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.

Pages: 552

ISBN: 9780819457615

Volume: PM147

- 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

**© SPIE.**Terms of Use