Cisco Systems, Inc.
`Exhibit 1042
`Page 1
`
`

`
`Optical Networl<s
`A Practical Perspective
`
`Second Edition
`
`Rajiv Ramaswami
`l<umar N. Sivarajan
`
`M( ... ®
`
`MORGAN KAUFMANN PUBLISHERS
`
`AN
`
`I M P R I NT OF ACADE M IC P RESS
`
`A D ivi sion of Har court, Inc
`
`Cisco Systems, Inc.
`Exhibit 1042
`Page 2
`
`

`
`Editor Rick Adams
`Publishing Services Manager Scott Norton
`Senior Production Editor Cheri Palmer
`Assistant Acquisitions Editor Karyn Johnson
`Cover Design Ross Carron Design
`Cover Image © Dominique Sarraute I Image Bank
`Text Design Windfall Software
`Copyeditor Ken DellaPenta
`Proofreader Jennifer McClain
`Indexer Steve Rath
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`
`This book has been author-typeset using NfEX·
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`Designations used by companies to distinguish their products are often claimed as trademarks or
`registered trademarks. In all instances in which Morgan Kaufmann Publishers is aware of a claim, the
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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.
`
`Cisco Systems, Inc.
`Exhibit 1042
`Page 3
`
`

`
`Contents
`
`Foreword
`
`ix
`
`Foreword to the First Edition
`
`xi
`
`Preface
`
`xxvii
`
`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
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`32
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`35
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`Page 4
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`XVl
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`CONTENTS
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`1.8.3 Optical Amplifiers and WDM . . . . . .
`1.8.4 Beyond Transmission Links to Networks
`Summary
`Further Reading .
`References . . . .
`
`I Technology
`
`47
`
`49
`
`2 Propagation of Signals in Optical Fiber
`2.1 Light Propagation in Optical Fiber
`2.1.1 Geometrical Optics Approach
`2. 1.2 Wave Theory Approach
`2.2 Loss and Bandwidth
`2.2.1 Bending Loss . . . . . .
`2.3 Chromatic Dispersion
`. . . . .
`2.3.1 Chirped Gaussian Pulses
`2.3.2 Controlling the Dispersion Profile
`2.4 Nonlinear Effects . . . . . . . . . . . .
`2.4.1 Effective Length and Area .. .
`2.4.2 Stimulated Brillouin Scattering .
`2.4.3 Stimulated Raman Scattering
`2.4.4 Propagation in a Nonlinear Medium
`2.4.5 Self-Phase Modulation . . . . . . . .
`2.4.6 SPM-Induced Chirp for Gaussian Pulses
`2.4.7 Cross-Phase Modulation .
`2.4.8 Four-Wave Mixing ....
`2.4.9 New Optical Fiber Types .
`2.5 Solitons
`. . . . . . . . . . . . . .
`2.5 .1 Dispersion-Managed Solitons
`Summary ....
`Further Reading .
`Problems.
`References . .
`
`107
`
`3 Components
`. . . . . . . .
`3.1 Couplers .
`3.1.1 Principle of Operation
`3.1.2 Conservation of Energy
`Isolators and Circulators ...
`3.2.1 Principle of Operation
`
`3.2
`
`37
`39
`40
`41
`42
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`50
`50
`55
`65
`67
`68
`69
`74
`76
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`87
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`100
`101
`102
`103
`104
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`108
`110
`111
`112
`113
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`CONTENTS
`
`3.3 Multiplexers and Filters
`3.3.1 Gratings . . . . . .
`3.3.2 Diffraction Pattern
`3.3.3 Bragg Gratings ..
`3.3.4 Fiber Gratings ...
`3.3.5 Fabry-Perot Filters
`3.3.6 Multilayer Dielectric Thin-Film Filters
`3.3.7 Mach-Zehnder Interferometers
`3.3.8 Arrayed Waveguide Grating . . . . . .
`3.3.9 Acousto-Optic Tunable Filter .... .
`3.3.10 High Channel Count Multiplexer Architectures
`3.4 Optical Amplifiers . . . . . .
`3.4.1 Stimulated Emission . . . . . .
`3.4.2 Spontaneous Emission .... .
`3.4.3 Erbium-Doped Fiber Amplifiers
`3.4.4 Raman Amplifiers . . . . . . .
`3.4.5 Semiconductor Optical Amplifiers .
`3.4.6 Crosstalk in SOAs
`3.5 Transmitters . . . . . . . . . .
`3.5.1 Lasers . . . . . . . . .
`3.5.2 Light-Emitting Diodes
`3.5.3 Tunable Lasers ....
`3.5.4 Direct and External Modulation .
`3.5.5 Pump Sources for Raman Amplifiers
`3.6 Detectors . . . . . . . . . . .
`3.6.1 Photodetectors ... .
`3.6.2 Front-End Amplifiers .
`3.7 Switches . . . . . . . . . . . .
`3.7.1 Large Optical Switches .
`3.7.2 Optical Switch Technologies .
`3.7.3 Large Electronic Switches
`3.8 Wavelength Converters .... . .
`3.8.1 Optoelectronic Approach
`3.8.2 Optical Gating . . . . . .
`3.8.3
`Interferometric Techniques .
`3.8.4 Wave Mixing
`Summary
`Further Reading .
`Problems ..
`References . . . .
`
`xvii
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`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
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`199
`201
`207
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`216
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`224
`225
`226
`232
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`Page 5
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`

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`xviii
`
`CONTENTS
`
`CONTENTS
`
`239
`
`4 Modulation and Demodulation
`4.1 Modulation . . . . . . . .
`4.1.1 Signal Formats
`. .
`4.2 Subcarrier Modulation and Multiplexing
`4.2.1 Clipping and Intermodulation Products .
`4.2.2 Applications of SCM . . . . . .
`4.3 Spectral Efficiency . . . . . . . . . . . . . . .
`4.3.1 Optical Duobinary Modulation .. .
`4.3.2 Optical Single Sideband Modulation
`4.3.3 Multilevel Modulation ..... .
`4.3.4 Capacity Limits of Optical Fiber .
`4.4 Demodulation . . . . . . . . . . . . . . .
`4.4.1 An Ideal Receiver . . . . . . . . .
`4.4.2 A Practical Direct Detection Receiver
`4.4.3 Front-End Amplifier Noise .
`4.4.4 APD Noise ..... .
`4.4.5 Optical Preamplifiers
`4.4.6 Bit Error Rates ...
`4.4.7 Coherent Detection .
`4.4.8 Timing Recovery ..
`4.4.9 Equalization .....
`4.5 Error Detection and Correction
`4.5 .1 Reed-Solomon Codes .
`4.5.2
`Interleaving
`Summary ....
`Further Reading .
`Problems.
`References . . . .
`
`283
`
`5 Transmission System Engineering
`5.1 System Model .
`5.2 Power Penalty .
`5.3 Transmitter ..
`5.4 Receiver . . . .
`5.5 Optical Amplifiers
`5.5.1 Gain Saturation in EDFAs
`5.5.2 Gain Equalization in EDFAs .
`5.5.3 Amplifier Cascades ....
`5.5.4 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
`
`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
`.
`. .
`5.7 Dispersion . . . . . . . . . . .
`5.7.1 Chromatic Dispersion Limits: NRZ Modulation .
`5.7.2 Chromatic Dispersion Limits: RZ Modulation
`5.7.3 Dispersion Compensation . . . . . . .
`5.7.4 Polarization-Mode Dispersion (PMD) .
`5.8 Fiber Nonlinearities . . . . . . . . . . . . . . .
`5.8.1 Effective Length in Amplified Systems .
`5.8.2 Stimulated Brillouin Scattering.
`5.8.3 Stimulated Raman Scattering
`5.8.4 Four-Wave Mixing . . . . . . .
`5.8.5 Self-/Cross-Phase Modulation
`5.8.6 Role of Chromatic Dispersion Management
`5.9 Wavelength Stabilization . . . . . . . . . . . . .
`5.10 Design of Soliton Systems .. .. . . . . . . . .
`5.11 Design of Dispersion-Managed Soliton Systems
`5.12 Overall Design Considerations . . . . . . . . .
`5.12.1 Fiber Type . . . . . . . . . . . . . . . .
`5 .12.2 Transmit Power and Amplifier Spacing
`5.12.3 Chromatic Dispersion Compensation
`5.12.4 Modulation . . . . . . . . . . . . . . .
`5.12.5 Nonlinearities . . . . . . . . . . . . . .
`5.12.6 Interchannel Spacing and Number of Wavelengths .
`5.12.7 All-Optical Networks
`5.12.8 Wavelength Planning
`5 .12.9 Transparency
`Summary ....
`Further Reading .
`Problems.
`References . . . .
`
`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
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`Cisco Systems, Inc.
`Exhibit 1042
`Page 6
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`

`
`XX
`
`CONTENTS
`
`II Networks
`
`361
`
`363
`
`6 Client Layers of the Optical Layer
`6.1 SONET/SDH . . . . . . . .
`6.1.1 Multiplexing .... .
`6.1.2 SONET/SDH Layers
`6.1.3 SONET Frame Structure .
`6.1.4 SONET/SDH Physical Layer .
`6.1.5 Elements of a SONET/SDH Infrastructure
`6.2 ATM . . . . . . . . . . . .
`6.2.1 Functions of ATM
`6.2.2 Adaptation Layers
`6.2.3 Quality of Service .
`6.2.4 Flow Control ...
`Signaling and Routing
`6.2.5
`IP ..
`Routing and Forwarding .
`6.3.1
`Quality of Service . . . . .
`6.3.2
`Multiprotocol Label Switching (MPLS)
`6.3.3
`Whither ATM?
`6.3.4
`6.4 Storage-Area Networks .
`6.4.1 ESCON ....
`6.4.2 Fibre Channel ..
`6.4.3 HIPPI . . . . . .
`6.5 Gigabit and 10-Gigabit Ethernet .
`Summary ....
`Further Reading .
`Problems .
`References . . . .
`
`6.3
`
`403
`
`7 WDM Network Elements
`7. 1 Optical Line Terminals
`7.2 Optical Line Amplifiers ....
`7.3 Optical Add/Drop Multiplexers
`7.3.1 OADM Architectures ..
`7.3.2 Reconfigurable OADMs
`7.4 Optical Crossconnects
`. . . . .
`7.4.1 All-Optical OXC Configurations
`Summary ....
`Further Reading . . . . . . . . . . . . . . . . .
`
`CO NTENTS
`
`Problems.
`References
`
`437
`8 WDM Network Design
`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 Interoperability . . . . .
`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 .
`
`XXl
`
`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
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`508
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`512
`513
`514
`519
`519
`
`364
`367
`370
`371
`375
`378
`381
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`385
`386
`387
`387
`388
`390
`392
`392
`394
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`396
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`397
`398
`398
`399
`399
`401
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`406
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`408
`411
`417
`419
`425
`428
`430
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`xxii
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`CONTENTS
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`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 Interworking 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
`
`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 NTT'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
`
`xxiii
`
`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
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`667
`669
`673
`681
`682
`683
`684
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`Page 8
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`

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`XXlV
`
`CONTENTS
`
`CONTENTS
`
`743
`G Multilayer Thin-Film Filters
`G.1 Wave Propagation at Dielectric Interfaces .
`G.2 Filter Design .
`References . . . . . . . . . . . . .
`
`751
`
`H Random Variables and Processes
`H.1 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 . . . . . . . .
`
`Receiver Noise Statistics
`1.1 Shot Noise ...
`1.2 Amplifier Noise
`References
`
`757
`
`Bibliography
`
`763
`
`Index
`
`797
`
`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 Metro 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)
`Fiber . . . . . . . . . . . . . . . . . . .
`C.1.1
`C.1.2
`SOH (Synchronous Digital Hierarchy) .
`C.1.3 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
`
`72 7
`
`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
`
`XXV
`
`743
`747
`750
`
`751
`752
`753
`753
`754
`755
`756
`756
`756
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`759
`760
`762
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`Cisco Systems, Inc.
`Exhibit 1042
`Page 9
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`

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`112
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`CoMPONENTS
`
`. 1 .
`follows merely from conserva-
`where I is the identity matrix. ~ote that tl~ls ~et~t:o~evice with an arbitrary number
`be readily genera 1ze
`d
`-
`~cl~~m~
`t uts
`· ce we can set S21 -
`f h d
`d
`t
`b
`of inputs an ou p
`.
`the s mmetry o t e evl
`'
`.
`2 x 2 directional coupler, y
`ll'fied scattering matnx, we ge
`y h'
`.
`F
`ora
`1 in (3.4)tot 1ss1mp
`s 12 =a and s22 = Sll =b. App y g
`(3.5)
`\a\2 + \b\2 = 1
`
`and
`ab* + ba* = 0.
`
`From (3.5), we can write
`
`\a\= cos(x) and \b\ = sin(x).
`.
`( )ei<Pa and b = sin(x)ei<Pb' (3.6) ylelds
`.
`If we wnte a = cos x
`
`(3.6)
`
`(3.7)
`
`(3.8)
`
`0
`
`cos(</>a- </>b)=
`f 12 The general form of (3.1)
`.
`·
`d. ff
`.
`by an odd multlple o n
`Thus 4> and </>b must 1 er
`f
`·m ortant consequences for the kinds o
`now follows from (3.7) and (3.8).
`The conservation of energy ha~l~o~:s~ :ate that for a 3 dB coupler, th.oughhthe
`. 1 components that we can bm
`'tude they have a relauve p ase
`'
`.
`the same magm
`opuca
`h
`'
`.
`f
`electric fields at the tw~ out:uts :~: which follows from the conservatwnh oz e~:~:r
`shift of n j2. This relatlVe p. ase sl ~ ' h design of devices such as the Mac - e
`rue1al ro e m t e
`1
`..
`. S
`.
`3 3 7
`as we just saw, pays a c
`interferometer that we will study m ectl~:io~ ~f· energy is that lossless combtntn~
`Another consequence of the co~serv d
`. e with three ports where the polw~
`nnot deslgn a evlC
`. d
`This resu t lS
`h
`1 1 delivered to the thlr port.
`is not possible. T us we c~
`of the ports lS comp ete y
`.
`mput at two
`demonstrated in Problem 3.2.
`
`3.2 -
`
`Isolators and Circulators
`. that the
`.
`·
`al dev1ces, m
`However,
`.
`o tical devices are rectproc
`Couplers and most other passlVaey i~ their inputs and outputs are revers~d.lator is an
`l d
`.
`· ce An zso
`.
`tly the same w
`.
`k
`e~l . . .
`devlces wor exac
`.
`d for a passive nonreczproca
`e direction
`in many systems there lS a nee
`tion is to allow transmlsswn m on
`used in
`. f
`example of such a device. Its mal.n .unc .
`the other direction. Isolators areflections
`ll transm1ss10n m
`bl k
`.
`ent re
`. 1
`through it but oc a
`lifiers and lasers primanly to prev
`ance. rhe
`systems at the output of. optlcahi:~ould otherwise degrade their perform
`from entering these devKes, w
`
`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.
`
`3.2.1
`
`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 direction 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
`h
`.
`.
`onzontal and vertical modes.
`. The principle of operation of an isolator is shown in Figure 3.4. Assume that the
`In~ut .light signal has the vertical SOP shown in the figure. It is passed through a
`~ 0 ~rzzer, which passes only light energy in the vertical SOP and blocks light energy
`In t e horizontal SOP. Such polarizers can be realized using crystals, called dichroics,
`
`Cisco Systems, Inc.
`Exhibit 1042
`Page 10
`
`

`
`114
`
`CoMPONENTS
`
`sorCD
`CD
`Ioc~iog liglll ~
`Polarizer
`
`...
`Blocked 8
`
`0 0 .,..
`Faraday ~ Pol~i=
`0 0
`
`rotator
`
`Reflected light
`
`sorE9
`
`FI 'ber in
`
`Faraday rotator
`
`SWP
`r-
`
`CD
`
`...
`
`0
`
`~
`1-.J 8
`
`I._ 0
`
`(a)
`
`IJ2 plate SWP
`
`..-- 8 .-
`~ EB
`
`CD
`
`'---
`
`I....J
`
`Fib~
`ut
`
`3.3 Multiplexers and Filters
`
`115
`
`IJ2 plate SWP
`
`,..;. 8r-
`~ EB
`(])
`
`'-
`
`'---
`
`Fiber
`out
`
`Faraday rotator
`,;....
`
`SWP
`
`~ 8
`
`0
`
`F iber in
`
`__._
`
`I....J
`
`(])
`
`L..J 0
`
`(b)
`
`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(cid:173)
`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 walk-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(cid:173)
`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 frorn
`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.
`
`3.3 -
`
`Figure 3.5 A polarization-independent isolator Th
`. I
`.
`e ISO a~or IS constructed along the
`same lines as a polarization-dependent isol t b .
`inputs and outputs. (a) Propagation from l:f~~o ~t ~;es(~)pPaual wal~-off polar.izers at the
`ng
`·
`ropagatwn from nght to left.
`
`.
`
`.
`
`In this section we
`
`·11
`
`d
`
`h
`
`Multiplexers and Filters
`~=~' 7! ::::~~~::::lo::: ,:c::O~~:::!." O~~~~ly~7!,:h:,~P=:::~~:I o!o~;::
`multiplex wavelen th ~s ems for at least two applications: to multiplex and de(cid:173)
`demultiplexers-a:d t~ lpnroavl'?d DM sl~ste~-thfese devices are called multiplexers/
`d fil
`·
`f
`.
`.
`e equa 1zat10n o the g ·
`.
`tical amplifiers Furth
`.
`.
`am an
`tenng o nOise m op-
`the operation ~f laserserl,autnd~rstha.ndlhng optical filtering is essential to understanding
`er m t IS c apter
`The different ap 1'
`t'
`f
`.
`.
`. 1
`p l~a wns o optiCal filters are shown in Figure 3 6 A
`filte
`.
`1
`.
`. .
`Simp e
`r IS a two-port device that selects
`h' one wave ength and reJects all others. It may
`have an additional th' d
`multiplexer combinesl:i po;t ond~f ICh the rejected wavelengths can be obtained. A
`mon output port and g;a s at. I erent wavelengths on its input ports onto a com-
`and demultiplex~rs ar: u:~;l~;;~~e;for~s the opposite f~nction. Multiplexers
`crossconnects and
`l
`h dd
`ermmals as well as m larger wavelength
`wave engt a
`!drop multiplexers.
`D
`.
`.
`emult1plexers and multiplexe
`b
`rs can e cascaded to reahze static wavelength
`crossconnects (WXC ) I
`.
`s . n a static WXC, the crossconnect pattern is fixed at the time
`
`Cisco Systems, Inc.
`Exhibit 1042
`Page 11
`
`

`
`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(cid:173)
`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 w- 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(cid:173)
`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(cid:173)
`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 application 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(cid:173)
`Pensate for their nonflat gain spectrum. As we will see, these devices serve as very
`
`1
`
`:s
`
`~ r
`ty
`1e
`he
`-4
`
`Cisco Systems, Inc.
`Exhibit 1042
`Page 12
`
`

`
`304
`
`TRANSMISSION SYSTEM ENGINEERING
`
`Intrachannel
`
`Interchannel
`
`-50
`
`-20
`-30
`-40
`Crosstalk level (dB)
`
`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 transmission 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 must 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
`
`Cisco Systems, Inc.
`Exhibit 1042
`Page 13