PoIarized light Second Edition, Revised and Expanded

The first edition was published as Polarized Light: Fundamentals and Applications, Edward Collett Marcel Dekker, Inc., 1993.. Single-Mode Fiber Optics: Principles and Applications, Second

Po I a r ized light

Second Edition, Revised and Expanded

Dennis Goldstein

Air Force Research Laboratory Eglin Air Force Base, Florida, U.S.A

Copyright © 2003 by Marcel Dekker, Inc All Rights Reserved.

Although great care has been taken to provide accurate and current information, neither the author(s) nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage, or liability directly or indirectly caused or alleged to be caused by this book The material contained herein is not intended to provide specific advice or recommendations for any specific situation

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The first edition was published as Polarized Light: Fundamentals and Applications, Edward Collett (Marcel Dekker, Inc., 1993)

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2 Acousto-Optic Signal Processing: Theory and Implementation, edited by Nor man

3 Electro-Optic and Acousto-Optic Scanning and Deflection, Milton Gofflieb, Clive L

4 Single-Mode Fiber Optics: Principles and Applications, Luc B Jeunhomme

5 Pulse Code Formats for Fiber Optical Data Communication: Basic Principles and

Applications, David J Monis

6 Optical Materials: An Introduction to Selection and Application, Solomon Musikant

7 Infrared Methods for Gaseous Measurements: Theory and Practice, edited by Joda Wonnhoudt

8 Laser Beam Scanning: Opto-Mechanical Devices, Systems, and Data Storage

Optics, edited by Gerald F Marshall

9 Opto-Mechanical Systems Design, Paul R Yoder, Jr

10 Optical Fiber Splices and Connectors: Theory and Methods, Calvin M Miller with Stephen C Meffler and /an A White

11 Laser Spectroscopy and Its Applications, edited by Leon J Radziemski, Richard

W Solan, and Jeffrey A Paisner

12 Infrared Optoelectronics: Devices and Applications, Wlliam Nunley and J Scoff Bechtel

13 Integrated Optical Circuits and Components: Design and Applications, edited by Lynn D Hufcheson

14 Handbook of Molecular Lasers, edited by Peter K Cheo

15 Handbook of Optical Fibers and Cables, Hiroshi Murata

16 Acousto-Optics, Adrian Korpel

17 Procedures in Applied Optics, John Strong

18 Handbook of Solid-state Lasers, edited by Peter K Cheo

19 Optical Computing: Digital and Symbolic, edited by Raymond Arrathoon

20 Laser Applications in Physical Chemistry, edited by D K, Evans

21 Laser-Induced Plasmas and Applications, edited by Leon J Radziemski and

David A Cremers

22 Infrared Technology Fundamentals, /wing J Spiro and Monroe Schlessinger

23 Single-Mode Fiber Optics: Principles and Applications, Second Edition, Re vised

24 Image Analysis Applications, edited by Rangachar Kasturi and Mohan M Trivedi

25 Photoconductivity: Art, Science, and Technology, N V Joshi

26 Principles of Optical Circuit Engineering, Mark A Mentzer

27 Lens Design, Milton Laikin

28 Optical Components, Systems, and Measurement Techniques, Rajpal S Sirohi

Lawrence E Mum

J Berg and John N Lee

M Ireland, and John Martin Ley

and Expanded, Luc B Jeunhomme

and M P Kothiyal

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29 Electron and Ion Microscopy and Microanalysis: Principles and Applications,

Second Edition, Revised and Expanded, Lawrence E Murr

30 Handbook of Infrared Optical Materials, edited by Paul KIocek

31 Optical Scanning, edited by Gerald F Marshall

32 Polymers for Lighbave and Integrated Optics: Technology and Applications,

33 Electro-Optical Displays, edited by Mohammad A Karim

34 Mathematical Morphology in Image Processing, edited by Edward R Dougherfy

35 Opto-Mechanical Systems Design: Second Edition, Revised and Expanded, Paul

R Yoder, Jr

36 Polarized Light: Fundamentals and Applications, Edward Colleff

37 Rare Earth Doped Fiber Lasers and Amplifiers, edited by Michel J f Digonnet

38 Speckle Metrology, edited by Rajpal S Sirohi

39 Organic Photoreceptors for Imaging Systems, Paul M Borsenberger and David S

40 Photonic Switching and Interconnects, edited by Abdellatif Marrakchi

41 Design and Fabrication of Acousto-Optic Devices, edited by Akis P Goutzoulis

42 Digital Image Processing Methods, edited by Edward R Doughetty

43 Visual Science and Engineering: Models and Applications, edited by D H Kelly

44 Handbook of Lens Design, Daniel Malacara and Zacarias Malacara

45 Photonic Devices and Systems, edited by Robert G Hunsberger

46 Infrared Technology Fundamentals: Second Edition, Revised and Expanded,

edited by Monroe Schlessinger

47 Spatial Light Modulator Technology: Materials, Devices, and Applications, edited

by Uzi Efron

48 Lens Design: Second Edition, Revised and Expanded, Milton Laikin

49 Thin Films for Optical Systems, edited by Francoise R Flory

50 Tunable Laser Applications, edited by f J Duarfe

51 Acousto-Optic Signal Processing: Theory and Implementation, Second Edition,

edited by Norman J Berg and John M Pellegrino

52 Handbook of Nonlinear Optics, Richard L Sutherland

53 Handbook of Optical Fibers and Cables: Second Edition, Hiroshi Murata

54 Optical Storage and Retrieval: Memory, Neural Networks, and Fractals, edited by

Francis T S Yo and Suganda Jutamulia

55 Devices for Optoelectronics, Wallace B Leigh

56 Practical Design and Production of Optical Thin Films, Ronald R Wlley

57 Acousto-Optics: Second Edition, Adrian Korpel

58 Diffraction Gratings and Applications, Erwin G Loewen and Evgeny Popov

59 Organic Photoreceptors for Xerography, Paul M Borsenberger and David S Weiss

60 Characterization Techniques and Tabulations for Organic Nonlinear Optical

Materials, edited by Ma& G, Kuzyk and Carl W Dirk

61 lnterferogram Analysis for Optical Testing, Daniel Malacara, Manuel Setvin, and Zacarias Malacara

62 Computational Modeling of Vision: The Role of Combination, William R Uttal, Ramakrishna Kakarala, Spiram Dayanand, Thomas Shepherd, Jagadeesh Kalki, Charles F Lunskis, Jr., and Ning Liu

63 Microoptics Technology: Fabrication and Applications of Lens Arrays and De-

vices, Nicholas Bomlli

64 Visual Information Representation, Communication, and Image Processing,

edited by Chang Wen Chen and Ya-Qin Zhang

65 Optical Methods of Measurement, Rajpal S Sirohi and F S Chau

66 Integrated Optical Circuits and Components: Design and Applications, edited by Edmond J Muvhy

edited by Lawrence A Homak

Weiss

and Dennis R Pape

67 Adaptive Optics Engineering Handbook, edited by Robert K Tyson

68 Entropy and Information Optics, Francis T S Yu

69 Computational Methods for Electromagnetic and Optical Systems, John M Jarem and Partha P Banerjee

70 Laser Beam Shaping, Fred M Dickey and Scott C Holswade

71 Rare-Earth-Doped Fiber Lasers and Amplifiers: Second Edition, Revised and

Expanded, edited by Michel J F Digonnet

72 Lens Design: Third Edition, Revised and Expanded, Milton Laikin

73 Handbook of Optical Engineering, edited by Daniel Malacara and Brian J Thompson

74 Handbook of Imaging Materials: Second Edition, Revised and Expanded, edited

by Arthur S Diamond and David S Weiss

75 Handbook of Image Quality: Characterization and Prediction, Brian W Keelan

76 Fiber Optic Sensors, edited by Francis T S Yu and Shizhuo Yin

77 Optical Switehing/Nelworking and Computing for Multimedia Systems, edited by Mohsen Guizani and Abdella Battou

78 Image Recognition and Classification: Algorithms, Systems, and Applications,

edited by Bahram Javidi

79 Practical Design and Production of Optical Thin Films: Second Edition, Revised

and Expanded, Ronald R Willey

80 Ultrafast Lasers: Technology and Applications, edited by Martin E Fennann, Almantas Galvanauskas, and Gregg Sucha

81 Light Propagation in Periodic Media: Differential Theory and Design, Michel Neviere and Evgeny Popov

82 Handbook of Nonlinear Optics, Second Edition, Revised and Expanded,

Richard L Sutherland

83 Polarized Light: Second Edition, Revised and Expanded, Dennis Goldstein

Additional Volumes in Preparation

Optical Remote Sensing: Science and Technology, Walter Egan Nonlinear Optics: Theory, Numerical Modeling, and Applications, Partha P Banerjee

Copyright © 2003 by Marcel Dekker, Inc All Rights Reserved.

Preface to the Second Edition

Where there is light, there is polarized light It is in fact difficult to find a source of light that is completely randomly polarized As soon as light interacts with anything, whether through reflection, transmission, or scattering, there is opportunity for polarization to be induced As pointed out in the first sentence of the Preface to the First Edition, polarization is a fundamental characteristic of the transverse wave that is light More than ever, it is a characteristic that must be addressed in modern optical systems and applications

Since 1993 when the first edition of this text appeared, there have been many new developments in the measurement and application of polarized light This revised edition includes revisions and corrections of the original text and substantive new material Most of the original figures have been redone Chapter 8has been expanded to include the derivation of the Fresnel equations with plots of the mag-nitude and phase of the reflection coefficients Also included in Part I is a chapter with in-depth discussion of the mathematics and meaning of the Mueller matrix In this chapter, there is a discussion of physical realizability and elimination of error sources with eigenvector techniques, and a discussion of Mueller matrix decomposi-tion The Lu–Chipman decomposition has shown that Mueller matrices are separ-able, so that a general Mueller matrix may be decomposed into a set of product matrices, each dependent on only one of the quantities of diattenuation, retardance,

or depolarization A chapter on devices and components has been added to Part III, Applications Those interested in use or measurement of polarized light should have knowledge of available devices and components that serve as polarizers and retar-ders for various wavelength regions and for various conditions of achromaticity Chapters on Stokes polarimetry and Mueller matrix polarimetry have been inserted

in Part III These polarimetric techniques are essential to an understanding of mea-surement of polarized light and characterization of optical elements

Appendixes have been added with summaries of the Jones and Stokes vectors for various states of polarized light, and with summaries of Jones and Mueller matrices for various optical elements An appendix has been included that gives the relations between the Jones and Mueller matrix elements Finally, a comprehen-sive bibliography has been included

Ed Collett collected a wonderful set of topics for students of polarized light for the first edition of this book, and he provided a resource that did not exist before It

is my hope that the revisions and additions contained in this second edition will make this text even more useful and thorough I express my gratitude to the follow-ing colleagues and friends for their critical comments durfollow-ing the creation of this work: Russell A Chipman of the University of Arizona, Robert R Kallman of the University of North Texas, J Scott Tyo of the University of New Mexico, and E.E (Gene) Youngblood and Lynn L Diebler of the Air Force Research Laboratory David Goetsch of Okaloosa-Walton Community College provided wise counsel Finally, I express gratitude to my wife, Carole, and daughters, Dianne and Laura, for their presence and support

Dennis Goldstein

Copyright © 2003 by Marcel Dekker, Inc All Rights Reserved.

Preface to the First Edition

Light is characterized by its intensity, wavelength, and polarization Remarkably, in spite of the importance of polarized light, no book is devoted just to this subject Nearly every book on optics contains several chapters on polarized light However, if one tries to obtain a deeper understanding of the subject, one quickly discovers that

it is almost always necessary to go to the original papers in the literature The objective of this book therefore is to provide a single source that describes the fundamental behavior of polarized light and its interaction with matter The book

is designed to be used by scientists and engineers working in the fields of physics, optics, opto-electronics, chemistry, biology, and mechanical and electrical engineer-ing as well as advanced undergraduate and graduate students

There are two well-known books on polarized light The first is W A Shurcliff ’s Polarized Light, an excellent introductory and reference book on the subject The other book, also excellent, is Ellipsometry and Polarized Light by

R M A Azzam and N M Bashara It is very advanced and is directed to those working in the field of ellipsometry While it contains much information on polarized light, its approach to the subject is very different Ellipsometry is important, how-ever, and an introductory discussion is included here in the final chapter

This book is divided into three parts One can begin the study of polarized light with Maxwell’s equations However, one soon discovers that in optics, unlike the field of microwave physics, Maxwell’s equations are not readily apparent; this was why in the nineteenth century Fresnel’s elastic equations were only slowly displaced

by Maxwell’s equations Much of the subject of polarized light can be studied and understood almost independently of Maxwell’s equations This is the approach taken in Part I We begin with the wave equation and quickly move on to the polarization ellipse At this point the observable concept of the optical field is intro-duced, and in succeeding chapters we discover that much new information is revealed on the nature as well as the description of polarized light and its interaction with polarizing elements Ultimately, however, it becomes necessary to describe the sourceof the radiation field and polarized light At this point no further progress can

be made without Maxwell’s equations Therefore, in Part II of this book, Maxwell’s equations are introduced and then used to describe the emission of polarized radia-tion by accelerating electrons In turn, the emitted radiaradia-tion is then formulated in

terms of the Stokes vector and Mueller matrices and applied to the description of unpolarized light, the Zeeman effect, synchrotron radiation, scattering, and the Faraday effect In particular, we shall see that the Stokes vector takes on a very interesting role in describing spectral lines In Part III, a number of important applications of polarized light are presented, namely, propagation in anisotropic media (crystals), opto-isolators, electro-optical modulation, reflection from metals, and a final introductory chapter on ellipsometry

The creation of this book could have happened only with the support of my family I wish to express my gratitude to my children Ronald Edward and Gregory Scott, and especially to my wife, Marilyn, for their continuous support, encourage-ment and interest Without it, this book would have never been completed

Edward Collett

Copyright © 2003 by Marcel Dekker, Inc All Rights Reserved.

Preface to the Second Edition

Preface to the First Edition

A Historical Note Edward Collett

PART I: THE CLASSICAL OPTICAL FIELD

Chapter 1 Introduction

References

Chapter 2 The Wave Equation in Classical Optics

2.1 Introduction 2.2 The Wave Equation 2.3 Young’s Interference Experiment 2.4 Reflection and Transmission of a Wave at an Interface References

Chapter 3 The Polarization Ellipse

3.1 Introduction 3.2 The Instantaneous Optical Field and the Polarization Ellipse

3.3 Specialized (Degenerate) Forms of the Polarization Ellipse

3.4 Elliptical Parameters of the Polarization Ellipse References

Chapter 4 The Stokes Polarization Parameters

4.1 Introduction 4.2 Derivation of the Stokes Polarization Parameters 4.3 The Stokes Vector

4.4 Classical Measurement of the Stokes Polarization Parameters