bragg mirror inscription on linbo3 waveguides by index microstructuration

Bragg mirror inscription on LiNbO3 waveguides byindex microstructuration

Richard Ferriere, Badr-Eddine Benkelfat, John M. Dudley, and Kamal Ghoumid

Numerous applications in integrated optics, especially those related to multiwavelength telecommuni-cations, require dichroic reflectors for use as narrowband or broadband wavelength-selective filters.Bragg mirrors are excellent candidates for this purpose, and we describe a method of fabricating Bragggrating reflectors in Ti-indiffused Lithium Niobate single-mode waveguides based on holographic mask-ing in association with proton exchange. The holographic setup is employed to record a photolithographicmask directly on the substrate, enabling the inscription of waveguides with both periodic and aperiodicdistributed parameters. © 2006 Optical Society of America

OCIS codes: 230.1480, 220.4000, 120.5790, 130.3120.

1. Introduction

Bragg grating inscription is commonly used in in-tegrated optics applications for the realization ofwavelength-dependent resonators, distributed Braggreflectors (DBRs), and fiber lasers,1,2 and there contin-ues to be significant interest in studying convenientand reproducible fabrication technologies. Fabrica-tion methods are usually based on the photorefrac-tive2,3 effect and dry etching,4 and ultraviolet-inducedsurface-relief gratings on LiNbO3 channel waveguideshave also been reported.5,6 More recently, a photore-fractive index difference induced by femtosecond la-ser pulses has been employed to realize gratings inoxides.7 In this paper we propose a simple and re-producable method to induce local refractive indexvariations based on a patterned proton-exchangetechnique in a Ti-indiffused waveguide.

The proton-exchange patterning technique requiresa mask to be deposited on the substrate. For the caseof a grating with a relatively large period, the photo-

lithographic mask reproducing a Bragg grating pat-tern can be fabricated by means of an e-beam mask.However, in applications where shorter periods areneeded, holographic methods are preferable due to thecost and difficulties involved in e-beam mask prepara-tion. Holographic inscription methods can be based onclassical interferometry,8,9 standing-wave configura-tions,10 and prism interferometers;11 but, from anindustrial perspective, the most frequently used tech-nique relies on a diffraction phenomenon using aquartz phase grating illuminated by UV radiation.This has been widely applied to the photoinscription ofgratings in Ge-doped fibers, where the interferencebetween the �1 and �1 orders produces a periodicvariation of luminous field intensity that, by the pho-torefractive effect, periodically modifies the value ofthe optical waveguide effective index. It has also beenapplied to DBR lasers where an interference patternis used to create a mask employed for corrugating asemiconductor surface.

In this paper we present a setup that has beendesigned to generate (using a holographic technique)a field of periodic or pseudoperiodic fringes, allowingthe inscription of a photolithographic mask directlyon a substrate. It is based on a triangular Sagnacinterferometer possessing high stability while allow-ing precise fringe spacing of the interference patternat the 3 nm scale. The device is of straightforwarddesign, uses standard and inexpensive optical com-ponents, and works equally well with continuous orpulsed sources of light. This paper is organized asfollows. In Section 2 we briefly review some designaspects of Bragg grating mirrors and report the re-sults of numerical modeling of a Bragg mirror struc-

R. Ferriere ([email protected]), J. M. Dudley, and K.Ghoumid are with the Franche-Comté Electronique, Mécanique,Thermique et Optique—Sciences et Technologies, Laboratoired’Optique P.M. Duffieux, Unité Mixte de Recherche 6174-16, routede Gray 25030, Besançon Cedex, France. B.-E. Benkelfat is withthe Groupe des Ecoles des Telecommunications—Institut Nationaldes Telecommunications, Laboratoire SAMOVAR, DépartementElectronique et Physique, Unité Mixte de Recherche 5157, 9 rueCharles Fourier, 91011 Evry Cedex, France.

Received 20 July 2005; revised 13 December 2005; accepted 28December 2005; posted 3 January 2006 (Doc. ID 63549).

0003-6935/06/153553-08$15.00/0© 2006 Optical Society of America

20 May 2006 � Vol. 45, No. 15 � APPLIED OPTICS 3553

ture optimized for 1550 nm operation. Section 3 thendescribes our experimental holographic setup, andSection 4 describes details of the fabrication processand presents experimental results. Section 5 containsour conclusions.

2. Principle of Bragg Grating Mirrors

We begin with a short review of the relevant theoryrelating to the design of Bragg grating mirrors, sum-marizing the main results required to determine theconditions associated with the reflection of light by aphase grating. This problem cannot be described by arigorous analytical theory but instead requires a nu-merical approach to simulate the Bragg reflectionphenomenon, and thus optimize the design of a struc-ture for a particular application. Figure 1 shows thebasic structure considered, consisting of a waveguideof index n1 indiffused in a substrate of index n3. Agrating is formed as a result of periodic index modu-lations �n � n2 � n1, and the whole structure isembedded in air with index n0 � 1. The substrateindex is n3 � 2.21, and the grating period is �.

Propagation in this structure can be described bycoupled-mode theory. In particular, from the propa-gation equation

��2 � �2��x, y��Em�x, y� � E�x, y�m2, (1)

the variation of the dielectric permittivity along thewaveguide is described as a linear combination ofpermittivity of the Ti-indiffused substrate �x, y� andthe variations of permittivity along the periodicallyperturbed zone ��x, y�:

�x, y� � 0�x, y� � ��x, y�. (2)

A Fourier expansion of ��x, y� allows us to deducethe coupling coefficient and conditions for phasematching between forward f and backward b trav-eling waves in the waveguide:

f � b � k2�

�, (3)

where k is the coupling order and � is the perturba-tion period. The maximum coupling coefficient is ob-tained when we satisfy the phase-matching conditionf � �c. The value of � that allows total reflection ofa traveling wave is

�Bragg � k�

2neff, (4)

where neff is the effective index of the guided mode.The numerical solution of the coupled-mode theory

can be used to optimize the structural parameters forany particular application. In our case, we have car-ried out a numerical study with the aim of designingBragg reflectors around 1550 nm for telecommunica-tions applications, and the results used in the struc-ture fabrication are shown in Figs. 2–5. Figure 2shows the calculated spectral response of a Braggmirror inscribed in a Ti:LiNbO3 waveguide corre-sponding to periodic variations of index: �n � 3 10�3, Bragg order k � 5, and �Bragg � 1.737 �m.The grating length for this calculation is �5.2 mm� 3000 �Bragg. The simulations also allow the study ofthe exact dependence of the peak reflectivity on struc-tural design. For example, Fig. 3 shows the variationin peak reflectivity on the number of grating periodsused, implying that at least 2500 periods are required

Fig. 1. Light beam is launched in a waveguide (n1) indiffused ina substrate (n3). Periodic index variations modulated the effectiveindex of the guide with an amplitude �n and a period �.

Fig. 2. Spectral response of a Bragg mirror inscribed in a Ti:LiNbO3 waveguide. Periodic variations of index: �n � 3 � 10�3,Bragg order is 5, �Bragg � 1.737 �m, grating length is approxi-mately 5.2 mm (�3000 �Bragg).

Fig. 3. Reflectivity of a Bragg mirror versus the number of grat-ing periods (�n � 5 � 10�3, Bragg order is 5).

3554 APPLIED OPTICS � Vol. 45, No. 15 � 20 May 2006

for near-unity reflectance. Figure 4 shows calcula-tions of peak reflectance as a function of the indexvariation, suggesting that �n � 4 10�3 is requiredfor high reflectivity. Finally Fig. 5 shows how thevariation in the grating periodicity (duty cycle) effectsthe peak reflectivity by perturbing the grating reso-nance. It is clear that a periodicity error of less than5% is essential for good performance characteristics.These results were taken into account in the choice ofparticular fabrication parameters used below.

3. On-Chip Mask for Inscription of Bragg Mirrors

As briefly discussed in Section 1, holographic meth-ods for mask preparation present a number of advan-tages when compared with conventional e-beamlithography techniques. In this section we describefurther details of our experimental technique used torealize Bragg mirrors, based on a holographic mask-ing setup in conjunction with localized proton ex-change in a Ti:LiNbO3 (TiPE) channel waveguide.

A. Description of the Experimental Setup

The Sagnac interferometer is of course well known,being used for fabrication of ring lasers and fibergyrometers for detection of rotational movement withmany applications in inertial navigation.12 Some ap-plications have also been developed in the field ofshearing interferometry,13 holography,14 and opticaldata processing.15 The holographic setup used here isbased on the classic Sagnac configuration with anillumination created by a focused converging beam.16

The setup is illustrated in Fig. 6. Source S is com-posed of a pinhole (diameter of 10 �m) placed at thefocal plane of a 20� microscope objective MO illumi-nated by a laser beam at � � 452.5 nm (Melles-Griot58BLD, power 400 mW cw). The beam emitted fromS is collimated by a lens Lc. A second lens L1 formsthe image of the source S on plane P2 at the inter-ferometer output. The interferometer consists of acube beam splitter �50�50� BS that divides the am-plitude of incident light into two beams propagatingin opposite directions. Beams are reflected by twomirrors tilted at an angle of ��8 in respect to theperpendicular direction to the optical axis of eacharm. Mirror M1 reflects beam 1 at an angle of ��4 inthe direction of mirror M2, which subsequently re-flects it in the direction of the beam splitter thatreflects back at an angle of ��2 in the direction of theinterferometer output. The same path is followed bybeam 2 in the opposite direction. If the distances OO1and OO2 are equal, images S1 and S2 of S formedthrough the interferometer are superposed exactly onplane P2. The optical field observed at the focal planeP3 of lens L2 is uniform and corresponds to a zero-

Fig. 4. Reflectivity versus the periodic phase modulation ofwaveguide by index variations.

Fig. 5. Reflectivity versus the duty cycle error on grating peri-ods.

Fig. 6. Holographic setup is based on a triangular interferometerconfiguration The key symbols used here and in subsequent figuresare MO, microscope objective; S, point source; Lc, collimating lens;L1, focusing lens; BS, beam splitter; M1, M2, mirrors; L2, outputlens; P2, image plane; P3, recording plane.


path-difference pattern (interference with infinitefringe spacing).

Mirror M2 is placed on a precision translation stage(Newport M-UTMMS.1 with a CV1000 controller) al-lowing a linear displacement along the � axis. A dis-placement � of M2 produces a lateral shift of thebeams traversing the two interferometer arms asshown in Fig. 7. The result of this is that imagesS1 and S2 of S, formed through the interferometer,are moved laterally and symmetrically on plane P2.The distance � between S1 and S2 is a function of thevalue �. (The setup then reduces to the well-knownYoung’s double-source configuration.) Point sourcesS1 and S2 are located at the focal plane of lens L2 andform two plane waves, tilted with respect to the axis, which interfere at the plane P3.

B. Geometric Analysis

The evaluation of the fringe spacing can be calculatedby means of simple geometric considerations asshown in Fig. 8. For simplicity, only the on-axis waveis considered. The input wave is divided by a beamsplitter into two waves (1 and 2). They are of equalamplitude and they propagate in opposite directionswith the same optical path length inside the inter-ferometer. The mirrors M1 and M2 are tilted at anglesof ��8 and reflect waves at angles of ��4.

The lateral shift of waves along path 1 and 2 are,respectively, equal to O1d1 and O2d2:

O1d1 � O2d2 � 2� sin��8�; (5)

therefore

��2 � O1d1 cos��8�� O2d2 cos��8�� 2� sin��8�cos��8�, (6)

��2 � � cos��4� � ��2�2. (7)

The angle between the surface waves �1 and �2corresponding to S1 and S2 is

� � arctan� �

2f. (8)

The fringe spacing i is thus given by

i��

2 sin��

�

2 sin arctan��22f

. (9)

Reciprocally, for a fringe spacing determined fromthe reflecting properties of the Bragg mirror, we canobtain the value of the displacement � of mirror M2that must be applied:

��i� �2f

�2tanarcsin� �

2i�. (10)

C. Composite Mask

The holographic configuration exhibits a peculiarproperty due to an optical conjugation between thefocal plane of lens L1 and the output plane of thesetup. The pair of lenses L1 and L2 can be consideredas an afocal device with a magnification coefficient �equal to the ratio of the focal lengths. Consequently,an object transparency placed in the P1 plane is im-aged on the output plane (Fig. 9). The optical functioncorresponding to transparency is multiplied by a pe-

Fig. 7. Linear displacement � of the mirror M2 induces the for-mation of twin sources symetrically with respect to the axis.

Fig. 8. Schematic drawing of light propagation. For simplicity,only an on-axis beam is represented.


riodic function corresponding to the interference phe-nomenon. This property allows us to record in onestep a composite mask. As a typical example of thetype of structure realizable with this technique,Fig. 10 shows an on-chip mask of a integrated Fabry–Perot interferometer composed of a cavity sur-rounded by two Bragg gratings. Further details of theproperties of the Bragg mirror structures themselvesare also given below.

D. Calibration of the Setup

The first operation consists of determining the par-ticular location of M2 for which ��2 � 0 corresponds tothe displacement origin �� 0�. This is carried out byvisual observation of the interference field in planeP3. By moving M2 forwards or backwards, we canlocate the position at which the distance between theinterference fringes tends to infinity, correspondingto zero optical path difference. This position can bemeasured with an accuracy of 0.1 �m.

The second step consists of characterizing the ab-errations of lens L2 according to the lateral shift � ofsources S1 and S2. More precisely, this means that weevaluate the variations in the focal length as a func-tion of �. This measurement is obtained by recordinginterference fringes for different positions of M2. Thepitch of the recorded gratings is measured using adiffraction method. The gratings are illuminated by aspectral lamp �Hg–Cd–Te� and the measurements ofthe angular positions of diffraction orders are ob-tained by means of a goniometer. Therefore, from Eq.(10), we can find variations in the focal length alongthe diameter of lens L2. The experimental setup isbuilt with commercially available optical compo-

nents. A mechanical translation stage that allows adisplacement of M2 with a precision of 0.1 �m en-sures an error on the fringe spacing less than 3 nm.

E. Modification of the Setup to Obtain Chirped Gratings

The initial setup designed to realize periodic gratingscan be modified simply to obtain linear chirped grat-ings as shown in Fig. 11. Chirped gratings can beused to obtain broadband Bragg mirrors with apo-dized wings. A phase plate with index n and thick-ness e is placed behind the beam splitter in the pathof beam 1. By refraction, it produces a displacementof the image S1 onto a plane P2� located behind planeP2. Wave �1 corresponding to S1 is a diverging spher-ical wave that interferes with the plane wave �2 pro-ducing a pseudoperiodic modulation of interferencefringes on plane P3.

The insertion of the phase plate produces a dis-placement P2�P2 of the axial localization of the sourceS2:

P2�P2 � e�1 �1n. (11)

The virtual image S1� of S1 formed by L2 is located ata distance z from the plane P3 and a distance x2 fromoptical axis (see Fig. 12) and has a magnificationcoefficient �:

� �x1

f �x2

z . (12)

Waves �1 and �2 corresponding to S1 and S2 can beexpressed as

�1�x0� � A expj2�

� �x02 � 2x2x0

2z �,

�2�x0� � A exp�j2�

� �x1x0

f �. (13)

Fig. 9. Image of a object transparency (contouring mask) disposedon the P1 plane is displayed at setup output in the P3 plane. Theoptical function associated with the object transparency is multi-plied by a periodic function due to the interference phenomenon.

Fig. 10. Photograph of a Fabry–Perot mask disposed on a Ti-indiffused waveguide. The mask is realized by the composite tech-nique described in Fig. 8: The cavity is obtained by the imaging ofa tranparency disposed on the P1 plane and gratings that sur-rounded the cavity.


Interference between �1 and �2 on plane P3 producesan optical field with an intensity distribution de-scribed by

I�x0� � ��1�x0� � �2�x0��1�x0� � �2�x0��*, (14)

I�x0� � 2A1 � cos2�

� ��x1x0

f �x0

2 � 2x2x0

2z ; (15)

and fringe spacing p(m) corresponding to an interfer-ence order m is thus expressed by

p�m� � �4y2z2 � 2m�z � �4�2z2 � 2�m � 1��z. (16)

This in fact results in a near-linear dependence offringe spacing versus interference order as shownin Fig. 13. The parameters used in calculating

this curve are f � 31 mm, n � 1.45, e � 6 mm,� � 452.5 nm, x1 � 4.01 mn.

4. Fabrication Process

To obtain maximum reflectivity with a Bragg grating,it is necessary to implement a periodic dielectricwaveguide with a significant index and�or lengthperturbation. The simulations indicate also that thefilter bandwidth is inversely proportional to gratinglength. One of the ways to increase and control thecoupling coefficient of the grating is to produce a largeand variable index modulation. The proton-exchangeprocess17 is expected to produce large changes in re-fractive indices: the extraordinary index increases��ne max �0.12� while the ordinary index decreasesby �0.04. This large and controllable change in re-fractive index will allow fabrication of high-efficiencyBragg filters.

Results of fabrication and characterization of proton-exchanged optical waveguides in X-cut, Y-cut, and Z-cutLiNbO3 have already been presented.18,19 The protonexchange takes place when a substrate is immersedin a proton source such as molten benzoic acid.Proton-exchanged waveguides present a steplike re-fractive index profile. They support only the TM modein Z-cut material and the TE mode in X- and Y-cutmaterials. The depth of the proton-exchanged layer isdetermined by immersion time and the diffusion co-efficient D(T) at different temperatures. Several au-thors20 have reported the diffusion coefficients ofTiPE layers for various melt temperatures. The maindrawback of the proton-exchange process is a largescattering loss when compared with the titanium dif-fusion process. One of the ways to reduce undesirableeffects is to anneal the samples in wet air at a tem-perature between 250° and 400 °C with a time rang-ing from minutes to hours. Such an annealing processincreases the depth of the proton-exchanged layerwhile reducing �ne. This results in more controllablerefractive index profiles.

Proton-exchanged grating waveguides were imple-mented in several steps as illustrated in Fig. 14. Inthe first step, single-mode optical waveguides inthe 1550 nm window were fabricated on Z-cut

Fig. 11. Modification of the basic holographic setup by insertion ofa phase plate to obtain a chirped grating.

Fig. 12. Phase plate displaces the location of image S1 from planeP2 to plane P2=. The fringes observed on plane P3 come from inter-ference between a plane wave �2 and a spherical wave �1.

Fig. 13. In a first approximation, values of fringe spacing versusinterference order can be considered as varying linearly.


(Y-propagating) LiNbO3 substrates by standard dif-fusion of 80 nm thickness and 7 �m wide Ti layers at1100 °C during 10 h in a wet Ar-O2 flow. Next, a200 nm thick SiO2 layer was deposited on the wave-guide to realize an on-chip proton-exchange masklayer. SiO2 was chosen for its excellent proton diffu-sion blocking, good adhesion to the substrate, andease of deposition and etching. The holographic maskis directly written in a resist layer deposited on a SiO2layer. The pattern was transferred in the SiO2 layerby chemical (or reactive ion) etching, and a electron-beam microscope photograph is shown in Fig. 15. Forthese results, the corresponding mask period is1.76 �m. The proton exchange was performed in mol-ten benzoic acid, and finally the SiO2 mask was re-moved by chemical etching. The waveguide wassubsequently annealed21 in wet air. As a conse-quence, the electro-optic effect is restored and prop-agation losses reduced.

The experimental parameters of the proton ex-change and annealing process are based on thepreliminary investigations (e.g, refractive index pro-file) that have been carried out on planar TiPEwaveguides in Z-cut LiNbO3 substrates. Sampleswere proton exchanged at a temperature between150° and 230 °C with a range time from 1 to 4 h. Theannealing process was performed at various temper-atures (from 250 °C to 400 °C) with different times(from 10 min to 3 h). To assess the spectral responseof the Bragg gratings, we employed a narrow-

bandwidth tunable �1510–1590 nm� laser diode(Tunics 1 mW) and a powermeter (ILX Lightwave) tomeasure the output power. Figure 16 shows the re-sults of this experimental characterization of theBragg gratings where we see strong narrowbandtransmission at the design wavelength of 1546 nmand a 3 dB transmission width �5 nm, in good agree-ment with the initial numerical design criteria.

5. Conclusion

The holographic setup described in this paper is de-signed to create periodic or pseudoperiodic patternson the surface of an integrated optical component,and has particular interest for use in the first stage offabrication of periodic and aperiodic distributed pa-rameter waveguides. The particular advantage of thesetup is that it enables a precise adjustment of fringespacing of an interference pattern. After a transfer ona photosensitive resist, it can be used to fabricate anon-chip photolithographic mask. Period adjustmentis made by adjustment of a single linear displace-ment. An accessible range of fringe spacing can be

Fig. 14. Experimental process employed to realize periodic vari-ations of index into the Ti:LiNbO3 waveguide.

Fig. 15. MEB photograph of a SiO2 mask on a surface of a LiNbO3

substrate (mask period is 1.76 �m).

Fig. 16. Spectral response of a 4 mm periodic distributed param-eter Ti:LiNbO3 waveguide. Peak reflection is observed at 1.546 �mwith an amplitude value of 94%. The sample was proton exchangedthrough a SiO2 periodic mask for 3 h at 230 °C and annealed at400 °C for 1 h and 10 min.


extended from several centimeters to a few hundrednanometers. The triangular configuration of the ho-lographic setup, in which two beams propagate inopposite directions, ensures perfect and rigorousequality of the lengths of optical paths in each arm.This characteristic makes the setup insensitive toexternal disturbances such as mechanical vibrationsor refractive index perturbations of air. The equalityof the optical paths in both arms of the interferometermeans that it can be equally used for both cw orpulsed optical sources.

We have also reported an implementation of theproton-exchange technique for fabrication of Bragggrating reflectors in Ti:LiNbO3 waveguides. This pro-cess offers great flexibility and simplifies fabricationsteps. Experimental results are in good agreementwith the modeling of the grating for which, in partic-ular, a reduction of its bandwidth is expected withoptimized technology parameters.

The annealing process reduces the refractive indexmodulation ��0.12� induced by proton exchange andthen allows the increase of the effective length of thedistributed parameter waveguide. Investigations arecurrently being carried out to improve reflector uni-formity and to reduce the grating period in the nano-meter range. Patterned proton-exchanged technologycan also be used to realize optical waveguide reflec-tors and tailored optical filters with specific spectralresponse characteristics.

We thank the ACI Nanosciences Committee of theFrench Ministry of Research for financial support.

References1. A. Yariv and M. Nakamura, “Periodic structure for integrated

optics,” IEEE J. Quantum Electron. 13, 233–251 (1977).2. C. Becker, A. Greiner, T. Oesselke, A. Pape, W. Sohler, and H.

Suche, “Integrated optical Ti:Er:LinbO3 distibuted Bragg re-flector laser with fixed photorefractive grating,” Opt. Lett. 23,1194–1196 (1998).

3. B. K. Das, R. Ricken, and W. Sohler, “Integrated optical dis-tributed feedback laser with Ti:Fe:LiNbO3 waveguide,” Appl.Phys. Lett. 82, 1515–1517 (2003).

4. J. Söchtig, “Ti:LiNbO3 stripe waveguide Bragg reflector grat-ings,” Electron. Lett. 24, 844–845 (1988).

5. B. Wu, P. L. Chu, H. Hu, and Z. Xiong, “UV-induced surface-relief gratings on LiNbO3 channel waveguides,” IEEE J.Quantum Electron. 35, 1369–1373 (1999).

6. Y. Sidorin and A. Cheng, “Integration of Bragg gratings onLiNbO3 channel waveguides using laser ablation,” Electron.Lett. 17, 312–314 (2001).

7. N. Takeshima, Y. Kuroiwa, Y. Narita, S. Tanaka, and K. Hirao,“Fabrication of a periodic structure with a high refractive-index difference by femtosecond laser pulses,” Opt. Express 12,4019–4021 (2004).

8. G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragggratings in optical fiber by a tranverse holographic method,”Opt. Lett. 14, 823–825 (1989).

9. T. Taunay, P. Bernage, M. Douay, W. Xie, G. Martinelli, P.Niay, J. Bayon, E. Delavaque, and H. Poignant, “Ultraviolet-enhanced photosensitivity in cerium-doped aluminisilicate fi-bers and glasses through high-pressure hydrogen loading,”J. Opt. Soc. Am. B 14, 912–924 (1997).

10. K. O. Hill, Y. Fujii, D. C. Jonhson, and B. S. Kawasaki, “Pho-tosensitivity in optical fiber waveguides: application to reflec-tion filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).

11. H. Patrick and S. L. Gilbert, “Growth of Bragg gratings pro-duced by continuous-wave ultraviolet light in optical fiber,”Opt. Lett. 18, 1484–1486 (1993).

12. P. Hariharan, “Sagnac or Michelson–Sagnac interferometer?,”Appl. Opt. 14, 2319–2321 (1975).

13. P. Hariharan and D. Sen, “Triangular path interferometer,” J.Opt. Soc. Am. 49, 1105–1106 (1959).

14. G. Cochran, “New method of making Fresnel transforms withincoherent light,” J. Opt. Soc. Am. 56, 1513–1517 (1966).

15. D. N. Grimes, “Optical correlator with special application toMTF measurement,” Appl. Opt. 11, 914–918 (1972).

16. R. Ferriere and B. E. Benkelfat, “Novel holographic setup torealize on-chip photolithographic mask for Bragg grating in-scription,” Opt. Commun. 206, 275–280 (2002).

17. J. L. Jackel, C. E. Rice, and J. J. Veselka, “Proton exchange forhigh index waveguide in LiNbO3,” Appl. Phys. Lett. 47, 607–608 (1982).

18. M. De Micheli, J. Botineau, S. Neveu, D. B. Ostrowsky, and M.Papuchon, “Independent control of index and profiles inproton-exchanged lithium niobate waveguides,” Opt. Lett. 8,114–115 (1983).

19. P. G. Suchoski, T. K. Findakly, and F. J. Leonberger, “Stablelow-loss proton-exchanged LiNbO3 waveguide devices with noelectro-optic degradation,” Opt. Lett. 13, 1050–1052 (1988).

20. A. L. Dawar, S. M. Al-Shukri, R. M. De La Rue, A. C. G. Nutt,and G. Stewart, “Fabrication and characterization of titaniumindiffused proton exchanged optical waveguides in z-cutLiNbO3,” Opt. Commun. 61, 100–104 (1987).

21. G. E. Betts, F. J. O’Donnell, and K. G. Ray, “Effect of annealingof photorefractive damage in titanium-indiffused LiNbO3 mod-ulators,” Photon. Technol. Lett. 6, 211–213 (1994).


bragg mirror inscription on linbo3 waveguides by index microstructuration

Documents