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Spie Press Book

Polarized Light in Fiber Optics
Author(s): Edward Collett
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Book Description

This book is both a coherent exposition and an in-depth mathematical analysis of polarized light in fiber optics. It also is an essential reference for scientists, optical and electrical engineers, optical physicists, and researchers working in the field of fiber optics and in related optical fields. Upper-level undergraduate, graduate, and continuing-education students will refer to it again and again.

Published by The PolaWave Group in association with SPIE Press.


Book Details

Date Published: 15 December 2003
Pages: 552
ISBN: 9780819457615
Volume: PM147

Table of Contents
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Preface /iii
Chapter 1 Introduction /1
Chapter 2 The Wave Equation and Young's Interference Experiment /3
2.1 Introduction /3
2.2 The Wave Equation /4
2.3 The Fourier Transform Method /10
2.4 Young's Interference Experiment /12
2.5 The Complex Representation of the Optical Field /15
2.6 The Concept of Optical Beats - The Beat Length /18
References /26
Chapter 3 The Polarization Ellipse /27
3.1 Introduction /27
3.2 The Instantaneous Optical Field and the Polarization Ellipse /28
3.3 Degenerate States of the Polarization Ellipse /32
3.4 The Elliptical Parameters of the Polarization Ellipse /35
References /43
Chapter 4 The Poincar� Sphere and the Polarization Ellipse /45
4.1 Introduction /45
4.2 The Poincar� Sphere /46
References /53
Chapter 5 The Stokes Polarization Parameters /55
5.1 Introduction /55
5.2 The Stokes Polarization Parameters /56
5.3 The Stokes Vector /61
5.4 The Classical Measurement of the Stokes Polarization Parameters /65
References /75
Chapter 6 The Mueller Matrices for Polarizing Components /77
6.1 Introduction /77
6.2 The Mueller Matrix Calculus /78
6.3 The Mueller Matrix of a Polarizer /79
6.4 The Mueller Matrix of a Waveplate /87
6.5 The Mueller Matrix of a Rotator /93
6.6 The Mueller Matrix for Rotated Polarizer Components /95
6.7 The Generation of Elliptically Polarized Light /103
6.8 Application - The Behavior of a Rotated Waveplate Placed between a Pair of Crossed Polarizers /107
6.9 The Mueller Matrix of a Depolarizer /110
References /113
Chapter 7 The Observable Polarization Sphere /115
7.1 Introduction /115
7.2 Mathematical Background of the Observable Polarization Sphere /117
7.3 The Relation between the Polarization Ellipse and the Coordinates of the Observable Polarization Sphere /123
7.4 Propagation through a Fixed Variable-Phase Waveplate /125
7.5 Propagation through a Rotator /127
7.6 Propagation through an Ideal Linear Polarizer /130
7.7 The Polarization Coverage on the Observable Polarization Sphere /132
Appendix I - Jerrard's Examples of the Polarizer-Analyzer and the S�narmont Compensator plotted on the Observable Polarization Sphere /136
Appendix II - A Note on Great and Small Circles on the Observable Polarization Sphere /144
References /148
Chapter 8 Application of the Mueller Matrices /149
8.1 Introduction /149
8.2 Propagation through a Rotating Quarter-Waveplate (QWP) /149
8.3 Propagation through a Rotating Half-Waveplate (HWP) /159
8.4 Propagation of a Polarized Beam through a Rotating Variable-Phase Waveplate /163
8.5 An Example - Determination of the Phase and Rotation Angle of a Variable Phase Waveplate to Generate a Specific Polarization State /171
8.6 Propagation of a Polarized Light Beam through Two Independently Rotating Quarter-Waveplates (QWP) /174
8.7 Propagation through a Rotated Ideal Linear Polarizer /179
References /181
Chapter 9 Polarization Controllers /183
9.1 Introduction /183
9.2 Analysis of a Birefringent Fiber /184
9.3 The Non-Rotating Variable-Phase Waveplate /186
9.4 The Rotating Variable-Phase (Waveplate) Fiber Optic /188
9.5 The Agilent 8169A Polarization Controller /189
9.6 The Agilent 11896A Polarization Controller /198
9.7 Lefevre's 3-Loop Polarization Controller /200
9.8 The Q-H-Q Waveplate Combination /208
9.9 The Corning PC-310 Polarization Controller /212
9.10 The Corning PC-410 Polarization Controller /215
9.11 The General Photonics PolaRite II Polarization Controller /219
References /225
Chapter 10 Optical Isolators and Optical Circulators /227
10.1 Introduction /227
10.2 The Faraday Effect /228
10.3 The Classical Optical Isolator /240
10.4 The Faraday Optical Isolator /245
10.5 Polarization Independent Isolators /253
10.6 Optical Circulators /257
10.7 An Application - Tuned Fiber Coil Isolators /262
Appendix - Spherical Spirals /276
References /279
Chapter 11 The Evolution of the Stokes Vector in a Fiber Optic /281
11.1 Introduction /281
11.2 Motion of a Vector on a Sphere /281
11.3 Motion of the Stokes Vector around the Vertical Axis /284
11.4 Motion of the Stokes Vector around an Arbitrarily Oriented Axis /286
11.5 Evolution of the Stokes Vector in a Birefringent Fiber /288
11.6 Coupled Mode Analysis of Propagation /299
11.7 Polarization Evolution in a Twisted Fiber /308
11.8 Random Polarization Coupling /311
References /317
Chapter 12 Optical Depolarizers and Scramblers /319
12.1 Introduction /319
12.2 The Monochromatic Depolarizer /320
12.3 The Rotating Waveplate Depolarizer /327
12.4 The Lyot Crystal Depolarizer /333
12.5 The Oz Optics Polarization Controller - Scrambler /336
12.6 The Single - Mode Fiber Lyot Depolarizer /343
References /353
Chapter 13 Polarization Measurements /355
13.1 Introduction /355
13.2 The Classical Measurement of the Stokes Polarization Parameters /356
13.3 Measurement of the Stokes Parameters using a Circular Polarizer /359
13.4 The Null Intensity Method /362
13.5 Determination of the Stokes Parameters using a Rotating Quarter-Waveplate - Fourier Analysis /365
13.6 The Four Channel Stokes Polarimeter /368
13.7 The Measurement of the Mueller Matrix /372
References /378
Chapter 14 The Jones Matrix Calculus and Wolf's Coherency Matrix /379
14.1 Introduction /379
14.2 The Jones Matrix Calculus /380
14.3 The Jones Matrices for a Polarizer, Waveplate, and Rotator /385
14.4 Eigenvalues and Eigenvectors of the Jones Matrices /390
14.5 The Circular Transformation and the Diagonalization of the Jones Matrices /393
14.6 Examples of the Jones Matrix Calculus /397
14.7 The Jones Matrices for Homogeneous Elliptical Polarizers and Retarders /402
14.8 Experimental Determination of the Jones Matrix /408
14.9 The Transmission Method to Measure the Experimental Jones Matrix /413
14.10 Wolf's Coherency Matrix /417
14.11 The Diagonalization of the Mueller Matrix - The ABCD Matrix /427
References /431
Chapter 15 Polarization Dependent Loss /433
15.1. Introduction /433
15.2. The Concept of Polarization Dependent Loss (PDL) /434
15.3. The Measurement of PDL - The All-States Method /448
15.4. The Measurement of PDL - The Random Polarization Scanning Technique /451
15.5. The Measurement of PDL - The Mueller Matrix Method and the Agilent 8169A Polarization Controller /463
15.6. The Measurement of PDL - The Jones Eigenvalue - Eigenvector Method /470
15.7. The Statistics of Polarization Dependent Losses /477
References /480
Chapter 16 Polarization Mode Dispersion /483
16.1. Introduction /483
16.2. The Concept of Phase Velocity and Group Velocity /484
16.3. The Experimental Measurement of Polarization Mode Dispersion in a Single Mode Fiber /491
16.4. The Phenomenological Model of Polarization Mode Dispersion of a Single Mode Fiber /500
16.5. The Statistical Behavior of Polarization Mode Dispersion /507
16.6. Mitigation and Compensation of Polarization Mode Dispersion /514
16.7. Measurement Techniques for Polarization Mode Dispersion /516
References /529
Index /531

Preface

Polarized Light has emerged as one of the most important topics in the current devel-opment of fiber optic transmission systems. Within the past two decades fiber optics has become increasingly important as telecommunications technology in the latter half of the twentieth century began to make a transition from the electrical domain to the optical domain. In large part this was due to the fact that fiber optics can inher-ently carry more channels of information than is possible with wire. Furthermore, for relatively low transmission rates, less that 1 Gbit/sec, the role of the orthogonal propagation modes that exist in an optical fiber do not affect the signals since power rather than amplitudes are detected. In the middle of the 1990s with the emergence of the internet and the World Wide Web and its seemingly insatiable demand for in-creased data rates, a new technological barrier began to appear, namely, chromatic and polarization dispersion. In large part the problems associated with chromatic dis-persion now appear to have been overcome. However, at this time the same cannot be said be said for polarization dispersion or as it is more often called polarization mode dispersion or simply PMD.

The phenomenon of PMD is readily understood. However, when one begins to read the literature to obtain more than a descriptive understanding of this subject as well as other polarization subjects such as optical scramblers, polarization control-lers, optical circulators, etc., one finds that the amount of information available, sim-ply put, is overwhelming. In fact, in order to understand the technical literature a very diverse background of information is required not only in polarized light but in other branches of optics and engineering as well. The result is that it is not at all easy from reading the published literature in a short time to obtain a coherent understanding of the field of polarized light in fiber optics. In order to obtain a more rapid and thor-ough understanding of polarized light and its applications it would appear that a text-book dealing with the major aspects of polarized light in fiber optics would be very useful. Therefore, one of the major objectives of the present textbook is to provide not only an understanding of the major developments of polarized light in fiber optics but to present the reader with the required background in polarized light. Very often the subject of the foundations of polarized light is discussed only in a cursory manner in either a one year course in physics or even in an optics course. Yet, in order to un-derstand the role of polarized light in fiber optics it is very useful the reader to under-stand and know this background. This information will greatly improve the reader�s understanding of polarized light as it relates to the numerous devices and measure-ment methods associated with fiber optics.

Edward Collett
Lincroft, New Jersey
USA


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