Access to eBooks is limited to institutions that have purchased or currently subscribe to the SPIE eBooks program. eBooks are not available via an individual subscription. SPIE books (print and digital) may be purchased individually on SPIE.Org.

Contact your librarian to recommend SPIE eBooks for your organization.
Ebook Topic:
Front Matter
Abstract
This front matter contains an introduction, table of contents, and symbol glossary.

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 Series

Welcome 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 Light

The 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 Contents

Glossary 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

Glossary

Frequently 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)

P

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

Vπ

half-wave voltage

Vm

maximum modulation voltage

WP

wave plate

x,y,z

Cartesian coordinate system

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

ϕ

phase shift

ϕx

phase shift (x)

ϕy

phase shift (y)

ω

angular frequency

ωc

cyclotron frequency

ωL

Larmor’s frequency

ωm

modulation frequency

spatial vector operator

TOPIC

SHARE
Back to Top