applications of compound fiber bragg grating structures in lightwave

Applications of compound fiber Bragg grating structures

in lightwave communications

by

Lawrence R. Chen, M. A. Sc.

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Graduate Department of Electrical and Computer Engineering University of Toronto

O Copyright by Lawrence R. Chen 2000

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A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

The Graduate Department of Electrical and Cornputer Engineering University of Toronto

Lawrence R. Chen

Doctoral Cornmittee

Professor T. E. van Deventer Department Chair Representative

Professor P. W. E. Smith Thesis Supervisor

Dr. K. O. Hill Extemal Examiner

Professor E. H. Sargent Voting Member

Professor P. R. Herman Voting Member

Professor F. R. Kschischang Voting Member

To m y family and for Brutus



A thesis for the degree of Doctor of Philosophy Lawrence R. Chen

Graduate Department of Electrical and Computer Engineering University of Toronto

Photonic networks have been identified as one solution that can satise

the growing demand for bandwidth due to increased Internet traflic and the

information superhighway. New enabling photonic technologies will be required

in order to successfidly implement, operate, and manage these dl-photonic

networks. In this thesis, we develop fiber Bragg grating technology for realizing

photonic components that can perform a wide variety of optical signal processing

fùnctions for aggressive network management and performance requirements.

First, we show how to tailor the spectral response of chirped moiré fiber

Bragg gratings so that they can be used as transmission passband filters. We

have fabricated filters having near ideal filter response which will be usefbl for

providing wavelength selectivity in wavelength-division-multiplexed and

wavelength routing networks.

Second, we demonstrate the first hybrid wavelength-encoding/time-

spreading optical code-division multiple-access system using chirped moiré fiber

Bragg gratings for encoding/decoding. Limitations imposed by the etectronic

bottleneck due to optical-to-electricd and electrical-to-optical conversions are

overcome since al1 encoding/decoding operations are performed all-optically.

Third, we realize a simple and cost-effective means usîng serial fiber

Bragg grating arrays for performing power equalization among different

wavelength channels in an erbium-doped fiber amplifier module. Such a module

will be critical for compensating the deleterious effects of gain nonuniformity

and transients in wavelength-division-multiplexed or wavelength routing

networks.

Finally, we demonstrate two different actively mode-locked erbium-doped

fiber lasers that simultaneously emit two wavelengths with stable room-

temperature operation. Wavelength spacings of 1.8 nm and 0.7 n m have been

achieved-the closest reported to date. These lasers will find applications in

high-performance transmission systems seeking to exploit combined wavelength-

division-multiplexingltime-division-multiplexing access and as a diagnostic tool

for photonic device testing/characterization.

ACKNOWLEDGIMEIUTS

This thesis presents a great deal of work which could not have been

completed (especially within my time constraints) without the encouragement,

support, and assistance of numerous people.

1 would like to thank my supervisor, Professor Peter Smith, for his advice

and guidance thmughout the course of my graduate studies. It has indeed been

a pleasure and honour to work with hun. He showed great confidence in my

abilities and gave me fieedorn to develop the independence that will undoubtedly

serve me well in my fùture endeavours.

1 thank the members of my supervisory committee for their comments and

suggestions as well as Dr. Kenneth Hill for serving as an extemal reviewer.

I would like to express my gratitude to two former members of OUT lab, Dr.

Seldon Benjamin and Dr. Hany Loka. 1 have acquired a great deal of

experimental skills fkom Seldon, who was always willing to lend a hand. 1 have

also learned fiom Hany's numerous experiences (and mistakes) and am grateful

to have him as a close, personal fiend.

1 certainly appreciated the extremely niendly environment that 1 had to

work in. My colleagues, Mr. David Cooper, Ms. Li Qian, Mr. Thomas Szkopek,

and Ms. Vani Pasupathy were always willing to lend a hand or a sympathetic

ear.

It is with pleasure that 1 acknowledge Dr. Robin Tarn (Photonics Research

Ontario) and Dr. Xijia Gu (E-TeklElectroPhotonics) for their patience in teaching

me the art of writing fiber gratings. 1 have benefited tremendously fkom their

experience.

1 would like to thank Dr. Martijn de Sterke (University of Sydney) for

introducing me to the concept of chirped moiré gratings during his visit to

Toronto. Certainly a great deal of the research presented in this thesis was

stimulated by ou. initial discussion on the optical properties of these grating

structures.

1 am very gratenil for having had the opportunity to work with several

visiting researchers in our lab. In particular, a special thanks goes to Dr.

Graham Town (University of Sydney) whose ideas initiated the work presented

in Chapter 7 of this thesis. 1 have learned a great deal from his experimental

expertise in fiber lasers. 1 would also like thank Mr. José Azaiïa (Universidad

Politecnica de Madrid) for the numerous stimulating discussions that we had,

and for introducing me to the-fkequency representations and their applications

to the analysis of fiber gratings.

1 thank Prof. Sophie LaRochelle and Dr. Pierre-Yves Cortès for fabricating

the serial grating arrays used in the experiments on the mode-locked fiber laser,

and for their generous hospitality during my stay at Université Laval.

Much of the experimental work presented in this thesis could not have

been performed without the following support. First, 1 thank E-

TeWElectroPhotonics, in particular Dr. Donna Zhou and Dr. Ming Gang Xu, for

making available the resources to do group delay measurements. Second, 1 a m

indebted to Prof. John Cartledge (Queen's University) for dlowing me access to

his 2.5 Gbit/s bit-error-rate test system and for his assistance with the

measurements. Third, 1 thank M.. Jaro Pristupa and Prof. C. Salama

(University of Toronto) for allowing me use of their pattern generator. Finally,

the Electromagnetics Croup (Universi@ of Toronto), especially Mr. Gerald

Dubois and Prof. John Long, were always willing to lend me the various bits of

equipment that were necessary in my experiments.

1 gratefully acknowledge financial support nom the Natural Sciences and

Engineering Research Council of Canada, the University of Toronto, the Walter

C. Sumner Foundation, and a V. L. Henderson Research Fellowship.

1 could not have completed this thesis without the support and

entertainment provided by my friends, Rabih Abouchakra, Eric Hazan, Mike

Vinke, Diego Batelich, Ayman Ghanem, Mae Abdalla, Margaret Cho, Natasha

Knechtel, and especially Malak Wahba.

Finally, last but not least, 1 thank my family for their unconditional love,

support, and constant encouragement. It is with them that 1 share this great

accomplishment.

Table of Contents

Chapter 1 Introduction

1.1. Motivation 1.2. Contributions and organization of thesis

Chapter 2 Fiber Bragg Gratings

2.1. General description 2 -2. Historical perspectives 2.3. Origin of photosensitivity

Colour center nodel Dipole model Compaction rnodel Stress- relief rnodel

2 -4. Fabrication techniques Bulk interferometer Phase mask technique Phase mask interferometer Scanning phase mask interferomter Point-by-point writing Types of gratings

2.5. Sources for writiag fiber gratings 2.6. Theory of fiber gratings

Wave equation Coupled-mode equations and the transmission mat&

Chapter 3 Chirped Mollé Gratings: Background

3.1. Grating resonator structures and chirped moiré gratings Fiber Bragg grating Fabry-Pérot Phase-shif2ed fiber Bragg grating Moiré phase-shified fiber Bragg grating Chirped Fabry -Péret resonators Chi rped moiré grating

3 -2. Fabrication of chirped moiré gratings

Chapter 4 Chirped Moiré Gratings for Wavelength-Division- Multiplexing

4.1. Filter requirements for WDM systems 57 4.2. Tailoring the spectral response of chirped moiré gratings for 58

bandpass filtering Principle of operation 59 Simulation results: spectral and group &lay responses 61 Cornparison with other fiber Bragg gmting-bwed filters 65

4.3. Experimental results 70 4.4. Discussion 75

Chapter 5 Chirped Moiré Gratings for Optical Code-Division Multiple-Gccess

5.1. Introduction 5.2. Ultrashort pulse reflection fiom CMGs 5.3. CMGs for encoding/decoding pulses

Qualitative &scription and implementation Numerical example: simulation Code design

5.4. Analysis of the proposed system Perfiormance Practical Issues

Fabrication of specially designed CMGs Chromatic fiber dispersion Time-gating Reconfigurability Other factors

5.5. Experimental results 5.6. Discussion and summary

Chapter 6 Transmission Edge Filters for Gain Equalization

6.1. Introduction 6.2. Transmission edge filters for gain equalization 6.3. Experimental results 6.4. Discussion

vii

Chapter 7 Multi-wavelength, Actively Mode-locked Erbium-Doped Fiber Lasers

7.1. Introduction 143 7.2. Design concept 148 7.3. First configuration based on chirped gratings and a 150

transmissive CMG 7.4. Second configuration using serial fiber Bragg grating arrays 156 7.5. Discussion 161

Chapter 8 Conclusion

8.1. Summary and conclusions 8.2. List of publications 8.2. Future work

References

List of Figures

2.1. Schematic representation and principle of operation of a fiber Bragg grating [4].

2.2. Diffraction of a light wave by a grating (101.

2.3. Ray-optic illustration of core-mode Bragg reflection by a fiber Bragg grating. The $-axis demonstrates the grating condition in Eq. (2.2) for m = -1. ncr and fi. are respectively the refractive index of the cladding and core of the optical fiber [IO].

2.4. UV absorption spectra before (solid line) and afkr (dashed line) writing an 81% peak reflectivity grating in an AT&T Accutether single-mode fiber. The squares denote the change in attenuation [211.

2.5. (a) Holographic setup for writing fiber Bragg gratings [4]. (b) Formation of a refractive index modulation proportional to the interference pattern of two UV beams in the core of an optical fiber [9].

2.6. Arrangement for formation of nonuniform gratings by the interference of two dissirnilar wavefkonts using cylindrical lenses in each a m of the interferometer [9 1 .

2.7. The Lloyd mirror interferometer [3].

2.8. Fabrication of gratings using the phase mask technique [18].

2.9. Phase mask used as a beam splitter in an interferometer for inscribing fiber Bragg gratings [3].

2.10. Phase mask used as a scanned interferometer [3].

2.11. Point-by-point writing of fiber gratings (41.

3.1. Illustrating the different configurations of FBGbased resonators: (a)FBG-based Fabry-Pérot, (b) phase-shifted FBG, (c) moiré phase-shifted FBG, (d) c hirped Fabry-Pérot resonator, and (e) chirped moiré grating .

3.2. (a) Caiculated transmission response of PS-FBGs having different values of phase-shift: $ = it/4 (dotted line), 9 = ir/2 (solid line), and @ = 3d4 (dashed line).

(b) nlustrating the effect of apodization on the transmission response of phase-shifted FBGs: d o m grating (solid line) and Gaussian apodization (dashed iine). The grating is 1 .O cm long with a grating period A = 533.747 n m and 6n = 2.5 x 104.

Illustrating the formation of a moiré grating 1421.

Calculated transmission response of a moiré PS-FBG. The grating is composed of two 1.0 cm long uniform FBGs having equal peak refractive index modulations hi = 6nz = 2.5 x 104 . The grating periods are Al = 533.747 nm and An = 533.802 nm.

Schematic of a wide-band chirped Fabry-Pérot resonator [45].

Calculated transmission response of a CFPR. The two linearly chirped FBGs comprising the CFPR are 8 mm long, each with a grating period A = 533.747 nm, chirp of 2 &cm (dl\ = 4.59 x 10-14 mVm) and equal peak refkactive index modulations &z = 5 x 104. (a) & = 12 mm and (b) 6z = 6 mm.

Illustrating the effects of varying the grating parameters on the spectral response of a CMG. In al1 three cases, the grating length is L = 3.0 cm and the chirp parameter is dA = 3.0 x 10-14 mVm. The other parameters are (a) peak refkactive index modulation 6n = 2 x IO-' and wavelength separation = 0.2 nm, (b) same as (a) except &z = 5 x IO4, and (cl same as (a) except AA = 0.4 nm.

Fabrication of chirped moiré gratings using dual-exposure of a single non-dedicated linearly chmped phase mask. The fiber is stretched between the two exposures [49].

Experimental measured (dotted line) and theoretically calculated (solid line) transmission response of a typical CMG w e fabncated. The parameters used to simulate the grating response are given in the text.

Embedding regions of constant refractive index in a CMG stnicture in order to obtain flattened passbands: (a) original CMG structure, (b) one region, (c) two regions, and (d) three regions embedded. The shaded regions marked by A2 have constant refiactive index; the hatched ones re~resent oriPinal sections fkom the CMG.

(a) - (g). Illustrating the eEects of introducing regions of constant 63,64 refractive index modulation in a CMG on the transmission response. The refractive index modulations of the new CMG structures appear in the leR column and the corresponding calculated transmission (solid üne) and group delay (dashed line) appear in the right column. The grating parameters are given in the text.

Calculated spectral response (solid line) and group delay (dashed line) of the five FBG filters whose phase responses are being compared. Reflection filters: (a) Gaussian apodization, (b) Blackman apodization, and (cl Gaussian + sinc apodization; transmission filters: (d) multiple- phase-shifted FBG and (el chirped moiré grating with one flattened passband. The heavy solid tines denote the 3 dB BW of the filters. The grating parameters are given in the text.

Calculated pulse broadening as a function of detuning.

Fabrication of CMGs with flattened passbands by dual-exposure of a chirped phase mask in conjunction with amplitude masks.

Experimentally measured transmission spectra (solid line) and group delay (dashed line) of CMGs fabricated to have a single or two flattened passbands: (a) Grating 1, corresponding to that in Fig. 4.2(b), (b) Grating 2, corresponding to that in 4.2(c), and (c) Grating 3, corresponding to that in Fig. 4.2(d).

Experimental setup for rneasuring BER of CMG filters.

(a) Measured transmission (solid line) and group delay (dashed line) of the CMG filter used in 2.5 Gbitls power penalty experiments; (b) measured power penalty at BER = 10-9 as a function of wavelength within the filter passband.

(a) Spectral phase encoding using an encoder based on a segmented fiber gratings (941. (b) Fast-nequency hopping using an encoder consisting of a serial Bragg grating array 1891.

Calculated reflection response of a 3 cm long CMG with ôn = 8.0 x IO-', AA = 0.2 nm, and equal chirp parameters &Al = 6A2 = 5.0 x 10-14 m*/m: (a) amplitude and reflected group delays for light incident on (b) the short wavelength and (c) long wavelength sides. The discontinuities in the group delay occur where the phase of the reflection coefficient changes by IC and the polarity is arbitrary.

Measured reflection response (solid line) and group delay (dashed line) 90 of (a) Grating 1, (b) Grating 2, and (c) Grating 3. These are the corresponding reflection responses for the three gratings shown in Fig. 4.6.

Time-fkequency representations of a short broadband input pulse 91,92 reflected nom (a) Grating 1, (b) Grating 2, and (c) Grating 3. The input is a transform-limited 0.5 ps Gaussian pulse incident on the short wavelength side of the gratings.

Measured reflection response fkom (a) Grating 1 (input pulse at A = 1542.35 nm), (b) Grating 2, (input pulse at A = 1542.9 nm), and ( c ) Grating 3 (input pulse at k = 1542.75 nm). The input is incident on the short wavelength side (solid iine) and the long wavelength side (dashed line).

Schematic illustration of (a) encoding and (b) decoding an ultrashort 95,96 broadband pulse using CMGs. The CMG is modeled as a multi- wavelength filter (or discrete set of wavelength filters) with corresponding time delay lines for each filtered wavelength component. Different users (codes) are defined by different spectral slicing patterns (Le. different wavelength filters) and their corresponding time delay patterns.

Schematic illustration of encoding and decoding processes. 98,99 (a) proper decoding of desired user, &) decoding an interferer having a strictly orthogonal code relative to the desired user, and (c) decoding an interferer having a quasi-orthogonal code relative to the desired user.

Implementation of CMG encoders/decoders in an OCDMA system. 100

Simulation of encoding a 0.5 ps transform-limited Gaussian pulse. 103 (a) spectral response of the CM& corresponding to the three codes outlined in the text and (b) corresponding encoded waveforms. The dotted lines in (a) show the wavelength bands and in (b) show the time slots (chips).

5.10 Simulation of proper and improper decoding of encoded waveforms 104 in Fig. 3b. Decoded waveforms: (a) cf (2) , (b) c,d (r) , and (c) cf (t) ; (dl the decoded waveform of c d t ) + cz(t) + c3(t). Note the similarity with cf (t) ; additional multi-user interference can be suppressed by time-gating. Al1 decoding was performed with the decoder for code C I .

The dotted lines show the time slots (chips).

5.11. Time-fkequency plots illustrating (a) the encoding and (b) proper 105 decoding processes. Note the difference in the time axes between the t w o plots.

5.12. P,,, as a h c t i o n of number of simultaneous users. 112

5.13. Number of simultaneous users at P e m r = 10-9 as a fiinction of code 113 length (N) for w = 3.

5.14. Experimental setup for demonstrating WE/TS OCDMA system using 120 CMGs. EDFA: erbium-doped fiber amplifier, W O MOD: electro-optic modulator, DSO: digital sampling oscilloscope, OSA: optical spectrum analyzer, TD: time delay, BPF: bandpass filter.

5.15. (a) Measured spectra of CMG encoders: desired user (solid line), 121 interferer 1 (dashed line), interfeer 2 (dotted line), interferer 3 (dash-dot line). (b) Comparing the spectral output of the decoder for the case when the desired user is transmitting only to the case when only a single interferer is transmitting: (i) interferer 1, (ii) interferer 2, and (iii) interferer 3.

5.16. (a) Measured encoded and decoded waveforms for the desired user. 123 The insets show the simulated temporal waveforms (including the = 100 ps detection response tirne) with the same time scale as the measurements. (kt) Measured temporal output of decoder for different users transmitthg.

5.17. Demonstrating the encoding and decoding of an RZ 8-bit pattern 125 "O O 1 O 1 1 O O" at 622.08 Mbit/s.

5.18. Measured eye diagrams of the output of the decoder: (a) only desired 126 user transmitting, (b) desired user and interferer 1 transmitting, (c) desired user and interferer 2 transmitting, (d) desired user and interferer 3 transmitting, and (e) al1 users transmitting.

6.1. Calculated transmission spectral (solid lines) of a tanh apodized and a 133 sin* apodized linearly chvped FBG, each having a background refractive index corresponding to its apodization profile. Also shown are the corresponding calculated group delays in transmission (dotted lines).

6.2. Schematic of using transmission edge filters for power equalization 135 among multiple WDM channels amplified by an EDFA.

Propagation of transfonn-limited Gaussian pulses through the transmission edge filter whose response is shown in Fig. 6.l(a). (a) The input pulse (solid line) is 10 ps long (corresponding 3 dB BW = 0.35 nm); the output pulses are for an input centered at 1549.2 n m (dashed line) and 1549.5 n m (dotted line). (b) The input pulse (solid line) are 5-ps long (corresponding 3 dB BW = 0.7 nm) and the output pulse (dashed line) is for an input centered at 1549.5 nm.

Typical spectral response of transmission edge filters fabricated: 139 spectrum (solid line), group delay (dotted line). (b) Amplitude variation of grating response over linearly-ramped edge fkom the ideal linear edge with slope - 13 dB/nm. Corresponding measured variation in relative transmitted power as a function of applied strain.

Illustration of transmission edge filters for providing power 140 equalization. Spectra of (a) input signals to EDFA, (b) output signals from EDFA with no power equalization, and (c) power equalized output. The additional 3 dB loss between the spectra in (b) and (c) is due to splicing loss between the EDFA and the gratings and not insertion loss of the gratings.

Schematic of dual-wavelength, actively mode-locked EDFL using temporal-spectral multiplexing. EOM: electro-optic modulator; WDM: 980/1550 n m coupler; EDFA: fiber amplifier; PC: polarization controller; LCFG: linearly chirped FBG; OSA: optical spectnun analyzer; PD: photodetector connected to digital sampling oscilloscope.

Measured spectral output of mode-locked EDFL showing the stable operation of two lasing wavelengths at 1544.6 nm and 1546.4 nrn with equal output power.

Measured temporal output of the laser. The upper trace shows the total intensity of the laser output. The lower traces show the temporal output for each lasing wavelength, obtained suing a tunable bandpass filter on the output of the 10% coupler.

Dual-loop configuration for multi-wavelength generation in an actively mode-locked EDFL using a serial FBG array [141].

Modified laser configuration for generating multiple wavelengths fkom an actively mode-locked EDFL.

xiv

7.6. Characteristics of the two serial grating arrays used in the laser: 159 (a) reflection spectnim and (b) group delay for light incident on the long wavelength side. Serial FBG array 1: top traces, serial FBG array 2: bottom traces.

7.7. Repeated scan of the spectral output of the laser showing stable, 160 dual-wavelength operation.

7.8. Measured temporal output of the laser measured. The upper trace 160 shows the total intensity of the laser output. The lower traces show the temporal output for each lasing wavelength ( h = 1532.06 nm, solid line; A = 1532.79 nm, dotted lîne), obtained using a tunable bandpass filter on the output of the 10% coupler.

List of Tables

5.1. Maximum number of codes and original rn codes for the different cases 113 used in the performance analysis.

Chapter 1

Introduction

1.1. Motivation 1.2. Contributions and organization of thesis

1.1. Motivation

We have reached the "tera-era". Only two decades ago, it was thought

unfathornable that the vast potential carrying capacity of optical fibers would

ever be required. However, we continually witness an explosive growth in

bandwidth demand (which approximately doubles every year) due to increased

Internet traffic fiom consumers requesting more and more data and information

of various types (voice, video, graphies, and multimedia) to be transferred over

communication networks.

T t has been recognized that the only way to accommodate current and

projected growth in bandwidth demand is to use photonic networks. Photonic

networks will be required to carry increasingly large amounts of data and it has

become evident that new optical network designs relying on new enabling

photonic technologies are needed to satisQ the bandwidth demand, especially at

the access points. Metropolitan Area Networks, Wide Area Networks, Storage

Area Networks, and Local Area Networks represent tributaries on the long-haul

photonic backbone which need to access the massive = 10 THz bandwidth

provided by the optical fiber. Currently, these access networks represent a

bottleneck in the interconnection network primarily due to

Chapter 1-Introduction 2

limitations in electronics and the tremendous burden imposed on them. While

forthcoming silicon integrated circuits are projected to operate at 10 GHz, this is

still three orders of magnitude less than the = 10 THz capacity of optical fibers.

There is clearly a need to multiplex low data rate streams onto the optical fiber

in order to increase the total system throughput and to manage the traffic

passing through the access nodes and networks.

All-photonic access networks are considered the most promising access

networks since they reduce the effects of the electronic bottleneck by minimizing

the number of electrical-to-optical and optical-toelectrical conversions. These

networks will rely on multi-access schemes which are needed for multiplexing

and demultiplexing traffic carried on a shared transmission medium L e . , optical

fiber). The three basic access techniques are wavelength-division-multiplexing

(WDM), time-division-multiplexing (TDM), and code-division multiplexing or

code-division multiple-access (CDMA). In WDM, each channel occupies a narrow

bandwidth centered about a specified carrier fkequency (or wavelength).

Furthermore, the modulation format and speed of a given channel are

independent of the other channels. In TDM, each channel occupies a time slot

which is interleaved with tirne slots &om other channels. Al1 channels are

transmitted on the same carrier fkequency. In CDMA, each channel occupies the

same fkequency and time space as the other channels; they are distinguished on

the basis of channel-specific (or user-specific) codes.

To achieve the requirements of an all-optical access network and network

management objectives, new enabhg component technologies will be required.

Active and passive elements, which can perform basic optical signal processing

b c t i o n s such as generating, routing, switching, and detecting the information,

are needed and in particular the following are critical:

optical filters for performing wavelength selective operations to facilitate

wavelength routing. These optical filters can be incorporated in

wavelength-add-drop-modules or in wavelength-cross-connects and

should enable WDM system performance with minimal penalty, Le., low

insertion loss, high channel selectivity (low channel cross-talk), and

minimum signal distortion due to filter dispersion.

dl-optical means to encodddecode signals to implement optical CDMA

(OCDMA). This will minimize the amount of electronic processing

required and high aggregate data rates are possible by designing the

system to support many users, each operating at a moderate rate.

devices that can be used to provide dynamic (active) power equalization

among different WDM channels aRer they have been amplified by a

single erbium-doped fiber amplifier (EDFA) or cascade of EDFAs. These

are necessary to compensate the nonuniform EDFA gain spectrum to

ensure that al1 WDM channels maintain high signal-to-noise ratios and

do not exceed the dynamic range of the receivers.

Chapter l-htroduction 4

optical sources capable of generating short pulses a t multiple

wavelengths. These sources are required for high-performance

transmission systems seeking to exploit combined WDMPTDM access

techniques or as a diagnostic tool for testingkharacterizing photonic

devices.

In recent years, fiber Bragg gratings (FBGs) have emerged as critical

components for enabling high-capacityhigh-speed transmission since their

response can be tailored to meet the needs of specific applications. Their

wavelength selective properties make them ideal for a number of optical filtering

applications including channel add/drop, wavelength routing, and taps for

network performance monitoring. They have also been incorporated with

EDFAs to produce single and multi-wavelength fiber lasers, both continuous

wave (cw) and mode-locked operation, and used in extemal cavity lasers. Their

dispersive properties make them suitable for dispersion compensation or pulse

shaping. They have also been used for gain flattening of the wavelength-

dependent gain spectrum of EDFAs and incorporated in more sophisticated

structures for performing various other signal processing functions. The above

list is far nom complete and in fact, the applications and possibilities in designs

of new grating structures are seerningly endless and continually attract

considerable research interest. This is evidenced by conferences [l], special

journal issues [2], and the recent publication of two textbooks solely devoted to

FBG technology [31, [4].

1.2. Contributions and organization of thesis

In this thesis, we focus on FBG technology for developing functional devices

that support future photonic networks. In particular, we propose, analyze, and

demonstrate novel applications of FBGs in lightwave communications. We

consider two types of compound FBG structures. The f i s t involves

superimposed linearly chirped FBGs, or chirped moiré gratings (CMGs), while

the second comprises physically separate FBGs, also known as a serial FBG

array (or cascaded FBGs). The significant contributions of this thesis include:

the design and realization of transmission bandpass filters having

near-ideal filter responses based on CMGs. These filters have flat

tops, high channel isolation, constant in-band group delay (they are

essentially dispersionless), and operate directly in transmission

without the need for incorporating them in sophisticated

interferometric structures or using circulators. They will have critical

roles in providing wavelength-selectivity in WDM and wavelength

routing networks.

the fkst demonstration of a novel hybrid wavelength-encodinghime-

spreading WEYTS) OCDMA system using CMGs. We capitalize on the

combined wavelength-selective and dispersive properties of CMGs in

reflection to encode broadband pulses simultaneously in both

wavelength and t h e . We have theoretically assessed the system

performance and experimentally verified the principle of

C hap ter I-Introduction 6

encoding/decoding in addition to operation of a four-user system

operating at OC-12 transmission speed. Limitations imposed by the

electronic bottleneck due to optical-to-electrical and electrical-to-

optical conversions are overcome since al1 encodingldecoding

operations are performed dl-optically.

the demonstration of a simple and costeffective means for providing

power equalization among WDM channels amplified by EDFAs using a

senal array of transmission edge filters based on apodized linearly

chirped FBGs. The equalization process is performed on a pershannel

basis and can be used to guarantee high performance by minimizing

the deleterious effects of the nonuniform EDFA gain spectrum and

transients arising £kom add/drop operations in recodigurable

networks.

r the demonstration of multi-wavelength, actively mode-locked erbium-

doped fiber lasers (EDFLs) having the closest wavelength spacings

reported to date and with stable, room-temperature operation. These

sources have a myriad of applications in time-resolved spectroscopy,

fiber sensors, and more importantly, as optical sources for photonic

device testingkharacterization and combined WDM/TDM lightwave

systems .

The remainder of this thesis is organized as follows. In Chapter 2, we

provide an overview of FBGs. We begin with a general description of their

C hapter 1-Introàuction 7

principle of operation and review some historical perspectives. We then discuss

the origins and models that explain the photosensitive phenornenon responsible

for allowing the formation of FBGs and the various fabrication techniques,

including the types of sources that can be used. We also review the derivation of

the wave equation, coupled-mode equations, and transmission matrix formalism,

al1 of which are necessary in modeling the response of FBG structures.

In Chapter 3, we provide a comprehensive discussion on the various types of

FBG-based resonator stmctures. We descnbe and compare the optical

properties and performance of the five basic resonator structures, paying special

attention to the similarities and differences. We consider in detail the CMG

structure since it forms a significant basis of the thesis.

In Chapter 4, we show how to tailor the spectral response of CMGs so that

they can be used as transmission filters for providing wavelength selectivity in

WDM systems. Design guidelines are introduced, followed by numerical

simulations. We dso compare the performance of our transmission filters with

other FBG-based implementations. We then describe their fabrication,

characterization, and examine their performance in 2.5 Gbit/s transmission

systems. We then conclude with a discussion of the dispersive properties of

optical filters and how these general results are related to the performance of

FBG-based filters, and ultimately our CMG filters.

In Chapter 5, we describe how CMGs can be used in reflection to

encodddecode short broadband pulses and implemented in WE/TS OCDMA

systems. We begin by considering the reflection properties of CMGs and their

Chapter 1--4ntroduction 8

short pulse reflection response. We then qualitatively describe how they can be

used for encoding/decoding pulses followed by a numerical simulation. The

OCDMA system is then presented: we discuss the design of suitable codes,

which takes into account the constraints imposed by the CMG encoder/decoder

structures, their corresponding performance, and the various practical issues

that are relevant to our proposed system. Finally, we present results of our

proof-of-principle experiments. These include measurements of

encoding/decoding short broadband pulses and successfûl operation of a four-

user system at the OC-12 transmission speed (622.08 Mbit/s).

In Chapter 6, we demonstrate how suitably apodized linearly chirped FBGs

can be used as transmission edge filters in order to perform (active) power

equalization of WDM channels amplified by an EDFA.

In Chapter 7, we present results on how FBGs can be incorporated in a

mode-locked fiber ring laser to produce short pulses at multiple wavelengths.

Two different laser configurations are constnicted. While both have the same

principle of operation, one configuration uses a CMG and the other a pair of

identical serial FBG arrays to d e h e the lasing wavelengths. The emphasis in

this work is on the use of FBGs for generating short pulses at multiple

wavelengths and not on the dynamics or the behaviour of the erbium gain

medium.

Finally, in Chapter 8 we summarize the main conclusions of the work and

suggest areas for future exploration.

Chapter M i b e r Bragg Gratings 1 O

Fig. 2.1. Schematic representation and principle of operation of a fiber Bragg grating [4l.

where 01 is the angle of the incident wave, & is the angle of the dieacted wave,

rn is the order of diffraction, n is the refkactive index of the medium light is

propagating in, and X is the wavelength. Short penod (Bragg) gratings are those

which couple modes travelling in opposite (counter-propagating) directions; in

contrast, long-period gratings which couple modes travelling in the same (CO-

propagating) direction [Il]. If the Bragg grating couples counter-propagating

waves of the same mode, then & = &. Since the propagation constant of a wave

21t 21t in the fiber is given by = -

A. n, = - n, sin 8 (nrr and nco are respectively the A.

effective refiactive index of the propagating mode and of the fiber core), the

difiaction equation (2.1) becomes

Chapter H i b e r Bragg Gratings 11

Fig. 2.2. Diffraction of a light wave by a grating [10].

Although higher order *action orders can exïst, the dominant contributions

for an FBG anse fkom first order difiaction, m = -1. Thus,

I f we identie negative values of B as those which propagate in the negative z-

direction, then for = - B i so that the resonant wavelength of a grating having a

period A is

A = 2ncf lA, (2.4)

the familiar resdt for Bragg reflection. In short, the Bragg reflection condition

is a statement of conservation of momentum as illustrated in Fig. 2.3.

Chapter 2-Fiber Bragg Gratings 12

Fig. 2.3. Ray-optic illustration of core-mode Bragg reflection by a fiber Bragg grating. The P- axis demonstrates the grating condition in Eq. (2.2) for m= -1. x~ and n, are respectively the

refkadive index of the cladding and core of the optical fiber [IO].

2.2. Historical perspectives

Photosensitivity in optical fibers was discovered accidentally by Hill et al. in

1978 during an expriment on nonlinear effects in a specially designed Ge-doped

silica fiber [6]. In the experiment, intense light fkom an Ar-ion laser was coupled

into the fiber. After prolonged exposure, they noticed a significant decrease in

the light transmitted. In subsequent experiments, Hill noticed a corresponding

increase in the light reflected, fkom the fiber, leading him to postulate the

formation of an in-fiber distributed reflector. The forward propagating wave was

interacting with the 4% Fresnel reflection fkom the cleaved output facet of the

fiber forming a standing wave pattern and indeed, the refkactive index in the

fiber was modified according to this standing wave pattern, increasing a t the

maxima of the standing wave pattern and creating a sinusoidal longitudinal

refkactive index modulation. This refkactive index modulation acted as a

Chapter M i b e r Bragg Gratings 13

distributed reflector (gratin@ which enhanced coupling into the backward

propagating mode thereby providing a mechanism for feedback. The enhanced

coupling to the backward propagating wave increased the amplitude of the

standing wave pattern which served to increase the refkactive index modulation

further, which in tum increased the feedback. This process continued until the

index modulation saturated. They immediately recognized that this distributed

reflector could be used as a narrowband reflection filter ta bandwidth of = 200

MHz was obtained) ['il; however, these gratings were reflective only at the

wavelength of the illuminating source and thus had limited applications.

During the next ten years, research interest in photosensitivity and fiber

gratings was sporadic since many attributed it to be a phenornenon associated

with the specially designed fiber. In this period, Lam and Garside made one

significant discovery: the peak refkactive index change was proportional to the

square of the intensiw of the writing beam, suggesting that a two-photon process

was responsible in the formation process of the in-fiber grating C121.

In the mid to late 1980's, results fkom several key simultaneous discoveries

renewed interest in photosensitivity. These included the works of Osterberg and

Margolis, who in 1986 demonstrated fkequency doubling in glass optical fibers

[13] and Stone, who in 1987 showed that any &Oz-doped silica fiber exhibits a

photosensitive response when illuminated by UV radiation [14]. Then in 1989,

Meltz et al. dernonstrated a new interferometric (holographie) fabrication

technique [15] which brought FBGs out of the research lab. This interferometric


technique gave the flexibility of producing gratings at any wavelength, not just

limited to that of the illuminating source thereby opening the possibility for

numerous applications. Furthemore, the use of UV radiation at 248 nm in this

approach capitalized on a single-photon absorption process where the fiber

exhibited an enhanced photosensitive response thereby significantly reducing

the times required to write gratings.

Additional contributions that continued to fuel interest in fiber gratings

included the developments of various techniques to enhance further the

photosensitive response of optical fibers, including hydrogen-loading [16] and

flame brushing [17] demonstrated respectively by Lemaire et al. and Bilodeau et

al., and the use of the phase masks, demonstrated independently and

simultaneously by Hill et al. [18] and Anderson et al. [191, as an even more

flexible means for producing more complicated grating structures. Today,

research on fiber gratings continues to progress and continually attracts

considerable interest fkom both academia and industry. Current research

focuses around five central areas: (i) an understanding into the nature of

photosensitivity, the ongin of the effect, and methods for its enhancement; (ii)

novel fabrication techniques which can provide greater flexibility in the types of

grating stnictures that can be fabricated; (iii) investigation of grating stability

and reliability; (iv) synthesis of grating structures with prescribed spectral

and/or phase responses, and (v) applications of fiber gratings in fiber-optic

sensing, biomedical physics, and optical communications [2] - [41. In the past


few years, fiber gratings have indeed emerged as cnticd building blocks for

many fiber-optic sensing and Lightwave communications applications.

2.3. Origin of photosensitidty

Although many different types of fiber gratings have been fabricated and

many applications already realized or envisioned, the photosensitive

phenornenon is not fully understood due to the complexity of the glass medium

[31, [41. Many different models explaining photosensitivity in optical fibers have

been proposed; however, no single explanation clearly describes the

photoinduced refkactive index changes and d l the observed effects. While it is

believed that each of the models contributes to the photoinduced refractive index

changes, the extent of each contribution is not known. The only consensus is

with regards to the mechanisms involved in initiating photosensitivity. The

photosensitive response is attributed to defects that are present in the glass

matrix and in particular, the so-called Ge oxygen vacancy defect [3]. Normally,

Ge bonds to four adjoinulg Si atoms via bndging oxygen atoms in the glass

matrix. However, during the fabrication of the fiber preforms and fiber drawing

process, Ge can bond directly with another Ge or Si atom forming Ge-Ge or Ge-Si

so-called "wrong" bonds. These defect sites, also called colour centers, have a

very strong absorption in the 240 - 250 nm (UV) range. Since exposure of the

fiber to UV radiation in this wavelength range can create very large changes in


the refractive index it is generally accepted that these wrong bonds are at the

root of fiber photosensitivity.1

CoZour center model

The colour center model [20] is based on photobleaching of the absorption

band associated with the wrong bond defect sites (see Fig. 2.4) and the

subsequent creation of new absorption bands [21]. The absorption of W

radiation at 245 nm ionizes the Ge-Ge or &-Si wrong bond forming in the

process a GeE' center and a £kee electron (a GeE' center is a Ge atom bonded to

three oxygen atoms and an unpaired electron). The fkee electron can recombine

immediately with its associated GeE' center to give recombination luminescence

or it can diffuse through the glass matrix until it is trapped at a Ge(1) or Ge(2)

center resulting in a Ge(1)- or Ge(2)- defect site. A Ge(n) center, where n refers

to the number of next nearest neighbor Ge (Si) atoms surrounding a Ge ion with

an unpaired single electron, is a well-known paramagnetic defect formed in the

Ge-doped silica core. The Ge(1)- and Ge(2)- defect sites have been shown to be

associated with absorption bands at 281 nm and 213 nm respectively. These

changes in the absorption spectrum of the fiber in the UV region create

refractive index changes in the visible spectrum through the Kramers-Kronig

relation:

' Recent research has shown that there is stmng absorption at 193 nm which can alço induce large refkactive index changes.

C hapter H i b e r Bragg Gratings 17

- E, (A) €,(A) = i + J d ~ -

A-A.

which relates the real ( ~ r ) and imaginary (ei) parts of the complex dielectric

constant (which in turn give the absorption and refractive index of the material).

Fig. 2.4. W absorption spectra before (solid line) and &r (dashed linel writing an 81% peak reflectivity grating in an AT&T Accutether single-mode fiber. The squares denote the change in

attenuation [2 11.

Photosensitivity has also been reported with illumination at other W

wavelengths including 260 nm and 193 nm [22]. This is likely due to defect sites

having absorptions at wavelengths other than in the 240 - 250 n m range.

DipoLe mode2

The dipole model, similar to the photorefkactive effect in crystals, is based

on the formation of built-in space charge electric fields arising fiom the

photoexcitation of the wrong-bond defects [23]. When the fiber core is exposed to

- -

Chapter 2-Fiber Bragg Gratinge 18

W illumination, the wrong bonds are ionized creating GE' centers and a free

electron. This occurs primarily in regions where the UV illumination has the

highest intensity (at the peaks of the standing wave pattern). The fkee electrons

then diffise through the glass until they are trapped a t Ge(1) or Ge(2) sites in

regions where the W intensity is low. This redistribution of charge creates a

periodic space-charge electric field that induces a change in the local refkactive

index through the DC Kerr effect [3]. However, the dipole mode1 is not expected

to contribute significantly to the photoinduced refkactive index changes due to

the relatively large number of GeE' centers and Ge(l), Ge(2) sites that would be

required. Furtherrnore, this effect only contributes to a refiactive index change

= at the breakdown voltage of the g l a s medium.

Compaction rnodel

The compaction mode1 is based on laser irradiation induced density changes

which create an associated refkactive index change [24], [25]. UV radiation, with

power levels below the breakdown tkeshold, can induce therrnally reversible

compaction in amorphous silicon. In particular, Fiori and Divine demonstrated

a 16% decrease in Si02 film thickness and an associated refiactive index change

during exposure to UV radiation [24]. Subsequent annealing of the sample

restored the original film thickness indicating that the W exposure did not

ablate the film surface. Simil= changes in refractive index were also obsemed

in hydrostatically compressed silica. These experiments confïrm that the

C hapter M i b e r Bragg Gratings 19

reeactive index changes due to laser and hydrostatically induced compaction are

due to similar physical mechanisms and that the photoinduced refkactive index

change is not stnctly a photochernical process involving the ionization of wrong-

bonds.

Stress-relief model

The stress-relief model [26] is based on the notion that refkactive index

increases when thermo-elastic stresses in the fiber core are alleviated. Therrno-

elastic stresses in the fiber core arise fiom differences in the thermal expansion

coefficients of the fiber core and cladding as the glass is cooled during the fiber

drawing process. It has been shown that tension reduces the refiactive index,

thus when wrong bonds are broken during UV illumination, built-in stresses are

reduced which accounts for the increase in the refkactive index.

2.4. Fabrication techniques

The first in-fiber gratings, fabricated using 488 n m or 514.5 nrn radiation

from an Ar-ion laser, were based on the formation of a refkactive index

modulation correlated to the standing wave pattern generated by the interfering

forward and backward counter-propagating beams, and are known as "Hill"

gratings. Although the use of these gratings for filtering operations was

immediately recognized, they were limited to operate near the wavelength of the

illuminating beam.

Chapter M i b e r Bragg Gratinge 20

Since the demonstration of the intederometric and phase mask techniques

to write gratings, there has been significant progress in modiS.uig and adapting

them to produce complicated grating structures for a variety of applications. In

this section, we overview some of the fabrication methods currently used.

Bulk interferorneter

The bulk interferometer technique fl5l is illustrated in Fig. 2.5. The W

light is divided into two parts and recombined a t an angle 9 relative to the

normal of the fiber. A compensating mirror can be inserted in the path of one of

the beams to ensure that both beams encounter the same number of reflections

so that a high degree of spatial coherence can be maintained at the intersection

of the two beams in the fiber. Simple geornetry shows that the resonant Bragg

wavelength of the grating inscribed in the fiber is

nu, sin - 2

The interferometric setup must be designed to accommodate the temporal

and spatial coherence properties of the source to allow the formation of high

contrast interference fiinges. Furthemore, it requires a stable interference

pattern of the two UV beams in order to produce the grating, otherwise the

interfering pattern is not stable over the time scale required to photoimprint the

grating. It must be free from mechanical vibrations and requires a W beam

with high spatial coherence. Although the setup generally produces gratings

C hapter H i b e r Bragg Gratings 2 1

with uniform periods, it is possible to Vary the grating period (i.e. make a

chirped grating) by exposing the fiber to the interference of two non-collimated

beams (at least one of which is diverging as shown in Fig. 2.6) 191. The grating

period is position dependent and is given by:

where Dr and D2 are the distances between the lenses and the fiber, and QI and

92 are the angles which the respective beams make with the fiber ax is .

interference fringes

r. f i

/ photosensitive

A

fi bm

Fig. 2.5. (a) Holographie setup for writing fiber 3ragg gratings [4]. (b) Formation of a refractive index modulation proportional to the interference pattern of two UV beams in the core of an optical fiber [9].


Fig. 2.6. -Arrangement for formation of nonuniform gratings by the interference of two dissimilar wavefkonts using cylindrical lenses in each a m of the interferometer [91-

The above-mentioned interferornetric techniques are based on amplitude

splitting whereby the power of a UV beam is divided in two separate paths

before they are allowed to intersect and interfere at the fiber. An alternate

interferometric approach is based on wavefkont splitting whereby part of the UV

beam is split before being recombined with itself. An example of wavefkont

splitting is based on the Lloyd mirror interferometer [27j, depicted in Fig. 2.7-

Since this method requires only a single optical component, it has increased

stability; however, it is limited to produce relatively short gratings.

Phase mask technique

This technique, a schematic of which is shown in Fig. 2.8, was proposed

independently by Hill et al. [18] and Anderson et al. [19]. In [18], a

transmission phase grating (phase mask) is used to diflkact a normally incident

UV beam into different orders according to the diffraction equation (2.1):


Fig. 2.7. The Lloyd mirror interferorneter [3].

et" Aw sin - = sine + m- 2 A PM

For normal incident illumination, 8i = O. If the phase mask is designed to

msilrimize the difiaction in the m= + 1 orders and minimize al1 other orders,

then the interfering 2 1 orders form a standing wave pattern perpendicular to

the fiber a i s and having a period

Ag = &V - -- A PM

O", 2sin r, 2

Thus, the inscribed grating has a Bragg wavelength


INCIDENT ULTRAVlOtET UGHT ôEAM

Fig. 2.8. Fabrication of gratings using the phase mask technique. 1181

Note that the Bragg wavelength is independent of the W writing wavelength.

However, the phase mask is usualiy optimized for operation at only one UV

wavelength, i.e., the rn = O diffraction is minimized at one wavelength. The

phase mask approach is very stable and repeatable, and it relaxes the

requirements on the characteristics of the illuminating W beam, especially its

temporal and spatial coherence. Many types of gratings, including chirped and

apodized, can be fabricated using the phase mask technique. Its only drawback

is that each phase mask only produces limited types of gratings so that different

phase masks are generally required to produce different grating structures.

Chapter M i b e r Bragg Grntings 25

Phase mask interferometer

The phase mask interferometer [28], illustrated below in Fig. 2.9, combines

the repeatability of the phase mask, used here as a wavelength defining element,

with the flelribility of the interferometric technique. The phase mask serves to

split the incident W light into the +- 1 diffraction orders. Mirrors are then

positioned to recombine the diffkacted beams on the fiber. The mirrors are

rotatable so that the two beams can intersect and interfere at any angle on the

fiber, giving control over the grating period. The change in the Bragg

wavelength as a f ic t ion of the change in the mutual angle between the two

intedering beams is given by

An advantage of this approach is that the zeroth order difiacted beam can be

physically blocked and eliminated so that any W wavelength c m be used for

illumination; however, it may be difficult to align.

, * , . . . - ' - .. . -. - -

-lIIIItJIIII --- Fibrr

Rotation for hlam

Fig. 2.9. Phase mask used as a beam splitter in an interferometer for inscnbing fiber Bragg gratings [3].


Scanning phase mask interferometer

In the scanning phase mask interferometer [29] (Fig. 2.101, the W beam is

scanned over the length of the phase mask. In this extremely powerfid

adaptation, we can control the intensity of the UV beam as it is scanned across

the phase mask so that we can obtain an apodized grating, even with a uniform

diffraction efficiency phase mask, by appropriately controlling the intensity at

the edges of the grating relative to the middle. If further the fiber is translated

while it is exposed to the radiation, then very long gratings, longer than the

length of the phase mask, c m be fabricated.

Filu; of W r m

Scanncd W bcani

Fihrr

Fig. 2.10. Phase mask used as a scanned interferometer [31.

Point-by-point writing

The basic premise of point-by-point writing [30] is illustrated in Fig. 2.11.

After passing through a narrow dit, the UV beam is focused onto the fiber and

the refkactive index is locally increased in the region exposed. The fiber is then

translated a distance h which corresponds to the grating period. Since

micropositioners are very precise, this is a very stable and repeatable means for

fabricating gratings, especially long ones. However, since the step size is ümited


to about 1 p by the precision of the micropositioners, then the gratings that can

be fabricated do not involve lowest order Bragg reflection at 1550 nm, but rather

higher order (m = 2, 3, ... ) reflection. The technique is more practical and suited

for fabricating long-period (possibly blazed) gratings which can be used to couple

CO-propagating modes.

Fig. 2.11. Point-by-point writing of fiber gratings [4].

Types of gratings

Three different types of gratings have been identified. These are the so-

called Type l, Type 2, and Type 3 (or Type 2A) gratings and their formation

depends on the type of UV exposure in the fabrication process [3]. Type 1

gratings are generated by exposure to cw radiation or multiple weak pulses. The

process is typically single-photon (although Type 1 gratings fabricated with 193

nm radiation appear to be two-photon) and the index change is uniform across

the entire cross-section of the fiber core. In most cases, these are the types of

gratings that are produced. Type 2 gratings mise fkom single pulse exposure.

Chapter H i b e r Bragg Gratinge 28

However, the behaviour is remarkably different depending on the energy of the

illuminating pulse. Below a certain threshold energy, a single pulse exposure

will produce a Type 1 grating. Above this threshold energy, a single pulse will

create an = 100% reflecting grating-these are known as Type 2 gratings [3 11.

The typical threshold fluence has been found to be = 1 Jlcm2 for a 20 ns pulse.

Specific features associated with these W s of gratings include a large index

modulation, strong coupling to cladding and radiation modes resulting in high

losses on the short wavelength side of the grating, and high thermal stability. It

has been shown that Type 2 gratings arise £kom a breakdown at the

core/cladding interface most likely due to a rapid heating of the glass beyond the

melting point [3 11.

While a grating is forming, the transmission within the vicinity of the

Bragg wavelength typically decreases. With prolonged exposure, the grating

partially or completely disappears. This corresponds to a complete saturation of

the index change. However, it was observed that with further exposure, a

second grating, with a reflectivity that can approach 100%, will form [32]. These

gratings are referred to as Type 3 gratings. Although the Bragg wavelength

nominally shifts towards longer values during exposure for the first grating

(consistent with the increase in background refkactive index), the Type 3 grating

actually shif'ts towards shorter wavelengths. Type 3 gratings have been

explained by the interplay of two mechanisms, one tending to increase the


reçactive index and the other tending to decrease the refkactive index. These

are consistent with the observed shifis in wavelength during fabrication.

2.5. Sources for umiting fiber gratings

The type of source chosen to photoimprint fiber gratings should be

compatible with the fabrication technique. The interferometric technique can

use any UV source but requires a stable interferorneter design in order for the

interference pattern to be transferred to the fiber. The phase mask technique

can in principle use any UV source, including a UV lamp, although better

efficiency is achieved with one having good spatial coherence. The point-by-point

fabrication method requires a UV source that provides s&cient energy to

induce a reçactive index change in the fiber.

For the interferometric method, the requirements on spatial coherence of

the W source can be relaxed if we ensure that the number of reflections for both

beams is the same. The primary concern then becomes the temporal coherence

which must be sufficiently long (= length of the grating). The long temporal

coherence ensures that, assuming the path lengths for both beams is the same,

the interference produces visible £kinges. A long temporal coherence requires a

narrow linewidth. While UV excimer lasers can operate at high repetition rates

and produce large energy per pulse, they usually have a short coherence length

due to the large bandwidth of the radiation. Thus these lasers are unsuitable for

use in the interferometric setup unless they are spectrally narrowed.


Another potential source is the fkequency-quadrupled YAG laser. This laser

has excellent temporal and spatial coherence; however, the amount of energy

available depends on the efficiency of the nonlinear conversion process. Also,

since YAG lasers normally emit at 1.06 pm, the UV radiation produced by the

fourth harmonic is - 266 nm which does not correspond to the main absorption

peak of the fiber. This reduces the overall efficiency of the writing process. An

alternative is a frequency-doubled Ar-ion laser. Again, these lasers have

excellent spatial coherence, narrow linewidth, and excellent beam pointing

stability and are likely the most suited for the formation of Type 1 gratings,

regardless of the fabrication technique,

2.6. Theory of fiber gratings

Wave Equation

We begin with Maxwell's equations in an isotropie medium with no sources:

V - & O (2.14)

V - B = o (2.15)

where Ë and H are the electric and magnetic field vectors, and fi and B are the

electric and magnetic flux densities. The flux densities are related to the field

vectors through the constitutive relations


where P and M are the induced electric and magnetic polarizations and EO and

p.^ are the permittivity and permeability of £kee space. For non-magnetic

materials, such as optical fibers, M = O . Using this result in conjunction with

(2.12) - (2.171, Maxwell's equations can be de-coupled to a vector wave equation

describing a single field quaatity, for example:

1 where c, = is the speed of light in f?ee space.

JG

The induced polarization is related to the electric field Ë through

where x"' is the jth order (delayed} susceptibility and is a tensor of rank + 1).

In this thesis, we will only be interested in linear effects so that al1 higher orders

of the susceptibility vanish and we have

If further the response of the medium is instantaneous, then (2.19) reduces to

- P = E 0 p E (2.21)

so that (2.18) becomes


By introducing the Fourier Transform for the electric field

Ë(F.o) = 9 [ Ë ( ~ , t ) ] = 1- -- d#(7,t)dW

we can represent (2.21) in the fkequency domain:

O' V x v x E(7 ,o ) = - ~ E ( F . ~ ) È ( F , c I I )

c- (2.23)

where ~ ( 7 , o ) is the fkequency dependent dielechic constant given by

E(?. O ) = 1 + x( ' ) ( 7 . 0 ) (2.24)

and X" ' (F,o) is the fiequency dependent susceptibility.

Since the susceptibility is in general a complex tensor, so is E ( F . o ) . In fact,

~ ( 7 , w ) gives the complex refkactive index N(7,cù) which in turn is related to the

refractive index n ( F , o ) and the absorption coefficient a ( T ,a) through

The refkactive index and absorption coefficient can be extracted fkom (2.24) and

(2.25) as

W a ( ~ . o) = h x'l) (F , W )

n(F, o)

Assuming a low-loss medium, ah) = O. Using the identity

v x v x E = V(V-Ë) -v2É


we derive the wave equation [331

Coupled-mode equations and the transmission m t r i x

Assuming a uniform distribution in the transverse direction, an FBG of

length L can be described fbndamentally by a longitudinally varying refractive

index modulation [IO]

where nefi is the effective refractive index of the fiber mode, 6n&z) is the

apodization function, u is the fringe visibility of the index change, Ao is the

nominal, or resonant, grating period, Mz) describes the spatially-varying phase

(chirp) of the grating, and the factor "1" allows for a background DC index

change proportional to the apodization function (in general, the background DC

index is not constrained to have the same functional form as the apodization

fùnction). If the fiber has a step-index profile, then = q6nm where q is the

confinement factor for the mode of interest.

In coupled-mode theory, we assume that the electric field can be written as

a superposition of the n ideal modes (Le. the modes of the fiber without the

grating perturbation):


where Adz) and Bab) are the slowly varying amplitudes of the nth mode

propagating in the forward and backward directions respectively, and Ën, (x . y) is

the corresponding transverse field distribution. In an "ideal" fiber, the modes

are orthogonal and do not exchange energy; however, the presence of the

perturbation causes the modes to couple according tu

where

is the transverse coupling coefficient between modes rn and n and & is the

perturbation, approximated by = 2ne+ef when Sneff cc 2 n e . The

longitudinal coupling coefficient is similarly defïned, but is generally smaller

than the transverse coupling coefficient and c m be neglected. If the induced

refractive index change is uniform across the fiber core and nonexistent in the

cladding, then the core reeactive index can be expressed by (2.29) with 5nco

replacing Gncff. Now defining two new coefficients,

the transverse coupling coefficient in (2.32) can be re-written as


If we now only consider coupling between forward and backward propagating

waves of the same mode (as in an ideal FBG) and make use of the synchronous

approximation, then the coupled-mode equations (2.30) simplify to2 [IO]

and 6 is the detuning parameter defined by

For a single-mode FBG, we find that

In uniform FBGs, &zef is independent of z and closed form solutions can be found

for the coupled-mode equations when appropriate boundary conditions are

imposed. The boundary conditions imposed are based on the assumption of a

forward propagating wave £kom z = -- [A+(O) = 11 and no backward propagating

' The coupled mode equations are vaiid if 6nln <cl. 6 cc 1, and the envelopes are slowly varying. Le.

Chapter M i b e r Bragg Grntings 36

wave for z 2 L [ A-(L) = O]. Eqs. (2.36) dong with these boundary conditions form

a boundary value problem. We can recast this into an initial value problem

(which is easier to solve) as follows. We know that there is a fornard

propagating wave at z = O and one quantiw that we seek is the forward

propagating wave at z = L. Rather than imposing a boundary condition at r = O

for the forward propagating wave, we can impose one at z = L in terms of a

normalized output, Le. A+U) = I . Then we can make the input A+(O) unknown.

In this manner, we can start nom the back of the grating, where the amplitudes

of the waves are known via the boundary conditions, and integrate "backwards"

to the front of the grating. The propagation of waves through the grating can

now be described by a 2 x 2 transmission matrix, [T1uni [31, [4], [IO] :

where

and y = Jir'-ô' . The reflection (r) and transmission ( t ) coeEcients can then be

calculated from the following:


We can determine the spectral response of a non-uniform grating by first

dividing the grating into p discrete segments of length Lkp , each of which can be

treated as a uniform segment. The T matrix defhed in (2.39) relates the input

and output fields of the individual grating segments (the length kp rather than

L is used) and once these are known, the total grating stnicture is then a

cascade of the p discrete segments. The input and output fields are related by

an expression similar to (2.38):

The reflectivity and transmissivity can be found as above.

Another usefbl property of FBGs are their group delays and dispersions.

The group delay and dispersion of a light wave reflected fkom a grating can be

determined f?om the phase of the corresponding reflection coefficient r. If & =

der resonant fiequency m. Since the first derivative -is directly proportional to do

a, then fkom linear systems theory, it can be identified as a time delay. Thus,

the relative time delay for wavelengths reflected by a grating is

Chapter H i b e r Bragg Gratiags 38

The corresponding dispersion, which is the rate of change of delay with

wavelength, is

drr - 2% d2er D,fps/ nm] = - - ---

d Â Â2 dm2

Similar expressions can be found for the group delay and dispersion in

transmission using the phase of the transmission coefficient 81.

The transfer mat* method requires certain conditions to be satisfied in

order to accurately simulate the grating response [l]. For gratings whose

parameters are position dependent (such as apodized or chirped gratings), it is

not true that increased accuracy can be obtained by dividing the grating into

more sections. In fact, the minimum section length is usually many grating

periods, with the maximum number of segments limited by ensuring that the

slowly varying envelope approximation is satisfied.

Chapter 3

Chirped Moiré Gratings: Background

3.1. Grating resonator structures and chirped moiré gratings 3.2. Fabrication of c-d moiré gratings

3.1. Grating resonator structures and chirped moiré gratings

The fkequency selective properties of optical resonators make them useful

for optical filtering applications. In this chapter, we consider several different

FBG-based resonators. The basic structures are shown illustratively in Fig. 3.1

and include the FBG Fabry-Pérot (FP) [34J, [35], phase-shifted (PS) FBGs [361 -

[41], moiré PS-FBG 1421 - [44, chvped FP resonator (CFPR) [45] - [48], and

chirped moiré gratings (CMGs) [49], [50]. Al1 structures differ in the origin of

their transmission resonances which can be deduced by observing the position-

dependent resonance conditions of the FBGs comprising the resonator

structures.

Fiber Bragg grating Fabry-Pérot

The bulk optics version of the FP resonator comprises two planar, partially

transmitting mirrors separated by a lossless medium (Le., no absorption) of

thickness d that is generally larger than the wavelength of the incident light

beam. Its spectral response is that of a comb filter: it is periodic in fiequency

Chapter =la-d Moiré Gratingu: Background 40

0, CFPR

C a - - a Z a

I Ci C s H

C

ri

rn c a - QI >

C

C rn C z

L C

position, z position, z

Fig. 3.1. Illustrating the different configurations of FBGbased resonators: (a) FBG-based Fabry-Pérot, (b) phase-shifted FBG, (cl moiré phase-shifted FBG, (dl chirped Fabry-Pbrot

resonator, and (e) chirped moiré grating.

2 P!' P!' position, z position, z position, z

4 FBG-FP

rn E - a 5 Q 3 e

d

with transmission peaks appearing within the reflection bandwidth of the

mirrms and separated by the fkee-spectral range (FSR):

d PS-FBG CL

P Q) - s m t 3 CI

gap size: fraction of a wavelength 5

V)

where CO is the speed of light and n is the refkactive index of the medium

moiré PS-FBG

AAI

between the mirrors. A figure of merit for the FP resonator is the finesse (3)

which relates the FSR to the fiiil-width at hawmaximum (FWHM) of the

transmission resonance. In the case where there is no absorption in the medium

between the mirrors and assuming ideal mimors with no phase aberrations,

Chapter Mhirped Moiré Gratings: Background 41

where R is the reflectivity of the mirror. The finesse is used as a measure of the

resolution of the FP resonator and also quantifies the amount of its loss (in the

lossless case and where 32 = 1, the transmission resonances are delta fhctions

located a t the resonant fkequencies).

An FBG-based FP nominally has 2 uniform FBGs s e ~ n g as distributed

reflectors (as opposed to the mirror reflectors in the bu& configuration). The

bandwidth and reflectivity of the two FBGs (which do not have to be identical)

and their physical separation cl determine the FSR and finesse of the FP. Note

that d i k e a bulk mirror, different wavelengths penetrate different depths into

an FBG so that the separation between the two FBG mirrors comprising the

FBG-based FP is wavelength dependent. We must then speak of an effective

separation, defined between the inner edges of the gratings plus twice the

effective length of the gratings. Off resonance, the penetration into the grating

is greater than on-resonance thereby creating a larger separation [35]. Thus, the

FSR is largest on resonance.

Phase-shifted fiber Bragg grating

The phase-shifted FBG is essentially an FBGbased FP filter in which the

separation d is less than one Bragg wavelength (see Fig. 3.1). PS-FBGs can be

modelled using the transfer matrix approach descnbed in section 2.6. The

complete transfer matrix for a phase-shifted FBG is

C hapter 3-Chirped Moiré Gratings: Background 42

[ T ] ~ ~ - ~ ~ ~ = [ T ] ~ [ T ] ~ ' [ T ] ' (3.3)

where [ T I ' (i = 1,2) are the transfer matrices representing the grating segments

before and after the phase-shifted region, and [IO], (371

@ is the transfer matrix representing the phase shiR. In (3.3), - is a discrete 2

phase shiR which can described by a discontinuity in the grating phase or

equivalently, be represented as 2 = =d where d is the length of fiber with 2 A

constant refractive index nefi that imparts the same phase shiR on a propagating

wave.

The principle of operation of a phase-shifted grating can be understood as

follows. First we assume that light satiswng the resonant Bragg condition is

reflected (coupled nom the foxward to backward propagating mode) at peaks in

the refkactive index modulation and not in between. These reflection centers are

spaced by the grating period A or 1J2. From the coupled-mode equations given in

(2.36), the counter propagating waves are d2 radians out of phase with each

other. In other words, each reflection fkom the reflection centers imparts a lr/2

phase shiR yielding a total phase shiR of x for the "doubly-reflected" light

relative to the straight through light. Thus, the total phase difference between

light that propagates through consecutive peaks and the "doubly-reflected" path

Chapter 342hirped Moiré Gratings: Background 43

4n ~r is + 4 = II + + d . Clearly, the transmission depends on the magnitude of

the discrete phase-shift.

reflected" light adds up

transmission resonance.

For the discrete phase shiR -= 2

in phase with the straight-through

In Fig. 3.2, we illustrate the transmission response of

I b - the "doubly- 3 y L

light creating a

a unifonn FBG

havulg different values of phase-shifts located at the center of the grating. The

FBG is 1.0 cm long, with grating period h = 533.747 nm, and has a peak

refractive index modulation 6n = 2.5 x 104. As discussed earlier, a single 7d4 or

d 2 phase shiR in the center of the grating will create a very narrow passband

having a Lorentzian shape within the middle of the stopband. PS-FBGs can be

fabricated using a variety of techniques. Discontinuities in the grating phase

can be obtained using the phase mask technique while effective phase shiRs can

be made with post processing techniques such as W tTimming or localized

thermal heating.

Generally the transmission passband appears within a fairly narrow

stopband even though a uniform grating of the same length but without the

phase-shift has a bandwidth approximately half that of the hl1 stop band of the

phase-shifted grating. There are also accompanying sidelobes on either side of

the stop band. Apodization can be used to reduce the sidelobes but since this

reduces the effective length of the grating, it also gives rise to a wider

transmission resonance. This is illustrated in Fig. 3.2 (b) where w e compare the

Chapter M h i r p c d Moiré Gratiags: Background 44

transmission response of a uniform and Gaussian apodized FBG having a single

d 2 phase shifi located in the center of the grating.

Fig. 33. (a) Calculated transmission response of PS-FBGs having different values of phase-SM: @ = rd4 (dotted linel, = d2 (solid line), and t$ = 3d4 (dashed linel. (bl Uustrating the eEect of apodization on the transmission response of phase-shifted FBGs: uniform grating (solid linel and Gaussian apodization (dashed line). The grating is 1.0 cm long with a grating period A =

533.747 nm and 6n = 2.5 x 104.

Moiré phase-shiped fiber Bragg gmting

The fabrication of PS-FBGs is very challenging due to the need to control

carefully and set the optical phase shiR. An alternative means for obtaining an

optical phase shiR is to superimpose two uniform FBGs having difTerent periods

to fonn a moiré pattern. This process is illustrated in Fig. 3.3. Consider two

uniform gratings havi~q central periodicities Ai and A2 and equal peak

refkactive index modulations 6nz = 6122 = (&/2). When the two gratings are

superimposed, the refkactive index modulation becomes [42]

Chapter Mhirped Moiré Gratingi: Background 45

which can be re-written as

where

and

Fig. 3.3. Illustrating the formation of a moiré grating (421-

Chapter Mhllped Moiré Gratings: Background 46

can be thought of as a sinusoidal apodization profile having a slowly varying

envelope with period

Due to the sinusoidal variation in the envelope, the phase of the grating changes

by n: intrinsically wherever there is a cross-over point in the refkactive index

modulation. This corresponds to an optical phase change of a U4 or rd2 [31.

Thus, a single period of the moiré grating incorporating a cross-over point is

equivalent to a A/4 or a d 2 phase-shitted grating. In principle, any value of

optical phase shiR can be obtained by simply superimposing two gratings having

difTerent amplitudes [42]. However, &om a fabrication point of view, this may be

difficult to do with a high degree of repeatability.

1549.6 1549.8 1550.0 1550.2 1550.4 1550.6

wavelength, nm

Fig. 3.4. Calculated transmission response of a moiré PS-FBG. The grating is composed of two 1.0 cm long uniform FBGs having equal peak refkactive index modulations 6n1= 6n2 = 2.5 x 10-4 .

The grating periods are Ai = 533.747 nm and A2 = 533.802 nm.

Chapter whirpecl Moiré Gratings: Background 47

In calculating the spectral response of a moiré PS-FBG, the use of the

transfer matrix [ ~ ] ' ~ ~ i v e n in (3.4) is not required to account for the phase shiR;

instead, the apodization profile given in (3.8) is used. In Fig. 3.4, we show the

calculated transmission response of a moiré PS-FBG composed to two

superimposed 1.0 cm long uniform FBGs, each with a peak refractive index

modulation Sn1 = 6n2 = 2.5 x 104 and central periodicities Ai = 533.747 n m and

A2 = 533.802 nm. Note that in this case, the transmission passband is broader

than that of a uniform FBG incorporating a phase-shift (see Fig. 3.2). This is

due to the apodized refkactive index modulation Bq. (3.8)] which makes the

coupling coefficient non-uniform (as opposed to a uniform PS-FBG) and thus, as

previously shown, reduces the effective length of the grating and widens the

transmission resonance.

Chirped Fabry-Pérot resonators

FBG-based FPs, PS-FBGs, and moiré PS-FBGs have been fabricated with

success. However, the transmission resonance generally appears in a fairly

narrow stopband resulting in a low finesse (note that unlike the bulk optics

definition, the finesse for PS-FBGs relates the 3 dB bandwidth of the

transmission resonance to that of the stopband within which the resonance

appears). The stopband can be increased, but only a t the expense of an

increased transmission resonance width. Thus, the finesse of these structures

can be limited [42], [43]. In order to increase the width of the stopband, it is

Chapter 3-Chirped Moiré Gratings: Background 48

necessary to use FBGs that have broader bandwidths. Since the bandwidth of a

uniform FBG cannot be increased indehitely, i t becomes necessary to use

chirped FBGs and the simplest implementation, of course, uses linearly chirped

FBGs. The grating periods can be written as

where A: is the initial periodicity of the ith grating, A: = A, (O), and dA [m2/mJ is

the chirp parameter.

A schematic of a Fabry-Pérot resonator comprising two linearly chirped

FBGs, also known as a chirped FP resonator (CFPR), is shown in Fig. 3.5.

Wavelengths transmitted through the structure (resonant wavelengths) are

reflected between the two gratings an even number of times. If the two gratings

are lossless and identical, the dispersion induced by reflection from one grating

is cancelled by reflection fkom the other grating so that al1 the wavelengths see

the same optical path length, i.e. the net dispersion is O [see Fig. 3.1(d)].

Fig. 3.5. Schematic of a wide-band c h q e d Fabry-Pérot resonator (451.

Chapter 3-Chirped Moiré Gratiags: Background 49

In Fig. 3.6(a), we show the calculated response of a CFPR comprising two

identical 8-mm long linearly chirped FBGs, each having an initial penodicity A!

= = 533.747 nm, period chirp of 2 ndcm (dAi = dA2 = 4.59 x 10-14 m2/m), and

separated by & = 12 mm. The FSR of the CFPR is determined by the spacing,

&, between the two linearly chllped FBGs. In order to increase the FSR, it is

necessary to decrease &, possibly to the point where the two linearly chirped

FBGs partially overlap. In Fig. 3.6(b) we show the calculated transmission

response of a CFPR comprising the same two linearly chirped FBGs as in Fig.

3.6(a) except that & = 6 mm so that the gratings partially overlap. Note that

the FSR in the latter case is now *ce that of the former, consistent with the

fact that the effective separation between the gratings is now half its initial

value.

Fig. 3.6. Calculated transmission response of a CFPR. The two liaearly chirped FBGs comprising the CFPR are 8 mm long, each with a grating period h = 533.747 nm, chwp of 2

n d c m (dh = 4.59 x 10-14 m2/m) and equal peak refkactive index modulations 6n = 5 x 10-4. (a) 6e = 1 2 m m a n d ( b ) 6 ~ = 6 m m .

Chapter Mhirped Moiré Gratiags: Background 50

Chirped moiré grating

A chirped moiré grating (CMG) is similar to the moiré PS-FBG except that

the two gratings are chirped. The two superimposed gratings are nominally

identical. They have the same length, peak refiactive index modulation, and

chirp rate, but differ in their initial periodicities (A: # -). The spectral

response of a CMG is determined by several different factors. For example, the

grating chirp determines in part the bandwidth of the stopband of each grating

and the corresponding stopband of their superposition. The wavelength

separation = )A: - -1, in conjunction with the length of the structure, sets the

number of periods in the moiré envelope L e . the number of cross-over points)

and determines the number of transmission resonances (passbands). As the

peak refkactive index modulation increases, both the filter strength and

sharpness of the transmission resonances increase (increased finesse).

Examples which illustrate the effect of varying the grating parameters on the

spectral response of a CMG are shown in Fig. 3.7. In al1 simulations, the length

of the grating and the chirp parameter are fked respectively at L = 3.0 cm and

d h = 3.0 x 10-14 m*/m (which corresponds to a grating period chirp of 0.56

ndcm). The other parameters are: (a) peak refkactive index modulation 6n = 2

x 104 and wavelength separation = 0.2 nm, (b) an increased peak refiactive

index modulation 6n = 5 x 10-4 but the same wavelength separation, and (c) the

same peak refiactive index modulation but an increased wavelength separation

A h = 0.4 nm.

Chapter x h i r p e d Moiré Gratings: Background 51

waveiength, nm

Fig. 3.7. ïllustrating the effects of varying the grating parameters on the spectral response of a CMG. In all three cases, the grating length is L = 3.0 cm and the chirp parameter is dA = 3.0 x 10-14 &/m. The other parameters are (a) peak refractive index modulation 6n = 2 x and wavelength separation AA = 0.2 nm, (b) same as (a) except ân = 5 x 10-~, and ( c ) same as (a)

except M = 0.4 nm.

Until now, the discussion on the various grating resonators has focused

stnctly on the transmission responses. For a lossless grating, the reflection

response can be calculated using the simple relation R(k) = 1 - T'(A). Obviously,

the passbands in transmission have the effect of creating spectrally separate

(distinct) stopbands in reflection. In most practical cases, resonator structures

are used in transmission and in Chapter 4, we will discuss the use of CMGs as

transmission filters for providing w avelength selectivity in WDM systems. We

C hapter S-Chirped Moiré Gratiags: Background 52

will consider the reflection characteristics of CMGs and their novel applications

in Chapter 5.

Before concluding this section, it is interesting to point out the similarities

and differences between a CFPR and a CMG. Both are composed of linearly

chirped FBGs and have very similar responses since they share the same basic

principle of operation. However, there is one subtle difference in their respective

origins of the FSR. For a CFPR, the FSR is determined by the physical

separation 6e of the two linearly chirped FBGs while on the other hand, there is

no physical separation between the gratings comprising a CMG. Only an

effective separation, created by the ciifference in the central wavelengths of the

two gratings exists, as illustrated in Fig. 3.1 (e). It is this separation which

would be used in determinhg the FSR of a CMG.

3.2. Fabrication of chirped moiré gratings

The best in-fiber grating resonator filters fabricated to date are those based

on the moiré technique. The moiré PS-FBG was first demonstrated by Reid et

al. as a surface relief grating formed in the core of an optical fiber [421. The fiber

was polished to expose the core, then coated with a thin layer of photoresist. A

moiré pattern was then formed in the photoresist by holographie exposure to t w o

interference patterns of differing periods using an Ar-ion laser. The grating was

then etched in the fiber and coated with a thin layer of aluminum oxide and an

Chapter x h i r p e d Moi& Gratingr: Background 53

index matching layer. A 0.04 nm wide passband was obtained and the resonator

had a finesse 3 = 20.

A significant drawback of a surface relief grating is the need to expose the

fiber core which reduces the mechanical strength of the fiber. It is thus more

desirable to have a non-invasive fabrication technique. Legoubin et al. reported

the first in-fiber moiré PS-FBG grating fabricated using UV holographie

exposure 1431- In this set-up, the difference in the periods of the two

superimposed uniform FBGs was obtained by tuning the wavelength of the W

wrîting beam [recall Eq. (2.6)]. With this approach, a resonator having a

transmission passband of 0.2 n m and finesse 9 = 10 was reported. Again,

though, the problem with the moiré PS-FBG incorporating uniform gratings is

the narrow stopband.

To increase the stop bandwidth, the use of linearly chirped FBGs to form

moiré PS-FBGs was demonstrated by Zhang et al. [Ml. The gratings were

fabricated using holographie exposure and the chirp was obtained using the

method of dissimilar wavefkonts (see section 2.4). The differenee in central

periodicities of the two gratings was obtained by moving the fiber paralle1 to the

bisector of the two-beam interferometer (by placing the fiber in different regions

of the dissimilar intersecting wavefkonts, different grating periods are achieved).

A resonator having a passband of 0.17 n m and finesse 3 = 25 was obtained. The

finesse was further increased by concatenating additional gratings to increase

the width of the stopband.


The fbst gratings written with a phase mask having a moiré apodization

were reported by Albert et al. [SI]. However, this technique for producing moiré

gratings is limited by the specifïc design of the phase mask. Recently, Everall et

al. [49] proposed an elegant and flexible technique for fabncating CMGs using a

single non-dedicated linearly chirped phase mask. The method, shown in Fig.

3.8, involves dual-exposure of a linearly chirped phase mask with the difference

in the central periodicities of the two gratings obtained by stretching the fiber

between the two exposures. Moiré resonator filters with as many as four

passbands within a 2 n m stopband were demonstrated.

Fig. 3.8. Fabrication of chirped moiré gratings using dual-exposure of a single non- dedicated linearly chllped phase mask. The fiber is stretched between the two exposures [491.

We have adopted the dual-exposure technique to fabricate CMGs. The

measured transmission response of a typical CMG that we have fabncated is

shown in Fig. 3.9. The grating was written in standard telecommunication fiber

(Corning SMF28) which had b e n hydrogen-loaded at - 125 atm. at room


temperature for more than 10 days. 248 nm UV radiation tkom an excimer laser

was scanned across a linearly chirped phase mask having a chirp of 1.0 d c m

(corresponding grating chirp of 0.5 nm/cm). The UV beam was translated a total

distance of 3.5 cm at a speed of 0.15 mm/s, and had a repetitian rate = 40 Hz

with a pulse energy = 35 mJ/pulse. A strain of 10 g (calibrated to provide a

wavelength separation = 0.16 nm) was applied to the fiber aRer the first

exposure. We obtained 6 transmission passbands, each with a bandwidth = O. f 5

nm, within a 6 nm stopband; the finesse is 9 = 4.

wavelength. nm

Fig. 3.9. Experimentally measured (solid line) and theoretically calculated (dotted line) transmission response of a typical CMG we fabricated. The parameters used to simulate the

grating response are given in the text.

One striking feature to note is that in the fabncated CMG, the FSR is not

constant as predicted by the simulationl. In fact, the FSR increases with

wavelength. This is an inherent result, previously not explained in [49], arising

' Note that the FSR is constant in frequency and not wavelength. However, for the values and over the range of waveiengths considered. the FSR is practically constant in wavelength and the observed variation in FSR is above and beyond that arising from this feature.

C hapter 3-Chirped Moiré Gratings: Background 56

£kom the dual-exposure process. If we assume that al1 the parameters are the

same for the two exposures, then the two gratings will have the same

characteristics, i-e. same length, index change, and chirp (note that in general,

the exposure process is not linear so inevitably, the two superimposed gratings

will not have identicd index changes). Applying a strain between the two

exposures changes the length and period of the second grating with respect to

the first. In fact, once the tension is removed, the physicai length of the second

grating is shorter (under tension the two gratings have the same length). This

has two effects: (1) the wavelength of the second grating is shifted to shorter

values relative to the Erst grating and (2 ) the chirp is larger than the first

grating since the phase mask imparts the same chirp but over a shorter length

for the second grating. The lines representing the position dependent resonant

condition shown in Fig. 3.l(e) are no longer parallel--the slope of the upper

branch (corresponding to the first grating) is smaller than that of the lower

branch (corresponding to the second grating). Thus the effective separation

between the gratings decreases with increasing wavelength, resulting in an

increase in the FSR, consistent with the experïmentally obsewed results. In

Fig. 3.9, we show the calculated transmission response of the fabricated CMG

using the following parameters: length L = 3.5 cm, 6n = 5 x IO4, AX = 0.13 nm,

and a 0.2% difference in the grating chirps. The agreement is excellent.

Chapter 4

Chirped Moiré Gratings for Wavelength-Division-Multiplexing

4.1. Filter requirements for WDM systems 4.2. Tailoring the spectral response of chirped moiré gratings for

bandpass filtering 4 -3. Experimental results 4.4. Discussion

4.1. Filter requirements for WDM systems

Optical filters have numerous applications in optical communications. In

particular, they can be used for selecting, routing, and adding/dropping channels

in WDM systems. In order to achieve these functions with good performance,

high data rate systems require filters which have (1) a square-like spectral

response (flat-top and steep edges) and (2) a linear phase response (constant

group delay or zero dispersion) within the filter bandwidth. The first

requirement accommodates wavelength drifts in either the filter position andior

laser source and ensures minimum cross-talk (leakage of optical power) fYom

adjacent WDM channels. The second requirement guarantees that no power

penalties due to intersymbol interference arising fkom dispersion-induced pulse

broadening are incurred.

The spectral response of an ideal optical bandpass filter centered at

frequency cm is given below:

Chapter M h i r p e d Moiré Gmtings for Wavclengtb-Division-Multiplcxing 58

The filter has a bandwidth of 2m and r is the group delay experienced by all

frequency components selected by the filter. However, such a filter is noncausal

(i.e., its correspondhg impulse response Mt) # O for t c 0 ) and thus not physically

realizable. For this reason, considerable research has focussed on the design and

realization of optical filters with properties that approximate the ideal response.

4.2. Tailoring the spectral response of chirped moiré gratings for bandpass filtering

FBGs have numerous applications for WDM and their wavelength

selectivity makes them ideal candidates for use as optical filters 1521, (531. In

particular, apodized FBGs can be designed to have very square-like spectral

responses. However, these FBGs typically operate in reflection and thus must

be used in conjunction with an optical circulator or incorporated in more

sophisticated structures, such as Michelson or Mach-Zehnder interferorneters, in

order to use them for wavelength selection, channel addkirop, or routing

purposes [54] - [58]. Furthermore, many applications involve the use of a

transmission, rather than a reflection, passband filter. The use of an optical

circulator may prove to be very costly, especially since one would be required for

each grating that is used to select a specific channel. Michelson and Mach-

Zehnder configurations are compact; however, since they are interferometric

type devices, they require strict tolerances on fabrication and must be

appropriately packaged to avoid, or at least reduce, performance degradation

arising fkom externd environmental factors such as temperature variations.

Chapter Q-Chirpcd Moiré Gmtings for Wavdengtb-Division-Multiple~ng 59

We showed in Chapter 3 how FBG resonator stmctures, and in particular

PS-FBGs and CMGs, can be directly used as transmission filters because their

spectral responses contain a well-defined transmission passband. However, we

also saw that the spectral features of these gratings are not necessarily ideal.

In particular, the passbands are Lorentzian in shape (which is typical of the

resonance) with narrow transmission peaks (no flat-top), and rounded, possibly

broad bottoms, thereby rendering them potentially unsuitable for system design.

Recently, several authors showed that a single flattened passband could be

obtained by introducing compound phase-shifts in an FBG [59] - [61]. In this

section, we show how to obtain flattened passbands and tailor the spectral

response of CMGs by selectively introducing regions of constant refkactive index

(i .e., no refractive index modulation) within the grating structure.

Principle of operation

In order to improve the transmission characteristics of a CMG, one or more

regions of constant refkactive index, denoted by dl, are embedded within the

onginal grating structure as illustrated schematically in Fig. 4.1. The principle

of operation is as follows: the A2 regions are positioned at the physical location

in the grating where an FP resonance associated with the original CMG occurs

(i-e., the cross-over point in the refkactive index modulation where the phase of

the grating changes by x). If, further, the value of dl is chosen to be near an

integer multiple of the length of a beat penod in the Moiré pattern, then

Chapter M h i r p e d Moiré Gratings for Wavdcngtb-Division-MultipleGng 60

consecutive FP resonances can be eliminated. Thus, two or more passbands are

combined resulting in a new passband with a flattened top. The new grating

structure resembles a concatenation of physically separate gratings, each

occupying its own wavelength interval.

Fig. 4.1. Embedding regions of constant refractive index in a CMG structure in order to obtain flattened passbands: (a) original CMG structure; (b) one region, (cl, two regions, and (dl three regions embedded. The shaded regions marked by LU have constant refiactive index; the

hatched ones represent original sections from the CMG.

The wavelength position and full-width half-maximum (FWHM) bandwidth

of the flattened passbands can be controlled by changing the positions and

length of the regions with constant refiactive index, Le.,, by preferentially

eliminating various consecutive FP resonances associated with the original

CMG. In particular, the wavelength position of a passband is determined by

Chapter 4-Chirped Moiré Cratings for Wavclengtb-Division-MultipIuOng 61

which of the (consecutive) FP resonances are eliminated while the passband

bandwidth is determined by the number of such resonances eliminated.

Simulation results: spectral and group &y responses

In Fig. 4.2(a), we show the calculated transmission response of a 3.5 cm

long CMG with a peak refkactive index modulation 6n = 5 x 10-1, equal chirp

parameters for both gratings 8A1 = 6A2 = 2.67 x10-14 d m (which corresponds to

a grating period chup of 0.5 nm/cm), and a wavelength separation = 0.16 nm.

We also show the corresponding envelope of the refkactive index modulation

profile. Notice that there are six cross-over points in the refiactive index

modulation, each associated with a transmission resonance. We now show how

to tai lor the transmission characteristics of the CMG by varying (i) the number

of AZ regions that are embedded into the grating structure, (ii) their positions

within the grating structure, and (iii) their lengths. For this CMG, Al = 0.5 - 0.6

cm in order to eiiminate two consecutive FP resonances. As a first illustrative

example, we place a single region of constant refkactive index, Ah = 0.5 cm, in

the center of the grating. The new grating structure resembles that in Fig.

4.l(a) with Li = L2 = 1.5 cm and Mi = 0.5 cm and the envelope of its refkactive

index modulation is shown in Fig. 4.2(b): the index modulation between the two

middle cross-over points is constant. The transmission spectrum is shown in

Fig. 4.2(b) and we can see that the comesponding resonances have been

eliminated, the region between them combined, and a new passband with a flat

Chapter H h i r p e d Moiré Gratiags for Wavdengtb-Dirision-Multiplclnng 62

top created. The passband has a flattened top with < 0.2 dB npple and provides

= 18 dB channel isolation with a Glter edge slope of = 110 dB/nm taken at the -

10 dB point. The 3 dB bandwidth is = 0.73 nm which is the same as the total

bandwidth occupied by and between two consecutive passbands in the original

grating response. As additional examples, we illustrate in Fig. 4.2W - (0, the

effects of introducing two regions of constant retiactive index so that the new

grating structure now resembles that in Fig. 4.l(c). We have complete fiexibility

in choosing the central wavelengths of the passbands and their 3 dB bandwidth

by simply specimng which FP resonances are to be eliminated. The grating

parameters are as follows: for Fig. 4.2(c), LI = 0.4 cm, Lz = 1.5 cm , and L3 = 0.4

cm with Ah = d l 2 = 0.6 cm; for Fig. 4.2(d), Lr = 1.5 cm, L2 = 0.5 cm, and L3 = 0.4

cm with LUI = 0.5 cm and d l 2 = 0.6 cm; for Fig. 4.2(e), LI = L2 = 1.0 cm, and L3 =

0.4 cm with d l 1 = AZ2 = 0.6 cm; and for Fig. 4.2(f), LI = 0.4 cm, L2 = 0.5 cm, and L3

= 1.0 cm with AI = 0.6 cm and d12 = 1.0 cm. In al1 cases, the passbands have a

ripple c 0.2 dB and a 3 dB bandwidth = 0.73 n m except for one passband in Fig.

4.2(0 which has a 3 dB bandwidth = 1.5 n m corresponding to the fact that three

consecutive FP resonances, rather than two as in al1 the other cases, have been

eliminated. Finally, in Fig. 4.2(g), we show the effect of introducing three

regions of constant refractive index so that the new grating structure resembles

that in Fig. 4.l(c): three identical passbands with flattened tops (al1 with c 0.2

dB npple) are obtained. The grating parameters are LI = L4 = 0.4 cm and L2 =

L~ = 0.5 cm e t h dlI = A3 = 0.6 cm and d12 = 0.5 cm. Note that the number of

regions having constant refkactive index intmduced into the grating structure is

the same as the number of flattened passbands.

Another important characteristic of optical filters is their phase response

(eom which we can obtain the group delay or dispersion). In Fig. 4.2, we also

show the calculated group delay in transmission for al1 of the grating filters.

Within the flattened passbands, the group delay is nearly constant. Physically,

this can be understood by observing that wavelengths in the passband no longer

experience any FP effects and the enhanced delay associated with multiple

reflections within the grating structure.

position, cm

Fig. 4.2. (a) - W. Illustrating the effects of introducing regions of constant refractive index modulation in a CMG on the transmission response. The refractive index modulations of the

new CMG structures appear in the left column and the comesponding caiculated transmission (solid line) and group delay (dashed line) appear in the right column. The grating parameters

are given in the text.

Chapter M h i t p e ù Moiré Gratings for Wavdcngth-Division-Mdtipluing 64

position, cm wavelength, nm

Fig. 4.2 (continued) (dl - (g). Illustrating the effects of introducing regions of constant refractive index modulation in a CMG on the transmission response. The refractive index modulations of the new CMG structures appear in the leR column and the corresponding

calcuiated transmission (solid line) and group delay (dashed linel appear in the right column. The grating parameters are given in the text.

As the examples above illustrate, for a given set of CMG parameters, the

number, length, and position of the regions with no refiactive index modulation

w i l determine the passband wavelength position, 3 dB bandwidth, and quality

of the filter (i.e., steepness of the dopes and amount of npple in the passband).

The quality of the filter is sensitive to the values and positions of the Al regions:

improperly eLimïnating consecutive FP resonances associated with the original

CMG structure results in increased npple and poor filter edges. In extreme

cases of incorrect values or positions of a AZ region, no useable passbands can be

generated. However, by suitably designing the grating structure, usefùl

transmission passband filters can be realized and tailored to suit the needs of

specific applications. Although this technique cannot always produce multiple

identical passbands with ideal transmission characteristics fiom a given CMG

(i.e., we cannot always obtain a spectral response similar to that shown in Fig.

4.2(g) where the modified response no longer has any narrow Lorentzian-shaped

passbands associated with the original CMG), it is a relatively simple means for

obtaining improved performance. The only additional step in the fabrication

process involves a modulation of the writing beam as it is s c a ~ e d across the

phase mask, the use of an amplitude mask to block selected parts of the phase

mask, or UV post processing. In all cases, there is of course the need to position

properly the regions with constant tefiactive index in order to obtain the

flattened passband characteristics.

Cornparison with other fiber Bragg grating-based filters

While considerable attention has been devoted to tailoring the amplitude

responses of FBG-based filters, the correspondhg phase responses and their

impact on the performance of WDM systems has only recently received attention

[62] - [66]. In this section, we evaluate the peflormance of various FBG-based

filters. In particular, we are interested in the impact of the phase response on

the propagation of short pulses "dropped" by 5 different FBG filters having

Chapter Q-Chirped Moiré Gratings for Wavdengh-Division-Multiple~ng 66

similar amplitude responses (Le., the same 3 dB bandwidth and edge slope).

The five FBG filters compared are:

1 [ z - ~ L D ~ J ( 1) an FBG with a Gaussian apodization, Gi, ( z ) = Gl exp - a

where 6n = 5.4 x 104, L = 1.0 cm, and a = 15;

( 2 ) an FBG with a Blackman apodization profile, 61, ( z ) = Gif (3 where

1+1.i9cos(~)+0.19cos(i') f (3 =

- h ( z - L / Z ) r z = , L = 0.75 cm,

2.38 L

and 6n = 5 x 10-4;

(3) an FBG with a combined Gaussian and sinc apodization profile [66),

cm, and Sn = 2.9 x 10-4;

(4) a uniform FBG of length L = 3.516 mm having six 7d2 phase-shifts

located at z = 0.22 mm, 0.752 mm, 1.411 mm, 2.405 mm, 2.764 mm,

and 3.296 mm, and a peak refractive index modulation 6rt = 1.0 x

10-3; and

( 5 ) a CMG of length L = 5.0 cm, peak refractive index modulation 6n =

8.5 x 104, chirp parameter dh = 2.3 x 10-14 mVm, AIL = 0.12 nm, and a

single region Al = 0.6 cm located at the center of the grating to create

a flattened passband.

Chapter H h i r p e d Moiré Gratings for Wavelength-Division-Mdtiplcxiag 67

The first three are reflection filters while the latter two are transmission-

based. In Fig. 4.3, we show the calculated amplitude and group delay responses

of these 5 filters. The FBG nIters are centered at 1550.0 nm, have negligible

ripple (c 0.2 dB) in the filter passband, a 3 dB bandwidth = 0.6 n m and an edge

slope of = 140 dB/nm at -10 dB. The filters have sirnilar amplitude responses

(except that the reflection filter having the Gaussian + sinc apodization is only

50% reflecting); they differ in their phase responses.

The performance of the filters is evaluated by examining the amount of

signal degradation arising fkom pulse broadening due primarily to filter

dispersion. The amount of pulse broadening is quantified as the ratio between

the FWHM or root-mean-square values of the output to input pulse widths. We

consider an input signal represented by a transform-limited 25 ps FWHM

Gaussian pulse, typical of return-to-zero signal format. For a bit rate of 10

GbitJs, this corresponds to a duty cycle of 25%.

In Fig. 4.4, we show the calculated pulse broadening factors as a function of

detuning fiom the central wavelength (within the filter passbands). As can be

seen, the filter based on a Gaussian apodized FBG clearly has the worst

performance: the pulse broadens by over 50% as the filter edges are approached,

corresponding to a power penalty in excess of 2 dB (these results would be even

more significant if a cascade of such filters were used)! Even in the central

portion of the filter, there is still non-negligible pulse broadening. The

remaining FBG nIters have comparable performance within the central portion

Chapter M h i r p e d Moiré Gratings for Wavdengtb-Division-Mdtiplexing 68

wavelength detuning, nm

Fig. 4.3. Calculated spectral response (solid line) and group delay (dashed line) of the five FBG f3ters whose phase responses are king compared. Reflection filters: (a) Gaussian

apodization, (b) Blackman apodization, and (c) Gaussian + sinc apodization; transmission filters: (dl multiple-phase-shiRed FBG and Ce) chirped moiré grating with one flattened passband. The

heavy solid lines denote the 3 dB BW of the filters. The grating parameters are given in the text.

of the filter with < 5% pulse broadening but induce greater broadening as the

filter edges are approached. The transmission filters have the best overall

performance. One factor to consider is that although the FBG with the combined

Gaussian and sinc apodization profile has comparable performance to the two

transmission filters with respect to the dispersive properties, it is only 50%

reflecting so that al1 filtered signals will immediately incur a 3 dB insertion loss.

Chapter H h i r p e à Moiré Gi~tings for Wavdength-Division-MulCipleKing 69

This undesirable feature is inherent in the design of the FBG and cannot be

avoided nor Mproved since any further increases in the grating reflectivity will

destroy its square-like amplitude response. If we use the common cntena that r

= 1/(4B) for Gaussian pulses, where T and B are the pulse width and bit rate

respectively, so that at least 95% of the pulse energy remains within the bit slot

[331, then clearly the CMG and phase-shifted FBG filters outperform the

reflection filters since they can be used over a greater portion of the filter

bandwidth while still satisfying this propem. We do point out, however, that

multiple phase-shifted FBGs (13 phase shifts) are very difficult to fabricate with

good performance characteristics [61] and so CMGs appear to be a very

promising solution.

Gaussian + Sinc -v- Multiple PSFBG

detuning, nm

Fig. 4.4. Calculated pulse broadening as a function of detuning.

Chapter M h i r p e d Moiré Gmtings for Waveleagth-Division-Mdtipluring 70

4.3. Experimental redts

In Section 3.2, we discussed the fabrication of CMGs by dual-exposure of a

single linearly chirped phase mask. The difference in the central wavelengths ( A

A) of the two superimposed gratings can be obtained by simply placing the fiber

under a strain between the two exposures (an initial calibration will provide a

relationship between the amount of strain and wavelength shiR). Several

different methods to obtain the fiattened passbands by introducing regions of no

refkactive index modulation were discussed in the previous section; we have

chosen the one that incorporates amplitude masks in the dual-exposure process.

A schematic of the fabrication setup is illustrated in Fig. 4.5.

define scanning range of UV beam

(reference mask) \r

provide regions of no /

index modulation

UV beam A- translation at uniform speed

phase mask

Fig. 4.5. Fabrication of CM& with flattened passbands by dual-exposure of a chirped phase mask in conjundion with amplitude masks.

Chapter 4-Chirpd Moiré Gratings for Wavdength-Division-Mdtiple~ng 71

We simultaneously used two or more amplitude masks. The first mask,

called the reference mask, had a designated opening which served to (il define

the scanning range of the UV beam on the phase mask and (ii) provide a

reference point for the start of the grating. The remaining amplitude masks

contained blocks of length d; the total number of such blocks corresponded to

the number of flattened passbands desired. These masks could also be moved

relative to the reference mask in order to position accurately the AZ regions for

eliminating the desired FP resonances.

Our 4 cm long phase mask has a chirp of 1 nmkm, equivalent to a grating

chirp parameter of 6A = 2.67 x 10-14 mVm. The reference amplitude mask had a

3.5 cm opening and we designed the other amplitude masks to yield the

calculated transmission responses shown in Figs. 4.2(b) - (dl. Specifically, the

amplitude masks resemble the structures illustrated in Figs. Q.l(b) and (cl with

the same values and positions of the Al regions used in the corresponding

grating simulations.

The gratings were written using 248 n m radiation fkom a KrF excimer laser

in standard telecommunication fiber (Corning SMF-28 or AT&T Accutether)

which had been hydrogen-loaded at = 125 atm at room temperature for more

than ten days. Once the appropriate amplitude masks which give the desired

transmission response were positioned behind the phase mask, we then scamed

the UV beam across the amplitude/phase mask combination, placed the fiber

under strain, and performed a second scan. Both scans were made at the same

Chapter H h i r p e â Moiré Gmtings for Wavclengtb-Dinsion-Mdtiple~ng 72

speed, pulse repetition rate, and pulse energies. Typical fabrication parameters

are 0.15 mm/s scan speed, 50 Hz repetition rate, and 50 - 60 mJ/pulse energy.

The pulse energies were kept sufnciently low so that the writing process was

linear (to obtain equal refractive index modulations for both gratings).

However, we typically observed different index changes for both exposures.

Fig. 4.6 shows the experimentally measured transmission spectra with 10

pm resolution, obtained using a tunable laser diode, of three CMGs (labelled

Grating 1, Grating 2, and Grating 3) with one or two flattened passbands

fabricated in SMF-28 fiber. The passbands have < 0.5 dB npple and exhibit > 12

dB isolation. The agreement between the calculated and measured results is

excellent, indicating the feasibiliw for fabricating such structures. We also

measured the group delay response [68] of these CMG filters and found that it

was nearly constant in the passbands, see Fig. 4.6. Clearly, our fabricated CMG-

based transmission filters approximate an ideal filter response. Note that the

bandwidth of the passbands increases with wavelength; this is due to the

increasing FSR associated with the original CMG structure and is inherent to

the fabrication process that we adopted (see the discussion in section 3.2). It can

be avoided by using a holographie exposure or phase mask interferorneter

technique since in these approaches, the wavelength separation Ah cari be

obtained without the need to strain the fiber between the exposures. The

channel isolation of the passbands can be fûrther improved by increasing the

grating strength. Nonetheless, the filters that we have fabricated have better

Chapter Q-Chirptd Moiré Gratings for Wavdengtb-Division-Mdtiplexiag 73

performance (with regards to channel isolation and in-band group delay) than

the best multiple-phase s h i h d FBG gratings realized to date [6l].

1542 1 544 1546 wavelength, nm

Fig. 4.6. Experimentally measwed transmission spectra (solid line) and group delay (dashed line) of CMGs fabricated to have a single or t w o flattened passbands: (a) Grating 1,

corresponding to that in Fig. 4,2(b), (b) Gratiag 2, correçponding to that in 4.2(c), and (cl Grating 3, corresponding to that in Fig. 4.2(d).

To characterize fimther the performance of our CMG filters, we inserted

them in the 2.5 Gbitls transmission system shown in Fig. 4.7 to determine

whether or not they introduce power penalties due to dispersion-induced pulse

broadening. Output £iom a tunable laser diode was intensity modulated by an

electro-optic modulator driven by a 223 - 1 NRZ pseudo-random bit sequence at

2.5 Gbit/s. The data was then sent through the CMG filter which could be used

in a real system for providing wavelength selectivity or dropping the channel.

Chapter 4-Chirpeà Moiré Gratiags for Wavdeagh-Division-Multiplerriag 74

The electro-optic modulator produced low-chirp output pulses so that any

dispersion-induced pulse broadening is primarily due to filter dispersion.

receiverl electro -optic

MZ modulator dock regenerator CMG filter

I > tunable LD

2.5 Gbit/s

data generator

Fig. 4.7. Experimental setup for measuRng BER of CMG filters.

The measured response of the CMG filter, fabricated in AT&T Accutether

fiber, that we used in the experiment is shown in Fig. 4.8 and is similar to that

shown in Fig. 4.6(a). We determined the power penalty at a given wavelength by

performing 2.5 GbiVs bit-error-rate (BER) measurements and comparing the

required optical power received for a BER = 10-9 to that of the back-to-back

configuration (with no filter). These measurements were then repeated for

wavelengths which span the passband of the filter and the results are shown in

Fig. 4.8(b). Negligible power penalty (< 0.2 dB) was obsenred, even near the

filter edges, since it is essentially dispersionless. Thus, our filters do not produce

any significant dispersion-induced power penalties when used for providing

wavelength selectivity in 2.5 GbiVs systems, i.e., dispersion does not limit the

Chapter 4-Chirped Moiré Gratings for WavdcngOi-DivUion-Mdtipldng 75

usable BW of the filter. Furthemore, based on the measured group delay, we

also expect similar results at 10 Gbit/s since the gmup delay variation is less

than 10 ps (at 10 Gbit/s, a 25 ps group delay variation would create a 1 dB power

penalty). This contrasts previously reported results [66] where power penalties

up to 3 dB were measured for a Gaussian apodized FBG used in reflection.

1549.6 1550.0 1550.4 1550.8 1551.2

wavelength, nm

Fig. 4.8. (a) Measured transmission (solid line) and group delay (dashed line) of the CMG filter used in 2.5 Gbi* power penalty experiments; (b) measured power penalty at BER = 10-9 as a

fundion of wavelength within the filter passband.

4.4. Discussion

In concluding this chapter, we make some general remarks on the

dispersive properties of optical filters and in particular, their implications for

FBG-based filters. Optical filters may be analyzed as digital filters and hence,

Cha p ter W b i r p e d Moiré Gmtings for Wavdem-Division-Multiplunng 76

treated with standard digital signal processing methods [65]. We first make two

distinctions on the types of filters: (1) those having a finite impulse response

iFIR) as opposed to those having an infinite impulse response (IIR) and (2) those

that are minimum phase (MP) as opposed to those that are not minimum phase.

The frequency response of an FIR nIter can be expressed as

while that for an IIR filter is given by

The frequency response of an FIR filter only contains zeros while that for an IIR

filter contains both zeros and poles. The latter is characteristic of a system

containing feedback. Since FBGs operate in either reflection or transmission,

they involve some mechanism of feedback and so they are inherently IIR filters.

A minimum phase filter is one in which the amplitude response uniquely

determines the phase response. In particular, the two are related by means of a

Hilbert transform (similar to the Kramers-Kronig relation in optical physics

which relates the absorption spectrum of a material to its fkequency-dependent

refractive index). In fact, it has been shown that the phase is related to the

derivative of the amplitude response on a log-log scale [65]:

Chapter H h i r p e d Moiré Gtatings for Wavdength-Division-Multiplcxing 77

where u = ln(+) is a normalized fhquency and A and B are a Hilbert

transform pair, the real and imaginary part or logarithm of magnitude and

phase. The significance of this transform relation is that having a square-like

amplitude response can only be obtained at the expense of an increased

nonlinear phase response. On the other hand, non-MP filters are free fiom this

constraint and in this case, the phase response is not uniquely determined by

the amplitude response. One important class of non-MP filters are dl-pass

filters which have a pure phase response (i.e., the phase can be tailored

independently of the amplitude response).

We now discuss how the above distinctions and consequences apply to FBG

filters. First, we note that an FBG filter can be thought of as a two-port junction

having four different responses: two reflection responses, H: (o) and H;(CW , and

two transmission responses, H;(o)and ~ : ( w ) , fiom the opposite ends of the

grating. The transmission response is identical regardless of which end the

input is incident so that H;l(o) = H F ( o ) . Reversibility imposes an additional

relation among the grating responses (assuming a lossless grating):

HL(%) = 1,- H P (~, - , ) td*(~~) (4.4)

From this relation, we derive that while the reflection amplitude responses are

the same, the group delays differ, depending on which end the input is incident,

d#; d#L1 1-e., - #- where @R denotes the phase responses of the filter in reflection.

do d o

Thus in general, the reflection response of FBG filters is non-MP. However for

Chapter H h i r p d Moiré Craüngp for Wavdenm-DinSion-Multiplexing 78

spatially symmetric structures, such as apodized or unapodized FBGs having

uniform grating periods, the phase responses q$ and @;' are identical and the

reflection response is MP [69]. In view of this discussion, we can now

understand the poorer peflormance of the reflection filters based on apodized

FBGs considered in section 4.2.3: although the apodization generates square-like

amplitude responses, this can corne only a t the expense of an increased

nonlinear phase response. Now if the grating is spatially asymmetric, then it is

non-MP in which case the phase response can not be uniquely determined by its

amplitude response. However, this does not imply that we can obtain a square

spectral response with a linear phase response and the reason is as follows. In

order for an FBG to have a spatially asymmetric structure (to avoid being MP),

two parameters can be changed: (1) introducing an asymmetric DC background

refractive index profile or (2) varying the grating period, i-e., chirp. Either of

these options gives rise to a spatially dependent resonant grating condition and

hence automatically, a non linear phase response (i.e., the group delay is not

constant).

We now turn our attention to the transmission response of an FBG. Since

the inverse Fourier Transform of Hdo) is identically zero for negative time, it is

a causal function. Furthemore, the inverse transmission coefficient 1/ Hdo) is

also causal. These two properties ensure that the transmission response is MP

[69]. This can also be derived by noting that Hdo) is an all-pole response. The

phase response of an FBG transmission-based filter is uniquely determined by

Chapter H h i r p e d Moiré Gntiags for Waveitngtb-Division-Multipldng 79

the amplitude response so that the amplitude response can be made more square

only at the expense of increased nonlinearity in the phase response. Thus, the

results on the filter cornparison presented in section 4.2.3 may appear somewhat

surprising. In particular, since al1 the FBG filters considered were MP, their

phase responses are uniquely determined by their corresponding amplitude

responses. If the FBG filters had similar amplitude responses, then they should

have had the same performance with respect to their dispersive pmperties. But

we emphasize that the similarïty in the amplitude response came only from

specification of the filter passband ripple, 3 dB bandwidth, and edge slope at the

-10 dB point. Clearly, simple observation of the amplitude responses of the FBG

filters shows that they are significantly different. For example the FBGs having

a Gaussian or Blackman apodization profile have amplitude responses with

sharp drop-offs beyond the -20 dB point in addition to the appearance of

sidelobes. On the other hand, for the FBG having a combined Gaussian and sinc

apodization as well as the two transmission-based FBG filters, there is a more

gradua1 change in the amplitude response. According to (4.3, the increased

sharpness in the amplitude response of the FBG filters having Gaussian and

Blackman apodization functions will create additional nonlinearity in the phase

response. Fewer variations in the amplitude response will result in a more

linear phase response. This is particularly true for the CMG-based transmission

filter. Another interpretation of the near linear phase response of the CMG is to

recall that the modified CMG is effectively a concatenation of physically separate

Chapter 4-Chirped Moiré Gratings for Wavelength-Division-Mdtipldg 80

gratings, each occupying its own wavelength interval. Wavelengths in the

passband effectively do not see any gratings though there are gratings on either

side. Thus these wavelengths are transmitted in the "wings" of the neighboring

gratings. It has been shown that the out-of-band dispersions from the adjacent

gratings can caneel, creating a region zero dispersion within the passband (641,

Vol, [W.

Chapter 5

Chirped Moiré Gratings for Optical Code-Division Multiple-Access

5.1. Introduction 5.2. Ultrashort pulse refïection from CMGs 5.3. CMGs for encoding/decoding pulses 5.4. Analysis of pmposed system 5.5. Experimental results 5.6. Discussion and s u m m a r y

5.1. Introduction

Optical code-division multiple-access (OCDMA) is a multiple access

technique for local area networks whereby user-specific code sequences are used

for channel discrimination. Multiple users can access and communicate over a

single transmission medium by encoding their data with user-specific codes. At

the receivers, matched decoders or filters are used with cross-correlation and

thresholding operations to ensure that data are detected only when they have

amved at the proper destination. In order to guarantee proper discrimination of

unwanted signals, multi-access is achieved by assignment of minimdly

interfering codes to each user.

Among the various attractive features of OCDMA are the ability to support

asynchronous, bursty t r a c , the potential for increased security, high capacity

(pnmarily through the interconnection of a large number of users operating at

modest data rates), and less stringent wavelength control compared with WDM

systems 3721, [73]. Many different implementations of OCDMA systems have

Chapter Whirped Moiré Gratings for Optical Code-Division MultipleAccess 82

been proposed. These are based on coherent or incoherent schemes, and the use

of optical orthogonal or truly orthogonal transmission with unipolar or bipolar

coding schemes.

Broadly speaking, OCDMA schemes can be divided into four general

categories: (1) direct-sequence (DS), (2) spectral amplitude encoding, (3) spectral

phase encoding, and (4) hybnd multiplexing techniques which combine two

domains, such as space and time or wavelength and time, for encoding signals.

DS-OCDMA schemes, also known as tirne addressingkode pulse positioning

CDMA, are based on suitable pulse positioning of the code bits (known as chips)

according to a specified code stmcture [74]. Implementations are based on

(tunable) delay lines or ladder networks [75] for the encoderddecoders,

incoherent detection, and the use of optical orthogonal codes I761.

Disadvantages of this scheme include the need for slot synchronization for

thresholding operations in the detection process and the use of inefficient, very

long code sequences to achieve optical orthogonality. Spectral amplitude

encoding schemes involve dispersing the fkequency components of a broadband

signal and spatially filtering them [77]. The various fkequency encoded patterns

that can be generated, the number of which depends on the resolution of the

spatially dispersed components, correspond to the different user codes. This

technique can achieve truly orthogonal transmission, especially when using

bipolar codes and balanced detection [78], 1791. Spectral phase encoding involves

the manipulation of the phases of the spectral content in a coherent ultrashort

Chapter 5-Chirped Moiré Gratings for Optical CodedXvision Multiple-Access 83

pulse B O 1 - [821. Encoding involves transforming an ultrashort coherent pulse

into a pseudo-noise burst while decoding involves subsequent reconstruction of

the coherent input pulse. Generally, this approach requires nonlinear optical

detection and thresholding and, unless properly accounted for, s e e r s severe

transmission impairments, especially from chromatic fiber dispersion, due to the

large bandwidth of the signals involved. Hybrid approaches seek to exploit the

simultaneous use of two domains, for example space and time [83] or wavelength

and time [841, f851, to provide flexibility in the selection of user codes and

achieve quasi-orthogonal requirements between multiple users.

Although many OCDMA implementations have been proposed and their

performance theoretically analyzed, there have been far fewer demonstrations of

encoding/decoding optical signals and even fewer system demonstrations.

Furthemore, existing proposals ofken involve bulk optic components which may

be difficult to package or ensure stability for proper operation, expensive

components (such as a mode-locked source for spectral phase encoding

approaches) which are not suitable for local area networks, and very cornplex

implementations.

FBGs have emerged as critical components and enabling technologies for

many lightwave communications applications. It is thus of no surprise that

there have been several proposals of using FBGs to irnplement various forms of

OCDMA [86] - [95]. We now bnefly describe two of the more thoroughly

investigated proposals which are based on spectral phase encoding [931, [941 and

Chapter M h i r p e d Moiré Gratings for Optical Code-Division Multiple-Access 84

a hybrid wavelength/time approach (also referred to as fast-fkequency hopping)

1861, [W, WI.

Templex Technology have proposed the use of segmented composite gratings

to perfom spectral phase encoding of ultrashort coherent pulses 1931, [941, see

Fig. 5.Ua). The encoder consists of a segmented fiber grating, Le., a linear array

of uniform gratings al1 having the same grating perïod, but with different peak

refractive index modulations and spatial phases relative to a fïxed coordinate

system. When a short input pulse is reflected fiom the grating, the reflected, or

encoded signal, comprises a train of time-delayed pulses of width equal to the

chip window. The relative amplitudes, temporal phases, and bandwidths of the

pulses in the encoded signal are determined by the peak refkactive index

modulation, phase, and length of the individual subgratings comprising the

composite structure. A matched grating decoder is used to de-spread the

encoded signal and reconstruct the original short pulse. This scheme involves

coherent pulses and in a practical system, would require a nonlinear threshold

detection process. A 15:l contrast ratio between the peaks of the properly

decoded desired and improperly decoded unwanted signal was achkved for a two

user, sparse OCDMA system (the encoded signds of the two users were not

allowed to overlap in tirne).

- --

Chapter Mhirped Moiré Gratings for Optical Code!-Division Multiple-Access 85

Fig. 5.1. (a) Spectrai phase encoding using an encoder based on a segmented fiber grating I941. (b) Fast-frequency hopping using an encoder consisting of a serial Bragg grating array 1891.

In a series of studies on the propagation of short pulses through FBGs [86],

[871, we realized the potential of eombining short pulse and FBG technology for

novel implementations of OCDMA systems. In particular, we demonstrated the

use of a serial FBG array to decompose a broadband input signal simultaneously

in both wavelength and time domains and proposed how this could form the

basis for encoding operations [86]. Our original idea was then fùrther developed

and analyzed by Fathallah et al. from Université Laval [89], [go]. As illustrated

in Fig. 5.l(b), encoding and decoding of a broadband signal are achieved by bi-

directional refiections (opposite ends) £!rom the grating structure. Here, the chip

Chapter Mhirped Moiré Gratings for Opticcil Code-Division Multiple-Access 86

duration, given by Tc = 2nWco where L is the spacing between gratings and n is

the reeactive index of the fiber, is the round-trip propagation tirne between two

adjacent gratings in the array. The total round-trip propagation time through

the grating structure, T = I2(N-I)Ln]lco where N is the number of gratùigs in the

array, determines the overall bit rate. This implementation allows both

wavelength and time domains to be used in defining user codes. However, it

requires very precise control in the fabrication of the grating encoder and

decoder stmctures-not only do the wavelengths of the gratings have to match,

but the spacing between them as well. Otherwise, the de-spreading operations

will degrade.

In this chapter, we descnbe how CMGs can be used as encoding and

decoding elements for implementing a hybrid wavelength-encoding/time-

spreading (WE/TS) OCDMA system. Our proposed scheme difXers Çom other

WE/TS implementations in the following ways:

in contrast with [84], no rapidly tunable source is required for providing

the wavelength encoding. The wavelengths are instead provided by the

use of a broadband input.

r wavelength-encoding and tirne-spreading are performed using a single

fiber grating stmcture, contrary to the approach presented in [96] where

an mayed waveguide grating is used to spectrally slice a broadband

input and f i ed delay lines are used to define the time-spreading

patterns.

Chapter 5-Chirped Moiré Gratings for Opticaï Code-Division MultipleAccees 87

Our approach builds on our initial proposai of using a serial FBG array to

decompose a broadband signai simultaneously in both wavelength and time

domains and has the same basic principle of operation as that of Fathallah et al.

However, in the present implementation, we use only a single grating to perform

encoding and decoding dl-optically and all in-fiber. This results in a cost-

effective implementation that limits the amount of electronic processing,

facilitates packaging (for stable and environmentally insensitive operation) of

the grating encoder and decoder structures, and relaxes the tight requirements

on the fabrication processes.

5.2. Ultrashort pulse refiection nom CMGs

W e first begin by examining the refiection properties of CMGs. Recall that

the crossover points of the beat in the grating &inge pattern correspond to TC

phase changes, each producing a passband in the transmission response. These

passbands have the effect of creating spectrally separated stopbands in

reflection.

In Fig. 5.2(a) we show the calculated spectral response of a 3 cm long CMG

with a peak refkactive index modulation 612 = 8.0 x 10-4, hi = 2 n o ~ : = 1550.0 nm,

1 2 = 2110~: =1550.2 nm, and equal chvp parameters for both gratings 6A1= 6A2 =

5.0 x 10-l4 m2h. This CMG has 7 reflection stopbands. Of greater interest is

the corresponding reflected group delay, shown in Fig. 5.2(b), which is linear as

expected since the individual gratings comprising the CMG are themselves

- - - --

Chapter 5-C-d Moiré Gratings for Opticaï Code-Divi~ion Multiple-Acceas 88

linearly chirped. The physically reversed CMG stnicture has the same

amplitude response (see the discussion in section 4.4); however it has, to first

order, an opposite group delay response as shown in Fig. 5.2(c) (this principle

has been demonstrated in an experiment in which pulses were broadened and

recompressed by bidïrectional reflection fiom a linearly chirped FBG [97] ).

wavelength, nm

Fig. 5.2. Caiculated reflection response of a 3 cm long CMG with 6n = 8.0 x 104, LU = 0.2 nm, and equal chirp parameters SA1 = 6 ~ 2 = 5.0 x 10-14 mVm: (a) amplitude and reflected group delays for light incident on (b) the short wavelength and (c) long wavelength sides. The

discontinuities in the group delay occur where the phase of the reflection coefficient changes by x and the polarïty is arbitrary.

We now consider the reflection of short broadband pulses from CMGs.

The short pulse response of FBGs, and in particular CMGs, c m be modeled

using simple Fourier analysis: the reflected signal ER(L) is the inverse Fourier

Transform of the product of the input pulse spectrum E d o ) and the grating

reflection response H R W :

Chapter 5-Chirped Moiré Grntings for Optical Code-Division Multiple-Access 89

Note that the phases of the signals are important which is why in the above

expression, we work with field quantities. Another usefùl representation in

modeling pulse propagation in FBGs is a two-dimensional joint time-fkequency

(TF) representation given by the spectrogram (SPI distribution [98]:

where g(o) is a frequency window function that determines the resolution of the

representation. The SP distribution provides the intensity of a signal as a

function of both fkequency (or wavelength) and time simultaneously.

Fig. 5.3 shows the measured reflection spectra and corresponding reflected

group delay of the same three CMG filters appearing in Fig. 4.6. As expected,

the reflection response comprises a series of stopbands separated by the

transmission passbands. The sharp separations between stopbands arise from

the narrowly peaked transmission resonances while the larger separations

between stopbands arise nom the flattened passbands in the transmission

response. Note that the linear relationship between reflected wavelengths and

time is still preserved even though regions of constant refkactive index have been

introduced within the grating structure Clearly each stopband is reflected in its

own time dot. Thus, a CMG operating in reflection can be used to decompose a

short broadband pulse simultaneously in both wavelength and time domains

and, in this sense, has similar functionality to a serial FBG array.

Chapter 5-Chirped Moiré Gratings for Optical Code-Division Multiple-Access 90

Furthemore, for the CMG there is a distinct phase relation that is maintained

between the wavelengths in the stopbands.

wavelength, nm

Fig. 5.3. Measured reflection response (solid line) and group delay (dashed line) of (a) Grating 1, (b) Grating 2, and (c) Grating 3. These are the corresponding reflection responses for

the three gratings shown in Fig. 4.6.

In Fig. 5.4 we show simulations for the reflection of a 0.5 ps transform-

limited Gaussian puise incident on the short wavelength side of the above three

gratings [the parameters used to calculate the grating response are the same as

those used in the grating simulations whose transmission responses appear in

Figs. 4.2(b) - (d)]. The leR plot shows the spectral content of the reflected signal

(which is essentially the grating fkequency response multiplied by the input

pulse spectrum), the bottom plot gives the reflected signal waveform [given by

Eq. (5.1)], and the center plot gives the SP distribution. The TF representation

- --

Chapter whirped Moiré Gratings for Optical Code-Division Multiple-Access 91

clearly demonstrates that the short broadband input pulse has been decomposed

simultaneously in both wavelength and t h e : each pulse in the reflected signal

occupies its own time slot and wavelength band.

r I 1

time, 50 ps/div

Fig. 5.4. Time-frequency representations of a short broadband input pulse reflected fiom (a) Grating 1, (b) Grating 2, and (c) Grating 3. Tbe input is a transform-limited 0.5 ps Gaussian

pulse incident on the short wavelength side of the gratings.

Chapter 5-Ch-d Moiré Gratings for Opticsü Code-Division Multiple-Access 92

time, 50 ps/div

Fig. 5.4 (cont'd). Time-fi-equency representations of a short broadband input pulse reflected h m (a) Grating 1, (b) Grating 2, and (c) Grating 3. The input is a transform-limiteà0.5 ps Gaussian pulse incident

on the short wavelength side of the gratings.

To demonstrate this concept experimentaliy, we launched near transform-

limited = 0.5 ps pulses with a F m bandwidth = 5 nrn Çom a wavelength-

tunable mode-locked (ML) EDFL and measured the reflected signals using a 25

GHz photodetector and 50 GHz sampling oscilloscope (combined overall response

time = 40 ps). The repetition rate of the EDFL is 6 MHz and the peak intensity

is = 2.5 x 107 WIcm2 so we do not expect to observe any nonlinear effects

(especially over the interaction lengths under consideration) [33]. The results

are shown in Fig. 5.5. When we tuned the wavelength of the EDFL to shorter

and longer wavelengths, we obsemed increases and decreases in the relative

peaks of the different pulses in the reflected signal depending on which stopband

saw more of the input pulse energy. This confirms that each pulse in the

Chapter u h i r p e d Moiré Gratings for Optical Code-Division Multiple-Access 9 3 -

reflected signal is at a different wavelength and that the reflected wavelengths

are spread in tirne.

Fig. 5.5. Measured reflection response ftom (a) Grating 1 (input pulse at A = 1542.35 nm), (b) Grating 2, (input pulse at A = 1542.9 nm), and (c) Grating 3 (input pulse at A = 1542.75 nm). The input is incident on the short wavelength side (soiid b e l and the long wavelength side (dashed

line).

As rnentioned earlier, a given CMG and its physically reversed structure

have the same reflectivity and, to fïrst order, opposite reflected group delay.

Thus the temporal reflection response depends on whether the input pulse is

incident on the short-wavelength or long-wavelength side of the grating. For

gratings with a symmetric spectral response, such as Gratings 1 and 2 in Fig.

3.5(a) and (b), the temporal reflection response will be simïlar regardless from

which end the input is incident. On the other hand, for gratings with an

asymmetric spectral response, such as Grating 3 in Fig. 5.5(c), the temporal

Chapter M h - d Moiré Gratings for Optical Code-Division Multiple-Access 94

reflection response will be Merent when the input is incident from opposite

ends of the grating. We cm, of course, always determine fkom which end of the

grating the input pulses are incident by simply tuning the input pulse towards

shorter or longer wavelengths and observing which of the peaks in the reflected

signal increase.

5.3. CMGs for encodingldecoding pulses

Qualitative description and irnplementation

Since a CMG and its physically reversed structure have the same ampli tude

response and to first order opposite group delay, we can envision encoding and

decoding broadband pulses by successive bi-directional reflections Çom a CMG

(encoding) and its physically reversed structure (decoding).

A CMG can be modeled as a multi-wavelength filter, or a set of w 5 N

discrete wavelength filters, with corresponding time delay lines for each filtered

wavelength component (w and N will be defined in the next paragraph). E t

serves two functions in encoding and decoding as illustrated in Fig. 5.6. First, by

selectively filtering wavelength components of the input pulse (i-e., spectral

slicing), it performs wavelength-encoding and second, by temporally arranging

these spectral components in a linear fashion, it performs time-spreading. If the

decoder is the physically reversed structure of the encoder, then the filtering

operations are identical and the temporal arrangements of the wavelength

components are complementary so that proper decoding can be achieved. To

Chapter S-Chirped Moiré Gratings for Opticai CodeDivision Multiple-Access 95

perfonn proper decoding, the decoder must recover d l of the wavelengths of the

encoded signal into the same time slot rather than simply re-arranging them in

time, Le., de-spreading the signal. Note that the original input puise will not be

fuliy reconstructed since we have performed spectral slicing (Le., eliminated

spectral contents fkom the pulse). However, properly and improperly decoded

signals can be distinguished on the basis of peak intensities, especially within

the time dot where al1 of the wavelengths of the properly decoded signal are

recovered.

chirped moiré gmting: encoding device

input signal

performs psdonns = bit rate spectral slicing time spreading

(wavekngthancoding)

output encoded signal

âetay

Fig. 5.6. Schematic illustration of (a) encoding and (b) decoding an ultrashort broadband pulse usiag CMGs. The CMG is modeled as a multi-wavelength filter (or discrete set of wavelength filters) with corresponding tirne delay lines for each filtered wavelength component. Dflerent users (codes) are defined by different spectral slicing patterns (i.e., different wavelength faters)

and their corresponding time delay patterns.

+

A L ; T= round-ttip propagation / time through gmting

5 CA C O 0 . 0 gm g" -

4 . T h - A

h b 2=c

t O Tc 2T, NT,

)k NT, T -

Chapter Mhirped Moiré Gratings for Optical CodeDïvision Multiple-Access 96

chi- I'n~ird gnting: dscoding device (phyrial reverse of encoding g d n g structure)

input encodcd signal

output decoôed signal

u u in this time dot

spectral decoding tim-de-spreading

Fig. 5.6. (con't). Schematic illustration of (a) encoding and (b) decoding an ultrashort broadband pulse using CM&. The CMG is modeled as a muiti-wavelength filter (or discrete set

of wavelength nIters) with corresponding tirne delay lines for each filtered wavelength component. Different users (codes) are dehed by different spectral slicing patterns Le.,

different wavelength filterd and their corresponding t h e delay patterns.

A given CMG has N spectrally separate reflection stopbands centered at hL ( 1

= 1, . . ., N) which occupy N time dots (or chips) each having a duration Tc = T / N

where T is the round-trip propagation time through the CMG (and could

correspond to the bit window). This results in a code length equal to N. A

convenient representation of the available codes is a 1 x N array,

denoted c, = [ci .ci .. . . . cr 1, where the index of the array defines the time slot (for

example, the fïrst entry corresponds to time dot 1, and so on) and the entry itself

gives the central wavelength of the stopband. Since the stopbands are reflected

sequentially in time due to the linear relationship between reflected

wavelengths and time as shown in Fig. 5.2, a given CMG gives rise to only one

C hapter 5-Chirped Moiré Gratings for Optical Code-Division Multiple-Access 97

code with a weight w = N, where the weight corresponds to the number of pulses

in the coded waveform (and equivalently, the number of spectral slices).

Suppose that from a given CMG we choose only q of the available N reflection

stopbands (wavelengths) for one code so that w = q < N. We are essentially

defining different spectral slicing patterns (wavelength-encoding patterns) which

would correspond to different codes. This can be accomplished by seiectively

eliminating stopbands from the CMG response as described in Chapter 4. The

code length is still N as defïned by the number of tirne slots corresponding to the

original CMG; however, N - w of the entries in the code are O (no signal) and the

w non-zero entries correspond to the wavelengths of retained stopbands. We can

then define a maximum of f i = L N / ~ J = L N / w ] codes that are strictly orthogonal

(i-e., the gratings corresponding to these codes have no spectral overlap), where

LeJ denotes the integer part of the argument. To generate additional codes, the

m 2 6 strictly orthogonal codes that we define can be simply wavelength shifted.

These new codes are only quasi-orthogonal since there may be some spectral

overlap between the gratings corresponding to the shifted and original codes. In

the above, strictly orthogonal codes refer to those which are strictly non-

interfering (the codes have a cross-correlation that is identically 0) ; quasi-

orthogonal codes are those which are minimally interfering (the codes have

specific cross-correlation properties which are defïned in Section 5.4.1). In Fig.

5.7, we show the concept of encoding and decoding with both strictly orthogonal

and quasi-orthogonal codes.

Chapter M h i r p e d Moiré Gratings for OpticaÏ Code-Division Multiple-Access 98

Output cacoded signai

Dccoding device for uscr 1

Encoding device for user 2 A iR l h . i !

hput A L, A4 1 I signal i 1 :+Tc+

-T- Output encoded signal

Decoding device for user 1

I 1 Input

encoded signal

no spectral overlap of codes => no output

Fig. 5.7. Schematic illustration of encoding and decoding processes. (a) proper decoding of desired user, (b) decoding an interferer having a strictly orthogonal code relative to the desired

user, and (c) decoding an interferer having a quasi-orthogonal code relative to the desired user.

C hapter 5-Chiiped Moiré Gratings for Opticaï Code-Division Multiple-Access 99

Input

Output encodcd s i g d

Dccodiag device for user 1 n

Fig. 5.7 (cont'd). Schematic iilustration of encoding and decoding processes. (a) proper decoding of desired user, (b) decoding an interferer having a strictly orthogonal code relative to the desired user, and (cl decoding and interferer having a quasi-orthogonal code relative to the

desired user.

t

Fig. 5.8 illustrates one possible implementation of an OCDMA network

which uses CMGs as encoder/decoders. Each transmitter comprises a broadband

source (mode-locked laser, gain-switched laser diode, amplified spontaneous

emission from an erbium-doped fiber amplifier, etc...), a modulator, and a CMG

encoder; each receiver comprises a CMG decoder and a detection unit

(photodiode, threshold electronics, etc. ..). A given user pair i communicates over

the network as follows. The output of the broadband source is modulated with

the data stream giving a string of pulses (bits) which are then reflected from the

CMG encoder. The encoded signal is then broadcast to al1 receivers in the

network via a star coupler. Following the decoding and threshold detection

L I . . . . .

Input 1 .

. . , I I nf@ l i , , . , , . . . . . - encodeâ -+ & $ k

Chapter 54Xairped MoVé Gratings for Opticaî CodeDivision Multiple!-Access 100

processes, only the desïred receiver which has the proper CMG decoder (i.e., the

physically reversed structure of the CMG encoder) will be able to recover the

information sent. Note that al1 the encoding/decoding operations are performed

in-fiber.

I I

I I I I

, I 1

: broadbmd modulaior source electronics i

0 I 1 , I

I 1 I

I I I CMG decoder CMG encoder I I I I 1 I I

1 I c

O L

I I I 1

6 I

Fig. 5.8. Implementation of CMG encoderddecoders in an OCDMA system.

Numerical exarnple: simulation

We now consider a concrete example that illustrates encoding and both

proper and improper decoding processes. Let N = 7 and LU = 3. We can define at

most two strictly orthogonal codes, for example ci = [0,2,3,0,0,6,0] and cz =

[1,0,0,4,0,0,7]. We can also define quasi-orthogonal codes which are wavelength-

shifted versions of cl and c2, one of which is c3 = [0,1,2,0,0,5,0]. The encoded and

decoded waveforms for a user with code cj are denoted as cdt) and

c: ( I ) respectively. In Fig. 5.9(a), we show the spectral responses of 3 CMGs

Chapter u h i r p e d Moiré Gratings for Opticd CodeDivision Multiple-Access 101

which generate the three codes ci, cz, and c3 (in the codes, Ai corresponds to the

stopband centered at =1550.5 n m and so on). These three CM& have the same

parameters (length, peak index modulation, difference in central periods or

wavelengths of the two superimposed gratings) as that in Fig. 5.2 except that

they incorporate regions of no refractive index modulation within the grating

structure in order to obtain the desired spectral response by suppressing

stopbands. Specifically, the CMG for cl has 3 regions of lengths 0.5 cm, 1.0 cm,

and 0.5 cm centered at z = 0.25 cm, 1.75 cm, and 2.75 cm respectively where

there is no index modulation; the CMG for c2 has two regions of equal length

0.75 cm centered at a = 0.875 cm and 2.125 cm where there is no index

modulation; and the CMG for c3 is identical to that for ci except for different

grating periods which shift the wavelengths by the width of a stopband. Codes

cl and c3 have the same tirne-spreading pattern but different wavelength-

encoding patterns. Thus the encoded signals ci(t) and c3W will have pulses in

the same time slots but the pulses will be at different wavelengths. In Fig.

5.9(b), we show the waveforms corresponding to the different codes assuming a

transform-limited 0.5 ps Gaussian pulse at 1 = 1554.25 nm as the input. In Fig.

5.10(a) - (c) , we show the result of decoding ci(t), d t ) , and «(t) using the decoder

for code c l . As expected, cy(t)has the largest signal due to proper decoding

whilec:(t) = O due to the orthogonality of ci and c2. Although there is some

spectral overlap between the CMGs defining ci and c2 [see Fig. 5.9(a)], so that

strictly cf (t) # O , the energy of cf (t) is clearly much greater than that of cf ( t ) .

Chapter 5-Chirped Moiré Grating~ for Opticai Code-Division Multiple+Access 102

Also, codes cr and c3 have one overlapping stopband at t = 1552 nm so that part

of c3W will be decoded by the decoder for code ci. However, its wavelength-time

relationship is such that the overlapping stopband will be recovered into a

different time slot than that for the stopbands in cr(t) as can be seen by

examining the wavelength-the relationships given by the codes. More

generally, if we assume chip synchronization, then a properly decoded signal will

have al1 of its wavelength components recovered into a different time slot fiom

that of an improperly decoded signal (in fact, they will be separated in time by

at hast Tc, the duration of a refiection stopband). In this case, properly and

improperly decoded signals can be W h e r distinguished by use of time-gating

(which selects the time slot within the bit window when the detector samples the

decoded signal) to suppress undesired signals. We also consider decoding the

input signal a ( t ) + cz(t) + c3(t) with the decoder for code CI. As shown in Fig.

5.10(d), the desired signal ci(t) can still be recovered even in the presence of

undesired signals (from c2 and c3) by using the appropriate decoder. Note that

similar results will be obtained if any incoherent pulsed broadband source

(rather than transforrn-limited pulse) is used except that there will be a decrease

in the peak of the signals since the energy d l be more spread in the time slots

(since there is no coherent interference). Finally in Fig. 5.11, we use the TF

representation to illustrate W h e r encoding and proper decoding processes. The

simulation shows how the wavelengths are temporally spread in the encoding

process and subsequently de-spread after decoding.

Chaptei Mhirped Moiré Gn*gs for Opticaï CodeIlivision Multiple-Access 103

1550 1 552 1 554 1556 1558

wavelength, nm

Tirne Slot: t 2 3 4 5 6 7

450 500 550 600 650 700 750 800 850

Time (ps)

Fig. 5.9. Simulation of encoding a 0.5 ps transform-limited Gaussian pulse. (a) spectral response of the CMGs corresponding to the three codes outiined in the text and (b) corresponding encoded waveforms. The dotted Iines in (a) show the wavelength bands and in (b) show the time

slots (chips).

Chapter Whirped Moiré Gratings for Optical Code-Division Multiple-Access 104

Fig. 5.10. Simulation of proper and irnproper decoding of encoded waveforms in Fig. 3b. Decoded waveforxns: (a) cf ( t ) , (b) cf (I) , and (c) c ) (t) ; (dl the decoded waveform of c d t ) + cz(t)

+ cd$). Note the similarity with cf ( t ) ; additional multi-user interference ean be suppressed by tirne-gating. Al1 decoding was performed with the decoder for code CI. The dotted lines show the

time slots (chips).

The number of codes (users) that can be supported is determined

primarily by the value of N. Depending on the code design (see below), this

number can Vary fkom one to a value greater than N (i.e., the number of codes

can exceed the number of bands defined by the CMG stmcture). Furthemore,

we can design L and N so that Tc = T / N = (%no) / (Nd, where c is the speed of

light, will be sufficiently long to allow the tirne-gating (if used) to be performed

Chapter Whirped Moiré Gratings for Optical Code-Division Multiple-Access 105

electronically. W e will have more to Say about the use of time-gating in Section

5.4.

I I 1 I 1 I 1

1

I . I I 1 _

time, 50 pddiv

time, 20 pddiv

Fig. 5.1 1. Time-fiequency plots ïllustrating (a) the encoding and (b) proper decoding processes. Note the difference in the time axes between the two plots.

Chapter Mhirped Moiré Gratings for Optical CoddW&xion M d t i p l ~ A c c e s s 106

Code Design

The design of two-dimensional codes for WEYTS OCDMA systems has been

considered in [991, [100]. In this section, we present the design of suitable codes

that take into account the physical constraints imposed by our grating encoders.

Assume that the N reflection stopbands of a given CMG occupy the range [hrnin,

hmaxl which spans the entire bandwidth of the broadband input pulse, Le., [Amn,

Lmax] = [xp,Az]. In the following, we d l use the notation where the

wavelengths represent the central wavelengths of the stopbands. We can then

write X- = Amin + (N - 1)Ak where AA is the bandwidth of a stopband. If we

measure wavelength in units of AL so that in these normalized uni ts AA = 1, then

hm, = Ami, + (37 - 1). As mentioned earlier, we can choose to define m (5

ni = L N I W ] ) codes that use only LU of the available N stopbands, (Le., a code of

length N having a weight w). These strictly orthogonal codes define m time-

spreading patterns coupled to rn wavelength-encoding patterns. We will refer to

them as the onginal m codes. Note that the combined wavelength selective and

dispersive natures of the CMGs are responsible for coupling the tirne-spreading

and wavelength-encoding patterns. They are not independent.

Additional codes can be obtained by wavelength-shifting the original rn

codes: al1 the wavelengths in each of the m tirne-spreading patterns are simply

shiRed by n M = n, an integer multiple of the bandwidth of a stopband. This can

be accomplished physically by strain or compression tuning the m CMG

structures cornespondhg to the original rn codes (15 n m and 100 n m tuning are

Cbapter Mhirped Moiré Gratings for Optical CobDivision Multiple-Access 107

achievable via strain and compression respectively, though the ultimate limit

depends on material properties). Since we have assumed that the N stopbands

span the entire pulse bandwidth, the new wavelengths in the shifked codes must

still lie in the range [Amin, A d . Let the w wavelengths for a given code c; occupy

[A&, ,AL,]. This code allows lotver and upper wavelength shiRs of ( AL, - L i n ) and

(hm, -A& ) respectively. From the time-spreading pattern corresponding to cl,

there are then a total of N - f - A&, ) wavelengthencoding patterns, al1 having

the same tirne-spreading pattern, that can be generated. Thus, from a given N,

w, and set of original m time-spreading patterns, we can obtain the following

maximum number of codes:

Max. numberofcodcs = N m - ( g [ L - G n ] ) (5.3) j = i

We now need to specim the original rn tirne-spreading patterns (or codes).

Simple combinatorid analysis shows that there are a total of

from which to choose these m codes. Mdti-user interference is controlled by the

cross-correlation of the code sequences. In order to minimize the interference,

the codes should have a maximum (Hamming) cross-correlation peak (defined in

section 5 -4) equal to 1 (so-called one-coïncidence sequences (10 11 ); thus certain

restrictions on the initial choices need to be imposed. Since the original m codes

are strictly orthogonal, the restrictions are made to affect their wavelength-

C hapter Mhirped Moiré Gratings for Opticai Code-Division Multiple-Access 108

shifted versions. First, we do not want a wavelength-shifted version of one the

original rn codes to coincide with (Le., have identical wavelenghs) another of the

original codes. Thus no two of the original rn codes can have similar time-

spreading patterns. For example, the two codes ci = [0,2,0,4,0,0,7,0,01 and c2 =

[1,0,3,0,0,6,0,0,0] will result in a wavelength-shified version of one code

coinciding with the other. Second, for any two of the original m codes, the same

number of time slots (chips) cannot separate any two wavelengths in their

respective codes, unless the amount of shift necessary to make a wavelength-

shiRed code have a cross-correlation peak > 1 exceeds the maximum allowed

lower or upper shiRs. For example, consider the two codes ci = [0,2,0,0,5,0,7,0,01

and cr = [1,0,0,4,0,0,0,9]. Wavelengths X2 and h in CI and hi and )c, in c2 are

separated by the 3 time slots; thus a wavelength-shifted version of ci, specifically

c:~'" = [0.1,0,0,4.0.6.0,0] and cz will have a crosscorrelation peak of 2. On the other

hand, the two codes ci = [1,0,0,4,0,6,0,0,0] and c2 = [0,0,3,0,5,0,0,0,9] cannot be

wavelength-shifted to give a cross-correlation peak > 1 even though wavelengths

h and b in cl and h3 and & in c2 are separated by the same number of time dots

(= 2). Note that the &st requirement is inherently contained in the second.

Clearly then, the number of available codes &om which the original m codes can

m-1 N - k W be chosen is less than ( 1. We propose the following algorithm to choose

k =O

the original rn codes:

Chapter M h i r p e d Moiré Gratings for Optical Code-Division MultipleAccess 109

1. Choose a code, cj fkom at most (N ilw) possible codes (k = j - 1). This

chosen code d l now form one of the original m codes.

2. Eliminate from the remaining possible codes those having a single

wavelength already used in existing codes CI, cz, . . . , cj.

3. Eliminate fkom the remaining possible codes those having similar

the-spreading patterns or same number of time slots between

consecutive wavelengths (unless wavelength-shifting cannot produce a

cross-correlation > 1) as in the existing codes cr, cz, . . ., cj.

4. Repeat the above until there are no more remaining possible codes.

The choice of the codes is not unique and in some cases, the maximum number

f i = LNIW ] C-ot be achieved, i.e., rn < n i . However, the generated codes, in

addition to the5 wavelength-shifted versions, will satise the properties of (il a

single autosorrelation peak (no sidelobes) and (ii) a maximum cross-correlation

peak of 1.

5.4. Analysis of the proposed system

Performance

We now consider a matched-filter receiver and analyze the system

performance in terms of multi-user interference (but neglecting al1 other sources

of noise) as a function of the number of sirnultaneous users (m. The following

analysis is only approximate and is based on the following assumptions: (1)

C hapter S-C hirped Moiré Gratingn for Optical Code-Division Multiple-Access 110

perfect time slot (chip) synchronization between al1 interfering users, ( 2 ) ideal

rectangdar-shaped temporal pulses and spectral slices for the encoded and

decoded signals, (3) incoherent superposition of multi-user interference (a pulsed

broadband source is used as the input to the encoderddecoders), (4) a Gaussian

distribution for multi-user interference, and (5) the variance of multi-user

interference, 0 2 , is approximated by the variance of the amplitude of the cross-

correlation of (K- 1) uncorrelated users [89]

<* is the average value of the variance of the cross-correlation between pairs of

codes ci and cj given in terms of the Hamming cross-correlation [101]:

where

y, is the average value ofHij

( i i ) (S + 7 ) is takea modulo N

1 ' ( i i i ) c, = [ci , c; . . . . , C; ] and c, = [ci, c; . . . . , cy ] are two codes of length N.

With the above assumptions and using the optimum detection threshold y =

1 4 2 + p , where p is the average value of the multi-user interference with

C hapter 5-C hirped Moiré Gratings for Optical CodeDivision Multiple-Access 111

corresponding variance 02 given in Eq. (5.5), the signal-to-interference ratio SIR

and probability of error Pemr are respectively [89]:

W' - wC SIR =- -

a' - (K- I ) ~ J

where

In Fig. 5.12 we show Perm., calculated using Eqs. (5.5) - (5.71, as a function of

the number of simultaneous users for two cases: (N = 12, w = 3, m = 3), and ( N =

15, w = 3, m = 3). The corresponding original m codes and the maximum

number of available codes [obtained using Eq. (5.311 for each case is given in

Table 5.1 (recall that once the original rn codes are specified, al1 the codes can be

defined). We have also considered the cases (N = 18, w = 3, m = 4) and (N = 21,

w = 3, m = 6) and found that the system could support 24 and 48 simultaneous

users at Perror = 10-9 respectively (the original m codes are also given in Table

5.1). In Fig. 5.13, we plot the number of simultaneous users at Permr = 10-9 as a

function of the code length N for codes having a weight w = 3.

Again, we point out that the above results are only approximate and are

based on a first-order analysis. In real systems, the encoded and decoded signals

will depend on the temporal reflection and spectral responses of the CMGs and

these are, in general, not rectangular in shape (see Figs. 5.9 and 5.10). The non-

ideal spectral slices can increase multi-user interference in the form of cross-

Chapter Mbirped Moiré Gratings for Optical Code-Division Multiple-Access 112

talk, thereby decreasing the SIR. Perfect slot synchronization assumes a

synchronous system. Furthermore, in our analysis, we have not incorporated

the use of time-gating which would fûrther minimize multi-user interference. In

an asynchronous system, slot synchronization among the different users is

neither guaranteed nor maintained. Thus, the cross-correlation peaks may

decrease due to imperfect temporal overlap of the pulses and in this case, the

variance of multi-user interference will be less than for a slot synchronous case.

Finally, as with most other publications in this field, we have calculated the SIR

using average variances for multi-user interference Bq. (5.511. In fact, the

variance depends on the sequence pairs under consideration and in extreme

cases, the corresponding performance can be far fkom average. A more accurate

estimation of Pe,, would require a more involved Monte-Carlo simulation.

-5 '

-10' C

-15'

-20 -

-25 ' 4 8 12 16 20 24

number of simuttaneous

Fig. 5.12. Pmt as a fundion of number of simultaneous users.

Chapter Mhirped Moiré Gratings for Optical Code-Division Multiple-Access 113

code weight w = 3

N. code length

Fig. 5.13. Number of simultaneous users at Pcmr = 10-9 as a function of code length (M for

M 1 Max. #of 1 original m codes 1

Table 5.1. Maximum number of codes and original m codes for the different cases used in the performance analysis.

Chapter 5-4-d Moiré Gra*gs for Optical Code-Division Multiple-Access 114

Practical issues

In this section, we discuss the various practical aspects that are relevant to

our proposed system.

FABRICATION OF SPECIALLY DESIGNED CMGS

The first practical aspect we consider is the realization and fabrication of

CMGs with specially designed spectral characteristics (i.e., the ability to

suppress selected stopbands). Reviously, CMGs were difficult to fabricate wîth

good performance characteristics; however, the numerous advances in grating

fabrication technology have overcome this problem. As we have seen in Chapter

4, the technique of fabricating CMGs using dualexposure of a single linearly

chirped phase mask has yielded very good results. We have adopted this

technique and included the use of amplitude masks in the exposure processes to

tailor the spectral characteristics of the CMGs and, as shown in Chapter 4,

obtained excellent agreement between measured and simulated results.

Furthexmore, there have been recent reports on the fabrication of very long (1 m

long) CMG structures using the scanning fibedphase mask technique [102].

These experimental successes show the feasibility of obtaining CMGs with good

performance characteristics. Finally, we note that for an individual user bit rate

a t the OC-3 (OC-12) standard of 155.52 MbiVs (622.08 MbiW the corresponding

bit window is = 6.43 ns (1.61 ns). To encode a signal so that it fully occupies this

Chapter 5-Chirped Moiré Gratingis for Opticd CodeDivision Muitiple-Access 115

time window (which is not necessary) requires a CMG approxhately 67 cm (17

cm) long, assuming a fiber index of 1.45-well within the available technology.

CHROMATIC FIBER DISPERSION

The second issue deah with chromatic fiber dispersion (CFD). Without

proper compensation, CFD is known to be a detrimental problem in optical

communication systems that require long distances of propagation or very high

speeds of operation (which require the use of very short optical puises) [BO] -

[82]. CFD can also be a significant problem in OCDMA systems which use

broadband sources, especially those based on phase encoding of ultrashort

optical pulses. These systerns distinguish properly and irnproperly decoded

signals on the basis of whether or not the ultrashort optical input pulse is fdly

reconstructed or remains a pseudo-random noise burst. In this type of OCDMA

system, the phases of al1 wavelength components must be accounted for and the

effects of CFD must be included. Otherwise if CFD is not compensated, the

ultrashort pulses cannot be reconstmcted properly.

Our proposed system does not require the use of coherent pulses and even if

they were used, we are not attempting to reconstmct the input pulses (the fact

that we perform spectral slicing and not phase encoding precludes this). For our

system, CFD becomes problematic only if it significantly spreads the spectral

slices in time so that the decoder CMG cannot recover them al1 into the same

time dot. b i c a l local area networks are less than 2 km in length. As an

Chapter Mhirpeâ Moiré Gratimgs for OpticPl Code-Division Multiple-Access 116

example, a dispersion of 17 psl(nm-km) [this is typical for a fiber that has zero

dispersion a t 1300 n m but is used at 1550 nm] results in a time spread of 340 ps

aRer propagation for a 10 n m wide signal. If the duration of the time slots is

much longer than 340 ps, then the wavelengths of a properly decoded signal will

still be recovered into the correct time slot. Thus, the use of longer CMGs can

give longer t h e dots so that the system is more tolerant to the effects of CFD.

Of course, requiring a time dot to accommodate the effects of CFD will place a

limit on the individual user bit rate since for a fixed code length N

(corresponding to N time slots), increasing their duration decreases the user bit

rate. For an individual bit rate at the OC-3 standard, using a time dot of 400-ps

to account for CFD would give a maximum code length N = 16. This system can

accommodate around 20 users for an aggregate data rate > 3 Gbit/s. Problems

associated with CFD can be significantly reduced, if not eliminated, by operating

the system near the zero dispersion wavelength (1300 nm), using dispersion-

shiRed fiber (Le., fiber where the zero dispersion wavelength is near 1550 nm),

or incorporating some form of dispersion compensation (for example with

dispersion-compensating fiber).

TIME-GATING

Time-gating is used to select the time slot within the bit window when the

detector samples the decoded signal. It is not a necessary requirement since we

can always ictegrate the detected optical power over the entire bit window.

Chapter 5-Chirped Moiré Gratings for Opticd Code-Division MultipleAccess 117

However, as multi-user interference increases, primarily outside the desired

time slot, incorporating a tirne-gate within the detection unit significantly

increases the performance of the system, especially for a chip synchronous

system using a fked threshold detector. This improvement results from

isolating the time slot in which al1 the energy of the properly decoded signal

occupies and so that the only multi-user interference arises &om the non-ideal or

non-rectangular spectral characteristics of the CMG encoderddecoders, see Fig.

5.10.

Time-gating can be performed electronicaily. With cwrent available

technology, this requires the duration of the tirne slot to be = 0.5 ns long. Given

that the time slot needs to be at least 340 ps long to accommodate CFD for a 10

nm wide signal in a 2 km link over standard fiber, the use of electronic tirne-

gating does not significantly change the individual user bit rates nor the overall

system capacity.

RECONFIGURABILITY

A reconfigurable local area network is desirable for flexible operation. This

requires a given user to be able to transmit on any of the available code

sequences or a receiver to tune its decoder to receive and recover data sent by

any of the transmitters. Reconfigurability is easy to achieve in our proposed

system. Recall that there are rn tirne-spreading patterns (corresponding to m

different CMG structures) that c m be distributed among the different users.

Chapter S-Chirped Moiré Gratings for Optical Code-Division Multiple+Access 118

Each jth tirne-spreading pattern has a total of N - ( &-A.& ) wavelength-

encoding patterns associated with it. The ciifferent wavelength-encoding

patterns can be obtained from the jth CMG structure simply by strain tuning.

Thus, transmitters having the jth CMG stmcture can actually transmit on any

one of the corresponding N - ( A& - G,, ) codes; similarly receivers having the jth

CMG structure c m receive any of these N - ( L - G , ) codes by simply strain

tuning the grating decoder. Of course this only provides limited

reconfigurability. However, if each trammitter and receiver is equipped with al1

m CMG structures, then users can transmit and/or receive on any of the codes.

A physical switch selects which of the tirne-spreading patterns is to be used (Le.,

which of the CMG structures) while strain tuning further selects the desired

wavelength-encoduig pattern. Since physical mechanisms are involved in these

processes, the reconfïguration speed will be limited to milliseconds (typical

SONET reconfiguratiodrestoration response times are 50 ms).

OTHER FACTORS

Although in our discussions, we have assumed that the N reflection

stopbands span the entire BW of the input pulse, [A-, hmJ = [A::= ,=], we

can easily extend our analysis to the case where the pulse bandwidth is larger

than the CMG spectral response, [A-, A d t [jib., . In this case, the

number of wavelengths to be used for wavelength-encoding is limited only by the

pulse bandwidth. Furthermore, a larger nurnber of codes can be obtained for the

Chapter tLChïrped M o M Gratings for Opticaï Code-Division ~ u l t i ~ l e - ~ c c e s ~ 119

same values of N and w-not only can we define more original m codes, we also

have a larger wavelength range in which to wavelength-shiff them (in this case,

the maximum oumber of original codes iE t LN/wJ). However, the amount of

CFD depends on the bandwidth of the broadband source and/or CMGs. While a

broader bandwidth potentially allows more codes to be defined, it cornes at the

expense of additional CFD.

We have also only considered a linear detection systern. An alternative

detection scheme, which may be more useful especially for asynchronous

transmission or coherent systems, is to use a non-linear optical detector which

distinguishes signals based on peak intensity andior duration rather than

average energy [103], [104].

5.5. Experimental results

The experimental setup for our proof-of-principle demonstration is shown in

Fig. 5.14. The system comprises four users, one desired and three interfering,

each having its own CMG encoder. The user codes are defined as follows: the

1 desired user, C&S = [0,2,0,4,0,0,7]; and the three interfering users, c,,, =

[0,2,3,0,5,0,0], ci, = [i,0,3,0,5,0,01, and CL, = [0,3,0,5,0,0,81. Interferer 1 (having

code cl:, 1 has a quasi-orthogonal code (there is one overlapping wavelength, hz)

while interferers 2 and 3 (having codes ci, and ci, respectively) have stnctly

orthogonal codes relative to the desired user. The decoder has the complement

code to c h s and is represented by &, = [7,0,0.4,0,2] . The CMG encoders, each 3.5

Chapter Mhirped Moiré Gratings for O p t i d CodeDivision Muitiple-Access 120

cm long with a grating period chvp of 0.5 n d c m , were fabrîcated using the

technique described in Chapter 4 and their spectra, shown in Fig. 5.15(a), were

tailored to the code specifications. Broadband pulses, either fkom an ML-EDFL

h o t shown) or the modulated ASE noise from an EDFA amplifier, were encoded

by reflection fkom the gratings (the pulses were incident on the short wavelength

side of the gratings). To simulate purely asynchronous transmission (i-e., no

chip synchronization), variable time delays were set in the paths of the users.

The encoded signals were then amplified and sent to the decoder. The decoded

signals were simultaneously observed using an optical spectrum analyzer and a

fast photodetector connected to a 20 GHz digital sampling oscilloscope.

I Y desired user encoder

interferor 11 eM0d.r interforer U2

EDFA encoder interforer 13

1 EDFA

BPF 1

Fig. 5.14. Experimental setup for demonstrating m S OCDMA system using CM&. EDFA: Erbium-doped fiber amplifier, EYO MOD: electro-optic modulator, DSO: digital sampling

oscilloscope, BPF: bandpass filter, OSA: optical spectrum analyzer, TD: tirne delay.

Chapter w h i r p e d Moiré Gratings for Optical CoddDivisîon Multiple-Access 12 1

wavelenglh. nm

(a)

Fig. 5.15. (a) Measured spectra of CMG encoders: desired user (solid line), interferer 1 (dashed line), interferer 2 (dotted linel, intei-fèrer 3 (dash-dot linel. (b) Comparing the spectral output of the decoder for the case when the desired user is transmitting only to the case when only a single interferer is transmitting: (i) interferer 1, (5) interferer 2, and (ci) interferer 3.

The first experiment illustrates the principle of encoding/decoding. Here,

the broadband pulses were generated by the same ML-EDFL used in the

experiments on measuring the short pulse response of CMGs. The spectral

output of the decoder is shown in Fig. 5.15(b). Clearly, the spectral content

associated with the desired user can be easily distinguished tkom those of the

interferers. Although interferer 1, which has a quasi-orthogonal code, has one

overlapping wavelength band with the desired user, other wavelengths are

rejected by more than 15 dB. Contrary to the ideal case, the non-zero spectral

output £kom the decoder when the t w o strictly orthogonal codes are transmitting

will result in interference. This is due only to the non-ideal characteristics of the

Chapter Mhirped Moiré Gratings for O p t i d CodeDivision Multiple-Access 122

respective CMG encoders used (the isolation of the wavelength bands is only =

10 dB). However, the rejection is typicdly > 10 dB and as shown below, does not

produce significant interference in decoding.

Fig. 5.16(a) shows the encoded and decoded waveform of the desired user

measured with a 5 GHz photodetector (combined detector/oscilloscope response

time = 100 ps). The encoded signal has three pulses, each at a different

wavelength, as defined by the WE/TS pattern of the CMG encoder. The total

duration is - 400 ps, in agreement with the round-trip propagation tirne through

the grating. The decoded signal consists of a single pulse and is shorter in

duration than the encoded signal. This clearly shows that the wavelength

components have been recovered (de-spread) in the same time dot (within the

response time of the detector). In Fig. 5.16(b), we show the output of the decoder

when different users are transmitting. In al1 cases, the auto-correlation peak

corresponding to the desired user is clearly distinguishable from the multi-user

interference. In particular, the contrast ratio between the autosomelation peak

and the multi-user interference for the case of strictly orthogonal codes is > 10:l

and larger values are expected with improved grating encoders. For the case of

the quasi-orthogonal user, the contrast ratio is = 3:l as expected since the codes

are defined by three wavelengths (w = 3), one of which is overlapping.

For cornparison, simulations of encoding and decoding for the desired user

are shown in the insets of Fig. 5.16(a); there is good agreement between

experiments and numerics. Ideally, al1 the pulses in the reflected signal would

Chapter 5-Chirped Moiré Gratings for Opticai Code-Division Multiple-Access 123

have the same energy; this is neither the case for the simulations or

measurements since the input broadband pulse does not have a flat energy

s p e c t m . Furthemore, the small differences in the temporal waveforms

between simulations and measurements are due to the non-ideal combined

WEmS response of the fabricated CMG encoder. However, the results show that

these features do not significantly affect the performance. In particular, for an

ideal input with a flat energy spectrum, the contrast ratio between the auto-

correlation and interference for a quasi-orthogonal code is 3:l; we have obtained

a comparable ratio, even with the uneven energy distribution.

I - output of 6scoder: onty desiml user mnsrnmg -

- - t L 1 1 I 1 I

time, 200 ps / div

(a)

* f i # i I I I 1 - 1 I I I

rnterference trom interlerer 2

9

interforence lrom miorforer 3

\

rn time. 2 nsldiv

Fig. 5.16. (a) Measured encoded and decoded waveforms for the desired user. The insets show the simdated temporal waveforms (including the == 100 ps detection response tirne) with the same time scale as the measurements. (b) Measwed temporal output of decoder for different

users transrnitting.

Chapter H h i r p e d Mo* Gratings for Optid CodeDivision Multiple-Access 124

In the second experiment, the broadband pulses were generated by

modulating the ASE noise nom an EDFA with the following 8-bit RZ pattern "O

O 1 O 1 1 O O" at 622.08 Mbit/s (OC-12 transmission speed). Each user

transmitted the same 8-bit pattern but with variable delays between them. A

bandpass filter having a 3 dB bandwidth = 5 n m is used to filter out additional

ASE before being detected by an 850 MHz photodetector. Fig. 5.17 shows the

results of encoding and decoding. In this case, the input broadband pulses (Le.,

the "1" bits) are = 800 ps long so that the encoded signals do not resemble that in

Fig. 5.16(a). However, the input signal to the decoder with d l users

transmitting comprises a mix of the waveforms transmitted by al1 the users and

clearly, the original 8-bit pattern is not identifiable. On the other hand, the

output of the decoder clearly demonstrates that the "O O 1 O 1 1 O 0" bit pattern

has been faithfully reproduced. The inset of Fig. 5.17 shows an enlargement of

the decoder output. When al1 the users are transmitting, most of the

interference in the decoded output is due to interferer 1 and the contrast ratio

between the auto-correlation and interference is again = 3: 1.

In Fig. 5.18, we show the measured eye diagrams for the output of the

decoder using the same &bit pattern: (a) is the desired user transmitting alone,

(b) - (d) are the desired user transmitting in the presence of a single interferer,

and (e) is for al1 users transmitting. Unfortunately, no bit-error-rate test

analyzer was available to assess the performance of our OCDMA system.

However, we can estirnate the Q-parameter which can be extracted fkom the eye

Chapter 5-Cbllped Moiré Gratings for Optical Code-Division Multiple-Access 125

diagram measurements. Assuming Gaussian statistics, the Q-parameter is

defined as [IO51

input signal to decoder. all usen transmitting

Fig. 5.17. Demonstrating the encoding and decoding of an RZ 8-bit pattern "O O 1 O 1 1 O O" at 622.08 Mbitls.

where Ir and Io are the mean signals of the "ln and "O" bits and al and ao are the

standard deviation of the "1" and "On bits. The probability of error is in turn

related to the Q-parameter by

Chapter u h i r p e d Moiré Gratings for O p t i d Code-Division Multiple-Access 126

In fact, we can identify approximately as the power signal-to-noise ratio and

hence Eq. (5.10) is equivalent to Eq. (5.7) which was used to analyze

theoretically the performance of the system. Of course, the measured Q-

parameter incorporates both multi-user interference and

example fiom the photodetector and the two EDFAs

amplie the signais).

al1 sources of noise (for

used to generate and

time, 200 psldiv

Fig. 5.18. Measured eye diagrams of the output of the decoder: (a) only desired user transmitting, (b) desired user and interferer 1 transmitting, (cl desired user and interferer 2 transmitting, (dl desired user and intederer 3 transmitting, and (e) ail users transmitting.

Chapter 5-C- Moiré Gratings for Opticaï Code-Division MultipleAccess 127

When the desired user is transmitting in the presence of an interferer

having a strictly orthogonal code wig. 5.18(c), (d)], the measured = 6 which

corresponds to a P e m r = 10-9. When the interferer has a quasi-orthogonal code,

the measured 0 = 3.8 or Pemr = 10-4 - 10-5. For transmission involving users

with strictly orthogonal codes, a lower P,,, can be expected with grating

encoders having improved characteristics. For quasi-orthogonal codes, a lower

P,,,, can be expected with longer codes (the codes used in this demonstration

only had a length N = 7 ) where a larger weight w can be used (and hence larger

signal-to-noise ratio). Nonetheless, the eye is reasonably open in d l cases except

for when al1 users are transmitting. In this last case, the measurement was

performed with al1 users transmitting continuously and having constant time

delays and represents a worst-case scenario. In typical system operation, due to

the bursty and asynchronous behaviour of the traffic, improved performance is

expected and the eye diagram wodd lie between those shown in Fig. 5.18(b) and

Figs. 5.18k) or (dl.

In our proof-of-principle demonstration, we used CMGs encoders which have

a code length N = 7 and weight w = 3. This is limited only by length of the

gratings that could be fabricated (i.e., the length of our available phase mask).

Also, the codes used do not f o m an optimal set as wodd be generated with the

algorithm presented in section 5.3 (the algorithm could not be applied efficiently

due to the limited code length). However, relative to the desired user, they are

representative of strictly and quasi-orthogonal code sequences. The contrast

Chapter Mhirped M o M Grntings for Optical Code-Division Multiple-Access 128

ratio of the autotorrelation and the interference from strictly orthogonal codes

is > 10:l. We anticipate higher values with improved gratings (our grating

encoders have 10 - 20 dB rejection; with more photosensitive fiber, stronger

gratings with greater rejection can be fabricated). For quasi-orthogonal codes,

the contrast ratio is = 3:l. Since optimal codes are one-coincidence, the contrast

ratio can be increased by using codes having longer lengths which can support

larger weights. Although interference h m quasi-orthogonal codes wiil

ultimately limit the number of simultaneous users, acceptable performance can

still be readily achieved. For example, we have shown that with an optimal set

of codes where N = 21 and w = 3, up to 48 simultaneous users at a BER =

can be supported.

5.6. Discussion and summary

In this chapter, we have proposed, analyzed, and demonstrated a hybrid

WEmS OCDMA system that uses in-fiber CMGS for performing

encoding/decoding. The approach presented here builds upon our initial studies

of short pulse propagation in serial FBG arrays and the system proposed by

Fathallah et al. However, contrary to the use of a serial FBG array, our

implementation involves only a single grating for encoding/decoding and is

advantageous since it requires (1) a less stringent fabrication process since we do

not need to ensure that the wavelengths and physical spacing between FBGs in

the array are eurctly identical (to obtain complementary -NE and TS patterns

Chapter Mbl lpad Moiré Gratings for O p t i d ~ode-~i&ion ~ulti~le-Access~ 129

between encoder and decoder grating structures) and (2) a simpler packaging

due to the shorter grating length. Furthemore, our system ean t 1) be designed

to be tolerant to the amount of CFD that would normally be expected in an LAN

network, ( 2 ) support a sufnciently large number of users operating at modest

data rates (we demonstrated transmission at OC-12 speeds), (3) can support

asynchronous transmission (although as discussed, there may be an advantage

of synchronous transmission since the-gating can be used to suppress multi-

user interference further), (4) is reconfigurable, and (5 ) performs

encoding/decoding dl-optically so that electronic processing is mllÿmized (which

is used only in the thresholding process). The drawback of our approach lies in

the constraint of the CMG structures. Due to the linear relationship between

reflected wavelengths and time, our codes cannot fully exploit the two-

dimensional nature provided by using both wavelength and time domains.

However, our codes still have comparable performance to previously proposed

two-dimensional ones as well as with one-dimensional optical orthogonal codes

but with shorter lengths. Thus, we believe that we have presented a simple,

innovative approach to hybrid WEITS OCDMA systems.

Chapter 6

Transmission Edge Filters for Power Equalization

6.1. Introduction 6 -2. Transmission edge filters for power equalization 6.3. Experimental results 6.4. Discussion

6.1. introduction

Erbium-doped fiber amplifiers (EDFAs) are indispensable tools for

providing optical amplification in WDM systems. However, it is difficult to

transmit and ampli@ many WDM channels using EDFAs since the gain profile

is wavelength dependent (non-uniform), while the transmission medium loss is,

to first order, wavelength independent. This creates significant differences in

the signal-to-noise ratios among the different amplified WDM channels which

may, depending on the system power budget or dynamic range of the receiver,

cause system impairments and degrade performance.

Although gain-tlattened EDFAs ( d o m gain profile) have been fahricated,

due to possible changes in operating conditions and to network reconfiguration

operations such as channel a d f i o p , variations can still exist among the power

levels of the WDM channels amplined by an EDFA. This problem will be M h e r

compounded by the fact that many EDFAs are generally used in transmission

systems. For example, an acceptable 0.5 dB variation after a single

amplification stage translates into an unacceptable 10 dB variation afbr twenty

stages. It is thus of critical importance to be able to equalize the power of the

Chapter &Transmission Edge Filtera for Gain Equalization 13 1

different WDM channels (&r amplification) in an active fashion in order to

compensate the variations in the signal levels. To this end, numerous different

techniques, both static and active, have been considered. These include the use

of optical filters (notch filters, acousto-optic tunable filters) [IO61 - 11121, optical

loop mirrors [113], and variable attenuation for each individual channel based

on tunable FBGs [Il41 - [117], or integrated array-waveguide grating routers

with phase shifters for independent loss tuning [IlSI, [119]. Implementations

based on FBGs are attractive since they are simple to fabricate, compact, and

can be packaged to reduce the* performance sensitivity to extemal

environmental factors. In this chapter, we propose and demonstrate the use of

transmission edge filters based on apodized linearly chirped FBGs to provide the

variable attenuation required for power equalization (a serial array of such

gratings can then be used for power equalization of multiple channels in WDM

systerns). Our approach is especially attractive since it can easily be extended to

provide active power equalization by simply incorporating a feedback loop.

6.2. Transmission edge filters for power equalization

A transmission edge filter is one in which the filter transmission varies

linearly, in either linear or dB scale, as a function of wavelength. They can be

realized in fibers using long-period gratings or tilted (blazed) linearly chirped

FBGs [120]. An alternative structure is a suitably apodized (unblazed) linearly

chirped FBG. Such gratings are routinely used in reflection for providing

dispersion compensation and have been extensively characterized with the view

Chapter Ci-'a.nsm.bsion Edge Filters for Gain Equalization 132

of determinhg the optimal structure for dispersion compensation [121], [1221. It

has been found that the presence of a background (DC) refkactive index

proportional to the apodization profile can significantly degrade the dispersion

compensating capabilities of these gratings by introducing non-ideal

characteristics in their dispersive properties. Thus, the preferred structures are

those with no background refiactive index. On the other hand, the presence of a

background refractive index in an apodized linearly chirped FBG creates an

asymmetric spectral response which, in transmission, approximates that of an

edge filter. In particular, the combination of a linear period chirp and an

background index creates the quadratic chirp which gives the linear

discrimination response. This cm be seen in Fig. 6.1 where for example, we

show the calculated transmission responses of taro apodized linearly chirped

FBGs, each having a background refkactive index proportional to its apodization

profile. The two apodization profiles 6n&) considered are:

( 1) a tanh-profile &cg (2) = ( 1 + tanh [ ( 1 - 2 Id)]} with 8 = 2.1, pk refrrctiue

index modulation 6n = 5.5 x 10-4, and grating length Lg =

(2) a raised-cosine-profile ih, ( 2 ) = sin ( with a pealt

modulation 6n = 5 x 104 and grating length Lg = 10 mm.

18 mm; and

reeactive index

Both gratings have a chirp of 0.5 ndcm (these values are typical of the gratings

that can be fabricated).

Chapter &Transmission Edge Filters for Gain Eqtdhation 133

wavelength, nm

Fig. 6.1. Calculated transmission spectra (solid Lines) of a tanh apodized and a sin2 apodized linearly chirped FBG, each having a background refractive index corresponding to its apodization profîle. Aiso shown are the corresponding calculateci group delays in transmission (dotted lines).

Introducing the background refractive index removes the symmetry in the

spectral response and in particular, the short wavelength side now has a linearly

ramped edge (in dB) while the long wavelength side has a steep rise. In fact,

simulations show that by simply varying the parameters in the apodization

profile and background reeactive index (which can be easily controlled with

available grating fabrication technology) the edge filter can be designed to have

a specified slope over a specified bandwidth (slope given in dB/nm). Note that

unlike the transmission edge filters reported in [120], here the Linear slope is

Chapter GTmnsmission Edge Fiiters for Gain Equaïization 134

due to a combination of the background refractive index and grating chirp, and

not f?om coupling of light into radiation modes. Thus the spectral response of

our transmission edge mters are shaped more like a right-angle triangle which

(1) occupies less bandwidth and (2) ensures that there is only a single linearly

ramped edge.

The use of edge filters in FBG sensor interrogation has been recognized

[1231. In these applications, the filters serve to convert strain-induced

wavelength variations into optical power measurements. In our application, the

linear variation in transmissivity is used as a means for providing variable

attenuation for a signal that is transmitted through the grating: different

amounts of power are transmitted simply by changing the wavelength of the

signal. For the case of a fixed wavelength signal, such as a WDM channel, the

transmitted power can be varied until the desired amount is obtained by simply

strain-tuning, tensile or compression, the grating (which can be accomplished by

mounting the grating onto a piezoelectric stack and applying the necessary

voltage). In fact, the linearly ramped edge nature of our transmission filters

allows us to determine exactly what wavelength shift, or amount of strain, is

necessary to obtain a desired attenuation. This forms the basic principle of

using transmission edge filters for providing power equalization of WDM

channels in EDFAs. A schematic of the proposed power-equalized EDFA module

is shown in Fig. 6.2. ARer amplification, a portion of the output power is tapped

(using a monitor tap) and used to determine the required attenuation for each

Chapter &Transmission Edge Faten, for Gain Equolizcrtion 135

WDM channel so that the appropriate electrical signals can be applied to each

individual transmission edge filter (e.g. a voltage to the piezo-electnc stack).

i EDFA

input WDM signals

output power

equalized signals

for strain tuning

Fig. 6.2. Schematic of using transmission edge flters for power equalization among multiple WDM channeb amplified by an EDFA.

One issue that needs to be addressed is the whether our equalization

scheme distorts the input signal. Specifically, due to the linearly ramped nature

of the edge filter, the different spectral components comprising a given input

signal (e-g. WDM channel) do not experience the same attenuation. For

example, with transmission edge filters having similar responses to those shown

in Fig. 6.1, the shorter wavelengths of the input signal would be attenuated

more than the longer wavelengths. This feature becomes more pmrninent for

signals whose BWs are comparable to that of the linear edge. Thus, to examine

whether this presents any problems or limitations in our proposed equalization

technique, we simulated the propagation of transform-limited Gaussian pulses

Chapter 6-Transmission Edge Filters for Gain Equaiization 136

through the edge filters. The input pulses had varying durations Le., different

BW) and were centered at different positions dong the linear edge. The results

are shown in Fig. 6.3. As can be seen, other than the desired attenuation of the

input signal, there is Little degradation of the pulse after it is transmitted

through the filter, even when the input pulse BW occupies a significant fraction

of the edge. Thus, we do not expect any signal degradation arising fkom the

non-uniform attenuation of the spectral components in the equalized signal.

time, 25 ps/div time. 10 psldiv

Fig. 6.3. Propagation of transform-limited Gaussian pulses through the transmission edge filter whose response is shown in Fig. 6,l(a). (a) The input pulse (solid line) is 10 ps long

(corresponding 3 dB B W = 0.35 am); the output pulses are for an input centered at 1549.2 nrn (dashed lhe ) and 1549.5 n m (dotted line). (b) The input pulse (solid linel are 5-ps long

(corresponding 3 dB BW = 0.7 nm) and the output pulse (dashed linel is for an input centered at 1549.5 nm.

6.3. Experimental results

We fabricated two transmission edge filters in hydrogen-loaded

telecommunication fiber using a 1.0 nmkm lineariy chvped phase mask and an

18 mm tanh-shaped amplitude mask having the same parameters as the grating

Chapter &Transmission Edge Filteis for Gain Equnliitation 137

used in the simulations in Fig. 6.1, tu provide apodization of the otherwise

uniform W beam. We used a KrF excimer laser producing pulses (at 248 nm)

having an energy of 6.5 mJ/pulse at a repetition rate of 50 Hz to write the

gratings; exposure times were = 5 minutes. A typicd transmission response of

the gratings we fabricated is shown in Fig. 6.4(a). The transmission varies

linearly on the short wavelength side with a slope of - -13 dB/nm over 1.1 nm

and has a sharp rise o n the long wavelength side. The amplitude variation for

this grating over the linearly ramped edge (1.1 n m range) fkom the ideal linear

case is = + 0.5 dB [see Fig. 6.4b)l. We also measured the relative transmitted

power as a function of strain applied to the gratings using a wavelength fixed on

the long wavelength side of the filters. The two ends of the grating were

clamped on separate stages, one fixed and one moveable; tensile strains were

applied by translating the free stage to increase the separation between the two

(in practical implementations, the gratings c m be strained by mounting them on

piezoelectnc stacks and applying voltages). For the grating shown in Fig. 6.4(a),

the wavelength was fked at 1551.05 nm. The results, shown in Fig. 6.4(c),

clearly demonstrate the linear relation between the relative transmitted power

and strain. The slope is = 13.5 dB/me, in agreement with the measured dope

from the spectral response. Note that a similar result can be obtained by setting

the wavelength of the input signal to the short wavelength side of the filter with

compression tilning.

Chapter &Transmission Edge Filters for Gain Equaïïzation 138

Another important propew of the edge Elters is the group delay response

which determines whether the compensated WDM signal experiences any

dispersion-induced pulse broadening due to filter dispersion. The measured

group delay in transmission of the grating is shown in Fig. 6.4(a). Clearly, over

the linearly ramped edge where the filter is designed to be used, the group delay

is essentially constant with c 10 ps variation and should not cause dispersion-

induced power penalties for signals at 10 Gbit/s (this can also be seen from the

simulated grating responses shown in Fig. 6.1).

The gratings we fabricated provide = 13 dB dynamic range; however, in

principle, any value can be obtained by adjusting the peak index modulation

A n o . We then used two of the gratings to provide power equalization among

input channels to a commercial EDFA. Three wavelength signals at 1544.79

nm, 1551.19 nm, and 1553.59 am, and having > 6 dB variation in their power

levels were multiplexed together and Iaunched into the EDFA; Figs. 6.4(a) and

6.4(b) shows the input signals before and after the EDFA without power

equalization. We used the output power for the signal at 1553.59 nm as the

reference, and the grating filters were strain-tuned to equalize the power of the

signals at 1544.79 n m and 1551.19 nm to that at 1553.59 nm. Fig. 6.4W shows

the three signals afbr amplification and power equal iza t io~lear ly , the power

variation has been compensated. The dips in the signal spectra result from a

reduction of the ASE background noise generated by the EDFA.

Chapter &Thmsmission Edge Filters for Gain EquolizPition 139

c over 1.1 nm 2 -16- c.

1 549 1550 1551

wavelength, nm

wavelength, nm

slope = 13.5 dB/m~

strain, me

Fig. 6.4. Typical spectral response of transmission edge filters fabncated: spectrum (solid line), group delay (dotted line). (b) Amplitude variation of grating response over the linearly-ramped edge from the ideal linear edge with dope 13 dB/nm. (c ) Corresponding measured variation in

relative transmitted power as a fùnction of applied strain.

Chapter &Tranmniesion Edge Filtera for Gain Equdhation 140

wavelength, nm wavelength, nrn wavelength, nm

Fig- 6.5. Illustration of transmission edge fiiters for proMding power equalization. Spectra of (a) input signals to EDF& (b) output signais h m EDFA with no power equalization, (cl power equalized output. The additional 3 dB loss between the spectra in (b) and (cl is due to splicing

1 0 s ~ between the EDFA and the gratings and not insertion loss of the gratings.

6.4. Discussion

Transmission edge filters can be realized using apodized linearly chirped

FBGs with a background refkactive index. The filters we fabncated have a

dynamic range of = 13 dB over = 1 nm. Similar spectral responses can also be

obtained within a 100 GHz spacing (or less) in order to support dense WDM.

Numencal simulations and experimental measurements show that these filters

have negligible in-band group delay in transmission, see for example Figs. 6.1

and 6.3. In particular, the group delay varies by < 10 ps on the short

wavelength side of the grating where the edge filters will be predominantly

used. Such a group delay response should not cause power penalties due to

dispersion-induced pulse broadening, especially for 10 Gbit/s signals.

Simulations also show that the non-uniform attenuation of the different

spectral components comprising an input signal that is to be power-equalized

does not degrade the signal. This is true even for input signals whose BW is a

Chapter &Transmission Edge Filters for Gain Eqdzat ion 14 1

significant fiaction of the linear edgel. Of course, this power equalization

technique is better suited for systems where the spectral efficiency < 0.5 b i m z

as in current WDM systems employing intensity-modulation/direct-detection.

Furthemore, since the power equalization is performed on a per channel

basis following amplification, each grating filter can be precisely tuned to

completely compensate power variations over the entire EDFA range. Of course,

this assumes that each filter has an ideal linearly-ramped edge (to provide

continuous compensation) and deviations can reduce overall perfurmance. Our

grating filters have an amplitude variation off 0.5 dB over the linearly-ramped

edge from the ideal linear case (smaller values are expected with improved

control in the fabrication process) and this value would correspond to the worst-

case signal variation aRer ampMcation. Nevertheless in our demonstration, we

were able to perform power equalization with no observable variation.

We also note that the edge filters can be placed before or f i e r the amplifier.

Filtering or power-equalization before amplification optimizes the output power

available while power-equalization aRer amplification optimizes the S M .

Finally, the use of transmission edge filters can be used in conjunction with

a discrete-sampled feedback loop to perforrn active power equalization. For a

specific WDM channel, once the required attenuation for equalization is

determined, the linear variation in transmission vs. strain (wavelength) allows

us to know exactly how much strain is needed to obtain that attenuation. The

This assumes digital transmission. Of course if an analog signal was transmitted, then clearly, it would undergo significant distortion aRer equalization.

Chapter &Transmission Edge Filters for Gain Equalization 142

necessary electrical signal can then be applied to effectuate the strain on the

grating. We emphasize that this process requires only a single iteration. Thus

the setting time of the device to achieve an equalized output corresponds to the

tuning speed which, for a grating mounted on a piezoelectnc stack, is on the

order of ms. Furthemore, the feedback process need not be continuous. That is,

once the output power level is specified, the signal level of a specific channel

does not have to be continuously tracked (which wouid reduce the overall speed

of operation) until the desired output is achieved. This would be the case for a

filter having a monotonie variation in transmission vs. wavelength, or strain,

since several iterations would be required to obtain the equalized output. In the

case of a non-monotonic variation, it is possible that the system will fail to

converge, even with continuous feedback.

In summary, we have proposed and demonstrated a simple and potentially

cost-effective means for achieving (active) power equalization of WDM channels

in EDFAs.

Chapter 7

Multi-Wavelength, Actively Mode-Locked Erbium-Doped Fiber Lasers

7.1. Introduction 143 7.2. Design concept 148 7.3. First configuration using chirped moiré gratings 150 7.4. Second configuration using serial fiber Bragg grating arrays 156 7.5. Si immary 161

7.1. lntroduction

There is considerable interest in developing erbium-doped fiber lasers

(EDFLs) for a varie@ of spectroscopie, fiber optic sensor, and optical

communications systems applications. EDFLs are attractive since they offer

great ease of adjustment, fkeedom &om mechanical dignment, and the potential

for increased stability as dl-fiber devices. Broadly speaking, EDFLs can be

categorized into four groups depending on their operation in fkequency (single-

wavelength or multi-wavelength) and in time (continuous wave, cw, or mode-

locked).

Multi-wavelength cw EDFLs are particularly usefid in WDM systems and

many different configurations have been reported. These include:

approaches similar to multi-wavelength semiconductor lasers whereby

an array of physically separate gain media, here EDFAs, are used in

conjunction with wavelength selective elements to define each lasing

wavelength. In these lasers, each wavelength sees its own laser cavity

and its own gain medium 11241.

a common CO-doped fiber gain medium where the different dopants

independently provide gain for the separate wavelengths. In one

specific configuration, the fiber was co-doped with both erbium and

neodymium atoms and simultaneous dual-wavelength operation at

1069 n m and 1550 n m was achieved using a dual-pumping scheme

[l25].

single gain media combined with intracavity optical filters to define

the lasing wavelengths [126] - [129].

While configurations based on the third approach are the most appealing since

compact structures can be fabricated, they s d e r fiom the problem of gain cross-

saturation (gain cornpetition) due to homogeneous broadening of the erbium-

doped fiber (EDF) gain medium at room temperature (the homogeneous

broadened linewidth is = 10 nm). Thus, room temperature operation is typically

limited to lasing wavelengths whose separation is larger than the homogeneous

linewidth, Le. > 10 nm. Closer spacing and more wavelengths are possible, but

this requires careful gain equalization for each wavelength resulting in less

stable operation. Increased stability is possible by cooling the EDF gain medium

to 77 K in order to reduce the homogeneous broadening and gaùi cross-

saturation effects; however this is not necessarily a desirable nor practical

solution.

Short pulse fiber laser sources are useful for dynamic component testing

and TDM applications. They can be generated using passive, active, or hybrid

Chapter 7-Multi-wavelength, Activelv Mode-Zacked Erbium-Doped Fiber Lasers 145

mode-locking techniques [130). With passively mode-locked EDFLs, short pulses

(< 1 ps) can be obtained. Although such lasers are environmentally insensitive,

they are not always self-starting and may be unstable (i.e. generate multiple

pulses with arbitrary repetition rates). On the other hand, actively mode-locked

EDFLs are self-starting and can be externally synchronized to (or even generate)

a clock signal via the mode-locking element (for example, a modulator). Actively

mode-locked EDFLs produce longer pulses than their passively mode-locked

counterparts; however with the right combination of dispersion and nonlinearity

(soliton pulse shaping) pulses < 10 ps long have b e n reported [130]. In this

thesis, we will be primarily concerned with actively mode-locked EDFLs.

Optical sources capable of producing short pulses at multiple wavelengths

will become critical components for lightwave communication systems seeking to

exploit combined WDMfi"l'M access techniques. Such sources should be capable

of producing multi-wavelength pulses, each c 100 ps long (to enable at least

single channel 10 Gbit/s operation), ofFer wavelength tunability, and stable

operation. In order to obtain these characteristics, mode-locking techniques

must be combined with approaches that allow for multi-wavelength operation.

Previous work in this area includes:

the use of a common mode-locking element yet separate gain media for

each wavelength [131]. Although these techniques do not suffer from

any gain cross-saturation effects, the implementations are complex

and have no cost benefit over an array of individual sources.

Chapter 74dti-wavelength, Activelv Mode-Lmcked Erbium-Doped Fiber Lasers 146

Furthemore, there is no phase syndvonism nor coherence among the

pulses generated at the different wavelengths.

the use of polarization dispersion in birefiingent components and

b i rehgen t fibers [132], [133]. Dual- and four-wavelength operation

with pulses several tens of ps long have been demonstrated in such

configurations; however, tuning and selection of wavelengths is

difficult .

dispersion tuning whereby different wavelengths in a ring Laser

configuration are mode-locked at different harmonies of the laser

cavity [l34], [1351. This is a very appealing technique in that the

wavelengths can be tuned by simply changing the modulation

frequency of the mode-locking element. It is even possible, under

specific conditions, to obtain two or three wavelengths, but the lasing

wavelengths are separated by more than the homogeneous broadened

linewidth or the multi-wavelength operation is unstable, even with

carefiil gain equalization techniques, due to gain cornpetition in the

EDF.

the use of FBGs as wavelength selective elements in a unidirectional

ring laser [136] - [140]. In order to make the cavity lengths for the

different wavelengths to be as sirnilar as possible so that the

modulation frequency of the mode-locking element is optimized for al1

wavelengths, there is the need to superimpose the FBGs. So far with

Chapter 7-Muiti-wavelength, Actively Modd,ocked Erbium-Doped Fiber Lasers 147

this approach, stable operation has been achieved only for two

wavelengths whose separation exceeds the homogeneous linewidth.

the use of a serial FBG array in a dual-loop unidirectional ring

configuration [l4l]. The dual-loop ensures that al1 wavelengths have

the same cavity length and avoids the need to superimpose the FBGs.

Furthexmore, the number of wavelengths that can be generated is not

limited by the number of FBGs that can be superimposed. Again,

stable operation was obtained only for two wavelengths having a

spacing in excess if 10 nm. Although the laser operated with a

narrower spacing of 3.5 nm, this required carefid gain equalization and

the laser was not stable. When the wavelength spacing was further

reduced to 1 nm, the laser failed to mode-lock altogether.

Although the results reported to date using the various approaches appear

promising, they are limited to producing only a few coarsely spaced wavelengths

( h o or three). Denser wavelength spacing has been achieved only with careful

gain equalization and thus the resdting operation is not very stable.

In this chapter, we describe our work aimed at developing multi-

wavelength mode-locked EDFLs that have a denser wavelength spacing (i.e. <<

homogeneous broadened linewidth of the gain medium) and stable operation at

room temperature. The emphasis here is on the use of FBGs to achieve these

goals and not on studying or understanding the dynamics or behaviour of the

EDF gain medium. Rather, it is a preliminary examination of the issues that

Chapter 74ulti-wavelength, Actively Mde-Locked Erbium-Doped Fiber Lasers 148

need to be examined for optimizing the conditions and parameters for fisture

implementations. Since the end results are the important aspects of this

chapter, the work presented herein is treated in less depth in comparison with

earlier chapters.

7.2. Design concept

The main difficulties in achieving multi-wavelength operation from the

EDF gain medium arise from the effects of gain cross-saturation due to

homogeneous broadening. Gain cross-saturation normally prevents lasing a t

multiple wavelengths since the fist wavelength to exceed threshold clamps the

gain for al1 other wavelengths, which then remain below threshold. Room

temperature multi-wavelength operation is relatively easily achieved if the

lasing wavelengths are separated by more than the homogeneous linewidth of

the EDF gain (> 10 nm). To obtain dense wavelength spacing, careful gain

equalization is required so that dl lasing wavelengths reach threshold at the

same time or the EDF must be cooled to 77K in order to make the EDF gain

medium inhomogeneously broadened.

Gain cross-saturation can be overcome by multipleKing the lasing

wavelengths in the gain medium. One technique is based on spatial-spectral

multiplelong [142]. In this approach, through the effects of spatial hole burning,

the gain medium effectively becomes inhomogeneously broadened. This enables

stable cw laser operation on multiple wavelengths and indeed three closely

Chapter 7-Multi-wavelength, Actively Mode-Locked ~ r b i G ~ o p e d Fiber Lasers 149

spaced wavelengths (S 0.6 nm) at room temperature were reported. In a series

of experiments, Town et al. have found that temporal-spectral multiplexing is

another means for reducing the effects of gain cross-saturation [143]. In this

approach, the different lasing wavelengths are temporally spread before passing

through the EDF gain medium so that each wavelength can experience gain in

its own temporal window (the effects of gain depletiodrecovery caused by one

pulse increases when the wavelengths are temporally overlapped). By using a

unidirectional ring laser configuration, the operation is analogous to a multi-

amplifier link where the pulses at different wavelengths play similar roles to

high-rate WDM channels passing through a chah of EDFAs.

For active mode-locking, multi-wavelength operation is only possible if the

pulses generated a t different wavelengths simultaneously pass through the

time-gating (mode-locking) element, typically an electro-optic modulator.

Consequently it is necessary to have either zero net cavity dispersion, or by

other means ensure that the round-trip propagation time is identical for al1 the

wavelengths that are to be mode-locked. The requirement of temporal spectral-

multiplexing, which is to have the different wavelengths pass through the gain

medium separated in time, conflicts with those mode-locking described above.

Thus, the process of temporally spreading the pulses at different wavelengths

before the gain medium must be compensated. Specifically, the pulses must be

de-spread before tirne-gating. If this can be achieved, then the temporal overlap

of the different wavelengths can be reduced while propagating through the

Chapter 7-Muiti-wavelength, Actively Mde-Locked ~ r b b - ~ o ~ e d Fiber Lasers 150

amplifier to reduce gain cornpetition, yet the net cavity dispersion is still near

zero to allow active mode-locking. In the next two sections, we present two

unidirectional ring cavity configurations that use FBGs to achieve stable multi-

wavelength mode-locked operation at room temperature based on temporal-

spectral multiplexing.

7.3. First configuration based on chirped gratings and a transmissive CMG

A schematic of the fïrst laser configuration is shown in Fig. 7.1. A pair of

dispersive elements, in this case linearly chirped FBGs, are used to spread and

de-spread the pulses before and after amplification. The lasing wavelengths are

defined by a transmissive comb filter based on a CMG. The linearly chirped

FBGs are = 18 mm long and were fabricated in hydrogen-loaded standard

telecommunication fiber (Corning SMF28) using a phase mask with a period

chirp of 1.0 nmkm. Each grating is more than 99% reflective over a bandwidth

of = 2.9 n m and centered at 1545 nm. They were fabricated to be as similar as

possible so that the dispersion (= 62 pdnm) of one would exactly cancel the

dispersion of the other. The gain medium consists of 10 m of commercially

available erbium-doped fiber with a numerical aperture of 0.22, core radius of 4

pm and 1000 ppm doping. The fiber was typically pumped with 125 mW from a

laser diode at 980.3 nm. The transmissive comb filter (CMG) has an average

FSR of 0.88 nm and a finesse of 4 (there are three transmissive fringes within

Chapter 7-Muiti-wavelength, Actively Mode-Locked Erbium-Doped Fiber Laserrr 151

the bandwidth of the linearly chirped gratings). The spectral response of the

CMG comb filter is shown in Fig. 3.9.

OSA 980 nm PUMP

b

EDFA

@- LCFG II LCFG 1)2 EOM

CHIRPED

GRATIN0

Fig. 7.1. Schematic of dual-wavelength, actively mode-locked EDFL using temporal-spectral multiplexing. EOM: electro-optic modulator; WDM: 980/1550 n m coupler; EDFA: fiber

amplifier; PC: polarization controiier; LCFG: iinearly chirped FBG; OSA: optical spectrum analyzer; PD: photodetector connected to digital sampling oscilloscope.

The fundamental fi-equency of the cavity was measured to be = 5.3 MHz.

However, the mode-locking element, an electro-optic modulator, was typically

driven near 2.5 GHz, (corresponding to at least the 470th harmonie). From

active mode-locking laser theory [144], we expect the pulses to have a duration

given by

where a m p m is the gain coefficient, & is the modulation depth of the modulator,

fm is the modulation frequency, and bf. is the gain bandwidth (here

Chapter 7-Muiti-wavelength, Actively Mode-Lockeà Erbium-Do@ Fiber Lasers 152

corresponding to the bandwidth of a transmission resonance). For f, = 2.5 GHz,

the pulses have an estimated theoretical FWHM pulse width of 100 ps

(assuming in steady state amPm = 1, & = 0.3, and dfo = 12.5 GHz).

The laser output was taken via a 10:90 fiber coupler, placed just afker the

first linearly chirped FBG, which was oriented to reflect long wavelengths first.

It was monitored simultaneously in both wavelength and time using an optical

spectrum analyzer and a fast photodetector connected to a digital sampling

oscilloscope (combined impulse response t h e = 100 ps). To monitor the

individual lasing wavelengths, a tunable bandpass filter with a 0.4 nm FWHM

bandwidth was temporarily inserted in the output arm of the 10% coupler.

The linearly chirped FBGs determine both the temporal and spectral

window over which the lasing pulses could be spread, 180 ps and 2.9 nm

respectively. Pulses separated by 0.8 nm (corresponding to the FSR of the CMG

comb filter), if synchronous when passing through the electro-optic modulator,

would be temporally separated by = 50 ps f?om each other after reflection corn

the first grating. We believe that this spreading is sufncient to reduce, though

not eliminate, gain cornpetition between the wavelengths as they pass through

the amplifier. Fig. 7.2 shows repeated scans of the laser spectral output when

the modulator was driven at 2543.25 MHz (480th harmonie). The two lasing

wavelengths are 1544.6 nm and 1546.4 nm, corresponding to a separation of

approximately twice the free spectral range of the CMG. Clearly, the laser has

long-term stable operation and in fact, we observed stable operation for at least

Chapter 7-Multi-wavelength Actively Mode-Locked Erbium-Doped Fiber Lasers 153

one hour. Fig. 7.3 shows the temporal output of the laser. The top and bottom

traces show respectively the output without and with the tunable bandpass filter

inserted for individual wavelength selection. It is evident from the bottom

trames that when passing through the amplifier, the two pulses are separated

in time by = 104 ps corresponding to the grating dispersion multiplied by the

wavelength separation (= 62 pdnm x 1.6 nm). We also measured the

polarization state of the two lasing wavelengths and found them to be the same

(there were no polarization-multiplexing effects in the laser).

1541.7 wavelength, nm

1549.7

Fig. 7.2. Measured spectral output of mode-locked EDFL showing the stable operation of two lasing wavelengths at 1544.6 nm and 1546.4 nm with equal output power.

The results clearly show that pulses at two wavelengths well within the

homogeneous linewidth of the EDF were simultaneously mode-locked. Careful

gain equalization techniques were not required to obtain the dual-wavelength

operation. In fact, we could adjust the polarization controller to arbitrarïly

change the cavity losses seen by either wavelength, thereby creating a

significant imbalance in output power while both wavelengths continued to lase.

- - -

Chapter 7-Multi-wavekngh, ~ c t i v & ~ o d e - k k d Erbium-Dopeà Fiber Lasers 154

Furthemore, tuming the RF drive to the electrooptic modulator on and off

caused the laser to switch between generating the two mode-locked wavelengths,

and one cw wavelength.

EDFL output without bandpass filtering

V)

b 15 I 1 I 1 I 1 1 1 I

!! EDFL output with banâpass filtenng

time, 100 ps / d i

Fig. 7.3. Measured temporal output of the laser. The upper trace shows the total intensity of the laser output. The lower traces show the temporal output for each lasing wavelength, obtained

using a tunable bandpass filter on the output of the 10% coupler.

To investigate the effect of temporal-spectral multiplexing during

amplification, we attempted to obtain multi-wavelength lasing without the two

chirped gratings in the cavity. Under these conditions, i.e. with the pulses

overlapped during amplification, we found that it was impossible to mode-lock

the same two wavelengths simultaneously. It was possible to mode-lock pulses

at two wavelengths spaced apart by = 2.5 nm (three times the FSR of the CMG

filter). However, this required carenil gain equalization without which only one

wavelength would lase. It was impossible to obtain a stable repeated scan of the

Chapter 7-Mdti-wavelength, Activelv M o d e - b k e d Erbium-Doped Fiber Lasers 155

laser output spectrum such as that shown in Fig. 7.2. Any perturbation to the

laser cavity, such as slight adjustments of the polarkation controller, would

result in only a single wavelength lasing. From these results, we conclude that

temporal-spectral multiplexing helps to enable stable rnulti-wavelength lasing

at two closely spaced wavelengths.

Based on the spectral characteristics of the gratings used in the laser

cavity, we had initially hoped to obtain three-wavelength operation. The non-

optimal performance may be explained as follows. First, the pulses are still

temporally overlapped, as can be seen in the lower trace of Fig. 7.3, even aRer

accounting for the response time of the photodetector/oscilloscope combination.

Hence, the gain competition is not completely rninimized in the amplifier. The

pulse associated with the middle wavelength (which can be seen in the spectral

output of Fig. 7.2 but is not lasing), would then have significant temporal

overlap with the pulses at the other two wavelengths and compte for gain with

both. The two wavelengths having a larger wavelength separation (and less

temporal overlap) would be favoured due to the reduced gain competition.

Second, if the two linearly chirped FBGs are not perfectly matched, then pulses

with longer durations would be generated compounding the previous problem.

Alternatively, if the modulation fkequency is not optimal for either wavelength

(when the cavity lengths are not the same), the laser may fail to mode-lock.

Even if the two gratings were perfectly matched, the net dispersion in the cavity

may still be non-zero.

Chapter 7-Multi-wavelength, Adively Mode&ocked Erbium-Doped Fiber Lasers 156

7.3. Second configuration using seriai fiber Bragg grating arrays

In the laser configuration described in the previous section, two different

types of gratings were used to pedorm temporal spreading and wavelength

selection. These two operations can be performed using a single grating

structure, specifically a serial FBG array. The use of a serial FBG array in a

dual-loop unidirectional ring configuration for dual-wavelength generation in an

actively mode-locked EDFL was proposed and demonstrated in [1411 and a

schematic of the laser is shown below in Fig. 7.4.

Fig. 7.4. Dual-loop configuration for multi-wavelength generation in an actively mode-locked EDFL using a serial FBG array [l4ll.

In this configuration, due to propagation in the dual-loops, the cavity

lengths for al1 wavelengths selected by the FBGs are intrinsically identical.

Thus, the modulation fkequency can be easily optimized for al1 the wavelengths.

Furthemore, any light not resonant with the FBGs that propagates in the upper

Chapter 7-Multi-wavelength, Acîively Mde-Locked Erbium-Do+ Fiber Lasers 157

loop L e . that is transmitted through the gratings) will be suppressed due to

detuned modulation when the modulator is driven at a harmonic of the

fundamental fkequency of the laser cavity length (given by the sum of loops 1

and 2). However, simple observation of this configuration reveals that the

problem of gain competition still exists-the wavelengths selected by the FBGs

propagate through the EDF gain overlapped in tirne. This explains the

relatively broad wavelength spacing (20.1 nm) required for stable operation or

the more sensitive operation when the spacing was reduced to 3.5 nm.

Our second laser configuration is the same as that in Fig. 7.4 except that

the EDF gain medium is moved fkom the upper loop to the lower loop in order to

take advantage of the effects of temporal-spectral multiplelcing in helping to

enable more stable multi-wavelength operation. The cavity lengths for al1 the

wavelengths selected by the FBGs are stiU the same; however, the wavelengths

are now temporally separated as they propagate through the EDF to reduce gain

competition. A new problem, though, &ses in this configuration. Light that is

non-resonant with the FBGs will propagate in the lower loop and experience less

loss than the mode-locked pulses that travel through both loops (especially since

modulators typically have insertion losses of = 6 dB). Thus, these wavelengths

will not be suppressed and in fact, if they start lasing (cw), this will prevent the

generation of any mode-locked pulses altogether. There are two ways to

overcome this problem. First, we can have the FBGs spectrally overlap to

ensure that there is no light transmitted. This will create the additional

Chapter 7-Multi-wavelengLh, Activelv Mde-Locked Erbium-Doped Fiber Lasers 158

problem that we do not necessarily know which grating in the array is

responsible for generating a specific wavelength (i.e. the wavelength may be

reflected by different gratings in the array so that al1 wavelengths no longer

necessarily have the same cavity length). The second solution is to use two

identical serial FBG arrays with opposite orientations. In this case, the problem

of cw lasing can be completely avoided. This cornes, though, at the price of

increased complexity (two serial arrays, rather than one, are used) and the need

to fabricate two identical arrays. Given the relative advances, including

repeatability, in grating fabrication technology, we have opted for the latter

approach. The modified laser configuration is shown in Fig. 7.5.

9CIO nm PUMP

I

Fig. 7.5. Modified laser configuration for generating multiple wavelengths from a . actively mode-locked EDFL.

We used a serial grating array comprising two 5 mm long apodized gratings

(having uniform period) separated by 15 mm (to give a temporal separation of

the pulses = 150 ps). The characteristics of the two grating arrays are shown

Chapter 7-Muiti-wavelength, ActiveIy Mode-Locked Erbium-Doped Fiber Lasers 159

below in Fig. 7.6 and clearly, they are well-matched. The EDF was pumped by =

50 mW from a laser diode at 980.3 nm and the modulator was dnven at 2599.7

MHz (at this fkequency, the estimated pulse widths are still = 100 ps long). Fig.

7.7 shows a repeated scan of the laser output spectrum. The two lasing

wavelengths are 1532.06 nm and 1532.79 nm. As can be seen fkom the repeated

scans, the laser has stable operation (this was over a period of one hour) for

wavelengths separated by only 0.7 nm! To our knowledge, this is the first report

of a dual-wavelength, actively mode-locked fiber laser having such a narrow

w avelength spacing.

wavelength. nm

lm 1 1532 1 s 1 s 1-

wavelength, nm

t= im 1% 1534 1536 9536

wavelength, nm

wavelength, nm

Fig. 7.6. Characteristics of the two serial grating arrays used in the laser: (a) reflection spectrum and (b) group delay for light incident on the long wavelength side. Serial FBG array 1:

top traces, serial FBG array 2: bottom traces.

The temporal output of the laser is shown in Fig. 7.8. The upper trace

shows the two wavelengths simultaneously lasing and the lower traces show

Chapter 74dti-wavelenflh, Actively de-~ockedËrb&-~oped Fiber Lasers 160

each individual wavelength (obtained as before using a 0.4 n m tunable bandpass

filter). The pulses are well-separated in time (150 ps) and hence we expect that

the reduced gain cornpetition allows for even more stable operation.

Fig. 7.7. Repeated scan of the spectral output of the laser showing stable, dual-wavelength operation.

time, 02nsldiv

Fig. 7.8. Measwed temporal output of the laser. The upper trace shows the total intensity of the laser output. The lower traces show the temporal output for each Iasing wavelength (A = 1532.06

nm, solid line; = 1532.79 nm, dotted line), obtained using a tunable bandpass filter on the output of the 10% coupler.

Chapter 7-Multi-wavelength, Actively Mode-Locked Erbium-Doped Fiber Lasers 161

We also measured the polarization states of the two lasing wavelengths and

again, found them to be the same. We then inserted a 5 nm, polarization

insensitive tunable bandpass filter within the laser cavity. By tuning the filter,

this allowed us to induce a differential loss befween the two wavelengths. Up to

10 dB variation in the output power of the two wavelengths could be induced

before the dual-wavelength operation stopped. As before, we could have a

significant imbalance in the output power with both wavelengths lasing. This

shows that gain equalization is not cntical in enabling dual-wavelength

operation. In the experiments reported in [141], the laser did not have stable

operation for a wavelength spacing of 1 nm, even with gain equalization. The

results of these experiments again support the idea of temporal-spectral

multiplexing in helping to enable stable multi-wavelength operation.

7.5. Siimmary

The requirements for temporal-spectral multiplexing and mode-locking are

conflicting: one requires the wavelenj$hs to be temporally separated before

amplification while the other requires the wavelengths to be temporally

overlapped for time-gating. Thus, the need to intentionally introduce dispersion

within the laser cavity to temporally separate the pulses at different

wavelengths before amplincation must be compensated before tirne-gating

(mode-locking). We have constructed two laser configurations, both

unidirectional, to implement temporal-spectral multiplexing. In the first

Chapter 7-Multi-wavelength, Activelv Mode-Locked Erbium-Doped Fiber Lasers 162

configuration, a pair of matched linearly chirped FBGs are used to introduce and

compensate for dispersion while a trammissive CMG comb filter is used to

provide wavelength selectivity (define the k i n g wavelengths). In the second

configuration, both the dispersive and wavelength selection operations are

performed by a pair of matched serial FBG arrays (with opposite orientations).

This latter configuration is extremely attractive since it permits wavelength

tunable operation by simply strain tuning the appropriate FBGs in both arrays.

Furthemore, if the FBGs in the arrays are written at the same wavelength,

then by strain tuning each FBG different arnounts, not only can we achieve

wavelength tunability, but we can also set the number of pulses (wavelengths)

that are to be generated. Specifically, the number of pulses generated

corresponds to the number of FBGs that are strain-tuned away fkom the initial

relaxed state. Of course, this requires the FBGs to be highly reflecting > 99 8

so that pulses at the same wavelength are not generated by different FBGs in

the array.

In summary, we have shown that temporal-spectral multiplexing helps to

enable stable, multi-wavelength operation of an actively mode-locked EDFL at

room temperature. Although the EDF gain medium is homogeneously

broadened, we believe that mdti-wavelength operation is possible since the

pulses at different wavelengths do not pass through the ampli*g medium

overlapped in time thereby reducing gain cornpetition. Again, we emphasize the

main points of this chapter are the results obtained. In particular, more detailed

Chapter 7-Muiti-wavelemgth, Actively Mode-Incked Erbium-Doped Fiber Lasers 163

study on the dynamics and behaviour of the EDF gain medium is necessary in

order to understand first, then optimize the conditions and parameters for

constmcting mode-locked EDFLs based on temporal-spectral multiplexing.

Chapter 8

Conclusion

8.1. Sumrnary and conclusions 8.2. List of publications 8.3. Future work

8.1. Sumrnary and conclusions

This thesis is concerned with a study of the optical properties of compound

FBG structures, particularly chirped moiré gratings and serial FBG arrays, and

their applications in lightwave communications. In Chapter 1, we identified

enabling components and technologies that will play critical roles in allowing

future optical networks to exploit the enormous bandwidth capacities of the fiber

transmission medium. These needs formed the basis for the investigations

carried out in the thesis.

In Chapter 2, we briefly reviewed FBG technology. This was followed in

Chapter 3 by a discussion on a specific class of compound FBG structures:

grating resonators. Specific attention was devoted to chirped moiré gratings,

which consist of superimposed linearly chirped FBGs. Once the fundamentals

were established, we then proceeded with proposhg and demonstrating

applications of CMGs and serial FBG arrays, as well as discussing their design.

The significant achievements reported in this thesis are:

the realization of transmission bandpass nIters with near-ideal filter

response for providing wavelength selectivity in WDM systems. Our

filters are inherently transmissive and do not require optical circulators

Chauter û-Concldons 165

nor incorporation of the gratings in interferometric structures. They are

based on specially designed CMGs and have a channel isolation = 15 dB

(typically > 12 dB), É 0.5 dB ripple in the passband, and near-constant

in-band group delay. Furthermore, BER measurements a t 2.5 Gbit/s

show that they do not produce any signincant power penalty (< 0.2 dB)

due to pulse broadening arising from filter dispersion. Al1 of our

measurements provide a complete characterization of filter performance

whereas previously published resuits have only focused on the spectral

properties of the transmission-based filters (see [43], [58] - [60]). The

isolation of our filters is comparable to previously reported results and

in some cases, is better than the best multiple-phase shifted FBGs

fabncated to date (15 dB isolation compared with 10 dB) [60]. While a

direct experimental comparison of the corresponding dispersive

properties is not possible (since these have not been published in [43]

nor [60]), simulations show that our filters have the better performance

in the sense that they do not introduce significant power penalties due to

pulse broadening from filter dispersion. These filters should prove to be

useful for providing wavelength selectivity in WDM and wavelength

routing systems. The results are presented in Chapter 4.

r the first operating hybrid WElTS OCDMA system that uses in-fiber

CMGs for encoding/decoding. We first examined the reflection response

of CMGs and showed that they have similar functionality to a serial

Chapter S-Conclusions 166

FBG array whereby they can be used to decompose short broadband

pulses simultaneously in both wavelength and tirne. We then analyzed

our proposed system by focusing on the design of suitable codes (which

take into account the physical constraints imposed by the CMG

encodeddecoder structures), system performance in the presence of

multi-user interference, and the practical issued associated with our

implementation. Finally, we provided a proof-of-principle demonstration

of a four-user system comprising one desired user and three interfering

users. In experiments that illustrated the encoding and decoding

processes, the contrast ratio between the auto-correlation peak (desired

user) and an interferer having strictly orthogonal codes is greater than

10:l while for interferers having quasi-orthogonal codes, the contrast is

- 3:l (correspondhg to the fact that the codes had only a weight of 3).

We also demonstrated data transmission at OC-12 speeds (622.08

Mbitk) in our system and measurements clearly show the rejection of

multiuser interference and proper recovery of the desired user's bit

sequence. This is one of the first experimental demonstrations of multi-

user OCDMA systems incorporating FBGs for encoding/decoding and is

the first to report the use of FBGs to implement hybrid WERS OCDMA.

These results are described in Chapter 5.

the proposal and successfbl demonstration of a simple, cost-effective

means for power equalization of WDM channels amplified by an EDFA.

C hapter 8-Conclusious 167

The approach uses a serial array of transmission edge filters based on

apodized linearly chirped FBGs for equalization on a per channel basis.

The filters that we fabricated can provide a dynamic range of 13 dB,

though in principle, any value can be obtained by suitably controlling

the grating fabrication process. With these grating filters, we

demonstrated power equalization of WDM signals amplified by a

commercial EDFA with no observable signal variation aRer

amplification. Furthermore, our nIters will not degrade the equalized

signal. We also discussed how this approach can be extended to provide

active power equalization. These filters will be extremely usefùl for

compensating the deleterious efFects of the non-uniform EDFA gain

spectrum and transients that occur dwing addidrop operation in

network reconfiguration. The results appear in Chapter 6.

the demonstration of multi-wavelength, actively mode-locked EDFLs

with stable, room temperature operation and the closest wavelength

spacing reported to date. The principle of operation is based on

temporal-spectral multiplexing, whereby pulses at different wavelengths

pass through the amplifying medium at different instants in tirne, in

order to reduce the effects of gain cornpetition. We assembled two

different laser configurations. The first uses linearly chirped FBGs to

add and subsequently compensate dispersion in the cavity and a CMG

comb filter to define the lasing wavelengths. Stable, dual-wavelength

C hapter 8-Concldons 168

operation with pulses = 100 ps at 1544.6 nm and 1546.4 nm with a

repetition rate of = 2.5 GHz was obtained at room temperature. In the

second configuration, a pair of identical serial FBG arrays with opposite

orientations are used to simultaneously add/compensate dispersion in

the cavity and define the lasing wavelengths. Again, stable dual-

wavelength operation with pulses = 100 ps at a repetition rate of 2.6

GHz was obtained at room temperature. In thîs case, the wavelength

spacing was reduced to 0.7 n m (the lasing wavelengths are 1532.06 nm

and 1532.79 nm). These results are reported in Chapter 7.

In this thesis, we have endeavoured and succeeded in developing FBG

technology and FBG-based devices for applications that are cntically important

in the realization of future photonic networks.

Chapter Monclusions 169

8.2. List of publications

The original research contributions of this thesis have been reported in the

following j oumals and conferences:

L. R Chen, D. J. F. Cooper, and P. W. E. Smith, "Transmission filters with multiple flattened passbands based on chirped moiré gratings," IEEE Photonics TechnoZogy Letters, vol. 10, no. 9, pp. 1283 - 1285, 1998.

L. R Chen, D. J. F. Cooper, and P. W. E. Smith, "Flattened passband transmission filters based on chirped moiré gratings for optical communications," OSA Annual Meeting (OSA'981, Baltimore, Maryland, 4 - 9 October 1998, paper ThPP26.

L. R C h e n and P. W. E. Smith, "Ultrashort pulse propagation in chirped moiré gratings: application to optical codedivision multiple-access," OSA Annual Meeting (OSA'Sa), Baltimore, Maryland, 4 - 9 October 1998, paper ThPP27.

L. R Chen, and P. W. E. Smith, T iber Bragg grating transmission filters with near-ideal filter response," Electronics Letters, vol. 34, no. 21, pp. 2048 - 2050,1998.

L. R Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, and X. Gu, "Fabrication of transmission filters with single or multiple flattened passbands based on chirped moiré gratings," Electronics Letters, vol. 35, no. 7, pp. 584 - 585,1999.

L. R Chen, P. W. E. Smith, and C. Martijn de Sterke, Wavelength- encoding/time-spreading optical code division multiple-access system with in- fiber chirped moiré gratings," Applied Optics, vol. 38, no. 21, pp. 4500 - 4508, 1999.

L. R. C h e n and P. W. E. Smith, 'Specially designed chirped moiré gratings for optical communications," European Conference on Optical Communications (ECOC'99), Nice, France, 26 - 30 September 1999, paper TuD 1.

G. E. Town, L. R Chen, and P. W. E. Smith, "Dual-wavelength, actively mode-locked erbium-doped fiber laser," Conference on Lasers and Electro- Optics (CLEO'OO), San Francisco, Califomia, 7 - 12 May 2000, paper CWE4.

Chapter û-Conclusions 170

9. L. R Chen, D. J. F. Cooper, and P. W. E. Smith, "Transmission edge filters for power equalization in erbium-doped fiber amplifiersr Conference on Lasers and Electro-Optics (CLEO'OO), San Francisco, Califomia, 7 - 12 May 2000, paper CFC5.

10.L. R. Chen and P. W. E. Smith, "Proof-of-principle demonstration of a wavelength-encoding/time-spreading optical code-division multiple-access system using in-fiber chirped moiré gratings," Conference on Lasers and Electro-Optics (CLEO'OO), San Francisco, California, 7 - 12 Mav 2000, paper CFC7.

11.L. R Chen, D. J. F. Cooper, and P. W. E. Smith, "Trmsmission edge filters based on apodized linearly chirped fiber Bragg gratings for power equalization of erbium-doped fiber ampliners," to appear in IEEE Photonics Technology Letters (July, 2000).

12.L. R Chen and P. W. E. Smith, "Tailorhg chirped moiré fiber Bragg gratings for wavelength-division-multiplexing and optical code-division multiple-access applications," (INVITED PAPER] to appear in Fiber and Integrated Optics, 2000.

13- L. R Chen and P. W. E. Smith, Pemonstration of incoherent wavelength- encodindtime-spreading optical CDMA using chirped moiré gratings," to appear in XEEE Photonics Technology Letters (September, 2000).

14.G. E. Town, L. Chen, and P. W. E. Smith, "Dual wavelength modelocked fiber laser," submitted to I E E Photonics Technology Letters (June, 2000).

8.3. Future work

In this thesis, we have explored the optical properties and use of two

specific compound FBG structures for a variety of lightwave communications

applications. The proposed applications have been analyzed theoretically and

expenmentally by means of proofsf-principle demonstrations. Nevertheless,

there is still room for follow-up work including the following:

Chapter onc cl dons 171

the fabrication and characterization of transmission nIters with greater

channel isolation by writing stronger gratings in more photosensitive

fiber. Based on the measured characteristics of the filters that we have

fabncated, we do not expect them to produce any power penalties (at 10

G b i W associated with pulse broadening arising fkom filter dispersion.

This can be venfied experimentally by inserting them in a 10 Gbitls

testbed.

a more detailed theoretical analysis of the proposed WElTS OCDMA

system using in-fiber CM&. In particular, an improved estimate of

system performance can be obtained by using fewer assumptions. For

example, the nomideal rectangular shapes for the spectral slices and

time waveforms can be incorporated, and a more realistic receiver that

accounts for noise sources above multi-user interference, such as shot

noise, thermal noise, and beat noise generated by the signals and ASE

fkom the amplifiers, should be used. Finally, the chip synchronous

assumption can be dropped thereby allowing a direct cornparison

between the synchronous (with the use of tirne-gating) and

asynchronous implementations.

additional experiments on the WE2TS OCDMA system. Future systems

should attempt to incorporate more users by employing codes with

longer lengths. Furthemore, to improve signal-to-noise ratios, larger

C hap ter û-Conclusions 172

weights can be used. Finally, BER measurements c m be performed to

quanti@ system performance.

an actual implementation of the scheme proposed in Chapter 6 for

performing active power equalization.

a detailed study into the dynamics and behaviour of the EDF gain

medium. The research presented in Chapter 7 focused on the use of

FBGs to obtain multi-wavelength operation fiom an actively mode-

locked EDFL. Although we experimentally observed that temporal-

spectral multiplexing helps to enable stable, multi-wavelength operation

at room temperature by reducing gain competition, the dynamics of the

processes involved within the actual erbium fiber are not fully

understood. The gain dynamics can be studied experimentdy by means

of standard dual-wavelength pumpprobe experiments, whereby the

effects of a pump signal at one wavelength on the gain medium can be

examined by a subsequent probe signal at a different wavelength.

There is no doubt that since their discovery only twenty years ago, FBGs

have emerged as critical components for numerous lightwave communications

applications. Although the field has reached a certain level of maturity,

additional opportunities exist for suitably designed novel grating stnictures or

incorporation of existing structures in innovative fashions in order to perform

more advanced optical signal processing funetions that are necessary in future

Chapter ~ o n c l u s ï o n s 173

all-photonic networks. The results presented in this thesis should stimulate

additional research dong these lines.

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