Optical Filter Design and Analysis(介绍目录)

xx_912 · 发表于 2006-3-19 02:29:11

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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
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
viii CONTENTS
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 × N Router 345
References 352
Problems 353
CONTENTS ix
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
x CONTENTS
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 domain.
These techniques are required for characterizing waveguide properties and individual
devices such as directional couplers; however, they can become cumbersome
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 important
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 independent
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 delays
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 quarterxi
wavelength thick. In this case, the splitters and combiners are the partial reflectances
at each interface. Just as capacitors, inductors, and resistors have underlying
electromagnetic models but are treated as lumped elements in analog filter designs,
each splitting and combining element is modeled from basic electromagnetic
theory and then treated as a lumped element in the optical filter design.
Another similarity with analog filters, but a major difference from digital filters,
is the level of precision and accuracy that can be achieved in the design parameters
for optical filters. For example, analog electrical components and optical components
cannot be specified to the tenth decimal place; whereas, such numerical precision
is commonplace for digital filters. Thus, a filter’s sensitivity to variations in the
design parameters must be considered. In addition, measurement and analysis techniques
are needed to identify where variations have occurred in the fabrication
process and what parameters are causing a filter to deviate from its nominal design.
These issues, which are characteristic of optical filters, are addressed in detail.
This book is intended for researchers and students who are interested in optical
filters and optical communication systems. Problem sets are given for use in a graduate
level course. The main focus is to present the theoretical background for various
architectures that can approximate any filter function. Planar waveguide devices
realized in silica are used as examples; however, the theory and underlying design
considerations are applicable to optical filters realized in other platforms such as
fiber, thin-film stacks, and microelectro-mechanical (MEMs) systems. We are at an
early point in the evolution of optical filters needed for full capacity optical communication
systems and networks. Many filters need experimental investigation, so
this book should be valuable to people interested in furthering their theoretical understanding
as well as those who are fabricating filters using a wide range of material
systems and fabrication techniques.
A detailed introduction to electromagnetic and signal processing theory is given
in Chapter 1. In Chapter 2 on electromagnetic theory, a complete discussion is provided
on waveguide modes, coupled-mode theory, and dispersion. In Chapter 3 on
signal processing theory, Fourier transforms, Z transforms, and digital filter design
techniques are discussed. The next three chapters (Chapters 4–6) cover optical filters
and include design examples that are relevant to wavelength division multiplexed
(WDM) optical communication systems. The examples include bandpass filters,
gain equalization filters for compensating the wavelength dependent gain of
optical amplifiers, and dispersion compensation filters. A particularly important filter
for WDM systems is the waveguide grating router (WGR), which is fundamentally
an integrated diffraction grating, because it filters many channels simultaneously.
Its operation is examined using Fourier transforms to provide insight into its
periodic frequency and spatial behavior. Filters using thin-film dielectric stacks,
Bragg gratings, acousto-optic coupling, and long period gratings are also examined.
Filters with a large number of periods such as Bragg and long period gratings are
typically analyzed using coupled-mode theory. We include the coupled-mode solutions
for these filters, thus offering the reader a comparison between signal processing
techniques and the coupled-mode approach. Measurement techniques and filter
xii PREFACE
analysis algorithms, which extract the filter’s component values from its spectral or
time domain response, are addressed in Chapter 7. Finally, areas that are expected to
have a dramatic effect on the evolution of optical filters are highlighted.
The authors gratefully acknowledge the review and suggestions provided by G.
Lenz, Y. P. Li, W. Lin, D. Muelhner, and A. E. White of Bell Laboratories Lucent
Technologies, S. Orfanidis of Rutgers University, B. Nyman of JDS Fitel, and T. Erdogan
of the University of Rochester.

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Optical Filter Design and Analysis(介绍目录)

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