Optical Networl<s
`A Practical Perspective
`
`Second Edition
`
`Rajiv Ramaswami
`l<umar N . Sivarajan
`
`MORGAN KAUFMANN PUBLISHERS
`
`AN IMPR I NT OF ACADE MI C
`A Division o f Harcourt, Inc.
`• SAN FRANCISCO SAN DIEGO NEW YORK BOSTON
`L ONDON SYDNEY TOKYO
`
`P R ESS
`
`LUMENTUM HOLDINGS, INC.
`Exhibit 1042, Page 1
`IPR2015-00731
`
`

`
`Editor Rick Adams
`Publishing Services Manager · Scott Norton
`Senior Production Editor Cheri Palmer
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`Cover Design Ross Carron Design
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`Designations used by companies to distinguish their products are often claimed as trademarks or
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`
`Morgan Kaufmann Publishers
`340 Pine Street, Sixth Floor, San Francisco, CA 94104-3205, USA
`http://www.mkp.com
`
`ACADEMIC PRESS
`A Division of Harcourt, Inc.
`525 B Street, Suite 1900, San Diego, CA 92101-4495, USA
`http://www.academicpress.com
`
`Academic Press
`Harcourt Place, 32 Jamestown Road, London, NW1 7BY, United Kingdom
`http://www.academicpress.com
`
`© 2002 by Academic Press
`All rights reserved
`Printed in the United States of America
`
`06 05 04 03 02
`
`5 4 3 2 1
`
`No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form
`or by any means-electronic, mechanical, photocopying, or otherwise-without the prior written
`permission of the publisher.
`
`Library of Congress Control Number: 2001094371
`
`ISBN 1-55860-655-6
`
`This book is printed on acid-free paper.
`
`LUMENTUM HOLDINGS, INC.
`Exhibit 1042, Page 2
`IPR2015-00731
`
`

`
`Contents
`
`Foreword
`
`tx
`
`Foreword to the First Edition
`
`xt
`
`Preface
`
`xxvn
`
`1
`
`1
`Introduction to Optical Networks
`1.1 Telecommunications Network Architecture .
`1.2 Services, Circuit Switching, and Packet Switching
`1.2.1 The Changing Services Landscape .
`1.3 Optical Networks ..... .. ........ .
`1.3.1 Multiplexing Techniques ...... . .
`1.3.2 Second-Generation Optical Networks .
`1.4 The Optical Layer . .... ... .. .. .
`1.5 Transparency and All-Optical Networks
`1.6 Optical Packet Switching . ....... .
`1.7 Transmission Basics ........... .
`1. 7.1 Wavelengths, Frequencies, and Channel Spacing
`1. 7.2 Wavelength Standards
`.
`1.7.3 Optical Power and Loss .. . .
`1.8 Network Evolution ... .. .. .
`.
`. .
`1.8.1 Early Days-Multimode Fiber .
`. · . .... .
`1.8.2 Single-Mode Fiber
`
`3
`6
`9
`10
`12
`14
`16
`24
`26
`28
`28
`30
`31
`32
`33
`35
`
`XV
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`XVI
`
`CONTENTS
`
`1.803 Optical Amplifiers and WDM 0 0 0 0 0 0
`1.8.4 Beyond Transmission Links to Networks
`Summary
`Further Reading 0
`References 0 0 0 0 0
`
`• 0
`
`I Technology
`
`47
`
`49
`
`2 Propagation of Signals in Optical Fiber
`201 Light Propagation in Optical Fiber
`20101 Geometrical Optics Approach
`201.2 Wave Theory Approach
`202 Loss and Bandwidth 0
`20201 Bending Loss 0 0 0 0 0 0
`203 Chromatic Dispersion 0 0 0 0 0
`20301 Chirped Gaussian Pulses
`2o3o2 Controlling the Dispersion Profile
`2.4 Nonlinear Effects 0 0 0 0 0 0 0 0 0 0 0 0
`2.401 Effective Length and Area 0 0 0
`2.402 Stimulated Brillouin Scattering 0
`2.403 Stimulated Raman Scattering 0
`2.4.4 Propagation in a Nonlinear Medium
`2.405 Self-Phase Modulation 0 0 0 0 0 0 0 0
`2.406 SPM-Induced Chirp for Gaussian Pulses
`2.407 Cross-Phase Modulation 0
`2.408 Four-Wave Mixing 0 0 0 0
`2.409 New Optical Fiber Types 0
`205 Solitons o o 0 0 0 0 0 0 0 0 0 0 0 0
`2o5o1 Dispersion-Managed Solitons
`Summary
`Further Reading 0
`Problems o
`References 0
`
`o
`
`o
`
`0
`
`0
`
`0
`
`107
`
`3 Components
`0 0 0 0 0 0 0 0
`301 Couplers 0
`301.1 Principle of Operation 0
`301.2 Conservation of Energy
`Isolators and Circulators 0 0 0
`30201 Principle of Operation 0
`
`302
`
`37
`39
`40
`41
`42
`
`50
`50
`55
`65
`67
`68
`69
`74
`76
`77
`79
`80
`81
`83
`87
`89
`90
`93 .
`98
`100
`101
`102
`103
`104
`
`108
`110
`111
`112
`113
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`LUMENTUM HOLDINGS, INC.
`Exhibit 1042, Page 4
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`CONTENTS
`
`303 M ultiplexers and Filters
`3o3o1 Gratings 0 0 0 0 o 0
`3o3 o2 Diffraction Pattern
`30303 Bragg Gratings o o
`303.4 Fiber Gratings 0 0 0
`303 05 Fabry-Perot Filters
`30306 Multilayer Dielectric Thin-Film Filters
`30307 Mach-Zehnder Interferometers
`30308 Arrayed Waveguide Grating 0 0 0 0 0 0
`3o3o9 Acousto-Optic Tunable Filter 0 0 0 0 0
`3o3o10 High Channel Count Multiplexer Architectures
`3.4 Optical Amplifiers o 0 o 0 0 0
`3.401 Stimulated Emission 0 0 0 0 0 0
`3.402 Spontaneous Emission 0 0 0 0 0
`3.403 Erbium-Doped Fiber Amplifiers
`3.4.4 Raman Amplifiers 0 0 0 0 0 0 0
`3.405 Semiconductor Optical Amplifiers 0
`3.406 Crosstalk in SOAs
`3o5 Transmitters 0 0 0 0 0 0 0 0 0 0
`3o5o1 Lasers 0 0 0 0 0 0 0 0 0
`3o5o2 Light-Emitting Diodes
`3o5o3 Tunable Lasers 0 0 0 0
`3o5.4 Direct and External Modulation 0
`3o5o5 Pump Sources for Raman Amplifiers
`306 Detectors o o o o o o o o o o 0
`3o6o1 Photodetectors o 0 o 0
`3o6o2 Front-End Amplifiers 0
`307 Switches 0 0 0 0 0 0 0 0 0 0 0 0
`3o 701 Large Optical Switches 0
`30702 Optical Switch Technologies
`30703 Large Electronic Switches
`308 Wavelength Converters 0 0 0 0 0 0
`30801 Optoelectronic Approach
`30802 Optical Gating 0 0 0 0 0 0
`30803
`Interferometric Techniques 0
`308.4 Wave Mixing
`Summary
`Further Reading 0
`Problems 0
`References 0 0 0 0
`
`xvn
`
`115
`118
`122
`123
`126
`130
`133
`135
`139
`143
`148
`151
`152
`153
`154
`159
`161
`165
`165
`166
`176
`178
`186
`190
`192
`192
`197
`199
`201
`207
`215
`216
`217
`218
`220
`223
`224
`225
`226
`232
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`LUMENTUM HOLDINGS, INC.
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`
`XVlll
`
`CO NTENTS
`
`239
`
`4 Modulation and Demodulation
`401 Modu lation 0 0 0 0 0 0 0 0
`4ol.1 Signal Formats 0 0
`4o2 Subcarrier Modulation and Multiplexing
`40201 Clipping and Intermodulation Products 0
`4o2o2 Applications of SCM 0 0 0 0 0 0
`4o3 Spectral Efficiency 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
`403 01 Optical Duobinary Modulation 0 0 0
`403 02 Optical Single Sideband Modulation
`40303 Multilevel Modulation 0 0 0 0 0 0
`403.4 Capacity Limits of Optical Fiber 0
`4.4 Demodulation 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
`4.401 An Ideal Receiver 0 0 0 0 0 0 0 0 0
`4.402 A Practical Direct Detection Receiver
`4.403 Front-End Amplifier Noise 0
`4.4.4 APD Noise o 0 0 o 0
`4.405 Optical Preamplifiers ·
`4.406 Bit Error Rates 0 0 0
`4.407 Coherent Detection 0
`4.408 Timing Recovery 0 0
`4.409 Equalization 0 0 0 0 0
`4o5 Error Detection and Correction
`40501 Reed-Solomon Codes 0
`405 02
`Interleaving
`Summary o 0 0 0
`Further Reading 0
`Problems 0
`References 0 0 0 0
`
`283
`
`5 Transmission System Engineering
`5 01 System Model 0
`5 02 Power Penalty 0
`5 03 Transmitter 0 0
`5.4 Receiver 0 0 0 0
`505 Optical Amplifiers
`50501 Gain Saturation in EDFAs
`50502 Gain Equalization in EDFAs
`50503 Amplifier Cascades 0 0 0 0
`505.4 Amplifier Spacing Penalty
`
`239
`240
`242
`243
`245
`245
`246
`248
`249
`249
`250
`252
`253
`254
`255
`255
`258
`263
`265
`266
`267
`270
`271
`272
`273
`274
`279
`
`283
`284
`287
`288
`289
`290
`292
`293
`294
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`CONTENTS
`
`5.5.5 Power Transients and Automatic Gain Control.
`5.5.6 Lasing Loops .... .
`5.6 Crosstalk .......... .
`5.6.1
`Intrachannel Crosstalk
`5.6.2
`Interchannel Crosstalk
`.5.6.3 Crosstalk in Networks
`5.6.4 Bidirectional Systems .
`5.6.5 Crosstalk Reduction
`5.6.6 Cascaded Filters o o o
`5. 7 Dispersion . 0 . . o . . . o o .
`5.701 Chromatic Dispersion Limits: NRZ Modulation
`5.702 Chromatic Dispersion Limits: RZ Modulation
`5.7.3 Dispersion Compensation
`. .. 0 0 ..
`5.7.4 Polarization-Mode Dispersion (PMD) .
`5 08 Fiber Nonlinearities o o o o ... o 0 0 0 0 0 ..
`5.8o1 Effective Length in Amplified Systems 0
`5.8o2 Stimulated Brillouin Scattering.
`508.3 Stimulated Raman Scattering
`5.8.4 Four-Wave Mixing ... o ...
`5o8o5 Self-/Cross-Phase Modulation .
`5o8.6 Role of Chromatic Dispersion Management
`5.9 Wavelength Stabilization . o o o o o . o .
`. o o o
`. o . o o ...... .
`5.10 Design of Soliton Systems
`5.11 Design of Dispersion-Managed Soliton Systems
`5 012 Overall Design Considerations . o . 0 0 ... 0
`5.1201 Fiber Type .. o . o o . .. ... 0 0 . 0
`5.1202 Transmit Power and Amplifier Spacing
`5.1203 Chromatic Dispersion Compensation
`5.12.4 Modulation . o o . ... o 0 ..... .
`5.1205 Nonlinearities . o o . ... 0 ..... .
`5012.6 Interchannel Spacing and Number of Wavelengths o
`5 012.7 All-Optical Networks
`5012.8 Wavelength Planning
`5 01209 Transparency
`Summary
`Further Reading .
`Problems.
`References . . . .
`
`0 • • •
`
`XIX
`
`296
`298
`299
`299
`301
`303
`303
`305
`307
`308
`309
`311
`314
`320
`323
`323
`325
`326
`329
`333
`335
`335
`336
`338
`341
`341
`342
`343
`343
`344
`344
`345
`346
`348
`348
`348
`349
`356
`
`LUMENTUM HOLDINGS, INC.
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`
`XX
`
`CO NTENTS
`
`II Networks
`
`361
`
`363
`
`6o2
`
`603
`
`6 Client Layers of the Optical Layer
`601 SONET/SDH o o o o 0 o 0 0
`601.1 Multiplexing 0 0 0 0
`6ol.2 SONET/SDHLayers
`601.3 SONET Frame Structure 0
`601.4 SONET/SDH Physical Layer o
`601.5 Elements of a SONET/SDH Infrastructure
`i\TM o o 0 0 o 0 0 0 o o o o
`6o2o1 Functions of i\TM
`60202
`i\daptation Layers
`6o2o3 Quality of Service o
`6o2.4 Flow Control 0 o o
`Signaling and Routing
`60205
`IP 0 0
`60301
`Routing and Forwarding o
`60302
`Quality of Service 0 0 0 0 o
`60303
`Multiprotocol Label Switching (MPLS)
`603.4
`Whither i\TM? o
`6.4 Storage-i\rea Networks 0
`6.401 ESCON o o o o
`6.402 Fibre Channel 0 0
`6.403 HIPPI 0 0 0 0 o 0
`605 Gigabit and 10-Gigabit Ethernet 0
`Summary 0 0 0 0
`Further Reading 0
`Problems 0
`References 0 0 0 0
`
`403
`
`7 WDM Network Elements
`701 Optical Line Terminals
`7o2 Optical Line i\mplifiers 0 0 0 0
`7o3 Optical i\dd/Drop Multiplexers
`70301 Oi\DM i\rchitectures o o
`70302 Reconfigurable Oi\DMs
`7.4 Optical Crossconnects 0 0 0 0 0
`7.401
`i\11-0ptical OXC Configurations
`Summary 0 0 0 0
`Further Reading 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
`
`364
`367
`370
`371
`375
`378
`381
`382
`385
`386
`387
`387
`388
`390
`392
`392
`394
`395
`396
`397
`397
`398
`398
`399
`399
`401
`
`406
`408
`408
`411
`41 7
`419
`425
`428
`430
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`LUMENTUM HOLDINGS, INC.
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`
`CO NTENTS
`
`Problems.
`References
`
`8 WDM Network Design
`437
`8.1 Cost Trade-Offs: A Detailed Ring Network Example
`8.2 LTD and RWA Problems .... ...... .
`8.2.1 Lightpath Topology Design
`. ... .
`8.2.2 Routing and Wavelength Assignment
`8.2.3 Wavelength Conversion
`.
`. ... . .
`8.2.4 Relationship to Graph Coloring .. .
`8.3 Dimensioning Wavelength-Routing Networks
`8.4 Statistical Dimensioning Models
`8.4.1 First-Passage Model ... .. .
`8.4.2 Blocking Model .. ...... .
`8.5 Maximum Load Dimensioning Models
`8.5.1 Offline Lightpath Requests .
`8.5.2 Online RWA in Rings .
`Summary
`. .. .
`Further Reading .
`Problems.
`References . . . .
`
`495
`9 Control and Management
`9.1 Network Management Functions
`9.1.1 Management Framework
`9.1.2
`Information Model ; ...
`9 .1.3 Management Protocols ..
`9.2 Optical Layer Services and Interfacing .
`9.3 Layers within the Optical Layer .. .
`9.4 Multivendor lnteroperability .. .. .
`9.5 Performance and Fault Management
`9.5 .1 The Impact of Transparency
`9.5.2 BER Measurement .
`. .. .
`9.5.3 Optical Trace .
`.
`.
`.
`9.5.4 Alarm Management .. . .
`9.5.5 Data Communication Network (DCN) and Signaling
`9.5.6 Policing ........ .
`.
`9.5.7 Optical Layer Overhead
`.
`9.6 Configuration Management
`.
`.
`9.6.1 Equipment Management .
`
`XXI
`
`431
`433
`
`441
`448
`449
`454
`457
`461
`462
`464
`466
`467
`475
`475
`481
`482
`484
`484
`488
`
`495
`497
`499
`500
`502
`504
`505
`507
`508
`509
`509
`510
`512
`513
`514
`519
`519
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`
`xxn
`
`C ONTENTS
`
`9.6.2 Connection Management
`9.6.3 Adaptation Management.
`9.7 Optical Safety ... .. .
`. ... .
`9.7.1 Open Fiber Control Protocol
`Summary
`. · .. .
`Further Reading .
`Problems.
`References . . . .
`
`537
`
`10 Network Survivability
`10.1 Basic Concepts
`.
`10.2 Protection in SONET/SDH .
`10.2.1 Point-to-Point Links
`10.2.2 Self-Healing Rings
`.
`10.2.3 Unidirectional Path-Switched Rings
`10.2.4 Bidirectional Line-Switched Rings .
`10.2.5 Ring Interconnection and Dual Homing
`10.3 Protection in IP Networks
`. ..... .. .
`10.4 Why Optical Layer Protection . ..... .
`10.4.1 Service Classes Based on Protection
`10.5 Optical Layer Protection Schemes
`10.5.1 1 + 1 OMS Protection
`10.5.2 1:1 OMS Protection
`10.5.3 OMS-DPRing .
`.
`.
`. .
`10.5.4 OMS-SPRing .. .. .
`10.5.5 1:N Transponder Protection
`10.5.6 1 + 1 OCh Dedicated Protection .
`10.5.7 OCh-SPRing ... ...... .
`10.5.8 OCh-Mesh Protection ... . .
`10.5.9 Choice of Protection Technique
`10.6 lnterworking between Layers
`Summary
`. ...
`Further Reading .
`Problems .
`References . . . .
`
`591
`11 Access Networks
`11.1 Network Architecture Overview .
`11.2 Enhanced HFC
`. . . . . .
`11.3 Fiber to the Curb (FTTC)
`11.3.1 PON Evolution ..
`
`520
`524
`526
`528
`530
`531
`532
`534
`
`539
`542
`544
`546
`549
`550
`555
`558
`560
`566
`567
`570
`571
`571
`571
`573
`574
`575
`576
`582
`582
`583
`584
`584
`587
`
`593
`598
`599
`609
`
`LUMENTUM HOLDINGS, INC.
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`
`CONTENTS
`
`Summary ... .
`Further Reading .
`Problems.
`References . . . .
`
`615
`12 Photonic Packet Switching
`12.1 Optical Time Division Multiplexing .
`12.1.1 Bit Interleaving ...
`12.1.2 Packet Interleaving .
`12.1.3 Optical AND Gates.
`12.2 Synchronization . . . . . . .
`12.2.1 Tunable Delays ...
`12.2.2 Optical Phase Lock Loop
`12.3 Header Processing .. .
`12.4 Buffering . . . . . . . . .
`12.4.1 Output Buffering
`12.4.2 Input Buffering .
`12.4.3 Recirculation Buffering .
`12.4.4 Using Wavelengths for Contention Resolution
`12.4.5 Deflection Routing
`12.5 Burst Switching
`12.6 Testbeds .. ..... .. .
`. .
`12.6.1 KEOPS ... .
`12.6.2 NIT's Optical ATM Switches
`12.6.3 BT Labs Testbeds ...... .
`12.6.4 Princeton University Testbed .
`12.6.5 AON
`.
`12.6.6 CORD .
`Summary ....
`Further Reading .
`Problems.
`References . . . .
`
`667
`13 Deployment Considerations
`13.1 The Evolving Telecommunications Network
`13.1.1 The SONET/SDH Core Network ..
`13.1.2 Architectural Choices for Next-Generation Transport Networks
`13.2 Designing the Transmission· Layer
`13.2.1 Using SDM .
`13.2.2 Using TDM .
`13.2.3 Using WDM
`
`XXlll
`
`610
`611
`611
`612
`
`619
`620
`623
`625
`631
`632
`633
`634
`635
`637
`639
`639
`641
`645
`649
`650
`650
`652
`654
`654
`655
`656
`657
`658
`659
`660
`
`667
`669
`673
`6 81
`682
`683
`684
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`XXIV
`
`CONTENTS
`
`13.2.4 Unidirectional versus Bidirectional WDM Systems
`13.2.5 Long-Haul Networks .... . .
`13.2.6 Long-Haul Network Case Study
`13.2.7 Long~Haul Undersea Networks
`13.2.8 Metro Networks ..... .. .
`13.2.9 Metto Ring Case Study .... .
`13.2.10 From Opaque Links to Agile All-Optical Networks
`Summary ....
`Further Reading .
`Problems.
`References
`
`A Acronyms
`
`711
`
`B Symbols and Parameters
`
`717
`
`721
`C Standards
`C.1
`International Telecommunications Union (ITU-T)
`C.l.1
`Fiber .... .. ... .... ... .. .
`C.l.2
`SDH (Synchronous Digital Hierarchy) .
`C.l.3 Optical Networking .
`C.1.4 Management ........ .
`C.2 Telcordia ............ .. .
`C.2.1
`Physical and Environmental
`C.2.2
`SONET .. ..... .
`.
`. .
`C.2.3 Optical Networking .... .
`C.3 American National Standards Institute (ANSI)
`C.3.1
`SONET ... .. ..... .
`C.3.2 ESCON and Fibre Channel .
`
`D Wave Equations
`
`727
`
`731
`E Pulse Propagation in Optical Fiber
`E.1 Propagation of Chirped Gaussian Pulses
`E.2 Nonlinear Effects on Pulse Propagation
`E.3 Soliton Pulse Propagation
`Further Reading .
`References . . . . . . .
`
`F Nonlinear Polarization
`
`741
`
`686
`688
`689
`697
`698
`700
`704
`705
`706
`706
`710
`
`721
`721
`721
`722
`722
`723
`723
`723
`724
`724
`724
`724
`
`734
`735
`738
`739
`739
`
`LUMENTUM HOLDINGS, INC.
`Exhibit 1042, Page 12
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`
`CONTENTS
`
`743
`G Multilayer Thin-Film Filters
`G.l Wave Propagation at Dielectric Interfaces .
`G.2 Filter Design .
`References . . . . . . . . . . . . .
`
`751
`
`H Rando~ Variables and Processes
`H.l Random Variables
`. . . . .
`H.1.1 Gaussian Distribution
`H.1.2 Maxwell Distribution
`H.1.3 Poisson Distribution
`.
`H.2 Random Processes
`. . . . . .
`H.2.1 Poisson Random Process .
`H.2.2 Gaussian Random Process
`Further Reading .
`References . . . . . . . .
`
`I Receiver Noise Statistics
`I.1 Shot Noise ...
`1.2 Amplifier Noise
`References
`
`757
`
`Bibliography
`
`763
`
`Index
`
`797
`
`XXV
`
`743
`747
`750
`
`751
`752
`753
`753
`754
`755
`756
`756
`756
`
`759
`760
`762
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`LUMENTUM HOLDINGS, INC.
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`
`112
`
`COMPONENTS
`
`where I is the identity matrix. Note that this relation follows merely from conserva-
`tion of energy and can be readily generalized to a device with an arbitrary number
`of inputs and outputs.
`For a 2 x 2 directional coupler, by the symmetry of the device, we can set s2 1 =
`s12 =a and s22 = Si! =b. Applying (3.4) to this simplified scattering matrix, we get
`
`(3.5)
`
`(3.6)
`
`and
`ab* + ba* = 0.
`From (3.5), we can write
`lal = cos(x) and lbl = sin(x).
`If we write a= cos(x)eicfla and b = sin(x)eicflh, (3.6) yields
`cos(¢a -¢b) = 0.
`Thus ¢a and ¢b must differ by an odd multiple of n j 2. The general form of (3.1)
`now follows from (3.7) and (3.8).
`The conservation of energy has some important consequences for the kinds of
`optical components that we can build. First, note that for a 3 dB coupler, though the
`electric fields at the two outputs have the same magnitude, they have a relative phase
`shift of n /2. This relative phase shift, which follows from the conservation of energy
`as we just saw, plays a crucial role in the design of devices such as the Mach-Zehnder
`interferometer that we will study· in Section 3.3.7.
`Another consequence of the conservation of energy is that lossless combining
`is not possible. Thus we cannot design a device with three ports where the power
`input at two of the ports is completely delivered to the third port. This result is
`demonstrated in Problem 3.2.
`
`(3.7)
`
`(3.8)
`
`3.2 -
`
`Isolators and Circulators
`Couplers and most other passive optical devices are recipmcal devices, in that the
`devices work exactly the same way if their inputs and outputs are reversed. However,
`in many system,s there is a need for a passive nonrecipmcal device. An isolator is an
`example of such a device. Its main function is to allow transmission in one direction
`through it but block all trans~ission in the other direction. Isolators are used in
`systems at the output of optical amplifiers and lasers primarily to prevent reflections
`from entering these devices, which would otherwise degrade their performance. The
`
`I
`
`LUMENTUM HOLDINGS, INC.
`Exhibit 1042, Page 14
`IPR2015-00731
`
`

`
`3.2
`
`Isolators and Circulators
`
`113
`
`(a)
`
`(b)
`
`Figure 3.3 Functional representation of circulators: (a) three-port and (b) four-port.
`The arrows represent the direction of signal flow.
`
`two key parameters of an isolator are its insertion loss, which is the loss in the
`forward direction, and which should be as small as possible, and its isolation, which
`is the loss in the reverse direction, and which should be as large as possible. The
`typical insertion loss is around 1 dB, and the isolation is around 40-50 dB.
`A circulator is similar to an isolator, except that it has multiple ports, typically
`three or four, as shown in Figure 3.3. In a three-port circulator, an input signal on
`port 1 is sent out on port 2, an input signal on port 2 is sent out on port 3, and
`an input signal on port 3 is sent out on port 1. Circulators are useful to construct
`optical add/drop elements, as we will see in Section 3.3.4. Circulators operate on the
`same principles as isolators; therefore we only describe the details of how isolators
`work next.
`
`Principle of Operation
`In order to understand the operation of an isolator, we need to understand the notion
`of polarization. Recall from Section 2.1 .2 that the state of polarization (SOP) of light
`propagating in a single-mode fiber refers to the orientation of its electric field vector
`on a plane that is orthogonal to its direct~on of propagation. At any time, the electric
`field vector can be expressed as a linear combination of the two orthogonal linear
`polarizations supported by the fiber. We will call these two polarization modes the
`horizontal and vertical modes.
`The pi'inciple of operation of an isolator is shown in Figure 3.4. Assume that the
`input light signal has the. vertical SOP shown in the figure. It is passed through a
`polarizer, which passes only light energy in the vertical SOP and blocks light energy
`in the horizontal SOP. Such polarizers can be realized using crystals, called dichroics,
`
`3.2.1
`
`LUMENTUM HOLDINGS, INC.
`Exhibit 1042, Page 15
`IPR2015-00731
`
`

`
`114
`
`COMPONENTS
`
`SOP CD
`
`CD
`
`locomlog llgh< ~
`Polarizer
`
`Blocked 8
`
`0
`0
`OF""'"' ~ '"'"'"'
`0
`0
`
`rotator
`
`Reflected light
`
`Figure 3.4 Principle of operation of an isolator that works only for a particular state
`of polarization of the input signal.
`
`which have the property of selectively absorbing light with one SOP. The polarizer
`is followed by a Faraday rotator. A Faraday rotator is a nonreciprocal device, made
`of a crystal that rotates the SOP, say, clockwise, by 45°, regardless of the direction
`of propagation. The Faraday rotator is followed by another polarizer that passes
`only SOPs with this 45° orientation. Thus the light signal from left to right is passed
`through the device without any loss. On the other hand, light entering the device
`from the right due to a reflection, with the same 45° SOP orientation, is rotated
`another 45° by the Faraday rotator, and thus blocked by the first polarizer.
`Note that the preceding explanation above assumes a particular SOP for the
`input light signal. In practice we cannot control the SOP of the input, and so
`the isolator must work regardless of the input SOP. This requires a more com-
`plicated design, and many different designs exist. One such design for a miniature
`polarization-independent isolator is shown in Figure 3.5. The input signal with an
`arbitrary SOP is first sent through a spatial wall~-off polarizer (SWP). The SWP splits
`the signal into its two orthogonally polarized components. Such an SWP can be
`realized using birefringent crystals whose refractive index is different for the two
`components. When light with an arbitrary SOP is incident on such a crystal, the two
`orthogonally polarized components are refracted at different angles. Each compo-
`nent goes through a Faraday rotator, which rotates the SOPs by 45°. The Faraday
`rotator is followed by a half-wave plate. The half-wave plate (a reciprocal device)
`rotates the SOPs by 45° in the clockwise direction for signals propagating from left
`to right, and by 45° in the counterclockwise direction for signals propagating from
`right to left. Therefore, the combination of the Faraday rotator and the half-wave
`plate converts, the horizontal polarization into a vertical polarization and vice versa,
`and the two signals are combined by another SWP at the output. For reflected signals
`in the reverse direction, the half-wave plate and Faraday rotator cancel each other's
`effects, and the SOPs remain unchanged as they pass through these two devices and
`are thus not recombined by the SWP at the input.
`
`LUMENTUM HOLDINGS, INC.
`Exhibit 1042, Page 16
`IPR2015-00731
`
`

`
`3.3 Multiplexers and Filters
`
`115
`
`SWP
`
`Faraday rotator
`
`IJ2 plate SWP
`
`Fiber in
`
`8
`
`6)
`
`(a)
`
`sorffi ~ CD ~ 0 ~:~
`~ 8 ~ 0 ~:~
`
`EB.
`
`Fiber out
`
`EB
`
`Fiber out
`
`SWP
`
`Faraday rotator
`
`IJ2 plate SWP
`
`Fiber in
`
`..
`
`CD
`
`6)
`
`3.3 -
`
`(b)
`
`Figure 3.5 A polarization-independent isolator. The isolator is constructed along the
`same lines as a polarization-dependent isolator but uses spatial walk-off polarizers at the
`inputs and outputs. (a) Propagation from left to right. (b) Propagation from right to left.
`
`Multiplexers and Filters
`In this section, we will study the principles underlying the operation of a va-
`riety of wavelength selection technologies. Optical filters are essential compo-
`nents in transmission systems for at least two applications: to multiplex and de-
`multiplex wavelengths in a WDM system-these devices are called multiplexers/
`demultiplexers-and to provide equalization of the gain and filtering of noise in op-
`tical amplifiers. Further, understanding optical filtering is essential to understanding
`the operation of lasers later in this chapter.
`The different applications of optical filters are shown in Figure 3.6. A simple
`filter is a two-port device that selects one wavelength and rejects all others. It may
`have an additional third port on which the rejected wavelengths can be obtained. A
`multiplexer combines signals at different wavelengths on its input ports onto a com-
`mon output port, and a demultiplexer performs the opposite function . Multiplexers
`and demultiplexers are used in WDM terminals as well as in larger wavelength
`cmsscom1,ects and wavelength add/drop multiplexers.
`Demultiplexers and multiplexers can be cascaded to realize static wavelength
`crossconnects (WXCs). In a static WXC, the crossconnect pattern is fixed at the time
`
`LUMENTUM HOLDINGS, INC.
`Exhibit 1042, Page 17
`IPR2015-00731
`
`

`
`3.3 Multiplexers and Filters
`
`127
`
`discussed the behavior of Bragg gratings in Section 3.3.3. Long-period gratings, on
`the other hand, have periods that are much greater than the wavelength, ranging
`from a few hundred micrometers to a few millimeters.
`
`Fiber Bragg Gratings
`Fiber Bragg gratings can be fabricated with extremely low loss (0.1 dB), high wave-
`length accuracy (± 0.05 nm is easily achieved), high adjacent channel crosstalk
`suppression (40 dB), as well as flat tops.
`The temperature coefficient of a fiber Bragg grating is typically 1.25 x 10-2 nm/°C
`due to the variation in fiber length with temperature. However, it is possible to
`compensate for this change by packaging the grating with a material that has a
`negative thermal expansion coefficient. These passively temperature-compensated
`gratings have temperature coefficients of around 0.07 x w-2 nm/0 C. This implies
`a very small 0.07 nm center wavelength shift over an operating temperature range
`of 100°C, which means that they can be operated without any active temperature
`control.
`These properties of fiber Bragg gratings make them very useful devices for sys-
`tem applications. Fiber Bragg gratings are finding a variety of uses in WDM systems,
`ranging from filters and optical add/drop elements to dispersion compensators. A
`simple optical drop element based on fiber Bragg gratings is shown in Figure 3.14(a).
`It consists of a three-port circulator with a fiber Bragg grating. The circulator trans-
`mits light coming in on port 1 out on port 2 and transmits light coming in on port
`2 out on port 3. In this case, the grating reflects the desired wavelength A.2, which is
`then dropped at port 3. The remaining three wavelengths are passed through. It is
`possible to implement an add/drop function along the same lines, by introducing a
`coupler to add the same wavelength that was dropped, as shown in Figure 3.14(b).
`Many variations of this simple add/drop element can be realized by using gratings
`in combination with couplers and circulators. A major concern in these designs is
`that the reflection of these gratings is not perfect, and as a result, some power at the
`selected wavelength leaks through the grating. This can cause undesirable crosstalk,
`and we will study this effect in Chapter 5.
`Fiber Bragg gratings can also be used to compensate for dispersion accumulated
`along the link. We will study this applicatiop in Chapter 5 in the context of dispersion
`compensation.
`
`Long-Period Fiber Gratings
`Long-period,fiber gratings are fabricated in the same manner as fiber Bragg gratings
`and are used today primarily as filters inside erbium-doped fiber amplifiers to com-
`pensate for their nonflat gain spectrum. As we will see, these devices serve as very
`
`LUMENTUM HOLDINGS, INC.
`Exhibit 1042, Page 18
`IPR2015-00731
`
`

`
`304
`
`TRANSMISSION SYSTEM ENGINEERING
`
`Intracbannel
`
`Interchannel
`
`5
`
`4.
`
`j
`
`2
`
`~
`£
`"" c ., 0.
`...
`.,
`~
`0 p..
`
`-50
`
`-20
`- 30
`-40
`Crosstalk level (dB)
`
`-10
`
`0
`
`Figure 5.12 Signal-spontaneous noise limited intrachannel and interchannel crosstalk
`penalties as a function of crosstalk level -10 logEs in a network. The parameter N denotes
`the number of crosstalk elements, all assumed to produce crosstalk at equal powers.
`
`Figure 5.13 A bidirectional tra~smission system.
`
`end, say, end A, will send a lot of power back into A's receiver, creating a large
`amount of crosstalk. In fact, the reflected power into A may be larger than the signal
`power received from the other end B. Reflections within the end equipment can
`be carefully controlled, but it is more difficult to restrict reflections from the fiber
`link itself. For this reason, bidirectional systems typically use different wavelengths
`\
`in different directions. The two directions can be separated at the ends either by
`using an optical circulator or a WDM mux/demux, as in Figure 5.14. (If the same
`wavelength mllst be used in both directions, one alternative that is sometimes used
`in short-distance access networks is to use time division multiplexing where only one
`·
`end transmits at a time.)
`If a WDM mux/demux is used to handle both directions of transmission, crosstalk
`can also arise because a signal at a transmitted wavelength is reflected within the mux
`
`LUMENTUM HOLDINGS, INC.
`Exhibit 1042, Page 19
`IPR2015-00731