Polarized light and the Mueller matrix approach

517 Pages·2022·39.936 MB·English

by  Razvigor Ossikovski, José Jorge Gil Pérez

i
Polarized Light and the
Mueller Matrix Approach
ii

Series in Optics and Optoelectronics
Handbook of Optoelectronic Device Modeling and Simulation (Two-Volume Set)
Joachim Piprek
Handbook of Optoelectronics, Second Edition (Three-Volume Set)
John P. Dakin, Robert G. W. Brown
Optical MEMS, Nanophotonics, and Their Applications
Guangya Zhou, Chengkuo Lee
Thin-Film Optical Filters, Fifth Edition
H. Angus Macleod
Laser Spectroscopy and Laser Imaging
An Introduction
Helmut H. Telle, Ángel González Ureña
Fourier Optics in Image Processing
Neil Collings
Holography
Principles and Applications
Raymond K. Kostuk
An Introduction to Quantum Optics, Second Edition
Photon and Biphoton Physics
Yanhua Shih
Polarized Light and the Mueller Matrix Approach, Second Edition
José J. Gil, Razvigor Ossikovski
For more information about this series, please visit: https://www.crcpress.com/Series-
in-Optics-and-Optoelectronics/book-series/TFOPTICSOPT
iii
Polarized Light and the Mueller
Matrix Approach
Second Edition
José J. Gil
Razvigor Ossikovski
iv
Second edition published 2022
by CRC Press
6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487- 2742
and by CRC Press
4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
CRC Press is an imprint of Taylor & Francis Group, LLC
© 2022 Taylor & Francis Group, LLC
First edition published by CRC Press 2016
Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot
assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers
have attempted to trace the copyright holders of all material reproduced in this publication and apologize to
copyright holders if permission to publish in this form has not been obtained. If any copyright material has not
been acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted,
or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including
photocopying, microfilming, and recording, or in any information storage or retrieval system, without written
permission from the publishers.
For permission to photocopy or use material electronically from this work, access www.copyright.com or contact
the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-7 50- 8400. For works
that are not available on CCC please contact [email protected]
Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for
identification and explanation without intent to infringe.
Library of Congress Cataloging‑in‑Publication Data
Names: Gil Pérez, José Jorge, author. | Ossikovski, Razvigor, author.
Title: Polarized light and the Mueller matrix approach / José J. Gil, Razvigor Ossikovski.
Description: Second edition. | Boca Raton : CRC Press, 2022. |
Series: Series in optics and optoelectronics |
Includes bibliographical references and index.
Identifiers: LCCN 2021050506 (print) | LCCN 2021050507 (ebook) |
ISBN 9780367407469 (hardback) | ISBN 9781032215112 (paperback) |
ISBN 9780367815578 (ebook)
Subjects: LCSH: Electromagnetic waves–Polarization. | Polarization (Light)
Classification: LCC QC441 .G55 2022 (print) |
LCC QC441 (ebook) | DDC 535.5/2–dc23/eng/20211217
LC record available at https://lccn.loc.gov/2021050506
LC ebook record available at https://lccn.loc.gov/2021050507
ISBN: 978-0-367-40746-9 (hbk)
ISBN: 978-1-03-221511-2 (pbk)
ISBN: 978-0-367-81557-8 (ebk)
DOI: 10.1201/ 9780367815578
Typeset in Palatino LT Std
by Newgen Publishing UK
José J. Gil dedicates this book to Mercedes.
Razvigor Ossikovski dedicates this book to Bojidar, Vania, Marie and Anne,
for their support, encouragement and patience.
vi
vii
Contents
Preface .....................................................................xvii
Preface to the second edition ...................................................xxi
Acknowledgements ........................................................ xxiii
Authors ....................................................................xxv
1 Polarized Electromagnetic Waves ............................................ 1
1.1 Introduction: Nature of Polarized Electromagnetic Waves ................... 1
1.2 The Polarization Ellipse ................................................. 4
1.3 The Analytic Signal Representation ...................................... 8
1.4 The Jones Vector ....................................................... 9
1.5 Polarization Matrix and Stokes Vector ................................... 13
1.5.1 Statistical Nature of Measurable Polarization Properties .............. 13
1.5.1.1 Stochastic (or Random) Process ........................... 14
1.5.1.2 Ensemble Average. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5.1.3 Stationarity ............................................. 15
1.5.1.4 Ergodicity .............................................. 15
1.5.1.5 Gaussian random processes .............................. 15
1.5.2 2D Polarization Matrix .......................................... 16
1.5.3 Stokes Vector ................................................... 18
1.6 2D Space– Time and Space– Frequency Representations of Coherence and
Polarization .......................................................... 24
1.6.1 2D Representations of Coherence and Polarization .................. 24
1.6.1.1 Coherence Matrix ....................................... 25
1.6.1.2 Space– Time Coherence Stokes Vector ...................... 26
1.6.1.3 Spectral Coherence Matrix ................................ 26
1.6.1.4 Spectral Coherence Stokes Parameters ..................... 28
1.6.2 Measures of the Degree of Coherence of 2D Electromagnetic
Fields ......................................................... 29
1.6.2.1 Complex Degree of Coherence ............................ 30
1.6.2.2 Complex Degree of Mutual Polarization .................... 31
1.6.2.3 Intrinsic Degrees of Coherence ............................ 31
1.6.2.4 Electromagnetic Degree of Coherence ...................... 34
1.6.2.5 Overall Degree of Coherence .............................. 36
1.6.3 Cross- Spectral Purity and Coherence– Polarization Purity ............ 37
1.7 Poincaré Sphere ...................................................... 41
1.8 Polarization Time ..................................................... 43
1.9 Intrinsic Polarization Matrix ............................................ 44
1.10 Concept of Spin of a Polarization State ................................... 49
1.11 Polarimetric Purity .................................................... 53
1.11.1 2D Degree of Polarization ........................................ 53
1.11.2 Components of purity of a 2D polarization state .................... 56
1.11.3 Degree of Mutual Coherence ..................................... 58
1.11.4 Polarization Entropy ............................................ 60
vii
viii
viii Contents
1.12 Composition and Decomposition of Two- Dimensional States of
Polarization .......................................................... 61
1.12.1 Coherent Composition and Decomposition of 2D Pure States ......... 61
1.12.2 Incoherent Composition and Decomposition of 2D Mixed States ...... 62
1.12.3 Partially Coherent Composition of 2D Pure States ................... 64
2 Three- Dimensional States of Polarization .................................... 67
2.1 Introduction .......................................................... 67
2.2 3D Analytic Signal and Jones Vector ..................................... 68
2.3 Sets of Orthonormal 3D Jones Vectors ................................... 71
2.3.1 Canonical Set of Orthonormal 3D Jones Vectors ..................... 71
2.3.2 General Form of Sets of Orthonormal 3D Jones Vectors .............. 72
2.4 3D Polarization Matrix ................................................ 74
2.5 3D Stokes Parameters ................................................. 77
2.6 Composition and Decomposition of 3D States of Polarization ............... 79
2.6.1 Coherent Composition of 3D Pure States ........................... 80
2.6.2 Partially Coherent Composition of 3D Pure States ................... 80
2.6.3 Arbitrary Decomposition of 3D States ............................. 80
2.6.4 Spectral Decomposition of 3D States ............................... 81
2.6.5 Characteristic Decomposition of 3D States .......................... 82
2.6.6 Smart Decomposition ........................................... 84
2.6.7 Polarimetric Subtraction ......................................... 85
2.7 3D Space– Time and Space– Frequency Representations of Coherence and
Polarization .......................................................... 86
2.7.1 3D Representations of Coherence and Polarization .................. 86
2.7.2 Measures of the 3D Degree of Coherence of Electromagnetic Fields .... 89
2.7.2.1 Intrinsic Degrees of Coherence ............................ 89
2.7.2.2 Electromagnetic Degree of Coherence ...................... 90
2.7.2.3 Overall Space– Frequency Degree of Coherence .............. 91
2.8 Intrinsic Polarization Matrix ............................................ 92
2.9 Intrinsic Stokes Parameters ............................................. 94
2.9.1 Intrinsic Stokes Parameters of a Polarization State ................... 95
2.9.2 Intrinsic Stokes Parameters for 2D States Embedded into the 3D
Representation ................................................. 98
2.10 Polarimetric Purity .................................................... 99
2.10.1 Norms of 3D Polarization Matrices and Stokes Parameters
Matrices ....................................................... 99
2.10.2 Degree of Polarimetric Purity .................................... 100
2.10.3 Sources of Polarimetric Purity ................................... 102
2.10.4 Indices of Polarimetric Purity .................................... 104
2.10.5 3D Purity Space ................................................ 106
2.10.6 Degrees of Mutual Coherence of a 3D Polarization State. . . . . . . . . . . . . 108
2.10.7 3D Polarization Entropy ........................................ 110
2.11 The Concept of Spin of a 3D Polarization State ........................... 110
2.12 Discriminating States and the Concept of Nonregularity .................. 112
2.12.1 Canonical Representation of a Discriminating State ................. 112
2.12.2 Degree of Nonregularity ........................................ 113
ix
Contents ix
2.12.3 Dependence of Spin Vector on Nonregularity ...................... 115
2.13 Invariant Quantities of a 3D Polarization State ........................... 116
2.14 Interpretation of the Polarization Matrix ................................ 117
3 Nondepolarizing Media .................................................. 125
3.1 Introduction ......................................................... 125
3.2 Basic Polarimetric Interaction: Jones Calculus ............................ 128
3.2.1 The Jones Matrix ............................................... 128
3.2.2 Jones Algebra and Its Physical Interpretation ...................... 130
3.2.2.1 Product of Jones Matrices ............................... 130
3.2.2.2 Product of a Jones Matrix and a Scalar .................... 131
3.2.2.3 Determinant and Norms of a Jones Matrix ................. 131
3.2.2.4 The Inverse of a Jones Matrix ............................ 132
3.2.2.5 Additive Composition of Jones Matrices ................... 132
3.2.3 Reciprocity in Jones Matrices .................................... 134
3.2.4 Changes of Coordinate System and Rotated Jones Matrices .......... 134
3.3 Pure Mueller Matrices ................................................ 135
3.3.1 The Concept of Pure Mueller Matrix .............................. 135
3.3.2 Partitioned Form of a Mueller Matrix ............................. 139
3.3.3 Reciprocity Properties of Mueller Matrices ........................ 139
3.3.4 Passivity Condition for Pure Mueller Matrices ..................... 140
3.3.5 Algebraic Operations with Pure Mueller Matrices and their
Physical Interpretation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
3.3.5.1 Product of Pure Mueller Matrices ......................... 141
3.3.5.2 Product of a Pure Mueller Matrix and a Non- negative
Scalar ................................................. 142
3.3.5.3 Determinant, Trace and Norms of a Pure Mueller
Matrix ................................................ 142
3.3.5.4 The Inverse of a Pure Mueller Matrix ..................... 143
3.3.5.5 Additive Composition of Mueller Matrices ................ 143
3.3.6 Changes of Coordinate System and Rotated Mueller Matrices ........ 144
3.4 Other Mathematical Representations of the Polarimetric Properties of
Nondepolarizing Systems ............................................. 145
3.4.1 Covariance Matrix ............................................. 145
3.4.2 Covariance Vector ............................................. 145
3.4.3 Coherency Vector and Coherency Matrix ......................... 146
3.4.4 The Complex Mueller Matrix .................................... 147
3.4.5 Matrix States .................................................. 147
3.4.6 Quaternion States .............................................. 147
3.4.7 The Jones Operator ............................................. 148
3.4.8 The Scattering Matrix: Sinclair Matrix and Kennaugh Matrix ........ 148
3.5 Singular States of Polarization ......................................... 150
3.6 Normality and Degeneracy of Jones and Mueller Matrices ................. 152
3.6.1 Normal Operators ............................................. 153
3.6.2 Non- normal Operators ......................................... 154
3.6.3 Degenerate Operators .......................................... 155