Optical filter design and analysis: a signal processing approach

417 Pages·1999·7.162 MB·English

by  Zhao, Jian H., Madsen, Christi K

Optical Filter Design and Analysis: A Signal Processing Approach
Christi K. Madsen, Jian H. Zhao
Copyright © 1999 John Wiley & Sons, Inc.
ISBNs: 0-471-18373-3 (Hardback); 0-471-21375-6 (Electronic)
Optical Filter Design
and Analysis
Constant Value Units
Speed of light in vacuum c 2.9979 × 108 m/s
Permittivity of free space (cid:1) 8.8542 × 10–12 F/m
0
Permeability of free space (cid:2) 1.2566 × 10–6 H/m
0
Electron charge q 1.6022 × 10–19 C
Planck’s constant h 6.6262 × 10–34 J·s
Boltzmann’s constant k 1.3807 × 10–23 J/K
B
Optical Filter Design
and Analysis
A Signal Processing Approach
CHRISTI K. MADSEN
Bell Laboratories
Lucent Technologies
JIAN H. ZHAO
Rutgers University
A WILEY-INTERSCIENCE PUBLICATION
JOHN WILEY & SONS, INC.
NEW YORK / CHICHESTER / WEINHEIM / BRISBANE / SINGAPORE / TORONTO
Designations used by companies to distinguish their products are often claimed as trademarks. In all
instances where John Wiley & Sons, Inc., is aware of a claim, the product names appear in initial
capital or ALL CAPITAL LETTERS. Readers, however, should contact the appropriate companies for
more complete information regarding trademarks and registration.
Copyright © 1999 by John Wiley & Sons, Inc. All rights reserved.
No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form
or by any means, electronic or mechanical, including uploading, downloading, printing, decompiling,
recording or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States
Copyright Act, without the prior written permission of the Publisher. Requests to the Publisher
for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc.,
605 Third Avenue, New York, NY 10158-0012, [phone], fax [phone], E-Mail:
[email protected].
This publication is designed to provide accurate and authoritative information in regard to the subject
matter covered. It is sold with the understanding that the publisher is not engaged in rendering
professional services. If professional advice or other expert assistance is required, the services of a
competent professional person should be sought.
ISBN 0-471-21375-6
This title is also available in print as ISBN 0-471-18373-3.
For more information about Wiley products, visit our web site at www.Wiley.com.
To our families:
Eric
Lucia, Suqing, and Yumao
Contents
Preface xi
1 Introduction 1
1.1 Optical Filters 1
1.2 Filter Applications in WDM Systems 7
1.2.1 Bandpass Filters for Multiplexing, Demultiplexing, and Add/Drop 8
1.2.2 Gain Equalization Filters 10
1.2.3 Dispersion Compensation Filters 13
1.3 Scope of the Book 14
References 15
2 Fundamentals of Electromagnetic Waves and Waveguides 19
2.1 The Plane Wave 19
2.1.1 Maxwell’s Equations 19
2.1.2 The Wave Equation in a Dielectric Medium 20
2.1.3 Solutions of the Wave Equation 22
2.1.4 Phase Velocity and Group Velocity 25
2.1.5 Reflection and Refraction at Dielectric Interfaces 27
2.2 Slab Waveguides 34
2.2.1 The Guided Wave Condition 34
2.2.2 Characteristic Equations for the Slab Waveguide 37
2.2.3 Waveguide Modes 39
2.2.4 Orthogonality and Completeness of Modes 42
2.3.5 Dispersion 44
2.2.6 Loss and Signal Attenuation 56
2.3 Rectangular Waveguides 64
vii
viii CONTENTS
2.3.1 Wave Equation Analysis 65
2.3.2 The Effective Index Method 67
2.3.3 Perturbation Corrections 68
2.4 Splitters and Combiners 69
2.4.1 Directional Couplers 69
2.4.2 Star Couplers 76
2.4.3 Multi-Mode Interference Couplers 78
2.5 Material Properties and Fabrication Processes 82
2.5.1 Materials 83
2.5.2 Fabrication 86
References 88
Problems 93
3 Digital Filter Concepts for Optical Filters 95
3.1 Linear Time-Invariant Systems 95
3.1.1 Continuous Signals 96
3.1.2 Discrete Signals 102
3.2 Digital Filters 106
3.2.1 The Z-Transform 106
3.2.2 Poles and Zeros 108
3.2.3 Stability and Causality 110
3.2.4 Magnitude Response 112
3.2.5 Group Delay and Dispersion 114
3.2.6 Minimum-, Maximum-, and Linear-Phase Filters 119
3.3 Single-Stage Optical Filters 126
3.3.1 A Single-Stage MA Filter 129
3.3.2 A Single-Stage AR Filter 131
3.3.3 Power Conservation and Reciprocity 134
3.3.4 Incoherent Optical Signal Processing 136
3.4 Digital Filter Design 137
3.4.1 Approximating Functions 137
3.4.2 Bandpass Filters 139
3.4.3 The Window Method for MA Bandpass Filters 140
3.4.4 Classical Filter Designs for ARMA Bandpass Filters 142
3.4.5 The Least Squares Method for AR Filter Design 148
3.4.6 Multi-Stage Filter Architectures 154
Appendix 161
References 162
Problems 164
4 Multi-Stage MA Architectures 165
4.1 Single-Stage MZI Design 165
4.1.1 Loss and Fabrication Induced Variations 166
4.1.2 A Tunable Coupler 168
4.2 Cascade Filters 171
CONTENTS ix
4.3 Transversal Filters 177
4.4. Multi-Port Filters 180
4.4.1 Diffraction Grating Filters 180
4.4.2 Waveguide Grating Routers 184
4.5 Lattice Filters 198
4.5.1 The Z-Transform Description and Synthesis Algorithm 199
4.5.2 Generalized Lattice Filters 216
4.6 Coupled-Mode Filters 224
References 232
Problems 236
5 Multi-Stage AR Architectures 237
5.1 Ring Cascade Filter 238
5.2 Ring Lattice Filter 241
5.2.1 The Z-Transform Description 242
5.2.2 Synthesis Algorithm 246
5.2.3 Sensitivity to Fabrication Variations 258
5.2.4 Bandpass Filter Design and Experimental Results 263
5.2.5 Gain Equalizer Design 267
5.2.6 Dispersion Compensator Design 270
5.3 Vernier Operation 272
5.4 Reflective Lattice Filters 276
5.4.1 Thin-Film Filters 277
5.4.2 Bragg Gratings 285
References 299
Problems 302
6 Multi-Stage ARMA Filters 305
6.1 A Maximally Flat ARMA Filter 305
6.2 A General ARMA Lattice Architecture 310
6.2.1 The Z-Transform Description 311
6.2.2 Synthesis Algorithm 314
6.2.3 Design Examples 317
6.3 All-Pass Filters 320
6.3.1 Optical All-Pass Filters 321
6.3.2 Fiber Dispersion Compensation 323
6.3.3 Filter Dispersion Compensation 325
6.3.4 Wavelength Dependent Delays 328
6.4 Bandpass Filters 330
6.4.1 All-Pass Decomposition for 2 × 2 Filters 333
6.4.2 An N × NRouter 345
References 352
Problems 353
x CONTENTS
7 Optical Measurements and Filter Analysis 355
7.1 Optical Measurements 355
7.1.2 Polarization Dependent Loss 360
7.1.3 Indirect Loss Measurements 365
7.1.4 Group Delay 372
7.2 Filter Analysis 378
7.2.1 Time Domain Measurement 378
7.2.2 Optical Low-Coherence Interferometry and Fourier Spectroscopy 380
7.2.3 The AR Analysis Algorithm 387
References 393
Problems 394
8 Future Directions 397
8.1 Communication System Applications 397
8.1.1 Ultra-Dense WDM Systems and Networks 397
8.1.2 Ultra-Fast TDM and Optical Codes 398
8.2 Materials and Processing 400
8.3 Summary 402
References 402
Index 405
Preface
Optical filters whose frequency characteristics can be tailored to a desired response
are an enabling technology for exploiting the full bandwidth potential of optical
fiber communication systems. Optical filter design is typically approached with
electromagnetic models where the fields are solved in the frequency or time do-
main. These techniques are required for characterizing waveguide properties and in-
dividual devices such as directional couplers; however, they can become cumber-
some and non-intuitive for filter design. A higher level approach that focuses on the
filter characteristics providing insight, fast calculation of the filter response, and
easy scaling for larger and more complex filters is addressed in this book. The im-
portant filter characteristics are the same as those for electrical and digital filters.
For example, passband width, stopband rejection, and the transition width between
the passband and stopband are all design parameters for bandpass filters. For high
bitrate optical communication systems, a filter’s dispersion characteristics must also
be understood and controlled. Given the large body of knowledge about analog and
digital filter design, it is advantageous to analyze optical filters in a similar manner.
In particular, this book is unique in presenting digital signal processing techniques
for the design of optical filters, providing both background material and theoretical
and experimental research results.
The optical filters described are fundamentally generalized interferometers
which split the incoming signal into many paths, in an essentially wavelength inde-
pendent manner, delayed and recombined. The splitting and recombining ratios, as
well as the delays, are varied to change the frequency response. With digital filters,
the splitting and recombining are done without concern for loss or the required
gain; whereas, filter loss is a major design consideration for optical filters. The de-
lays are typically integer multiples of a smallest common delay. A well-known
example is a stack of thin-film dielectric materials where each layer is a quarter-
xi