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Library of Congress Cataloging-in-Publication Data Collett, Edward, 1934- Field guide to polarized light / Edward Collett. p. cm. – (SPIE field guides; v. FG05) Includes bibliographical references and index. ISBN 0-8194-5868-6 1. Polarization (Light) I. Title. II. Series. QC441.C63 2005 535.5′2--dc22 2005006346 Published by SPIE—The International Society for Optical Engineering P.O. Box 10 Bellingham, Washington 98227-0010 USA Phone: +1 360 676 3290 Fax: +1 360 647 1445 Email: spie@spie.org Web: http://spie.org The content of this book reflects the work and thought of the author. Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon. SPIE Terms of Use: This SPIE eBook is DRM-free for your convenience. You may install this eBook on any device you own, but not post it publicly or transmit it to others. SPIE eBooks are for personal use only. For details, see the SPIE Terms of Use. To order a print version, visit SPIE. Printed in the United States of America. Introduction to the SeriesWelcome to the SPIE Field Guides! This volume is one of the first in a new series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series. Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as related material outside the main scope of the volume, key mathematical relationships and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field. The SPIE Field Guides are intended to be living documents. The modular page-based presentation format allows them to be easily updated and expanded. We are interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at fieldguides@SPIE.org. John E. Greivenkamp, Series Editor Optical Sciences Center The University of Arizona Field Guide to Polarized LightThe polarization of light is one of the most remarkable phenomena in nature and has led to numerous discoveries and applications. Today it continues to play a vital role in optics. Before the 1950s there was very little activity on the foundations of polarized light. For example, answers to questions such as the nature and mathematical formulation of unpolarized light and partially polarized light were not readily forthcoming. Today there is a very good understanding of polarized light. In particular, the mathematical difficulties that had hindered complex polarization calculations were finally overcome with the introduction of the Mueller-Stokes matrix calculus and the Jones matrix calculus. Research in polarized light continues with much vigor as witnessed by the continued appearance of numerous publications and conferences. The primary objective of this Guide is to provide an introduction to the developments in polarized light that have taken place over the past half-century. In this Guide I have tried to present the most salient topics on the subject. Hopefully, this Field Guide will enable the reader to have a good grasp of the material and most of all to allow him or her to be comfortable and even delighted with the beauty and subject of polarized light. Finally, this Field Guide is dedicated to my wife, Mary Ann, and my children Ron and Greg. Their encouragement and support greatly simplified the task of writing this Guide. Edward Collett Georgian Court University Lakewood, New Jersey Table of ContentsGlossary x The Foundations of Polarized Light 1 The Ray Theory of Light 1 The Polarization of Light 2 Malus’s Law 3 Brewster’s Law 4 The Wave Theory of Light 5 Fresnel’s Wave Theory 5 The Polarization Ellipse 7 Degenerate Polarization States 8 The Parameters of the Polarization Ellipse 9 The Poincaré Sphere 10 Degenerate States on the Poincaré Sphere 11 The Observables of Polarized Light 12 The Stokes Polarization Parameters 12 Stokes Parameter Relations 14 Classical Measurement of the Stokes Parameters 16 The Mueller Matrices for Polarizing Components 17 Polarizers 18 Wave Plates 20 Rotators 22 Mueller Matrices for Rotated Components 23 Mueller Matrix Applications-Malus’s Law 25 Mueller Matrix Applications-The Optical Shutter 26 Mueller Matrix Applications-Stokes Parameters 27 The Observable Polarization Sphere 28 The Observable Polarization Sphere 28 Plotting the Quarter-Wave Plate on the OPS 32 The Rotating Quarter-Wave Plate 34 The Babinet-Soleil Compensator 35 Linear and Circular Polarizers 36 The Generation of Elliptically Polarized Light 37 Measurement Methods of the Stokes Parameters 38 The Rotating Quarter-Wave Plate Measurement 39 Birefringent Crystals and Wave Plates 40 Multiple and Zero-Order Wave Plates 41 Reflection and Transmission 42 Mueller Matrices for Reflection and Transmission 42 Reflection and Transmission Stokes Parameters 43 Reflection and Transmission Mueller Matrices 47 Total Internal Reflection 48 The Fresnel Rhomb 49 Single and Multiple Dielectric Plates 50 Pile of Polarizing Dielectric Plates 52 Fresnel’s Reflection and Transmission Coefficients 55 Other Polarization Matrix Calculi 57 The Jones Matrix Calculus 57 Wolfs Coherency Matrix Calculus 62 Optical Activity and Optical Rotation 63 Optical Activity and Optical Rotation 63 Faraday Rotation 64 Optical Isolators 66 Depolarizers 72 Wave Plate Depolarizers 72 The Lyot Crystal Depolarizer 74 Polarizing Materials 75 Polarizers 75 Polarizing Prisms 76 Characterizing Polarizers 78 Wave Plate Materials 81 Superposition and Decomposition of Polarized Beams 82 Incoherent Superposition and Decomposition 82 Incoherent Decomposition-Ellipses 83 Coherent Superposition and Decomposition 84 The Electro-Optical Effect 85 The Electro-Optical Effect - Modulators 85 The Pockels Cell 87 Refractive Index Measurements 88 Incidence Refractive Index Measurement 88 The Radiation Field 91 Maxwell’s Equations 91 The Radiation Equation and the Stokes Parameters 92 The Linear Oscillating Bound Charge 93 The Randomly Oscillating Bound Charge 94 A Charge Moving in a Circle 95 A Charge Moving in a Magnetic Field 96 The Classical Zeeman Effect 98 Optical Scattering 101 The Optics of Metals and Semiconductors 105 The Optics of Metals and Semiconductors 105 Refractive Index and Absorption Coefficient 106 Incidence Angle Reflectivity 107 Complex Reflection Coefficients 109 The Principal Angle of Incidence Measurement 110 Appendix 114 Equation Summary 124 Bibliography 128 GlossaryFrequently used variables and symbols: B birefringence B(r, t) magnetic induction vector c speed of light in a vacuum cp circularly polarized db decibels D(r, t) electric displacement vector e- extraordinary ray ɛ permittivity constant E0x maximum amplitude in the x direction E0y maximum amplitude in the y direction Ex(r, t) x component of the optical field Ey(r, t) y component of the optical field E Jones vector E(r, t) electric field vector F force vector H0 Transmission of two parallel polarizers H90 Transmission of two crossed polarizers H(r, t) magnetic field vector HWP half wave plate i angle of incidence iB Brewster angle i,j,k Cartesian unit vectors J Jones matrix j(r, t) electric current density vector, JPOL Jones matrix for a polarizer JWP Jones matrix for a wave plate JROT Jones matrix for a rotator JQWP Jones matrix for a quarter-wave plate JHWP Jones matrix for a half-wave plate J(θ) Jones matrix for a rotated polarizing element k wave number k wave vector k1 major transmittance of a polarizer k2 minor transmittance of a polarizer KDP potassium dihydrogen phosphate L−45P linear −45 polarization L+45P linear +45 polarization LCP Left circular polarization LHP linear horizontal polarization LVP linear vertical polarization μ permeability constant M Mueller matrix MHWP Mueller matrix of a half-wave plate MLP Mueller matrix of a linear polarizer MPOL Mueller matrix of a polarizer MQWP Mueller matrix of a quarter-wave plate MR Mueller matrix for reflection MROT Mueller matrix of a rotator MT Mueller matrix for transmission MWP Mueller matrix of a wave plate M(θ) Mueller matrix of a rotated polarizing element n complex refractive index ne refractive index of the extraordinary ray no refractive index of the ordinary ray np parallel refractive index ns perpendicular refractive index nL levo-rotary refractive index nR dextro-rotary refractive index n refractive index o- ordinary ray OPS observable polarization sphere p- parallel polarization state px polarizer transmission coefficient (x) py polarizer transmission coefficient (y) degree of polarization PBS polarizing beam splitter QWP quarter wave plate r angle of refraction r radius vector RCP right circular polarization s- perpendicular polarization state S Stokes vector S0 first Stokes parameter S1 second Stokes parameter S2 third Stokes parameter S3 fourth Stokes parameter SR Stokes vector for reflection ST Stokes vector for transmission TIR total internal reflection UNP unpolarized v(r, t) velocity vector vx,vy,vz principal velocities V Verdet’s constant half-wave voltage Vm maximum modulation voltage WP wave plate x,y,z Cartesian coordinate system 2α coordinate on the observable polarization sphere 2Ψ coordinate angle on the Poincaré sphere 2X coordinate angle on the Poincaré sphere α auxiliary angle ε complex dielectric constant εx, εy, εz principal dielectric constants δ coordinate on the observable polarization sphere δ phase difference δx phase of the wave (x) δy phase of the wave (y) θ angle of rotation κ absorption coefficient Ψ orientation angle X ellipticity angle ρs,p Fresnel reflection coefficients ρ(r,t) electric charge density σ conductivity τs,p Fresnel transmission coefficients phase shift phase shift (x) phase shift (y) ω angular frequency ωc cyclotron frequency ωL Larmor’s frequency ωm modulation frequency spatial vector operator |
CITATIONS
Cited by 1 scholarly publication.
Dielectric polarization
Wave plates
Geometrical optics
Calculus
Mueller matrices
Polarization
Polarizers
