Table Of ContentPhotonic Signal Processing
Photonic Signal Processing
Second Edition
Le Nguyen Binh
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Library of Congress Cataloging‑in‑Publication Data
Names: Binh, Le Nguyen, author.
Title: Photonic signal processing / Le Nguyen Binh.
Description: Second edition. | Boca Raton : Taylor & Francis, a CRC title,
part of the Taylor & Francis imprint, a member of the Taylor & Francis
Group, the academic division of T&F Informa, plc, [2019] | Includes
bibliographical references.
Identifiers: LCCN 2018024823 (print) | LCCN 2018026380 (ebook) | ISBN
9780429436994 (eBook General) | ISBN 9780429792632 (Pdf) | ISBN
9780429792625 (ePub) | ISBN 9780429792618 (Mobipocket) | ISBN
9781498769938 (hardback : acid-free paper)
Subjects: LCSH: Optical communications. | Signal processing. | Photonics. |
Optoelectronic devices.
Classification: LCC TK5103.59 (ebook) | LCC TK5103.59 .B5243 2019 (print) |
DDC 621.36/5--dc23
LC record available at https://lccn.loc.gov/2018024823
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Dedication
To the memory of my father
To my mother, Mrs. Nguyen Thi Huong
To Phuong Nguyen and Lam
Contents
Preface............................................................................................................................................xvii
Author .............................................................................................................................................xix
Chapter 1 Introduction ..................................................................................................................1
Acronyms .....................................................................................................................1
1.1 Preamble ............................................................................................................1
1.2 Introductory Remarks ........................................................................................2
1.3 Organization of Chapters ..................................................................................4
Chapter 2 Photonic Signal Processing Via Signal-Flow Graph ....................................................7
2.1 Introduction .......................................................................................................7
2.2 Incoherent Photonic Signal Processing .............................................................8
2.2.1 Fiber-Optic Delay Lines .....................................................................10
2.2.1.1 Fiber-Optic Directional Couplers .......................................10
2.2.2 Fiber-Optic and Semiconductor Amplifiers .......................................11
2.3 Coherent Integrated-Optic Signal Processing .................................................12
2.3.1 Integrated-Optic Delay Lines .............................................................15
2.3.2 Integrated-Optic Phase Shifters .........................................................16
2.3.3 Integrated-Optic Directional Couplers ...............................................16
2.3.4 Integrated-Optic Amplifiers ...............................................................18
2.4 Remarks ...........................................................................................................19
2.5 Signal-Flow Graph Approach and Photonic Circuits ......................................20
2.5.1 Introductory Remarks ........................................................................21
2.5.2 Signal-Flow Graph Theory ................................................................21
2.5.3 Definitions of SFG Elements ..............................................................22
2.6 Rules of SFG....................................................................................................23
2.6.1 Rule 1: Transmission Rule ..................................................................23
2.6.2 Rule 2: Addition Rule .........................................................................23
2.6.3 Rule 3: Product Rule ..........................................................................24
2.7 Mason’s Gain Formula ....................................................................................25
2.7.1 Analysis of an Incoherent Recursive Fiber-Optic Signal
Processor (RFOSP) ............................................................................25
2.7.2 SFG Representation of the Incoherent RFOSP ..................................25
2.7.3 Derivation of the Transfer Functions of the Incoherent RFOSP ........27
2.7.4 Stability Analysis of the Incoherent RFOSP ......................................29
2.7.5 Design of the Incoherent RFOSP .......................................................29
2.7.6 Remarks ..............................................................................................30
2.8 Optmason: A Program for Automatic Derivation of the Optical Transfer
Functions of Photonic Circuits from Their Connection Graphs .....................31
2.8.1 Overview ............................................................................................31
2.8.2 Using OPTMASON ...........................................................................33
2.8.3 Contents of the Input File for above Examples ..................................35
2.8.4 The OPTMASON Program Structure ...............................................36
2.9 Appendix: Z-Transform ...................................................................................40
vii
viii Contents
2.10 Appendix: OPTMASON.PAS Program Listing ............................................42
2.11 Appendix: Using “OPTIMASON” the Computer Aided Generator .............66
Chapter 3 Bandpass Optical Filters by DSP Techniques ............................................................71
3.1 Optical Fixed Bandpass Filter .......................................................................71
3.1.1 Introductory Remarks ......................................................................71
3.1.2 Chebyshev Optical Filter Specification and Synthesis Algorithm .....71
3.1.3 Basic Characteristics of Chebyshev Lowpass Filters .......................72
3.1.3.1 Chebyshev-Type Optical Bandpass Filter
Specification .....................................................................72
3.1.3.2 Illustration of a Chebyshev Bandpass Optical Filter ........74
3.1.3.3 Optical Components for Chebyshev Filters ......................75
3.1.3.4 Realization of the Chebyshev Optical Bandpass Filters .......78
3.1.3.5 The COF1 .........................................................................78
3.1.3.6 Parallel Realization ...........................................................79
3.1.3.7 The COF2 .........................................................................81
3.1.3.8 Discussions .......................................................................83
3.1.4 Concluding Remarks ........................................................................83
3.2 Tunable Optical Bandpass Waveguide Filters ...............................................84
3.2.1 Introductory Remarks ......................................................................84
3.2.2 Transfer Function of IIR Digital Filters to Be Synthesized .............85
3.2.3 Basic Building Blocks of Tunable Optical Filters ............................86
3.2.3.1 Tunable Coupler ................................................................86
3.2.3.2 All-Pole Filter ...................................................................87
3.2.3.3 All-Zero Filter ...................................................................89
3.2.4 Tunable Optical Filter .......................................................................91
3.2.5 Synthesis of Tunable Optical Filters ................................................91
3.2.5.1 Design Equations for the Synthesis of Tunable
Optical Filters ...................................................................91
3.2.5.2 Synthesis of Second-Order Butterworth Bandpass
and Bandstop Tunable Optical Filters...............................92
3.2.5.3 Designed Parameter Values of the Bandpass and
Bandstop Tunable Optical Filters .....................................92
3.2.5.4 Tuning Parameters of the Synthesized Bandpass
and Bandstop Tunable Optical Filters...............................94
3.2.6 Synthesis of Bandpass and Bandstop Tunable Optical Filters
with Variable Bandwidths and Fixed Center Frequencies ...............98
3.2.6.1 Synthesis of Tunable Optical Filters with Fixed
Bandwidths and Tunable Center Frequencies ..................98
3.2.6.2 Fabrication Tolerances of Filter Parameters ...................100
3.2.7 Concluding Remarks ......................................................................104
References ................................................................................................................105
Chapter 4 Photonic Computing Processors ..............................................................................107
4.1 Incoherent Fiber-Optic Systolic Array Processors ......................................107
4.1.1 Introduction ....................................................................................107
4.1.2 Digital-Multiplication-by-Analog-Convolution Algorithm
and Its Extended Version ................................................................109
4.1.2.1 Multiplication of Two Digital Numbers ..........................109
Contents ix
4.1.2.2 High-Order Digital Multiplication....................................110
4.1.2.3 Sum of Products of Two Digital Numbers ........................112
4.1.2.4 Two’s Complement Binary Arithmetic .............................112
4.1.3 Elemental Optical Signal Processors ...............................................113
4.1.3.1 Optical Splitter and Combiner ..........................................113
4.1.3.2 Binary Programmable Incoherent Fiber-Optic
Transversal Filter ..............................................................114
4.1.4 Incoherent Fiber-Optic Systolic Array Processors for Digital
Matrix Multiplications .....................................................................116
4.1.4.1 Matrix–Vector Multiplication ...........................................116
4.1.4.2 Matrix–Matrix Multiplication ..........................................117
4.1.4.3 Cascaded Matrix Multiplication .......................................118
4.1.4.4 Performance Comparison .................................................121
4.1.4.5 Fiber-Optic Systolic Array Processors Using
Non-Binary Data ...............................................................122
4.1.4.6 High-Order Fiber-Optic Systolic Array Processors .........123
4.1.5 Remarks ............................................................................................124
4.2 Programmable Incoherent Newton–Cotes Optical Integrator ......................125
4.2.1 Introductory Remarks ......................................................................125
4.2.2 Newton–Cotes Digital Integrators ...................................................126
4.2.2.1 Transfer Function ..............................................................126
4.2.2.2 Synthesis ...........................................................................127
4.2.2.3 Design of a Programmable Optical Integrating
Processor ...........................................................................130
4.2.2.4 Analysis of the FIR Fiber-Optic Signal Processor ...........132
4.2.2.5 Analysis of the IIR Fiber-Optic Signal Processor ............133
4.2.3 Section Remarks ...............................................................................143
4.3 Higher-Derivative FIR Optical Differentiators .............................................143
4.3.1 Introduction ......................................................................................144
4.3.2 Higher-Derivative FIR Digital Differentiators .................................146
4.3.3 Synthesis of Higher-Derivative FIR Optical Differentiators ...........147
4.3.4 Computed Differentiators of First and Higher Orders .....................150
4.3.4.1 First-Derivative Differentiators ........................................150
4.3.4.2 Second-Derivative Differentiators ....................................152
4.3.4.3 Third-Derivative Differentiators.......................................154
4.3.4.4 Fourth-Derivative Differentiator ......................................158
4.3.5 Remarks ............................................................................................159
4.4 Appendix A: Generalized Theory of the Newton–Cotes Digital
Integrators .....................................................................................................160
4.4.1 Definition of Numerical Integration .................................................161
4.4.2 Newton’s Interpolating Polynomial ..................................................162
4.4.3 General Form of the Newton–Cotes Closed Integration
Formulas ..........................................................................................164
4.4.4 Generalized Theory of the Newton–Cotes Digital Integrators ........164
Chapter 5 Optical Dispersion Compensation and Gain Flattening ..........................................167
5.1 Introductory Remarks ....................................................................................167
5.2 Dispersion Compensation Using Optical Resonators ....................................167
5.2.1 Signal-Flow Graph Application in Optical Resonators ....................170
5.2.2 Stability Test .....................................................................................175
