuned to first maximum (d = λ / (2Δn) = 1.7 μm), in the whole visiblerange. The switching on and switching off times in a 1.5 μm thick LCLV with W1898driven by voltage of 10 V are not longer than 0.4 ms and 4 ms, respectively, inoperating temperature range from 20 °C to 60 °C.

Acknowledgements – This work was supported by the Grant No. NN507 471837 from the Polish Ministryof Science and Higher Education.

References [1] DĄBROWSKI R., DZIADUSZEK J., SZCZUCIŃSKI T., Mesomorphic characteristics ofthe some new

homologous series with the isothiocyanato terminal group, Molecular Crystals and Liquid Crystals124(1), 1985, pp. 241–257.

[2] SPADŁO A., DĄBROWSKI R., FILIPOWICZ M., BOGUN M., GAUZA S., WU S.T., Synthesis, mesomorphicand optical properties of 4'-alkyl-3,5-difluoro-4-isothiocyanatotolaqnes and 4'-alkylphenyl-3,5-difluoro-4-isothiocyanatotolanes, Conference Proceedings, XVI Conference on Liquid Crystals,Stare Jabłonki, 2005, Poland, pp. 53–58.

[3] DĄBROWSKI R., DZIADUSZEK J., ZIÓŁEK A., SZCZUCIŃSKI Ł., STOLARZ Z., SASNOUSKI G., BEZBORODOV V.,LAPANIK W., GAUZA S., WU S.T., Low viscosity, high birefringence liquid crystalline compounds andmixtures, Opto-Electronics Review 15(1), 2007, pp. 47–51.

[4] GAUZA S., WEN C.H., WU B., WU S.T., SPADŁO A., DĄBROWSKI R., High figure-of-merit nematicmixtures based on totally unsaturated isothiocyanate liquid crystals, Liquid Crystals 33(6), 2006,pp. 705–710.

[5] DĄBROWSKI R., DZIADUSZEK J., GARBAT K., FILIPOWICZ M., URBAN S., GAUZA S., SASNOUSKI G.,Synthesis and mesogenic properties of three- and four-ring compounds with a fluoroisothio-cyanatobiphenyl moiety, Liquid Crystals 37(12), 2010, pp. 1529–1537.


[6] RASZEWSKI Z., Measurement permittivityof liquidcrystalline substances, Electron Technology 20,1987, pp. 99–113.

[7] PERKOWSKI P., Dielectric spectroscopy of liquid crystals. Theoretical model of ITO electrodesinfluence on dielectric measurements, Opto-Electronics Review 17(2), 2009, pp. 180–186.

[8] BARAN J.W., RASZEWSKI Z., DABROWSKI R., KĘDZIERSKI J., RUTKOWSKA J., Some physical propertiesof mesogenic 4-(trans-4'-n-alkylcyclohexyl)-isothiocyanatobenzenes, Molecular Crystals and LiquidCrystals 123(1), 1985, pp. 237–245.

[9] KĘDZIERSKI J., KOJDECKI M.A., RASZEWSKI Z., ZIELIŃSKI J., LIPIŃSKA L., Determination of anchoringenergy, diamagnetic susceptibility anisotropy and elasticity of some nematics by means ofsemiempirical metod of self-consistent director field, Proceedings of SPIE 6023, 2005,article 602305.

[10] KĘDZIERSKI J., RASZEWSKI Z., KOJDECKI M.A., KRUSZELNICKI-NOWINOWSKI E., PERKOWSKI P.,PIECEK W., MISZCZYK E., ZIELIŃSKI J., MORAWIAK P., OGRODNIK K., Determination of ordinary andextraordinary refractive indices of nematic liquid crystals by using wedge cells, Opto-ElectronicsReview 18(2), 2010, pp. 214–218.

[11] MISZCZYK E., RASZEWSKI Z., KĘDZIERSKI J., NOWINOWSKI-KRUSZELNICKI E., KOJDECKI M.A.,PERKOWSKI P., PIECEK W., OLIFIERCZUK M., Interference method for determining dispersion ofrefractive indices of liquid crystals, Molecular Crystals and Liquid Crystals 544(1), 2011, pp. 22–36.

[12] KĘDZIERSKI J., RASZEWSKI Z., NOWINOWSKI-KRUSZELNICKI E., KOJDECKI M.A., PIECEK W.,PERKOWSKI P., MISZCZYK E., Composite method for measurement of splay, twist and bend nematicelastic constants by use of single special in-plane-switched cell, Molecular Crystals andLiquid Crystals 544(1), 2011, pp. 56–68.

[13] TARUMI K., FINKENZELLER U., SCHULER B., Dynamic behaviour of twisted nematic liquid crystals,Japanese Journal of Applied Physics Part 1 31(9A), 1992, pp. 2829–2836.

[14] NOWINOWSKI-KRUSZELNICKI E., JAROSZEWICZ L., RASZEWSKI Z., SOMS L., PIECEK W., PERKOWSKI P.,KĘDZIERSKI J., DĄBROWSKI R., OLIFIERCZUK M., MISZCZYK E., Liquid crystal cell for space-bornelaser rangefinder to space mission applications, Opto-Electronics Review, 2011, (in press).

[15] RASZEWSKI Z., KRUSZELNICKI-NOWINOWSKI E., KĘDZIERSKI J., PERKOWSKI P., PIECEK W.,DĄBROWSKI R., MORAWIAK P., OGRODNIK K., Electrically tunable liquid crystal filters, MolecularCrystals and Liquid Crystals 525(1), 2010 pp. 112–127.

Received September 4, 2011in revised form October 24, 2011


Direct determination of the refraction index normal dispersion for thin films of 3, 4, 9, 10-perylene tetracarboxylic dianhydride (PTCDA)

JAN CISOWSKI1*, BOŻENA JARZĄBEK2, JAN JURUSIK2, MARIAN DOMAŃSKI2

1Institute of Physics, Cracow University of Technology, ul. Podchorążych 1, 30-084 Kraków, Poland

2Centre of Polymer and Carbon Materials, Polish Academy of Sciences, ul. M. Curie-Skłodowskiej 34, 41-819 Zabrze, Poland


The improved approach for analysis of the thin film optical spectra exhibiting the interferencefringes is presented. It is shown that, based on the positions of adjacent extrema, the interferenceorder numbers can be easily identified allowing for determination of a model-free normaldispersion of the refraction coefficient provided the film thickness is known from an independentmeasurement. The usefulness of the presented method is illustrated by the analysis of the reflectionspectra obtained for thin films of 3, 4, 9, 10-perylene tetracarboxylic dianhydride (PTCDA) withvarious thicknesses determined with the atomic force microscopy (AFM).

Keywords: optical spectra, interference fringes, refraction coefficient, PTCDA thin films.

1. IntroductionResearch on optical properties belongs to basic tools for characterising thin films ofvarious materials. The theory of the optical transmittance (T ) and reflectance (R ) ofthin films on transparent substrates yields complicated expressions being functions ofthe refraction (n) and extinction (k ) coefficients (which, in turn, depend on the wave-length) as well as on the film thickness d [1], thus requiring elaborated computerprocedures. A much simpler procedure has been devised for the region of weakabsorption (i.e., for the case n2 >> k2) involving the construction of continuousenvelopes around the extrema of the interference fringes [2, 3]. This procedure, knownas the Swanepoel method (see [4, 5] and references therein), was first applied to the trans-mission spectrum and was subsequently extended over the reflection spectrum [6].However, the derived expressions for T and R concern homogeneous smooth films

182 J. CISOWSKI et al.

with uniform thickness; moreover, both quantities have to be measured with an extremeaccuracy. For real thin films, all these requirements can seldom be fulfilled leading tosignificant errors in the calculated values of the optical constants and the film thickness(even up to 100%), as already pointed out by Swanepoel himself [7].

Apart from this, it appears that various types of inhomogeneities may compensateeach other resulting in a quasi-ideal spectrum for a non-ideal thin film. Namely, the geo-metrical inhomogeneities, such as non-uniform film thickness and surface roughness,reduce the magnitude of the interference extrema [4, 8–12], while the optical inhomo-geneity may increase the transmittance even over that of the uncoated substrate incertain spectral regions [13].

Quite recently, the Swanepoel formulae were questioned [14] which gave rise tofurther uncertainties concerning the determination of the optical and geometricalparameters of thin films by the envelope method.

Contrary to transmittance and reflectance, the positions of the interference extremacan be determined with high accuracy and independently of the factors influencingthe magnitudes of both quantities. Therefore, we propose an improved description ofinterference fringes in thin films resulting in a model-free refraction index in the regionof normal dispersion provided that the basic geometrical parameter, i.e., the filmthickness, is determined by an independent method. The usefulness of our approachis illustrated by the analysis of the reflection spectra obtained for thin films ofthe model organic compound, PTCDA, with various thicknesses determined by AFM.

2. Spectral dependence of the refraction index from the interference fringes

At normal incidence and in the region of weak absorption, i.e., where n2 >> k2,the order number m of a given extremum of the interference fringes for a film ofthickness d results from the basic equation

4nd = mλextr (1)

where the convention of treating m’s as integers [2, 6], that may be simply calledthe interference numbers, has been used. For n > ns (the refraction index of the sub-strate), an odd number m (1, 3, 5, …) corresponds to the wavelength λextr for whichthe reflection spectrum has a maximum, while an even m (2, 4, 6, …) corresponds toa minimum; the situation is reversed in the case of the transmission spectrum.

As pointed out in [15], it is better to present the optical spectra as functions ofthe photon energy E = hc/λ (with h the Planck constant and c the light speed in vacuum)instead of λ since, in the region of weak dispersion of the refractive index, the positionsof extrema are almost equidistant and, moreover, at higher photon energies, the inter-ference extrema are much better resolved.

Direct determination of the refraction index normal dispersion... 183

The extremum position Em for a particular interference number m is thereforegiven by

(2)

where nm is the refraction index corresponding to the photon energy Em . Forthe subsequent extremum located at a higher photon energy Em + 1, we have

(3)

Combining Eqs. (2) and (3) results in

(4)

The positions of the interference extrema can be determined quite easily fromexperiment, and for two consecutive ones (i.e., maximum and minimum or minimumand maximum) Em and Em + 1, the quantity mexp can be defined as

(5)

which generally is not an integer. The difference between mexp and m is equal to

(6)

and is positive in the region of normal dispersion of the refractive index consideredhere (i.e., in the region where the refraction index increases with the photon energy:nm + 1 > nm). It is also clear that with decreasing dispersion, δ approaches zero.These features of δ allow us to determine the actual interference number m as beingnot only an integer closest to mexp but also being smaller than mexp since m = mexp – δ.

For thicker samples with many interference fringes, the adjacent extreme positionsare close to each other and the denominator of Eq. (5) may be quite small leading toan uncertainty in determining m; in such a case we can take into account a furtherextremum at energy Em + l and then

(7)

Emhc

4nmd------------------- m=

Em 1+hc

4nm 1+ d-------------------------- m 1+( )=

mEm nm

Em 1+ nm 1+ Em nm–-------------------------------------------------------=

mexpEm

Em 1+ Em–---------------------------------=

δEm Em 1+ nm 1+ nm–( )

Em 1+ Em–( ) Em 1+ nm 1+ Em nm–( )----------------------------------------------------------------------------------------------=

mexpl Em

Em l+ Em–--------------------------------=


For example, the transmission spectrum for a 106.4 μm thick film of polyethyleneterephthalate (PET) in the wavelength range 740–760 nm [16] reveals the presenceof 25 interference extrema (l = 24) between the first minimum with the interferencenumber as high as m = 923±2 at 1.6318 eV and the last minimum with m = 947±2at 1.6742 eV.

Knowing m for a chosen extremum at low photon energy (in the low-dispersionregion), we can easily number the consecutive extrema at higher energies simply asm + 1, m + 2, etc. (see Fig. 3).

Having determined the interference numbers, we can make a plot of Em vs. m (seeEq. (2)) and its deviation from linearity will be a measure of the refractive indexdispersion.

Equation (2) yields the photon energy dependence of the product nmd, demon-strating in fact the relative dispersion of the refractive index, as being multiplied bythe constant thickness d

(8)

Finally, a model-free absolute dispersion of the refractive index can be determinedprovided the film thickness is known from an independent measurement such asprofilometry, scanning electron microscopy (SEM) or AFM as in this work

(9)

Frequently, d is claimed to be calculated from Eq. (8) with a very small uncertainty,even of the order of 1%, using, however, the value of n calculated from formulae forthe ideal thin film which is seldom the case. For example, assuming a uniform thicknessfor an amorphous As-S film, d = 806 nm is found, while applying very complicatedmathematical procedure that takes into account a small average surface roughnessAr ≅ 20 nm, a much higher value is obtained, namely d = 878 nm which favorablycompares with d = 864 nm obtained directly with a profilometer [11].

3. Experiment In order to illustrate the usefulness of our approach, we have chosen the model organicmaterial, i.e., 3, 4, 9, 10-perylene tetracarboxylic dianhydride, abbreviated as PTCDA.Thin films of PTCDA have been deposited onto glass substrates by thermal vacuumevaporation of bulk material (from Aldrich). Five films studied have been examinedwith an Explorer ToMetrix AFM working in the contact mode. The films arepolycrystalline, as checked by X-ray diffraction study, and possess smooth surfacesas evidenced by a small root-mean square (rms) surface roughness presented incolumn 3 of the Table.

nmd hc4

----------- mEm

------------=

nmhc4d

----------- mEm

------------ 309.96d nm( )

--------------------- mEm eV( )

-------------------------= =


As for the film thickness (column 2 in the Table), the films were scratched witha scalpel down to the glass substrate and the thicknesses were calculated by measuringthe vertical distance between the substrate and the film surface with an AFM tip (forvery thin organic films which are usually soft, an AFM tip may be used also forscratching [17]). An example of the AFM profile after scratching is shown in Fig. 1.

The optical spectra of the PTCDA films under investigation have been gatheredwith a JASCO V-570 double-beam spectrophotometer operating in the range from 190to 2500 nm. For reflection measurements, a special two-beam JASCO unit has beenused with an Al mirror in the reference beam as a reflectance standard. The angle ofincident light is approximately 5°, which is very close to the normal incidence.


The optical reflection spectra of the PTCDA films investigated (see the Table) areshown in Fig. 2 demonstrating clear interference fringes, the number of which dependson the film thickness.

T a b l e. Characteristics of the PTCDA thin films investigated.

d and σrms denote the film thickness and rms (root-mean square) roughness, respectively, both determinedby AFM; s is the slope of the dashed straight lines from Fig. 4; and are the zero-energy limitsof the refraction coefficient as determined experimentally (from the slope s and thickness d ) and fromfitting Eq. (12) to the experimental data (Fig. 5), respectively.

Sample d [nm] σrms [nm] s [eV]1 216 ± 15 11 0.857 1.67 1.652 365 ± 10 7 0.511 1.66 1.663 725 ± 40 10 0.250 1.71 1.684 1260 ± 50 29 0.142 1.73 1.705 2050 ± 70 38 0.087 1.74 1.73

n0exp n0

fit

n0exp n0

fit

600

400

200

00 2 4 6 8 10

PTCDAsample 2

Distance [μm]

Z da

ta [n

m]

Fig. 1. AFM profile of PTCDA layer on glass (sample 2) after scratching. Height of the step yieldsthe sample thickness d = 365±10 nm.


40

30

20

10

00.5 1.0 1.5 2.0

PTCDA

1

2 3

4

5

R [%

]

E [eV]

Fig. 2. Reflectance of the PTCDA films with various thicknesses.

Fig. 3. Transmittance (a), reflectance (b) and relative reflectance change (c) for PTCDA sample 5.Integers indicate the interference numbers of extrema and Rb (dashed line) represents the non-oscillatorybackground reflectance fitted with a second order polynomial.

100

0.5 1.0 1.5 2.0

PTCDA, sample 5

R [%

]

E [eV]

90

80

70

6020

15

10

5

0

(R –

Rb)/

Rb

T [%

]

0.5

0.0

–0.5

a

b

c


We have also measured the transmission spectra T and such a spectrum forthe thickest sample 5, treated as an example, is shown in Fig. 3a, in order to compareit with the reflection spectrum R presented once again, in greater detail, in Fig. 3b.A clear onset of absorption results in vanishing of the interference fringes in T above1.5 eV. However, the fringes are still observed in R up to 2 eV.

The effect of absorption on the optical spectra is such that Eq. (1) is not exactlyvalid at the interference extrema, as it is in the transparent region, but at the tangentpoints, i.e., at the points where the envelopes, usually computer-drawn, are tangentialto the actual spectrum [4, 5, 8, 18]. In order to eliminate the shift between the tangent-and extreme points, we propose a subtraction of the non-oscillatory backgroundfrom the total optical spectrum by fitting it with, e.g., a polynomial, as shown in Fig. 3bfor the reflectance. The resulting relative reflectance change, shown in Fig. 3c, allowsthe interference extrema to emerge up to 2.08 eV. Applying Eq. (4), we havedetermined the interference numbers (see Fig. 3), clearly showing that the relativereflectance change enables one to observe much more interference fringes (up tom = 30) than in the case of the transmission spectrum (only to m = 18).

The positions of extrema versus the interference numbers for all the samplesstudied are presented in Fig. 4, indicating a clear deviation from linearity above1.5 eV. On the other hand, the low-energy linear part of this dependence, extrapolatedto E = 0, yields m = 0, evidencing the correct interference numbering and inequalityn > ns .

The slope of the linear part (column 4 in the Table) gives the product n0d (atleast its upper limit for the thinnest sample), with n0 being the zero-energy limit ofthe refraction coefficient. Knowing the film thicknesses d from AFM, we havecalculated the values of n0 (column 5 in the Table).

Finally, the experimentally determined photon energy dependences of the refrac-tive index n(E ) for the samples studied at the extreme points are presented in Fig. 5.

2.5

2.0

1.5

1.0

0.5

0.00 5 10 15 20 25 30

1 2 3 4 5

PTCDA

m

Em

[eV

]

Fig. 4. Energies of the reflectance extrema vs. the interference numbers for the PTCDA films investigated.Dashed lines demonstrate a linear character of this dependence at low energy.


The relative uncertainty Δn /n is, at least, equal to Δd /d = 3%–7% depending onthe sample (see the Table), which means that differences between the n(E)-depen-dences for our PTCDA samples lie within the film thickness uncertainty. Moreover,the films under investigation may be more or less compact, which can also contributeto these differences, as clearly seen for a number of TiO2 thin films [19].

For comparison, we have also inserted in Fig. 5 some ellipsometric results (requir-ing, however, a model to calculate n) obtained for thin films of PTCDA [20–22]. Itshould be mentioned that the refraction coefficient of PTCDA samples may change ina wide range, depending on their structure. The highest values are reported for PTCDAsingle crystals, with the maximal value of n0 = 2.3 [23]. Therefore, the n (E)-depen-dences for PTCDA thin films, which may be polycrystalline and/or less compact thanthe bulk material, are expected to lie below the highest n (E )-dependence of the singlecrystal, as actually observed in Fig. 5, where n = 2.3 is just the upper limit on the scalefor the refraction coefficient.

Applying the commonly used phenomenological Cauchy and Sellmeier relations,we came to the conclusion that they did not fit our model-free experimental data well.Therefore, following [24], we have made use of the physically-based Solomonapproach [25]. Considering a simple two-band model, the variation in the refractiveindex takes the form [25]

(10)

2.01.51.00.5

1 2 34

5

PTCDA

n

E [eV]

2.3

2.2

2.1

2.0

1.9

1.8

1.7

1.6

Fig. 5. Dispersion relation of the refractive index of PTCDA thin films. Various symbols represent ourexperimental data and solid curves – fitting with Eq. (12). For comparison, the ellipsometric results fromRefs. [20], [21] and [22] are also shown as dotted, dash-dotted and dashed curves, respectively.

n2 1– n02 1–⎝ ⎠

⎛ ⎞ 1 E4Δ

-------------EM

2 Δ E–( )2–

EM2 Δ E+( )2–

------------------------------------------ln+=


where Δ is the bandwidth, assumed to be the same for both bands, and EM is the averagegap, i.e., the energy difference between the “centres of gravity” of the bands. Withinthis model, one can introduce the optical gap Eopt and then [25]

(11)

Substituting Eq. (11) into Eq. (10) we get the final n (E )-dependence in the form

(12)

clearly showing that the Solomon model is valid for E < Eopt. In view of this, it is worthnoticing that fitting the exact formula (12) to a 1120 nm thick As–S–Se glassy alloyfilm from [24], the value of Eopt = 2.78 eV is found, while fitting the approximationof Eq. (10) yields Eopt = 2.08 eV making the impression that the n(E )-dependence maybe extended beyond Eopt [24].

Solid lines in Fig. 5 represent the global fit of the Solomon relationship yieldingEM = 4.33±0.15 eV and Eopt = 2.10±0.02 eV, in excellent agreement with the absorp-tion data [26]. The assumption of weak absorption used in this work (n2 >> k2) is verywell fulfilled up to Eopt = 2.10 eV, since for this energy n ≈ 2 and k ≈ 0.1 [20–23].The fitting of Eq. (12) to the experimental data gives also the values of n0 (column 6in the Table) consistent with those found previously from the slopes in Fig. 4 (column 5in the Table).

The interference numbering for thin films of PTCDA (see Fig. 3) is a consequenceof inequality n > ns, as mentioned in Section 4. For the opposite case (n < ns),the interference numbering is reversed, i.e., odd m’s correspond to maxima in T andminima in R, while even m’s – on the contrary. This can be illustrated, for example,by the reflection spectrum for a 525 nm thick thermal SiO2 layer on Si [27]. Inthe wavelength range 400–800 nm, the spectrum reveals the presence of 4 interferenceextrema between the first maximum at 1.653 eV and the last minimum at 2.886 eV forwhich our approach yields the interference numbers m = 4 and m = 7, respectively.This indicates that n < ns as expected, since n = 1.42–1.44 [27], while ns ≥ 3.42 [28].

In a quite recent paper [12], it is stated that the interference numbering requiresthe prior knowledge whether n > ns or n < ns; our approach, including extrapolationto E = 0 (see Fig. 4), clearly demonstrates that it is not necessary.

The possibility of verifying whether n > ns or vice versa may be very useful indescription of various thin film structures, especially new ones. An interesting exampleis provided by the optical data for amorphous GdN thin films of various thicknessesdeposited onto glass with ns = 1.51 [29]. The quantitative analysis of the transmissionspectra based on the Swanepoel method (assuming a priori that n > ns) yieldsthe minimal value (at 1.1 μm) n = 1.62 > ns, in contradiction with the interference

EM Eopt Δ+=

n2 1– n02 1–⎝ ⎠

⎛ ⎞ 1 E4 EM Eopt–( )

--------------------------------------2EM Eopt– E–( ) Eopt E+( )2EM Eopt– E+( ) Eopt E–( )

------------------------------------------------------------------------ln+=


numbers being odd and even m’s for the transmittance maxima and minima,respectively, which means just the opposite, i.e., n < ns.

This example clearly shows that the interference numbering should be treated asa primary feature when analyzing the optical spectra of thin film structures.

5. ConclusionsThis work presents the improved approach for analysis of the thin film optical spectraexhibiting the interference fringes. It has been shown how to determine easilythe correct interference order numbers without the knowledge of the film thickness.The correct interference numbers, in turn, enable one to distinguish whetherthe refraction coefficient of a particular thin film is smaller or greater than the refractioncoefficient of the substrate. It has also been demonstrated how to determine the exactpositions of the interference extrema by subtracting the non-oscillatory background ofan optical spectrum. All these procedures serve as a tool for determination of a model--free normal dispersion of the refraction coefficient n (E ), provided the film thicknessis known from an independent measurement. It has to be stressed that the directlymeasured film thickness allows one to determine reliable values of the optical constantsand to avoid the use of complicated and frequently uncertain mathematical procedures.

The usefulness of our approach has been illustrated by the analysis of the reflectionspectra obtained for thin films of PTCDA with various thicknesses determinedby AFM, and the experimentally obtained n (E)-dependences have been describedwithin the physically-based Solomon model.

The values of n (E ), fixed below the optical gap Eopt, can also serve as an anchoringpoint when analyzing the ellipsometric data which require a model for calculation ofn (E) in the whole photon energy range under investigation, including that beyond Eopt.

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[10] RUIZ-PEREZ J.J., GONZALEZ-LEAL J.M., MINKOV D.A., MARQUEZ E., Method for determining the opticalconstants of thin dielectric films with variable thickness using only their shrunk reflection spectra,Journal of Physics D: Applied Physics 34(16), 2001, pp. 2489–2496.

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Theoretical study of slab waveguide optical sensor with left-handed material as a core layer

SOFYAN A. TAYA1*, TAHER M. EL-AGEZ1, HANI M. KULLAB1, MAZEN M. ABADLA2, MOHAMED M. SHABAT1

1Physics Department, Islamic University of Gaza, Gaza, Palestine

2Physics Department, Alaqsa University, Gaza, Palestine


A three-layer planar waveguide sensor consisting of thin left-handed material core layer isinvestigated for sensing applications. The sensitivity of the proposed sensor to the changes inthe refractive index of the cladding is presented and studied for TE-polarized light. It is observedthat the sensitivity of the proposed sensor is improved compared to that of the conventionalthree-layer slab waveguide sensor. It is also found that the sensitivity of the structure proposed isnegative and critically dependent on the dispersive permittivity and permeability of the core layer.

Keywords: slab waveguides, optical sensors, left-handed material, sensitivity, power.

1. Introduction

Optical waveguide sensors have been used for analytical purposes for a number ofyears [1–6]. The sensing operation of the slab waveguide sensors is performed bythe evanescent tail of the modal field in the cover medium (cladding). The guidedelectromagnetic field of the waveguide mode extends as an evanescent field intothe cladding and the substrate media and senses an effective refractive index ofthe waveguide mode. The effective refractive index of the propagating mode dependson the structure parameters, e.g., the guiding layer thickness and dielectric permittivityand magnetic permeability of the media constituting the waveguide. As a result, anychange in the refractive index of the cladding results in a change in the effectiverefractive index of the guided mode. The basic sensing principle of the planarwaveguide sensor is to measure the changes in the effective refractive index due tochanges in the refractive index of the cladding [1]. Many theoretical and experimentalstudies have been conducted to improve the sensitivity of slab waveguide sensors.

194 S.A. TAYA et al.

TAYA et al. [7–10] proposed optical waveguide sensors in which one or both ofthe surrounding media have an intensity dependent refractive index. It is found thatutilizing nonlinear media can enhance the sensitivity of slab waveguide sensors.Another class of optical waveguide sensors has been proposed with the so-calledreverse symmetry design [11–13]. In these structures the substrate has a refractiveindex being less than that of the cladding medium. This design offers evanescentoptical fields deeply penetrating into the cover sample analyzed. Therefore, the sensi-tivity has shown an improvement in the reverse symmetry configuration.

Slab waveguide sensors have been used for a wide range of applications such ason-line bacteria [14], and living cell monitoring [15], multidepth screening of livingcells [16], detection of protein adsorption [17], lipid bilayers [18], and affinity bind-ing [19].

Metamaterials are artificial media, in which man-made structural units play the roleof atoms. Thus, the complex phenomena in metamaterials result from the character-istics of the individual elements as well as from the way they are arranged in a lattice.In other words, metamaterials gain emerging properties that were not available in theirconstitutive elements alone. This provides enormous flexibility in tailoring the re-sponse of metamaterials to external waves or fields. The history of these materialsbegan with the paper of VESELAGO [20], who predicted a number of remarkableproperties of waves in a material with simultaneously negative dielectric permittivityε and magnetic permeability μ. Such media are usually termed as left-handed materials(LHMs), since the electric and magnetic fields form a left-handed set of vectors withthe wave vector. Recent experimental demonstration of the novel composite materialwith a negative index refraction, opens up a unique possibility of designing novel typesof devices, where electromagnetic waves do not propagate in a conventional way [21].One of the first applications of LHMs was reported by PENDRY [22], who demonstratedthat a slab of a lossless LHM can provide a perfect image of a point source. GRIBC andELEFTHERIADES [23] verified by simulation the enhancement of evanescent waves in atransmission-line network by using a negative refractive index material. In 2003, itwas shown that left-handed materials can enhance the evanescent field in planar slabwaveguides [24]. Recently, left-handed materials have been proposed as a mechanismof building cloaking devices [25]. TAYA et al. proposed an optical slab waveguidesensor using LHM layer [6]. They showed that the sensitivity can be enhanced usingLHMs in the field of optical evanescent sensors.

In this paper, bulk polaritons propagating along a slab waveguide with a lossynegative index material film are investigated. The dispersion relation and the sensi-tivity of the effective refractive index to variations in the refractive index ofthe cladding are derived. The power flowing in each layer of the structures proposedis also investigated. The variation of the sensitivity with the parameters of the pro-posed structure is presented. Goos–Hänchen shift and the penetration depth both inthe cladding and the substrate layers are also presented.

Theoretical study of slab waveguide optical sensor... 195

2. Theory

We consider an asymmetric slab waveguide with an LHM layer occupying the region0 < z < d, which is characterized by an electric permittivity ε2 and magnetic perme-ability μ2 such that

(1)

(2)

where ωp is the plasma frequency, ωo is the resonance frequency, γ is the electronscattering rate, and F is the fractional area of the unit cell occupied by the splitring [26]. The slab is sandwiched between a dielectric cladding occupying the regionz > d with ε3 and μ3 and a dielectric substrate occupying the region z < 0 with ε1and μ1, as shown in Fig. 1.

The time harmonic electromagnetic fields in the region z < 0 are

(3)

(4)

In the region 0 < z < d, the fields are in the form

(5)

ε2 ω( ) 1ω p

2

ω 2 iγω+------------------------------–=

μ2 ω( ) 1 Fω 2

ω 2 ω o2– iγω+

-------------------------------------------–=

z

0d

x

Cover

LHM film

Substrate

ε3, μ3

ε2, μ2

ε1, μ1

Fig. 1. Schematic diagram of a left-handed material slabsandwiched between two semi-infinite dielectric media.

E1 x z,( ) yA e β1zeikx x=

H1 x z,( ) Aωμ0μ1

---------------------- e β1z iβ1 x kxz+( )eikx x=

E2 x z,( ) y Beikz 2, z Ce i– kz 2, z+ eikx x=


(6)

For the region z > d,

(7)

(8)

where , and are the unit vectors in x, y, and z directions, respectively.The constants A, B, C, D and the longitudinal propagation constant (kx) are chosen tosatisfy the boundary conditions. The relation between βj ( j = 1, 2, 3) and the normalvector component kz, j is given by

(9)

where kx = k0N, k0 = 2π/λ , λ is the vacuum wavelength of the guided light, and N isthe effective refractive index. It is worth noting that the sign of βj should be shifted tothe minus sign in the case where Re(εjμj) > Re(N ) [27].

The surface wave mode can be obtained with kz, 2 being replaced by iβ2. The bound-ary conditions require that the tangential components of E and H be continuous atz = 0 and z = d, yielding a set of homogeneous linear equations for the coefficients A,B, C, and D. The determinant of this set must be zero for nontrivial solution to exist.After some manipulations, the following equation, which is the bulk-polaritondispersion relation for TE waves, is obtained [26]

(10)

The sensitivity of the evanescent field sensor is defined as the change of the effec-tive refractive index with respect to the change of the cladding refractive index n3, i.e.,

(11)

Differentiating the dispersion relation with respect to N yields

(12)

H2 x z,( ) Aωμ0μ2

---------------------- Beikz 2, z kz 2, x kxz–( )– Ce ikz 2, z– kz 2, x kxz+( )+ eikx x=

E3 x z,( ) yD e β– 3 z d–( )eikx x=

H3 x z,( ) Dωμ0μ3

----------------------– e β– 3 z d–( ) iβ3 x kx z–( )eikx x=

x y z

βj ikz j,– kx2 εj μj k0

2–⎝ ⎠⎛ ⎞1 2⁄

±= =

kz 2,

μ2--------------⎝ ⎠⎜ ⎟⎛ ⎞

2β3

μ3----------

β1

μ1-----------+

⎝ ⎠⎜ ⎟⎛ ⎞ kz 2,

μ2-------------- kz 2, d( )cot–

β3

μ3----------

β1

μ1----------– 0=

S ∂N∂n3

--------------=

Sn3

N---------

μ3kz 2,2

β3 μ22β3

2 μ32kz 2,

2+( )------------------------------------------------- d

μ2---------

μ1 kz 2,2 β1

2+⎝ ⎠⎛ ⎞

β1 μ22β1

2 μ12kz 2,

2+⎝ ⎠⎛ ⎞

--------------------------------------------------μ3 kz 2,

2 β32+⎝ ⎠

⎛ ⎞

β3 μ22β3

2 μ32kz 2,

2+⎝ ⎠⎛ ⎞

-------------------------------------------------+ +

1–

=


It is worthwhile to find the total time-averaged power transported by the waveguide,

(13)

Therefore, the time-averaged power flowing in the substrate, the film, and the claddinglayers are respectively given by

(14)

(15)and

(16)

It is instructive to study the percentage of time-averaged power contained in eachregion. To quantify the fractional power within the j-th layer, we define the filmconfinement factor Γj as

(17)

The following relation must hold between the confinement factors

(18)

The effective waveguide thickness is an important factor in the dispersion ofthe effective refractive index and in the application of optical sensing. Knowing this,we calculate the effective waveguide thickness from the ray penetrations at the upperand lower boundaries of the guiding layer. The penetration of the guided wave fromthe guiding layer into the surrounding media can be written as

(19)

(20)

Ptotalkx

2ω--------------

Ey z( ) 2

μi z( )------------------------- d z

∞–

∞

∫=

P1kx A 2

4ωμ0 μ3 β1--------------------------------=

P2kx

4ωμ0 μ2-------------------------- B 2

2kz 2,------------------ 1 e 2kz 2, d––⎝ ⎠

⎛ ⎞ C 2

2kz 2,----------------- 1 e2kz 2, d–⎝ ⎠

⎛ ⎞– 2BCd+=

P3kx D 2

4ωμ0 μ3 β3--------------------------------=

ΓjTime Average power transported in the j-th region–

Total time Average power transported by the waveguide–--------------------------------------------------------------------------------------------------------------------------------------------------=

Γjj 1=

3

∑ 1=

λ1μ1 μ2

β1-----------------

kz 2,2 β1

2+

μ22 β1

2 μ12 kz 2,

2+-------------------------------------------=

λ 3μ3 μ2

β3-----------------

kz 2,2 β3

2+

μ22 β3

2 μ32 kz 2,

2+-------------------------------------------=


When a light beam undergoes a total internal reflection at the interface betweentwo different media, the reflected light beam experiences a lateral shift in the planeof incidence from the position predicted by the geometrical optics because eachplane wave component undergoes a different phase change [13]. This shift is knownas Goos–Hänchen (GH) shift. GH-shifts at the film-substrate and the film-claddinginterfaces are given by

(21)

(22)

with being the angle of incidence.

3. Numerical resultsFigure 1 shows the slab waveguide geometry under consideration. In the analysisbelow, we have assumed the wavelength of Nd:YAG laser λ = 1064 nm, the substrateto be SiO2 with n1 = 1.5341 (ε1 = 2.35), the cladding to be water of n3 = 1.33(ε3 = 1.77), and μ1 = μ3 = 1. Figures 2 and 3 show the variation of the real andimaginary parts of the sensitivity of the proposed sensor with the thickness of the LHMlayer and the electron scattering rate γ. As can be seen from the figures, the sensitivityis negative and has a peak at a specific value of the guiding layer thickness d. It thendecays towards lower values for high values of d due to the high field confinement.

GH1λπ

-------- γ( )tan

N 2 n12–

--------------------------=

GH3λπ

-------- γ( )tan

N 2 n32–

--------------------------=

γ sin 1– Nn2

----------⎝ ⎠⎛ ⎞=

100 150 200 250 300–0.40

–0.36

–0.32

–0.28

–0.24

–0.20

γ = 0.010 ωp

γ = 0.011 ωp

γ = 0.012 ωp

d [nm]

Re(

S)

Fig. 2. The real part of the sensitivity of the proposed sensor versus the thickness of the guiding layer fordifferent values of the electron scattering rate for λ = 1064 nm, ε1 = 2.35, ε3 = 1.77, μ1 = μ3 = 1, ωp = 2ω,ωo = 0.4ωp, and F = 0.56.


The absolute values of the real and imaginary parts of the sensitivity increase asγ decreases.

It is very important to compare the sensitivity of the proposed sensor to that ofthe conventional three-layer slab waveguide sensor with positive index guiding layer.Figure 4 shows the absolute value of the real part of the sensitivity of the proposedsensor and that of the conventional three-layer slab waveguide sensor with positiveindex material guiding layer. It is clear from the figure that the sensor proposed hasan improved sensitivity. The improvement may be attributed to the property ofamplification of evanescent waves observed in LHMs [28].

The negative value of the sensitivity of the structure proposed is considered asa new feature that has not been observed in slab waveguide optical sensors. To clarify

100 150 200 250 300

–0.30

–0.24

–0.18

–0.12

–0.06

γ = 0.010 ωp γ = 0.011 ωp γ = 0.012 ωp

d [nm]

Im(S

)

Fig. 3. The imaginary part of the sensitivity of the proposed sensor versus the thickness of the guidinglayer for different values of the electron scattering rate for λ = 1064 nm, ε1 = 2.35, ε3 = 1.77, μ1 = μ3 = 1,ωp = 2ω, ωo = 0.4ωp, and F = 0.56.

150 200 250 300 350 400–0.1

0.0

0.1

0.2

0.3

0.4

abs(Re(S))

S1

d [nm]

Sen

sitiv

ity

Fig. 4. Comparison between the sensitivity of the proposed sensor and that of the conventional sensorfor λ = 1064 nm, ε1 = 2.35, ε3 = 1.77, μ1 = μ3 = 1, ωp = 2ω, ωo = 0.4ωp, γ = 0.012ωp and F = 0.56 (S1 isthe sensitivity of conventional structure).


this point, we plot the real part of the effective refractive index as a function of d fordifferent values of the cladding index. In the case of the proposed sensor, the effectiverefractive index N decreases as the cladding index n3 increases, as shown in Fig. 5.This explains the negative value of the sensitivity which is the differentiation of N withrespect to n3. For the conventional sensor, N increases as n3 increases.

In Figures 6 and 7, the real and imaginary parts of the sensitivity are plotted versusthe thickness of the guiding layer for different values of the fractional area of the unitcell occupied by the split ring. As can be seen from the figures, Re(S ) and Im(S ) exhibit

150 200 250 3001.35

1.50

1.65

1.80 n3= 1.33 n

3= 1.41

Conventional sensor

Proposed sensor

d [nm]

Re(

N)

Fig. 5. The real part of the effective refractive index of the proposed sensor and that of the conventionalsensor versus the thickness of the guiding layer for different values of the index of the cladding forλ = 1064 nm, ε1 = 2.35, μ1 = μ3 = 1, ωp = 2ω, ωo = 0.4ωp, γ = 0.012ωp and F = 0.56.

100 150 200 250 300–0.40

–0.36

–0.32

–0.28

–0.24

–0.20

F = 0.56

F = 0.57

F = 0.58

Fig. 6. The real part of the sensitivity of the proposed sensor versus the thickness of the guiding layer fordifferent values of the fractional area of the unit cell occupied by the split ring for λ = 1064 nm, ε1 = 2.35,ε3 = 1.77, μ1 = μ3 = 1, ωp = 2ω, ωo = 0.4ωp, γ = 0.012ωp.

Fig. 7. The imaginary part of the sensitivity of the proposed sensor versus the thickness of the guidinglayer for different values of the fractional area of the unit cell occupied by the split ring for λ = 1064 nm,ε1 = 2.35, ε3 = 1.77, μ1 = μ3 = 1, ωp = 2ω, ωo = 0.4ωp, γ = 0.012ωp.

d [nm]

Re(

S)

F = 0.56

F = 0.57 F = 0.58

100 150 200 250 300

–0.24

–0.20

–0.16

–0.12

–0.08

–0.04

d [nm]

Im(S

)


different behaviors with varying F. Contrary to Im(S ), the absolute value of Re(S )increases with increasing F for a given value of d.

Figures 8, 9, and 10 show the power transported in the substrate, the guiding film,and the cladding, respectively. Many interesting features can be observed in thesefigures. First, the powers transported in the substrate and the cladding show the samebehavior with γ. Decreasing γ enhances both of the powers. The enhancement ofRe(P3) with decreasing γ explains the improvement of Re(S ) with decreasing γ, asobserved in Fig. 2. The sensitivity of evanescent field sensors is totally dependent onthe power transported in the analyte medium (the material to be detected in the cladding

100 150 200 250 3000.112

0.126

0.140

0.154

γ = 0.010 ωp

γ = 0.011 ωp γ = 0.012 ωp

d [nm]

Re(

P1)

[W/n

m]

100 150 200 250 300–1.2

–1.0

–0.8

–0.6

–0.4

γ = 0.010 ωp γ = 0.011 ω

p γ = 0.012 ωp

d [nm]

Re(

P 2) [

W/n

m]

Fig. 8. The real part of the power flowing within the substrate layer versus the thickness of the guidinglayer for different values of the electron scattering rate for λ = 1064 nm, ε1 = 2.35, ε3 = 1.77, μ1 = μ3 = 1,ωp = 2ω, ωo = 0.4ωp, and F = 0.56.

Fig. 9. The real part of the power flowing through the guiding layer versus the thickness of the core layerfor different values of the electron scattering rate for λ = 1064 nm, ε1 = 2.35, ε3 = 1.77, μ1 = μ3 = 1,ωp = 2ω, ωo = 0.4ωp, and F = 0.56.

100 150 200 250 300

0.125

0.150

0.175

0.200

γ = 0.010 ωp

γ = 0.011 ω

p

γ = 0.012 ωp

d [nm]

Re(

P3)

[W/n

m]

Fig. 10. The real part of the power flowing through the cladding layer versus the thickness of the guidinglayer for different values of the electron scattering rate for λ = 1064 nm, ε1 = 2.35, ε3 = 1.77, μ1 = μ3 = 1,ωp = 2ω, ωo = 0.4ωp, and F = 0.56.


layer). Second, the negative value of the film power is the most important feature thatcan be seen in Fig. 9. This is one of the main differences between LHM andconventional materials. In LHM, the Poynting vector S always forms a left-handed setwith the vectors E and H. Accordingly, S and the propagation vector k are in oppositedirections. Thus, it is clear that LHMs are substances with the so-called negative groupvelocity, which occurs in particular in anisotropic substances or when there is spatialdispersion. In brief, Fig. 9 emphasizes the fact that in LHMs the phase velocity isopposite to the energy flow. Third, the effect of γ on the power transported in the filmis barely detectable in the range considered for γ due to the large value of Re(P2)compared to Re(P1) and Re(P3).

In order to study some additional parameters of the structure proposed, we plotthe penetration depth and the GH shifts as a function of the guiding layer thicknessfor different values of the electron scattering rate γ , as shown in Figs. 11 and 12, respec-

100 150 200 250 300

–10

0

10

20

30

40

50

60

70 γ = 0.010ωp γ = 0.011ωp γ = 0.012ωp

Re(λ1)

Re(λ3)

d [nm]

Pene

tratio

n de

pth

[nm

]

Fig. 11. The penetration depth in the substrate and the cladding layers versus the thickness of the guidinglayer for different values of the electron scattering rate for λ = 1064 nm, ε1 = 2.35, ε3 = 1.77, μ1 = μ3 = 1,ωp = 2ω, ωo = 0.4ωp, and F = 0.56.

100 150 200 250 3000

100

200

300

400

500

600

γ = 0.010 ωp γ = 0.011 ω

p γ = 0.012 ωp

GH1

GH3

d [nm]

Goo

s–H

änch

en s

hift

[nm

]

Fig. 12. The Goos–Hänchen shift in the substrate and the cladding layers versus the thickness ofthe guiding layer for different values of the electron scattering rate for λ = 1064 nm, ε1 = 2.35, ε3 = 1.77,μ1 = μ3 = 1, ωp = 2ω, ωo = 0.4ωp, and F = 0.56.


tively. Both of them can be treated as a probe for detecting changes in the refractiveindex of an aqueous cladding. In the above analysis, we have adopted the effectiverefractive index as a probe for detecting the cladding index changes which is oneof the most commonly used techniques in slab waveguide sensors. Generally, anycladding-index dependent waveguide parameter can be used as the probe foroptical sensing purposes, provided that this parameter is practically measurable. Boththe penetration depth and the GH shift are dependent on the cladding index and aremeasurable. For example, several techniques have been developed for measuringthe GH shift. BRETENAKER et al. investigated experimentally the measurement ofthe GH shift for only one reflection [29]. Their method uses the high sensitivityof the eigenstates of a quasi-isotropic laser to small perturbations to measure GH shiftfor angles of incidence both below and above the critical angle. Another approach wasproposed to measure the GH shift [30] based on the modulation of the polarizationstate of a laser by an electro-optic modulator combined with a precise measurementof the resulting spatial displacement with a position-sensitive detector. The sensitivityof any waveguide parameter to changes in the cladding index is given as the differ-entiation of that parameter with respect to n3.

Finally, we investigate the behavior of the proposed sensor in reverse symmetryconfiguration because of the high sensitivity shown in the literature [11–13] forthe conventional slab waveguide sensors in reverse symmetry. To achieve the reversesymmetry configuration, we assume the substrate to be air with ε1 = 1.00 and the clad-ding to be water of ε3 = 1.77. Figure 13 shows the absolute value of the real part ofthe sensitivity of the proposed sensor and the sensitivity S1 of the conventionalthree-layer slab waveguide sensor both in reverse symmetry configuration. As can beseen from the figure the proposed sensor has an improved sensitivity in a specificrange of the thickness of the guiding layer.

100 150 200 250 3000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

abs(Re(S))

S1

d [nm]

Sen

sitiv

ity

Fig. 13. Comparison between the real part of the sensitivity of the proposed sensor in a reverse-symmetryconfiguration and that of the conventional sensor S1 for λ = 1064 nm, ε1 = 1.00, ε3 = 1.77, μ1 = μ3 = 1,ωp = 2ω, ωo = 0.4ωp, γ = 0, and F = 0.7.


4. Conclusions

In this paper, we have proposed a three-layer slab waveguide optical sensor consistingof a left-handed material core layer. The sensitivity of the proposed sensor to the changesin the refractive index of the cladding is found to be enhanced using the negative indexmaterial guiding layer. Moreover, the sensitivity showed a critical dependence onthe parameters of the LHM, which means that it can be maximized through properchoice of these parameters. LHMs of simultaneously negative and dispersive ε and μare currently receiving high interest due to many potential applications. We believethat optical waveguide sensing is one of such applications.

References

[1] TIEFENTHALER K., LUKOSZ W., Sensitivity of grating couplers as integrated-optical chemical sensors,Journal of the Optical Society of America B 6(2), 1989, pp. 209–220.

[2] PARRIAUX O., DIERAUER P., Normalized expressions for the optical sensitivity of evanescent wavesensors, Optics Letters 19(7), 1994, pp. 508–510.

[3] HORVATH R., SKIVESEN N., PEDERSEN H.C., Measurement of guided light-mode intensity:An alternative waveguide sensing principle, Applied Physics Letters 84(20), 2004, pp. 4044–4046.

[4] TAYA S.A., EL-AGEZ T.M., Comparing optical sensing using slab waveguides and total internalreflection ellipsometry, Turkish Journal of Physics 35(1), 2011 pp. 31–36.

[5] EL-AGEZ T., TAYA S., Theoretical spectroscopic scan of the sensitivity of asymmetric slab waveguidesensors, Optica Applicata 41(1), 2011, pp. 89–95.

[6] TAYA S.A., SHABAT M.M., KHALIL H.M., Enhancement of sensitivity in optical waveguide sensorsusing left-handed materials, Optik – International Journal for Light and Electron Optics 120(10),2009, pp. 504–508.

[7] TAYA S.A., SHABAT M.M., KHALIL H.M., Nonlinear planar asymmetrical optical waveguides forsensing applications, Optik – International Journal for Light and Electron Optics 121(9), 2010,pp. 860–865.

[8] TAYA S.A., SHABAT M.M., KHALIL H.M., JÄGER D.S., Theoretical analysis of TM nonlinearasymmetrical waveguide optical sensors, Sensors and Actuators A 147(1), 2008, pp. 137–141.

[9] SHABAT M.M., KHALIL H.M., TAYA S.A., ABADLA M.M., Analysis of the sensitivity of self-focusednonlinear optical evanescent waveguide sensors, International Journal of Optomechatronics 1(3),2007, pp. 284–296.

[10] KHALIL H.M., SHABAT M.M., TAYA S.A., ABADLA M.M., Nonlinear optical waveguide structurefor sensor application: TM case, International Journal of Modern Physics B 21(30), 2007,pp. 5075–5089.

[11] HORVATH R., LINDVOLD L., LARSEN N., Reverse-symmetry waveguides: Theory and fabrication,Applied Physics B 74(4–5), 2002, pp. 383–393.

[12] HORVATH R., PEDERSEN H.C., LARSEN N.B., Demonstration of reverse symmetry waveguide sensingin aqueous solutions, Applied Physics Letters 81(12), 2002, pp. 2166–2168.

[13] TAYA S.A., EL-AGEZ T.M., Reverse symmetry optical waveguide sensor using plasma substrate,Journal of Optics 13(7), 2011, article 075701.

[14] DUDAK F.C., BOYACI I.H., Rapid and label-free bacteria detection by surface plasmon resonance(SPR) biosensors, Biotechnology Journal 4(7), 2009 pp. 1003–1011.

[15] YE FANG, FERRIE A.M., FONTAINE N.H., MAURO J., BALAKRISHNAN J., Resonant waveguide gratingbiosensor for living cell sensing, Biophysical Journal 91(5), 2006 pp. 1925–1940.


[16] HORVATH R., COTTIER K., PEDERSEN H.C., RAMSDEN J.J., Multidepth screening of living cells usingoptical waveguides, Biosensors and Bioelectronics 24(4), 2008 pp. 799–804.

[17] VÖRÖS J., The density and refractive index of adsorbing protein layers, Biophysical Journal 87(1),2004 pp. 553–561.

[18] RAMSDEN J.J., Partial molar volume of solutes in bilayer lipid membranes, Journal of PhysicalChemistry 97(17), 1993, pp. 4479–4483.

[19] DÜBENDORFER J., KUNZ R.E., Compact integrated optical immunosensor using replicated chirpedgrating coupler sensor chips, Applied Optics 37(10), 1998 pp. 1890–1894.

[20] VESELAGO V.G., The electrodynamics of substances with simultaneously negative values of ε and μ,Soviet Physics Uspekhi 10(4), 1968, pp. 509–514.

[21] ZI HUA WANG, ZHONG YIN XIAO, SU PING LI, Guided modes in slab waveguides with a left handedmaterial cover or substrate, Optics Communications 281(4), 2008, pp. 607–613.

[22] PENDRY J.B., Negative refraction makes a perfect lens, Physical Review Letters 85(18), 2000,pp. 3966–3969.

[23] GRIBC A., ELEFTHERIADES G.V., Growing evanescent waves in negative-refractive indextransmission-line media, Applied Physics Letters 82(12), 2003, pp. 1815–1817.

[24] DE-KUI QING, GANG CHEN, Enhancement of evanescent waves in waveguides using metamaterialsof negative permittivity and permeability, Applied Physics Letters 84(5), 2004, pp. 669–671.

[25] ALU A., ENGHETA N., Achieving transparency with plasmonic and metamaterial coatings, PhysicalReview E 72(1), 2005, article 016623.

[26] KEUNHAN PARK, BONG JAE LEE, CEJI FU, ZHUOMIN M. ZHANG, Study of the surface and bulk polaritonswith a negative index metamaterial, Journal of the Optical Society of America B 22(5), 2005,pp. 1016–1023.

[27] SKIVESEN N., HORVATH R., PEDERSEN H.C., Optimization of metal-clad waveguide sensors, Sensorsand Actuators B 106(2), 2005, pp. 668–676.

[28] CHANGCHUN YAN, QIONG WANG, YIPING CUI, Generating mechanism of the energy-stream loops forthe evanescent waves in a left-handed material slab, Optik – International Journal for Light andElectron Optics 121(1), 2010, pp. 63–67.

[29] BRETENAKER F., LE FLOCH A., DUTRIAUX L., Direct measurement of the optical Goos–Hänchen effectin lasers, Physical Review Letters 68(7), 1992, pp. 931–933.

[30] GILLES H., GIRARD S., HAMEL J., A simple measurement technique of the Goos–Hänchen effect withpolarization modulation and position sensitive detector, Optics Letters 27(16), 2002, pp. 1421–1423.

Received May 24, 2011in revised form September 5, 2011


Photoinduced anisotropy and polarization holography on UV exposure in films of N-benzylideneaniline in PMMA matrix

DETELINA ILIEVA1, LIAN NEDELCHEV2*

1Varna Medical University, 55 Marin Drinov St., 9002 Varna, Bulgaria

2Institute of Optical Materials and Technology, Bulgarian Academy of Sciences, Acad. G. Bonchev St., bl. 109., P.O. Box 95, 1113 Sofia, Bulgaria


In this paper, we present a study of the photoinduced processes in films of N-benzylideneanilineincorporated in a polymethylmethacrylate (PMMA) matrix both by spectrophotometric and holo-graphic methods. Photodichroism of the order of ΔD = 0.15 is induced in the films by polarizedUV light at room temperature. We are also able to record stable holographic gratings in thesematerials for the first time to the best of our knowledge.

Keywords: photoinduced anisotropy, polarization holography, UV recording, polarization diffractiongrating, N-benzylideneanilines.

1. IntroductionPolarization holography has been a field of intensive research during the last threedecades since TODOROV et al. [1] established in 1984 the possibility to record high--efficient polarization diffraction gratings in azobenzene materials. In contrast toconventional holography, where the intensity and phase of an object beam are recordedusing a second beam as a reference, in polarization holography also the polarizationstate is recorded on a suitable medium [2].

Numerous materials have been studied by researchers all over the world orientedtowards different applications – understanding the mechanism of the recording [3, 4],formation of surface relief structures [5–11] and chiral structures [12–16], recordingpolarization holographic gratings and optical elements with specific polarizationproperties [17–21] and last but not least – for reversible optical storage of information[4, 22–26].

In most of these studies though the wavelength of the recording laser is fromthe visible part of the spectrum, usually at 488 nm or 514 nm. This is related with

208 D. ILIEVA, L. NEDELCHEV

the sensitivity of the materials used, mainly azo-dyes or azopolymers. On the otherhand, it is well known that reducing the wavelength allows the density and capacityof optical storage media to be increased. Therefore, we focus our attention in this paperon investigating materials with absorbance in the UV, which at the same time havestructure similar to the azobenzene compounds, namely the N-benzylideneanilines.

N-benzylideneanilines (NBA) are imines-type compounds. They have two aromaticrings linked by a –C=N– bridge. Just like the azobenzenes and stilbenes they havetwo isomeric forms: trans-NBA and cis-NBA. They absorb in the UV region ofthe spectrum with the absorption extending into the visible region. The photoinducedprocesses and, in particular, the trans–cis photoisomerization play an important rolein the investigations on N-benzylideneaniline structure [27–33]. It has been estab-lished that on exposure to UV light NBA undergoes cis–trans isomerization aboutthe carbon–nitrogen bond with the trans isomer being stable in the dark, yieldingthe cis isomer on exposure to light. The kinetic properties of this process have beenstudied and the lifetime of the cis isomer was estimated to be of the order of 1 sec atroom temperature [27, 28]. Hence NBA is representative of a group of compoundswhich can apparently undergo trans–cis–trans isomerization and as a result, reorientperpendicularly to the polarization of the exciting light. Therefore, these materials arepossible candidates for polarization holographic storage.

The main objective of this paper is to study the photoinduced processes, inparticular, the photoinduced anisotropy in N-benzylideneaniline incorporated ina polymethylmethacrylate (PMMA) matrix. We are looking for optical storagematerials sensitive to UV light and transparent in the visible range. It is expected thatanisotropy can be induced in these materials due to the difference in the opticalproperties of the trans isomer in different directions. As a result, we demonstratethe possibility to record a stable holographic grating in NBA by UV laser at 257 nm.

2. Materials and methodsThe material used in our study is N-benzylideneaniline incorporated in a poly-methylmethacrylate matrix (NBA/PMMA). The chemical structure of the NBA isgiven in Fig. 1.

The N-benzylideneaniline may isomerize by –C=N– bond torsion (Θ ) and bya mechanism that involves the inversion of the CNC bond angle (φ ) at one ofthe nitrogen atoms via a semi-linear transition state [30, 33]. In our experiments,

C

N

φ

Θ

γ

β

C

N

φ

Θ

γ

βFig. 1. Chemical structure of the N-benzylideneaniline (NBA).

Photoinduced anisotropy and polarization holography... 209

the N-benzylideneaniline was added to a solution of polymethylmethacrylate (5%)in chloroform. The NBA concentration with respect to the PMMA is 1:1 wt%.The samples were dried for one week at room temperatures for elimination of residualsolvent. Films with thickness about 0.5 μm were obtained by solution casting ontoclean quartz substrates for the spectrophotometric investigation and onto glass platesfor the holographic experiments.

Linearly polarized light from a high pressure mercury lamp (HBO 200 withλmax ≈ 365 nm) was used to induce isomerization in the NBA/PMMA films. The lightintensity at the surface of the samples was 0.05 mW/cm2. The illumination wasdone directly with the lamp. The polarization of the beam was at 45° with respectto the horizontal. The spectral measurements were carried out with a Cary 5E(UV Vis NIR) spectrophotometer. For the holographic experiments a frequency dou-bled Ar+ laser was used with wavelength λ = 257 nm. The optical set-up in this caseis shown in Fig. 2. Using a half-wave plate (HWP) followed by a polarization beamsplitter allows us to control and equalize the intensity of the two beams. Introducingthe quarter-wave plates (QWP) in the optical scheme varies the polarizations ofthe recording beams from linear to circular.

3. Experimental resultsIn Figure 3, we compare the absorption spectra of films of N-benzylideneanilineincorporated in a polymethylmethacrylate matrix (NBA/PMMA) before and aftera 2-hour exposure directly with mercury lamp with light intensity 0.05 mW/cm2. Bothnon-irradiated and irradiated films are measured through polarizer oriented parallellyand perpendicularly to the exciting light polarization direction. For the non-irradiatedfilms the two measurements coincide and are equal to D0 – the optical density beforeillumination. The absorption maximum is about 255 nm. The corresponding opticaldensities after the exposure differ and are denoted as Dpar and Dort.

UV laser (257 nm)

HWP PBS

M

M

Sample

D

POL

Probe laser(635 nm)

QWP

QWP

QWP

Fig. 2. Optical set-up for the holographic experiments. PBS – polarization beam splitter, HWP – λ /2 plate,QWP – λ /4 plates, M – mirrors, POL – linear polarizer, D – photodetector.


Most significant changes are seen in the maximum of the absorption spectrum inNBA/PMMA films, mainly of the trans-band. The maximal photoinduced dichroismof the sample was ΔD = Dort – Dpar = 0.15, which coincides with the absorbancemaximum of the trans-molecules (about 255 nm). The relative dichroism is alsoshown in Fig. 3b and as seen, it does not vary significantly over the entire absorbanceband. The effect is also stable in time – we did not observe considerable changes inthe photoinduced dichroism ΔD in a NBA/PMMA films during one month followingthe exposure.

Along with the dichroism, birefringence is induced in the samples on illuminationwith polarized light from the mercury lamp. Using a He-Ne laser we measuredthe photoinduced birefringence (Δn) at λ = 633 nm, outside the absorption band.For the NBA/PMMA films we obtained Δn = 3×10–4. This value is small becausethe illumination was done with relatively low light intensity.

Further we investigated the possibility for holographic storage in the NBA/PMMAfilms using a frequency doubled Ar+ laser at 257 nm. As shown in Fig. 2, the laserbeam was split in two beams with orthogonal linear polarizations by a polarizationbeam splitter. In some of the experiments each of the beams passed through QWP andtheir polarizations were converted to circular. The half-angle between the recordingbeams was 8° (corresponding to a grating with 540 lines/mm).

Depending on the recording polarizations, two types of experiments wereconducted: i) with two waves with the same polarization (leading to modulation onlyof the intensity of the interference light field) and ii ) with two beams with orthogonalpolarizations (leading to modulation of the polarization only, but not the intensity ofthe interference light field). The total light intensity in all these cases was approx-imately 160 mW/cm2. The recorded holographic gratings were probed by a red laserbeam. In Figure 4, the time evolution of the diffraction efficiency in the +1 order ofthese two gratings is shown. As seen from the figure, the maximum efficiency of

250 300 350 400 4500.0

0.5

1.0

1.5

2.0Dort

D0Dpar

Wavelength [nm]

Opt

ical

den

sity

Rel

ativ

e di

chro

ism

ΔD

/D0

0.15

0.10

0.05

0.00225 275250 300 325 350

Wavelength [nm]

a b

Fig. 3. Photoinduced changes in the absorption of the NBA/PMMA film. D0 – the optical densitybefore the illumination, Dort and Dpar – the polarized spectra after 2 h exposure with mercury lamp,I = 0.05 mW/cm2 (a); relative change of the optical density: (Dort – Dpar) /D0 = ΔD /D0 (b).


the polarization grating (about 1.1%) is more than two times higher than the efficiencyof the intensity grating (0.47%). They are stable for a long time after the exciting lightis switched off.

4. Discussion

In this paper, we present the results from the spectral investigation of the photoinducedanisotropy in films of N-benzylideneaniline incorporated in a polymethylmethacrylatematrix. Following the exposure to polarized UV light, significant dichroism wasinduced in the absorbance maximum (the main trans-band) and though being smalleris also noticeable in the region of the cis-band (about 235 nm and 315 nm). MAEDAand FISCHER [31] also investigated UV irradiation of solution of the trans-isomers atreduced temperature. This resulted in extensive (80%–90%) conversion of the trans--isomers into cis-isomers. The process was found to be reversible both thermally andphotochemically. In this case, the cis-isomers were stable only at low temperatures(less than –80 °C).

As seen in Fig. 3, the observed changes in the absorption in our experiments areanisotropic if the illumination is done with polarized UV light at wavelengths absorbedby both trans- and cis-isomers. It is well known that the cis molecules are not stableat room temperature and the cis–trans isomerization is very rapid [31–33]. Hence, itmight not be necessary to use an optical-pumping scheme to reorient the moleculesback to trans state and one can use the strong π–π* transition at 310 nm forthe absorption and reorientation [33]. After the exposure the absolute value ofthe optical density for light polarized orthogonally to the exciting light polariza-tion (Dort) increases mainly in the trans-band region (Fig. 3a). Therefore, we believethat the trans-isomers are reoriented into directions perpendicular to the exciting lightpolarization, similarly to the photoprocesses in azobenzene and stilbene molecules.

0 1000 2000 3000 40000.0

0.1

0.2

0.3

0.4

0.5

UV laser off

Time [s]

Diff

ract

ion

effic

ienc

y [%

]

a

0 2000 4000 6000 80000.0

0.4

0.8

1.2

UV laser off

Time [s]

Diff

ract

ion

effic

ienc

y [%

]

b

Fig. 4. Time evolution of the diffraction efficiency of the holographic grating recorded in NBA/PMMAfilms by a frequency doubled Ar+ laser, λ = 257 nm, I = 160 mW/cm2 with two beams with: the samecircular polarizations (a) and orthogonal linear (s-p) polarizations (b).


The absorption spectra after the illumination remain stable in darkness or on exposureto normal daylight. There are not detectable changes in them during the followingmonth.

We have also recorded for the first time stable holographic gratings in NBA/PMMAfilms. In order to compare conventional holographic recording (where only the intensityof the light field is modulated) to pure polarization recording (where only the polariza-tion is modulated), we used different combinations of polarizations of the recordingbeams. Initially, we recorded a set of conventional holographic gratings – with parallellinear polarizations (s-s and p-p) and with circular polarizations with the samehandedness. They showed similar behavior and close maximal values of the diffractionefficiency, the one recorded with same circular polarizations showing the highestefficiency. Afterwards we recorded a sequence of pure polarization gratings, againwith similar dynamics and highest value of the diffraction efficiency for the case oforthogonal linear (s-p) polarizations. In this case we have also measured the polari-zation of the first order diffraction beam and established that it has polarizationorthogonal to the zero order beam.

The conclusion is that the diffraction efficiency of the gratings recorded bymodulation of the polarization of the interference pattern (Fig. 4b) is higher thanthe efficiency of the ones recorded by modulation of only the intensity of the field(Fig. 4a) and therefore these materials are more sensitive to polarization recordingthan to conventional holographic recording. Most probably the diffraction at 633 nmcan be further increased by modifying the chemical structure of the photosensitivecompound or alternatively increasing the intensity of the recording beams.

The shape of the curves in Fig. 4 can be attributed to the presence of “fast” and“slow” processes as observed in azopolymers [34], where the growth of birefringenceis described by biexponential functions. The “slow” process may also have certainexposure threshold and is activated after the “fast” one has achieved saturation.

We believe that the NBA/PMMA films could be used for fabrication of opticalelements in the visible range.

5. Conclusions

In summary, we have obtained considerable photoinduced dichroism in the absorptionspectra of PMMA films containing N-benzylideneaniline on illumination with polar-ized UV light. We believe that the exposure leads to reorientation of the trans-isomersinto direction perpendicular to the exciting light polarization in a way similar tothe azobenzene and stilbene compounds. We have also recorded stable holographicgratings in these films and showed that the diffraction efficiency of the polarizationgratings is higher than of the intensity ones.

Acknowledgments – The authors are grateful to Dr. P.S. Ramanujam for the fruitful collaboration as wellas to Dr. L. Nikolova and Dr. Ts. Petrova for useful discussions. Dr. Ilieva would also like to express her


acknowledgements to the Short Term Scientific Mission (STSM)–COST committee for the opportunityto visit Risoe National Laboratory, Roskilde, Denmark.

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[17] NIKOLOVA L., TODOROV T., IVANOV M., ANDRUZZI F., HVILSTED S., RAMANUJAM P.S., Polarizationholographic gratings in side-chain azobenzene polyesters with linear and circular photoanisotropy,Applied Optics 35(20), 1996, pp. 3835–3840.


[18] NEDELCHEV L., TODOROV T., NIKOLOVA L., PETROVA TZ., TOMOVA N., DRAGOSTINOVA V., Charac-teristics of high-efficient polarization holographic gratings, Proceedings of SPIE 4397, 2001,pp. 338–342.

[19] MARTINEZ-PONCE G., PETROVA T., TOMOVA N., DRAGOSTINOVA V., TODOROV T., NIKOLOVA L.,Bifocal-polarization holographic lens, Optics Letters 29(9), 2004, pp. 1001–1003.

[20] RAMANUJAM P.S., DAM-HANSEN C., BERG R.H., HVILSTED S., NIKOLOVA L., Polarisation-sensitiveoptical elements in azobenzene polyesters and peptides, Optics and Lasers in Engineering 44(9),2006, pp. 912–925.

[21] KAWATSUKI N., KONDO M., OKADA M., MATSUI S., ONO H., EMOTO A., Surface relief formation inphoto-cross-linkable polymer/benzophenone composite films using 325 nm laser, Japanese Journalof Applied Physics 49, 2010, article 080207.

[22] HVILSTED S., ANDRUZZI F., KULINNA C., SIESLER H.W., RAMANUJAM P.S., Novel side-chain liquidcrystalline polyester architecture for reversible optical storage, Macromolecules 28(7), 1995,pp. 2172–2183.

[23] RASMUSSEN P.H., RAMANUJAM P.S., HVILSTED S., BERG R.H., A remarkably efficient azobenzenepeptide for holographic information storage, Journal of the American Chemical Society 121(20),1999, pp. 4738–4743.

[24] RAMANUJAM P.S., HVILSTED S., UJHELYI F., KOPPA P., LÖRINCZ E., ERDEI G., SZARVAS G., Physicsand technology of optical storage in polymer thin films, Synthetic Metals 124(1), 2001, pp. 145–150.

[25] NEDELCHEV L., MATHARU A.S., HVILSTED S., RAMANUJAM P.S., Photoinduced anisotropy ina family of amorphous azobenzene polyesters for optical storage, Applied Optics 42(29), 2003,pp. 5918–5927.

[26] AUDORFF H., KREGER K., WALKER R., HAARER D., KADOR L., SCHMIDT H.-W., Holographic gratingsand data storage in azobenzene-containing block copolymers and molecular glasses, Advances inPolymer Science 228, 2010, pp. 59–121.

[27] ANDERSON D.G., WETTERMARK G., Photoinduced isomerizations in anils, Journal of the AmericanChemical Society 87(7), 1965, pp. 1433–1438.

[28] WETTERMARK G., WEINSTEIN J., SOUSA J., DOGLIOTTI L., Kinetics of cis–trans isomerization ofpara-substituted N-benzylideneanilines, Journal of Physical Chemistry 69(5), 1965, pp. 1584–1587.

[29] HASELBACH E., HEILBRONNER E., Elektronenstruktur und physikalisch-chemische Eigenschaften vonAzo-Verbindungen. Teil XIV: Die Konformation des Benzalanilins, Helvetica Chimica Acta 51(1),1968, pp. 16–34.

[30] WARREN C.H., WETTERMARK G., WEISS K., Cis–trans isomerization about the carbon–nitrogendouble bond. Structures of the isomers of N-benzylideneaniline, Journal of the American ChemicalSociety 93(19), 1971, pp. 4658–4663.

[31] MAEDA K., FISCHER E., Photoformation of (Z)-isomers in diarylazomethines. Part IV. Direct andsensitized photoisomerization of pyridyl analogues of benzylidene-aniline and absorption spectraof their (Z)-isomers, Helvetica Chimica Acta 66(7), 1983, pp. 1961–1965.

[32] KING N.R., WHALE E.A., DAVIS F.J., GILBERT A., MITCHELL G.R., Effect of media polarity onthe photoisomerization of substututed stilbene, azobenzene and imine chromophores, Journal ofMaterials Chemistry 7(4), 1997, pp. 625–630.

[33] GAENKO A.V., DEVARAJAN A., GAGLIARDI L., LINDH R., ORLANDI G., Ab initio DFT study of Z–Eisomerization pathways of N-benzylideneaniline, Theoretica Chimica Acta 118(1), 2007,pp. 271–279.

[34] HO M.S., NATANSOHN A., ROCHON P., Azo polymers for reversible optical storage. 7. The effect ofthe size of the photochromic groups, Macromolecules 28(18), 1995, pp. 6124–6127.

Received October 6, 2011in revised form November 17, 2011


Wavelet transform method of phase-step determination

YEU-JENT HU1, JIN-YI SHEU1, JIUNN-CHYI LEE1, YA-FEN WU2*

1Department of Electrical Engineering, Taipei Chengshih University of Science and Technology, Taipei, 112 Taiwan

2Department of Electronic Engineering, Ming Chi University of Technology, New Taipei City, 243 Taiwan


The phase-shifting technique is the most popular phase-retrieving technique applied in opticaltesting. Most of the phase retrieval algorithms rely on stability and accuracy of phase steps.A sufficiently exact phase-step calibration is necessary for phase measurements with highaccuracy. We introduce a new method for phase-step calibration between interferograms.The method is based on a recently introduced continuous wavelet transform demodulationtechnique. For the method proposed here only two phase-stepped images are required. Simulationresults indicate that the phase shift error of the proposed method is less than 0.05%.

Keywords: continuous wavelet transform, interferometry, phase measurement, fringe pattern.

1. IntroductionThe phase-shifting interferometry (PSI) is the most popular phase-retrieving techniqueapplied in optical testing. In PSI, most of the phase retrieval algorithms rely onthe stability and accuracy of the phase steps. Phase-shifter miscalibration is a majorsource of systematic error that limits the phase measurement accuracy. Therefore,a sufficiently exact phase-step calibration is a necessary and important task in phasemeasurements with high accuracy. Many calibration techniques [1–5] have beendeveloped to measure an unknown phase step. In the techniques using the Carréalgorithm [6] four phase-stepped images are required. This algorithm was constructednot only to obtain the phase step but also to obtain information on all four unknownquantities, i.e., the background intensity, the modulation, the phase step, and, mostimportant, the phase to be measured. The assumption in the Carré approach is thatthe phase step δ, the background intensity Ib, and the modulation depth M are constantfor all recordings.

In recent years, the wavelet transform (WT) was found to be applicable to differenttasks, such as pattern recognition, image compression and sound analysis [7, 8].

216 YEU-JENT HU et al.

Continuous wavelet transform (CWT) was also used for phase extraction on differenttypes of fringe patterns with spatial carrier [9, 10]. The WT is an important lineartime-frequency (space-frequency) representation, which can represent a signal by itslocalization both in the time space and frequency planes [11–13].

In this study, continuous wavelet transform is applied to extract the phase-stepfrom two fringe patterns. The phase-step calibration can be obtained by extractingthe ridge of the wavelet coefficients. The principle of the method proposed is demon-strated by simulation of phase demodulation of fringe pattern using CWT technique.In Section 2, we introduce a continuous wavelet transform and discuss the space-fre-quency localization properties of wavelets. A new CWT demodulation technique isdescribed in this section, where the phase-step between two images can be obtainedfrom the wavelet ridge. In Section 3, the CWT method is applied to phase-stepcalibration, where results of the simulations are presented. The conclusions arediscussed in Section 4.

2. Phase-step calibration by wavelet transformThe wavelet transform has become an effective tool in many research areas, forexample, being a useful mathematical tool, it can be employed in this application.The CWT of a signal f (x) is defined as its inner product with a family of waveletfunctions ψa, b(x ) [14, 15]

(1)

(2)

where ψ (x) is the mother wavelet, ψa, b(x) is a set of basis functions, called daughterwavelet and obtained from the mother wavelet, a is the scaling parameter related tothe frequency, b is the translation parameter, and asterisk denotes a complex conjugate.The factor 1/ in Eq. (2) is used to keep the energy of ψa, b(x) constant duringdilation and translation. In this study, the wavelet ridge is applied to determinethe phase step between two fringe patterns. To illustrate the properties of the ridge,the Morlet wavelet is chosen as mother wavelet because it gives a better resolution inspatial and frequency domains. The Morlet wavelet can be written as [13]

(3)

where μ is the mother frequency, g (x) is a symmetric window function this is,generally, a Gaussian function as it provides the smallest Heisenberg box. Supposethat the intensity distribution of the two images I0(x, y) and I (x, y) can be expressed as

Wf a b,( ) f x( )ψa b,* x( )dx∞–

∞

∫=

ψa b, x( ) 1a

----------ψ x b–a

-----------------⎝ ⎠⎛ ⎞ ,= b R,∈ a 0>

a

ψ x( ) g x( ) iη x( )exp=

Wavelet transform method of phase-step determination 217

(4)

(5)

where A and A0 are the background intensities, B and B0 are the modulation intensities,ψ (x, y) is the phase of the image I0(x, y), and δ is the phase step.

For clarity, let I0(x) and I(x) represent a row of the fringe patterns I0(x, y) andI(x, y), respectively. The wavelet transforms of I0(x) and I(x) on the ridge are thengiven by [14]

(6)

(7)

From Eqs. (6) and (7), the phase step is calculated by

(8)

where denotes the imaginary part of the wavelet transform of I (x),am denotes the value of a at instant b on the ridge.

3. Computer simulationFor the method proposed here only two phase-stepped images are required. To testthe method described above, we created two fringe patterns that can be written as

(9)

(10)

where ψ (x, y) = 0.55(x2 + y2)2 + 1.5y (x2 + y2) + 0.5(x2 + 3y2) + 1.2(x2 + y2 ) + 8x.The global phase shift between the two interferograms is 1.0472 rad, n (x, y) is

random noise, the noise mean and variance are preset at 0 and 0.14, the data areuniformly sampled 129×129 points in the unit square, which are shown in Fig. 1.Figures 2a and 2b represent the one-dimensional signals of the row 50 of Figs. 1aand 1b, respectively.

I0 x y,( ) A0 B0 ψ x y,( )cos+=

I x y,( ) A B ψ x y,( ) δ+cos+=

WI am b,( )am

2-------------B i ψ b( ) δ+

⎩ ⎭⎨ ⎬⎧ ⎫ g 0( )exp=

WI 0a0m b,( )

a0m

2---------------B0 i ψ b( )

⎩ ⎭⎨ ⎬⎧ ⎫ g 0( )exp=

δ Im WI am b,( )ln⎩ ⎭⎨ ⎬⎧ ⎫ Im WI 0

a0m b,( )ln⎩ ⎭⎨ ⎬⎧ ⎫–=

Im WI am b,( )[ ]ln{ }

I0 x y,( ) A0 B0 2πψ x y,( )cos n x y,( )+ +=

I x y,( ) A B 2πψ x y,( ) δ+cos n x y,( )+ +=


Processed by CWT technique in the above case, Figs. 2c and 2d show the modulusof CWT coefficient of Figs. 2a and 2b, respectively. The solid curve shows the ridgewhere the maximum modulus is formed. The maximum modulus value is determinedby computing the maximum correlation coefficients of the original signal and daughterwavelets, which reflect similarity between the wavelet and load signal. To avoid

Pixel Pixel

Pix

el

Pix

el

a b

Fig. 1. Simulated interferograms with phase-step value of 0 (a), and 1.0472 rad (b).

1.5

1.0

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–0.520 40 60 80 100 120

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50

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nsity

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les

[pix

el]

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10

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40

50

6020 40 60 80 100 120

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nsity

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les

[pix

el]

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c d

Fig. 2. The one-dimensional signals of the row 50 of Fig. 1a (a), and Fig. 1b (b); modulus of the CWTand corresponding ridge of Fig. 2a (c), and modulus of the CWT and corresponding ridge of Fig. 2b (d).


the inherent edge distortion error of the CWT, we ignore 20 pixels at the boundary.From Eqs. (6) and (7), the unwrapped phase can be retrieved, which is shown in Fig. 3a.A very accurate estimation of δ can be obtained if we calculate the phase-step for eachrow and finally average the values obtained from each row. The phase-step value errorcan be estimated, which is shown in Fig. 3b.

The phase-step calibration results are summarized in the Table and shown in Fig. 4.Before the noise was added, the phase-step estimated by the new algorithm had shownhigh accuracy. After the noise was introduced, it was found that the error in the obtained

20

Unw

rap

phas

e [ra

d]

Pixel number

a

Pixel number

10 30 40 50 60 70 80 90 100

50

40

30

20

10

0

0.4

0.2

0.0

–0.2

–0.42010 30 40 50 60 70 80 90 100

– – – Phase-step value of π/3—— Phase-step value of 0

b

Pha

se-s

tep

valu

e er

ror [

rad]

Fig. 3. Phase error analysis by CWT algorithm: calculated phase distribution (a), and phase-step valueerror (b).

T a b l e. Phase-step calibration results.

Simulated phase step value [rad]

Calibration result without noise[rad]

Error [%]

Calibration result with noise[rad]

Error[%]

0.3142 0.3141 –0.039 0.3128 –0.340.3491 0.3490 –0.045 0.3476 –0.410.3927 0.3926 –0.040 0.3910 –0.440.4488 0.4485 –0.037 0.4469 –0.420.5236 0.5235 –0.025 0.5222 –0.270.6283 0.6280 –0.028 0.6259 –0.380.7854 0.7850 –0.021 0.7837 –0.221.0472 1.0470 –0.019 1.0456 –0.15


phase step was less than 0.5%. It can be seen that the simulated results agree well withtheoretical ones.

4. ConclusionsThe phase step calibration algorithm described in this paper allows an arbitrary phasestep to be calibrated between two interferograms. We have proposed a simple methodfor phase-shift measurement between two interferograms. The main feature ofthe method proposed is to determine accurate phase-step values from two fringepatterns using wavelet coefficients along the wavelet ridge. Compared with the tradi-tional methods used for the same purpose, our method has the advantages of highaccuracy and high antinoise ability. We believe that it may find practical applicationsin related fields, especially in phase-shifting interferometry, for elimination ofthe phase-shift error. The wavelet transform method proposed in this paper hasdemonstrated the validity of the new phase-step calibration method.

References[1] CHENG Y.Y., WYANT J.C., Phase shifter calibration in phase-shifting interferometry, Applied

Optics 24(18), 1985, pp. 3049–3052.[2] JAMBUNATHAN K., WANG L.S., DOBBINS B.N., HE S.P., Semi-automatic phase shift calibration using

digital speckle pattern interferometry, Optics and Laser Technology 27(3), 1995, pp. 145–151.[3] VAN BRUG H., Phase-step calibration for phase-stepped interferometry, Applied Optics 38(16),

1999, pp. 3549–3555.[4] CHEN X., GRAMAGLIA M., YEAZELL J.A., Phase-shift calibration algorithm for phase-shifting

interferometry, Journal of the Optical Society of America A 17(11), 2000, pp. 2061–2066.

a

Interferogram number

1.2

1

– – – Simulated phase-step value without noise• Calculated phase-step value without noise

b

Phas

e-st

ep v

alue

[rad

]

2 3 4 5 6 7 8

1.0

0.8

0.6

0.4

0.2

1.2

1.0

0.8

0.6

0.4

0.2Pha

se-s

tep

valu

e [ra

d]

Interferogram number1 2 3 4 5 6 7 8

– – – Simulated phase-step value with noise• Calculated phase-step value with noise

Fig. 4. Calibration curve for the phase-step: without added noise (a), and with added noise (b).


[5] GOLDBERG K.A., BOKOR J., Fourier-transform method of phase-shift determination, AppliedOptics 40(17), 2001, pp. 2886–2894.

[6] MALACARA D., Optical Shop Testing, in Pure and Applied Optics, Wiley, 1992.[7] FREYSZ E., POULIGNY B., ARGOUL F., ARNEODO A., Optical wavelet transform of fractal aggregates,

Physical Review Letters 64(7), 1990, pp. 745–748.[8] KRONLAND-MARTINET R., MORLET J., GROSSMANN A., Analysis of sound patterns through wavelet

transforms, International Journal of Pattern Recognition and Artificial Intelligence 1(2), 1987,pp. 273–302.

[9] WATKINS L.R., TAN S.M., BARNES T.H., Determination of interferometer phase distributions by useof wavelets, Optics Letters 24(13), 1999, pp. 905–907.

[10] FANG J., XIONG C.Y., YANG Z.L., Digital transform processing of carrier fringe patterns fromspeckle-shearing interferometry, Journal of Modern Optics 48(3), 2001, pp. 507–520.

[11] COMBES J.M., GROSSMANN A., TCHAMITCHIAN P., Wavelets: Time-Frequency Methods and PhaseSpace, Springer, 1989.

[12] MALLAT S.G., A theory for multiresolution signal decomposition: The wavelet representation,IEEE Transactions on Pattern Analysis and Machine Intelligence 11(7), 1989, pp. 674–693.

[13] DAUBECHIES I., The wavelet transform, time-frequency localization and signal analysis,IEEE Transactions on Information Theory 36(5), 1990, pp. 961–1005.

[14] MALLAT S., A Wavelet Tour of Signal Processing, Academic Press, 1999.[15] DAUBECHIES I., Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.

Received April 2, 2011in revised form August 18, 2011


Metastability exchange optical pumping low field polarizer for lung magnetic resonance imaging

GUILHEM COLLIER1*, MATEUSZ SUCHANEK3, ANNA WOJNA1, KATARZYNA CIESLAR4, TADEUSZ PALASZ1, BARTOSZ GLOWACZ1, ZBIGNIEW OLEJNICZAK2, TOMASZ DOHNALIK1

1Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

2Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Kraków, Poland

3Department of Chemistry and Physics, Agricultural University, al. Mickiewicza 21, 31-120 Kraków, Poland

4Université de Lyon, CREATIS-LRMN, CNRS, UMR5220, INSERM U630, Villeurbanne, France


An extensive improvement of our low field polarizer is described. It produces 3He gas polarizedup to 40% in a 6 h decay time storage cell. Production rate was raised by a factor of 10 to4–5 scc/min1 thanks to the implementation of a new 10 W laser and a new design of a peristalticcompressor, easier to handle. Some applications of polarized gas are also presented: dynamicimages of gas inhalation in the rat as well as a static image of human lungs using hyperpolarizedgas were obtained.

Keywords: optical pumping, 3He, table-top polarizer, magnetic resonance imaging (MRI) of the lungs.

1. IntroductionDespite its relative scarcity, hyperpolarized 3He has become an important alternativetool to study the lung functions. In the last decade, magnetic resonance imaging (MRI)using 3He has been successfully implemented in clinical research of asthma, cysticfibrosis, emphysema and lung cancer allowing one to perform well resolved ventilation

1scc is an acronym for standard cubic centimeter, corresponding to the number of atoms included in onemL (cubic centimeter) for a gas at atmospheric pressure (1013 mbar) and normal temperature (273.15 K).

224 G. COLLIER et al.

and dynamic imaging, diffusion measurement and regional oxygen uptake assess-ment [1]. The main interest in 3He for lung imaging is its property of being a highcontrast agent once it has been hyperpolarized. Indeed, a high nuclear polarization of3He gas can be obtained by the metastability exchange optical pumping (MEOP)method. It consists of two steps. First, the optical pumping of the 23S–23P transition(see notation in [2]) is performed, using circularly polarized laser light at 1083 nm, inthe presence of a radio-frequency (rf) discharge, ensuring sufficient density ofmetastable atoms. A high electronic polarization of metastable atoms is transferred tonuclei by the hyperfine interaction. In the second step, the collisions of helium atomsin the metastable state and in the ground state lead to the transfer of nuclear polarizationto helium atoms in the ground state.

The method was demonstrated for the first time in [3] and a detailed microscopicmodel for the MEOP was developed in [4]. In the standard operating conditions a lowmagnetic field, of the order of a few mT, plays the role of the guiding field forthe nuclear polarization, and a low 3He gas pressure, of the order of a few mbar is used.In most favorable conditions, the nuclear polarization achieved can exceed 80% [5].In practice, achieving a good polarization level and production of 3He usable in MRIis far from being straightforward. Regarding MEOP technique, different strategies ofgas production have been established. A global and central massive production hasbeen chosen in Mainz [6]. This group has designed an advanced bulky polarizerreaching an efficient gas production of 20 scc/min with a nuclear polarization of 75%.The disadvantages, however, are the high price due to the non-magnetic titanium alloycompressor driven by a hydraulic system, the big size of the polarizer containing fiveoptical pumping cells of 2.4 m for a total volume of 36 L, as well as difficulties inadjusting to user demands with regard to gas shipment over large distances.

Another approach is to design smaller polarizers [7–10], easy to handle, storableand placed close to the MRI system for on-site production. Such polarizer hasthe advantage of having lower cost and less constraints but usually only allows one toreach lower polarisation level and much lower throughput than the system in Mainz.A similar table-top polarizer was designed a few years ago by our group [10], buttypically had throughput of only 0.4 scc/min for an estimated final polarization of onlyfew percent when extracted into a syringe. We present in this paper an extensiveupgrade of this polarizer, whose main novelties are a new 10 W laser and a new designof a peristaltic compressor, which different groups have always been attempting toimprove.

In Section 2, all the different modifications of the polarizer are listed. We thendescribe briefly the MRI facilities used for our applications in Section 3. In the lastsection, results are presented and discussed.

2. Low-field polarizer

In Figure 1, a general design of our table-top polarizer is schematically described anda picture of it is presented in Fig. 2. The main framework and the coils frame were

Metastability exchange optical pumping low field polarizer... 225

Fig. 1. Scheme of the table-top polarizer (see text). Six coils (cross-section) produce a homogeneousmagnetic field. A gas handling system located under a 12 mm aluminium plate (G: getter, F: 50 μm filter)deliver gas to the optical pumping cell where it is being polarized by a laser tuned at 1083 nm(BS: polarizing beam splitter). The gas is then compressed to a storage cell (V: one-way valve, PI: pressuresensor) with a peristaltic compressor. The same gas can be compressed a second time to atmosphericpressure inside a syringe for rat lung experiment using a bypass between the input and output ofthe compressor.

Fig. 2. Picture of the low field polarizer.


copied from the Protlab polarizer made in Paris [7, 8]. The supporting frame is madeof fifteen square aluminium profiles of 6 cm in width inside which a main 12 mm thickaluminium plate is mounted. Wheels were added on the bottom of the framework,allowing an easy handling and transportation of the polarizer. The gas handling systemwas built inside a separate rectangular cuboid frame made of aluminium and Plexiglas.MEOP efficiency being strongly dependent of the gas purity, a particular care wastaken to keep all the system airtight. All necessary needle valves (4172G6Y/MM byHoke, Spartanburg, SC, USA) were helium leak-tight certified, and connectionbetween the different elements was made using a 6 mm OD electropolishednon-magnetic 316/316L stainless steel (Swagelok, Solon, Ohio, USA). The gashandling system is composed of a turbomolecular pump that can achieve a vacuum of10–8 mbar and a bottle of 4He for cleaning purposes of the optical pumping cell.The 1 L 3He bottle at a pressure of 15 bar (Spectra Gases Inc., Stewartsville, NewJersey, USA) has a purity of 99.999% but for further cleaning, the gas passes througha PS2-GC50 SAES Getters S.p.A. (Lainate, Italy) getter, and an additional mechanicalporous 0.5 μm filter. A pressure sensor (24PC, Honeywell, Morristown, New Jersey,USA) was mounted at the output of it to control the pressure inside the optical pumpingcell. Connection between gas handling system and the optical pumping cell is madeusing a flexible pipe from the CT convoluted metal tubing series and a glass metalconnection (G304-4-GM3, Cajon Co, Solon, Ohio, USA). All the gas handling systemfits inside a 40×60×90 cage that can be placed under the main plate of the polarizer.The actual dimensions of the main framework plus gas handling system are70×160×170 and make it easily transportable to any MRI facility.

2.1. Guiding fieldA guiding field of 16.4 gauss is produced by 3 pairs of square coils of 20 cm side.The frame of the coils is made of 2 mm thick aluminium whose cross-section hasan open square shape. Grooves of the 2 inner pairs of coils have a 14 mm thicknessand 22 mm for the external ones. Positions and number of turns for each coil wereoptimized by a Matlab program, taking into account the different filling height ofthe groove depending on the number of turns of a 0.8 mm diameter copper wire. Tobe more realistic, the filled groove was not assimilated to one loop of current butdiscretized into nine equally spaced loops centered around the center of the groove.

An optimized configuration was found to be 85, 100 and 225 turns respectively forthe 6, 19.1 and 36.8 cm distances from the center of symmetry of the system (seeFig. 3). The simulations were experimentally verified with a three axis MAG-03 MSfluxgate magnetometer (Bartington Instruments Ltd, Witney, Oxfordshire, UnitedKingdom). The power supply of the probe was home made and gave a precision of0.01%. The probe was mounted on a Plexiglas structure that allowed investigation ofa matrix of 3.5 cm steps along transverse direction and it was manually moved witha step of 1 cm along the magnetic field direction. The experimental results gave a goodagreement with the simulation and a final homogeneity of 0.15% was obtained inthe location of a cylindrical optical pumping cell 48 cm long, 0.01% for a 100 mL


storage cell which serves to perform the NMR measurement, and 0.06% for the secondNMR system dedicated to a 1.1 L storage cell.

2.2. LaserThe 50 mW DBR diode laser was replaced by a new ytterbium 10 W doped fiber laser(2.1 GHz FWHM, CUS-BT-YFL-1083-HE-100-COL, Keopsys, Lannion, France)with the same wavelength of 1083 nm. An APC collimator (model F220APC,Thorlabs, Newton, New Jersey, USA), coated for 1064 nm with a focus length of11.17 mm was mounted directly on the output of the fiber. To improve efficiency ofoptical pumping inside the 5 cm diameter optical pumping cell, the beam was expandedby a Kepler-like telescope F2/F1 = 7 (EKSMA OPTICS, Vilnius, Lithuania). The finalfull width at half maximum of the Gaussian beam profile was 4.9 mm. The beam wascircularly polarized with a 5 cm cube polarizing beam splitter and a multiple orderplate with λ /4 retardation. The beam was back-reflected by a dielectric mirror afterfirst passage through the cell to double the efficiency.

2.3. Optical pumping cellThanks to the new guiding field, a new longer Pyrex optical pumping cell of 48 cm inlength, 5 cm in diameter with optical windows have been implemented. Apiezon Lgrease was used for lubrication of input and output valves. Some 5 cm glass capillaries

0.2

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d in

hom

ogen

eitie

s [%

]

z distance from the center [cm]z distance from the center [cm]–20 –10 0 10 20

a b

Fig. 3. Computation and experimental data of the magnetic guiding field deviation (1000×ΔB/B) insidethe set of 6 square coils. The magnetic field is along the z direction. a – Matlab computation of ourmagnetic field inhomogeneities for three different distances from the symmetric axis of the square frames(solid line, dotted line and dashed line are respectively 0, 3.5 and 7 cm from the axis in the diagonaldirection of the square frame). b – Comparison between computed (solid line) and experimentalvalues (dotted and dashed lines) measured with a Bartington magnetometer. The dotted line correspondsto the left side of the axis where the 48 cm long optical pumping cell is lying and the dashed line tothe right side where the NMR and the 100 mL, 5 cm long storage cell is located.


of 1.8 mm in diameter were located at the input and output of the cell to constraintthe gas flowing in one direction only and keep impurities out of the storage cell andgas handling system. The cell was located 3.5 cm off the center of the coils symmetryaxis.

2.4. Storage cell and gas transportationTo store the polarized 3He after compression, three different storage cells were used.A small 100 mL Pyrex cell was dedicated to short rat lung imaging experiments in our0.088 T permanent magnet based system and optical calibration of the NMR signal.This cell was previously demagnetized [11]. Following this procedure, a decay timeof 54 min was measured by NMR. A 500 mL quartz cell with a longer decay time of4 h was used to store larger quantities of helium for longer experiments. Thanks toa bypass system implemented between the output and the input of the peristalticcompressor (see Fig. 1) a portion of the gas can be compressed a second time toatmospheric pressure into a 12 mL syringe. This latter is used to transfer 3He fromthe low field polarizer to the low-field MRI system located 10 m away in ourlaboratory. Previously polarized 3He was mixed in the storage cell with a buffer gas(4He or N2) to reach a pressure higher than 1 atm and only a small amount of 3Hewas retrieved by distending the mixture inside a plastic syringe. This new process ofextracting helium avoids losses due to gas mixing and shows a factor of 3 increase intotal magnetization inside the syringe. Losses due to the first and the secondcompression inside the peristaltic compressor and also during transportation inthe presence of a non-homogeneous magnetic field are difficult to accurately assessbut the relaxation time of 3He inside the syringe in the low-field MRI system wasmeasured to be longer than 3 min (see Fig. 4).

Fig. 4. Relaxation of magnetization inside a 12 mL polypropylene/polyethylene syringe in our 0.088 Tpermanent magnet. Plastic syringe was used to transport polarized 3He from the storage cell to the scannerand to inflate lungs of the tracheotomised rat. Time before application was reduced as much as possibleand kept below 20 s, which is equivalent to a total magnetization loss lower than 10%.

5×105

4×105

3×105

2×105

1×105

00 2 4 6 8 10 12 14 16

Experimental dataExponential decay fit

Equation: y = A1exp(–x/t1) + y0

y0 = –2546 ± 1238

A1 = 5.025×105 ± 1984t1 = 3.279 ± 0.033

Sig

nal a

mpl

itude

[a. u

.]

Time [min]


For human lung experiments, storage cells of 1.1 L volume were bought togetherwith a magnetic transport box (Fig. 5) from Arbeitsgruppe Helium-3, Institut fürPhysik, Universität Mainz [12]. As was shown in [13] that short relaxation times couldbe attributed to ferromagnetic contaminants, the vessels were made by Schott AG(Mainz, Germany) from a special aluminosilicate-glass containing a minimum of theseparamagnetic centers and the best flask was certified to have a 150 h wall relaxationtime. In practice, our gas handling system at the output of the compressor being notas clean as it is at the input of the OP cell, an additional relaxation due to impuritiesshortened this time. The NMR measurement gave a decay time of polarization insidethe cell of 6 h. To store and keep the vessels inside a magnetic homogeneousguiding field, the transport box is magnetically shielded with permanent magnet andpieces of mu-metal. It produces a field of 10 gauss with relative gradients lower than10–3 cm–1. This gives a relaxation time due to gradient inhomogeneities close to 150 hat 1 bar. Once in the hospital and the preliminary calibrations on patient executed,the transport box was placed close to the end of the fringe field of the scanner. Afteropening the box, gas was extracted into a 1 L Tedlar gas sampling bag (modelGST001S-0707, Jensen Inert Products, Coral Springs, Florida, USA) using a similardesign of the peristaltic compressor as the one used in the table-top polarizer.The sample bag was pre-filled with 100 mL of nitrogen to avoid too fast a relaxationwith its inner surface during the beginning of helium compression. After a first rinseof the lungs with nitrogen, gas mixture was directly administrated to the volunteerthrough the sample bag. Delay between the end of 3He polarization and the time ofthe scan was approximately 1.5 h, including 45 min of transportation.

2.5. Peristaltic compressor

To replace the peristaltic compressor borrowed from the Kastler Brossel Laboratory [14],a new transparent design was developed, tested and experimentally approved (see

Fig. 5. Transport box and vessels from Mainz University group for 3He storage during journey to hospital.


Fig. 6). The compressor is built of the following fixed elements: the main body madeof polycarbonate, two Plexiglas lids with bearing shells, Plexiglas pressing bar,radiators, peristaltic tube and Plexiglas oil chamber. The rotor of the compressor ismade of polyamide and turns on the antimagnetic steel axis. The pressing polyamiderollers rotating on non-magnetic steel axis play the role of the compressor’s valves.The main motivation for this new design was to facilitate the replacement of the innerperistaltic tube. The replacement procedure was then shortened from 30 min to 15 min.To lengthen the lifetime of the tube, inorganic oil was inserted inside the compressorand two radiators were mounted on both sides of the main body to dissipate the heatenergy released during friction. To improve the flow circulation, a vacuum of the orderof a few mbar was maintained by a rotary pump inside the body of the compressor,while operating. This vacuum prevents the tube from shrinking under atmosphericpressure while compressing helium that is polarized in the optical pumping cell at2–3 mbar. A small gas reservoir is located between the compressor and the vacuumchamber to keep the oil inside the main body. Several peristaltic tubes from Masterflex(Cole-Parmer, Vernon Hills, Illinois, USA), models C-FLEX (50 A), Pharmed BPT,Norprene (A 60 G) and BioPharm Plus silicone have been tested, of which onlythe first two showed satisfactory parameters to be used inside the compressor. NMRmeasurements on the storage cell showed that both of them gave similar andreproducible polarization levels but for mechanical considerations the Pharmed tubewas chosen due to a more rigid property, allowing for a longer lifetime up to 20 h.Compressors of two different sizes were produced. The first one with a similar corediameter of 8 cm as the older compressor was built to work with the Pharmed BPTtube model 06508-17, inside diameter of 6.4 mm. A larger model, core diameter of

Fig. 6. Picture of the new peristaltic compressordesign.


9.5 cm and 12.7 mm 06508-82 tube model, was also tested to increase the productionof polarized 3He.

2.6. Nuclear magnetic resonance (NMR)

The nuclear magnetic resonance (NMR) system was completely rebuilt (see Fig. 7).New square Helmholtz transmitter coils, of 107 cm radius, 20 turns each, weremounted on the main aluminium frame to give a homogeneous B1 field over the storagecells volume and an easy access to different elements. They have been tuned to 55 kHz(inductance L = 3.85 mH, resistance R = 12.63 Ω). Radio-frequency pulse at a fre-quency of 53.3 kHz, is produced by a generator (GW Instek GFG 3015), whoseexternal trigger option allows a precise control of the number of oscillations, andamplified with a 100 W DMOS audio amplifier (model TDA 7294). Concerningthe pick-up coils, two different systems were built. The first one consists of two circularcoils of 40 turns, 30 mm apart from each other (R = 24 Ω, L = 1.55 mH) and whosediameter (72 mm) was chosen to fit the size of the 1.1 L storage cell. A smaller onewas dedicated to a 5 cm long and 5 cm diameter storage cell and was made of tworectangular coils of 120 turns each (R = 50 Ω, L = 3.76 mH). Litz wire was used forboth pick-coils and each of them has their own tuning and matching circuits. A similarQ factor of 20–25 was achieved in both coils.

Fig. 7. Scheme of the NMR acquisition (see text). (TB: tuning and matching circuit, I: input, O: output,SC: storage cell, E.T.: external trigger). A microprocessor at the center of the NMR system is used tocontrol the different elements.


During NMR experiment a chosen pulse was sent through transmitter coils thatcauses free precession of the storage cell magnetization. This free induction decay(FID) signal at 53.3 kHz was then detected by the pick-up coils and a digital lock-inamplifier (LIA, SR 830, Stanford Research Systems, Sunnyvale, California, USA)applied synchronous detection. The output of the lock-in amplifier was recorded ona numerical oscilloscope that had the possibility to transfer saved waveforms from itsmemory to a personal computer via USB connector. The free induction decay wasrevealed by the LIA using its internal clock a little off resonance to get a sufficientnumber of oscillations during the decay. Data analysis was performed on a standalonePC by performing a peak-to-peak analysis of the oscillations and fitting them to retrievethe initial amplitude of the FID. A proper gating circuit protects the LIA at the timeof the rf pulse and turns off the discharge during data acquisition to minimize the noise.The key element of the NMR system is a programmable microprocessor (ATmega 8,Atmel, San Jose, California, USA) which is synchronizing all the different elementstogether. Four output signals are delivered by the microprocessor:

– one switches off the radio-frequency discharge inside the OP cell just beforethe rf pulse,

– a second signal is sent to the external trigger of the generator and commandsthe NMR pulse length,

– an opto-isolator coupled to flip flop diodes opens the gate and lets the signal gothrough to the LIA after the ringing time of the transmitter coils,

– a last logic signal triggers the acquisition of the oscilloscope.It is possible to program the length of the pulse, the delay between two pulses,

the ringing off time after the pulse and the acquisition time through a simple interfacewith display (LCD panel). This home made device therefore offers an easy control ofall the parameters and facilitates the NMR acquisition.

At last, NMR was calibrated against an optical detection method [15, 16]. A sealedcell with the exact same shape as the 100 mL storage cell, filled with 1 torr of pure3He was polarized inside the NMR system by the pump laser. The optical detectionrelies on the absorption of a longitudinal attenuated probe laser tuned at 1083 nm onC9 or C8 lines of 3He. Indeed, the ratio of absorption rates for positively and negativelypolarized probe beam is directly related to the spin temperature distribution inmetastable state and then to the nuclear polarization. This method is very accurate anddoes not depend on pressure. Knowing precisely the polarization and the total amountof 3He inside our sealed cell, nuclear magnetization inside the storage cell can be easilydeduced.

3. MRI facilities

3.1. Low field (0.088 T) scannerThe imaging of rat lungs was performed at a low field MRI scanner described in detailelsewhere [17]. It was specially designed for small animal lung imaging usingpolarized 3He gas. The scanner is based on a 0.088 T permanent magnet (AMAG,


Poland) equipped with a biplanar actively shielded gradient coils (30 mT/m, NRC,Winnipeg, Canada) controlled by commercial MR Research System (previously SIMS,Surrey, Great Britain) MR4200 Narrow Band console. Dual-frequency 2.84 MHzfor 3He (alternatively 3.73 MHz for 1H) solenoid coil was used for NMR signaldetection.

For in vivo animal study three adult rats (race: Wistar, 400 g) were used. Allexperiments using animals were approved by national research ethics committees andconducted in accordance with Polish regulations and animal protection law. Eachanimal was anesthetized by intraperitoneal injection of chloral hydrate (40 mg/100 gbody weight) and afterwards tracheotomized to simplify 3He gas injection. Aftereach hour 1/3 of the anesthetic dose was injected again to prevent animal wake up.The animals were placed in a supine position on a home-built holder in the center ofthe rf coil. Just before imaging the volume of 7 mL of polarized 3He gas was introducedto the rats lung directly from the syringe via the trachea catheter.

For image acquisition we employed standard FLASH sequence (flip angle 7°,FOV = 80 mm, 128×128 matrix, slice thickness 80 mm, sampling bandwidth 10 Hz,no averages, total acquisition time 1.6 s). Additionally, a radial sequence was devel-oped for both static and dynamic imaging. The technique uses the followingparameters: flip angle 7°, FOV = 80 mm, number of samples 128, total acquisitiontime 4 s and 20 s, for static and dynamic imaging, respectively. Both protocols utilizedlow-field excitation pulses optimal for polarized 3He imaging. The importantadvantage of radial sequence as compared to FLASH is that it allows performingdynamic imaging of gas inflow with a good temporal resolution, following a singlegas injection.

3.2. Clinical 1.5 T scannerThe clinical experiments were performed at a Siemens Sonata scanner at 1.5 T (seeFig. 8) in collaboration with the team at the John Paul II Hospital in Kraków (Poland).

Fig. 8. Sonata scanner at the John Paul II Hospital with 3He coil from RAPID Biomedical. In the centerof the coil, a first phantom (see text) is placed for angle calibration experiment.


A necessary update of the scanner’s software and the purchase of a 3He birdcage lungcoil from RAPID Biomedicals allowed us to perform 3He experiments at a frequencyof 48.5 MHz. In order to test the system, a first phantom consisting of a 250 mL vesselfilled with 1.363 bar of 3He and 440 mbar of O2 was realized. A similar phantom wasused already in Orsay [18]. Only 14.02 mmol of thermally polarized 3He is sufficientto get an FID from the phantom and the oxygen is used to shorten the longitudinalrelaxation time T1 [19].

Using a spectroscopic sequence from Siemens, adapted for multinuclearexperiments, a T1 of 3.1 s was found and the flip angle calibrated. Gradient recalledecho sequences being the most commonly used sequences in MRI of hyperpolarizednuclei, a multinuclear multislice 2D spoiled gradient echo (SPGR) sequence, alsoknown as fast low-angle shot (FLASH), was written and implemented on the scanner.

4. Results

4.1. 3He production using the table-top polarizer

Thanks to all the improvements described above (optimized guiding field, new laser,optical pumping and storage cells, peristaltic compressor), the table-top polarizer isnow able to work in a continuous mode. The new framework gives an easier openaccess to the elements inside and the possibility to transport the polarizer. The newcalibrated NMR system gives the value of polarization inside the storage cell.The system was verified to give reproducible 30–40% of polarization for a pressurebetween 2.5 and 3 mbar inside OP cell during optical pumping. At this pressure andfor a rotation speed of 4 to 5 Hz, the first design of peristaltic compressor hasa production rate of 0.8–1 scc/min. The second larger version, working with a peri-staltic tube of two times bigger diameter, also appeared to work satisfactorily andreaches 3.5–4 scc/min. As a reference, approximately 10 scc of gas are needed fora single rat lung experiment. Which means that within 3 min of compression the nec-essary volume of 3He can be polarized. For human experiment, the required volumeis much higher: around 250–300 scc. This is obtained after about 1 h and 15 min ofcompression.

4.2. Small animal experiments

Preliminary tests were performed on a syringe phantom. The first test was made usinga spectroscopy sequence to check the increase of total magnetization and compare thisvalue to our previous experiments [10]. Results showed an increase of a factor of 7 inthe total magnetization contained in a 10 mL syringe. The new way to extract the gasfrom the storage cell was responsible for an additional increase of a factor of 3, whichmeans that new MRI experiments were possible with at least 20 times higher signal.New radial static and dynamic sequences were first implemented and tested with thisphantom (Fig. 9). The static radial image is shown on the left. The 2 mm diameternozzle and the 1 mm thick septum are well visible at the top and the bottom of


the image, respectively. An artifact inherent to the radial reconstruction is responsiblefor the white vertical band pattern outside the syringe. On the right side of Fig. 9,a series of 10 images obtained using the projection sliding window sequence arepresented. The sequence started before 3He entered the syringe, which explainsthe first 2 empty images of the series. The syringe was completely filled on the 8-thimage. Then, total magnetization is decreasing due to the relaxation process andthe rf pulsing. That is why the image SNR gradually decreases in the 9-th and 10-thimage.

Fig. 9. Preliminary tests of the radial sequence made with a syringe phantom filled with 3He ina 0.088 T permanent scanner. Left: static radial 2D projection image acquired with 256 samples and200 views, 10 cm field of view (FOV), 25 kHz bandwidth, 6.1° flip angle, acquisition time tac of 4 s,TR = 20 ms. Right: dynamic series of radial 2D projection sliding window images with 128 samples and100 views, 10 cm FOV, 33 kHz bandwidth, 8° flip angle, tac = 21 s.

Fig. 10. Transverse 3He images of rat lungs in vivo acquired with the (left) FLASH sequence(slice thickness 80 mm, FOV = 80 mm, 128×128 imaging matrix, 8° flip angle, 10 kHz bandwidth,no averaging, echo time = 7 ms, repetition time = 32 ms, tac = 4 s) and the (right) projection radial one(FOV = 80 mm, 128 samples per 200 views, repetition time = 20 ms, tac = 4 s, 10 kHz bandwidth, flipangle 7°, no averaging).


These tests were followed by in vivo experiments with rats. Compared to the resultspreviously reported by our group [17], a two-fold increase in spatial resolution anda four-fold increase in the SNR were observed, significantly improving the quality ofthe static images acquired during breath-hold (Fig. 10) as well as the dynamic imagesrepresenting the gas inflow into the animal’s lung (Fig. 11).

4.3. Human lung images

Preliminary tests were required to validate the sequence. The signal coming fromthe first phantom described in Section 3.2 being too low for an imaging sequence, wedecided to optically pump a 11.5 cm long cell of 15 mm inner diameter filled with128 mbar of 3He directly inside the scanner. The cell had a volume of approximately20 mL, which corresponds to 2.5 scc but a polarization of the level of 30% can beobtained at 2 T. The different mechanisms and features of metastability exchangeoptical pumping in high field are not the subject of this article and are describedelsewhere [20, 21]. A 500 mW laser was tuned at 1083 nm on the f 2m pumping line(see notation in [20]). After waiting a few minutes for the steady state polarization tobe reached, the FLASH sequence was successfully tested with this phantom.

Fig. 11. Transverse 3He radial projection sliding window images of rat lungs in vivo (100 mm fieldof view, 128 samples and 100 views, 33 kHz bandwidth, 8° flip angle, tac = 20 s).


Thanks to the new larger design of the peristaltic compressor, a few boluses of 3Hecould be carried to hospital inside the transport box and the storage cell. The polar-ization process takes 1 h to get 240 scc of 3He. The polarized gas was then mixedwith N2 until reaching the atmospheric pressure inside the 1.1 L storage cell. Once inhospital, 81% of the total gas was extracted to the Tedlar bag previously rinsedwith 4He. Lungs of a healthy volunteer were washed with 1 L of clean N2 beforeinhalation from the Tedlar bag. The image was taken 1 h after the end of the polari-zation process. The FLASH sequence was launched directly after inhalation. The fieldof view was 35×35 cm for a 64×64 matrix. A bandwidth of 16.64 kHz was used witha slice thickness of 20 cm to cover the whole lungs. There was no averaging andthe sequence lasted approximately 500 ms (TE = 3.6 ms and TR = 7.5 ms). An 11° flipangle used in the experiment was calculated to be optimal [22]. The result is shown inFig. 12. This image is the first MRI picture of human lungs using hyperpolarized gasmade in Poland.

5. Conclusions

Improvements in our table-top polarizer, leading to the efficiency of 3.5–4 scc/minand a reproducible corresponding polarization of about 30–40% inside storage cellhave been presented in this paper. The improvements are mainly due to the imple-mentation of a broader bandwidth 10 W laser and a new design of the peristalticcompressor. Thanks to these modifications the magnetization was increased by a factorof 20, which allowed improved FLASH rat lungs pictures to be taken and moreover,to implement radial dynamic and static sequences. These ventilation images showa sufficient resolution and SNR to be used for diagnostic or medical tests. In additionwe were also able to polarize a necessary quantity of 3He to take the first picture ofhuman lungs made in Poland. Compared to rat images, the resolution of human lung

50

100

150

200

25050 100 150 200 250

Fig. 12. Transverse 3He image of healthy volunteer’s lungs using a FLASH sequence (20 cm slicethickness, 35 cm FOV, 64×64 matrix, 11° flip angle, 16.64 kHz bandwidth, TE = 3.6 ms, TR = 7.5 ms).


images is still low. A major issue for this problem is probably the loss of polarizationduring transportation and extraction. The losses due to relaxation time inside transportbox and storage cell are minimal and can be easily assessed: the decay time is ofthe order of 6 h and the transport lasts 1 h (corresponding to 15% loss of magneti-zation), the losses due to the transfer of storage cell inside transport box were checkedto be around 7%, only 81% of the gas mixture was compressed inside the Tedlar bag.But the main loss is probably due to the time spent (around 1.5 min) duringcompression inside the Tedlar bag in the non-homogeneous fringe field of the magnet.The transport of the bag inside the scanner is probably adding some losses. An easysolution to this problem would be to build a second smaller guiding field close tothe magnet for minimizing the losses during the second compression. In the same waythe table-top polarizer could be transported close to magnet in hospital and the gasdirectly produced few meters away from it.

But none of these solutions have been chosen by our group for future experiments.As evoked briefly earlier in Section 4.3, an alternative solution would be to performMEOP at higher magnetic field and build a high field polarizer [23]. Previouspromising experiments have been done and showed a great increase in production rateefficiency. This would solve both the problem of transportation and polarization timeand will be tested in the near future.

Acknowledgements – We gratefully acknowledge Pierre-Jean Nacher from LKB in Paris for his supportand advice. This work was partially supported by the Polish Ministry of Science and HigherEducation (SPUB 547/6.PRUE/2008/07), the Marie Curie Research and Training Network PHeLINet(MRTN-CT-2006-036002) and the European Regional Development Fund under Operational ProgrammeInnovative Economy Operational Program NLTK.

References[1] KAUCZOR H.-U., MRI of the Lung, Springer, Heidelberg, 2009, pp. 36–56.[2] COLEGROVE F.D., SCHEARER L.D., WALTERS G.K., Polarization of He3 by optical pumping, Physical

Review 132(6), 1963, pp. 2561–2572.[3] WALTERS G.K., COLEGROVE F.D., SCHEARER L.D., Nuclear polarization of He3 gas by metastability

exchange with optically pumped metastable He3 atoms, Physical Review Letters 8(11), 1962,pp. 439–442.

[4] NACHER P.J., LEDUC M., Optical pumping in 3He with a laser, Journal de Physique 46(12), 1985,pp. 2057–2073.

[5] STOLTZ E., MEYERHOFF M., BIGELOW N., LEDUC M., NACHER P.-J., TASTEVIN G., High nuclearpolarization in 3He and 3He–4He gas mixtures by optical pumping with a laser diode, AppliedPhysics B 63(6), 1996, pp. 629–633.

[6] WOLF M., Highest He-3 nuclear spin polarization production by metastable exchange pumping,Dissertation zur Erlangung des Grades Doktor der Naturwissenschaften am Fachbereich Physik derJohannes Gutenberg-Universität in Mainz, 2004, available online: http://ubm.opus.hbz-mrw.de/volltexte/2005/655/.

[7] NACHER P.-J., TASTEVIN G., MAITRE X., DOLLAT X., LEMAIRE B., OLEJNIK B., A peristaltic compressorfor hyperpolarized helium, European Radiology 9, 1999, article B18.


[8] CHOUKEIFE J., MAITRE X., NACHER P.-J., TASTEVIN G., On-site production of hyperpolarizedhelium-3 gas for lung MRI, Proceedings of the 11th ISMRM Scientific Meeting and Exhibition,July 10–16, 2003, Toronto, Canada, p. 1391.

[9] GENTILE T.R., RICH D.R., THOMSON A.K., SNOW W.M., JONES G.L., Compressing spin-polarized 3Hewith a modified diaphragm pump, Journal of Research of the National Institute of Standards andTechnology 106(4), 2001, pp. 709–729.

[10] SUCHANEK K., CIESLAR K., OLEJNICZAK Z., PALASZ T., SUCHANEK M., DOHNALIK T., Hyperpolarized3He gas production by metastability exchange optical pumping for magnetic resonance imaging,Optica Applicata 35(2), 2005, pp. 263–276.

[11] THIEL T., SCHNABEL A., KNAPPE-GRÜNEBERG S., STOLLFUß D., BURGHOFF M., Demagnetization ofmagnetically shielded rooms, Review of Scientific Instruments 78(3), 2007, article 035106.

[12] HIEBEL S., GROßMANN T., KISELEV D., SCHMIEDESKAMP J., GUSEV Y., HEIL W., KARPUK S., KRIMMER J.,OTTEN E.W., SALHI Z., Magnetized boxes for housing polarized spins in homogeneous fields, Journalof Magnetic Resonance 204(1), 2010, pp. 37–49.

[13] SCHMIEDESKAMP J., ELMERS H.-J., HEIL W., OTTEN E.W., SOBOLEV YU., KILIAN W., RINNEBERG H.,SANDER-THÖMMES T., SEIFERT F., ZIMMER J., Relaxation of spin polarized 3He by magnetizedferromagnetic contaminants – Part III, The European Physical Journal D 38(3), 2006, pp. 445–454.

[14] NACHER P.J., Peristaltic compressors suitable for relaxation-free compression of polarized gas,United State Patent No. US6655931B2, 2003.

[15] COURTADE E., MARION F., NACHER P.-J., TASTEVIN G., KIERSNOWSKI K., DOHNALIK T., Magnetic fieldeffects on the 1083 nm atomic line of helium – Optical pumping of helium and optical polarisationmeasurement in high magnetic field, The European Physical Journal D 21(1), 2002, pp. 25–55.

[16] TALBOT C., BATZ M., NACHER P.-J., TASTEVIN G., An accurate opical technique for measuringthe nuclear polarisation of 3He gas, Journal of Physics: Conference Series 294, 2011, article 012008.

[17] SUCHANEK M., CIESLAR K., PALASZ T., SUCHANEK K., DOHNALIK T., OLEJNICZAK Z., Magneticresonance imaging at low magnetic field using hyperpolarized 3He gas, Acta PhysicaPolonica A 107(3), 2005, pp. 491–506.

[18] VIGNAUD A., Influence de l’intensité du champ magnétique sur l’imagerie RMN des poumons à l’aided’hélium-3 hyperpolarisé, Dissertation to get the grade of Docteur en science de l’université ParisXI, Orsay, 2003, p. 85, available online: http://tel.archives-ouvertes.fr/tel-00003668/en/.

[19] SAAM B., HAPPER W., MIDDLETON H., Nuclear relaxation of 3He in the presence of O2, PhysicalReview A 52(1), 1995, pp. 862–865.

[20] NIKIEL A., PALASZ T., SUCHANEK M., ABBOUD M., SINATRA A., OLEJNICZAK Z., DOHNALIK T.,TASTEVIN G., NACHER P.-J., Metastability exchange optical pumping of 3He at high pressure andhigh magnetic field for medical applications, The European Physical Journal Special Topics 144,2007, pp. 255–263.

[21] DOHNALIK T., NIKIEL A., PALASZ T., SUCHANEK M., COLLIER G., GRENCZUK M., GLOWACZ B.,OLEJNICZAK Z., Optimization of the pumping laser beam spatial profile in the MEOP experimentperformed at elevated 3He pressures, The European Physical Journal – Applied Physics, (in press).

[22] LEE R.F., JOHNSON G., GROSSMAN R.I., STOECKEL B., TRAMPEL R., MCGUINNESS G., Advantages ofparallel imaging in conjunction with hyperpolarized helium – A new approach to MRI of the lung,Magnetic Resonance in Medicine 55(5), 2006, pp. 1132–1141.

[23] COLLIER G., NIKIEL G., PALASZ T., SUCHANEK M., GLOWACZ B., WOJNA A., OLEJNICZAK Z., DOHNALIK

T., Metastability exchange optical pumping of 3He at 1.5 T for an in-situ polariser, Poster presentedin JCNS Workshop on Modern Trends in Production and Applications of Polarized 3He, Munich,2010, available online: http://flux.if.uj.edu.pl/posters/Munich2010.pdf.


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