3rd Edition

Polarized Light

ISBN 9781439830406
Published December 16, 2010 by CRC Press
808 Pages 306 B/W Illustrations

USD $290.00

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Book Description

Polarized light is a pervasive influence in our world—and scientists and engineers in a variety of fields require the tools to understand, measure, and apply it to their advantage. Offering an in-depth examination of the subject and a description of its applications, Polarized Light, Third Edition serves as a comprehensive self-study tool complete with an extensive mathematical analysis of the Mueller matrix and coverage of Maxwell’s equations.

Links Historical Developments to Current Applications and Future Innovations

This book starts with a general description of light and continues with a complete exploration of polarized light, including how it is produced and its practical applications. The author incorporates basic topics, such as polarization by refraction and reflection, polarization elements, anisotropic materials, polarization formalisms (Mueller–Stokes and Jones) and associated mathematics, and polarimetry, or the science of polarization measurement.

New to the Third Edition:

  • A new introductory chapter
  • Chapters on: polarized light in nature, and form birefringence
  • A review of the history of polarized light, and a chapter on the interference laws of Fresnel and Arago—both completely re-written
  • A new appendix on conventions used in polarized light
  • New graphics, and black-and-white photos and color plates

Divided into four parts, this book covers the fundamental concepts and theoretical framework of polarized light. Next, it thoroughly explores the science of polarimetry, followed by discussion of polarized light applications. The author concludes by discussing how our polarized light framework is applied to physics concepts, such as accelerating charges and quantum systems.

Building on the solid foundation of the first two editions, this book reorganizes and updates existing material on fundamentals, theory, polarimetry, and applications. It adds new chapters, graphics, and color photos, as well as a new appendix on conventions used in polarized light. As a result, the author has re-established this book’s lofty status in the pantheon of literature on this important field.

Table of Contents

Part I: Introduction to Polarized Light


Polarization in the Natural Environment

Sources of Polarized Light

Polarized Light in the Atmosphere

Production of Polarized Light by Animals

Polarization Vision in the Animal Kingdom

Wave Equation in Classical Optics

The Wave Equation

Young’s Interference Experiment

Reflection and Transmission of a Wave at an Interface

The Polarization Ellipse

The Instantaneous Optical Field and the Polarization Ellipse

Specialized (Degenerate) Forms of the Polarization Ellipse

Elliptical Parameters of the Polarization Ellipse

Stokes Polarization Parameters

Derivation of Stokes Polarization Parameters

Stokes Vector

Classical Measurement of Stokes Polarization Parameters

Stokes Parameters for Unpolarized and Partially Polarized Light

Additional Properties of Stokes Polarization Parameters

Stokes Parameters and the Coherency Matrix

Stokes Parameters and the Pauli Matrices

Mueller Matrices for Polarizing Components

Mueller Matrix of a Linear Diattenuator (Polarizer)

Mueller Matrix of a Linear Retarder

Mueller Matrix of a Rotator

Mueller Matrices for Rotated Polarizing Components

Generation of Elliptically Polarized Light

Mueller Matrix of a Depolarizer

Fresnel Equations: Derivation and Mueller Matrix Formulation

Fresnel Equations for Reflection and Transmission

Mueller Matrices for Reflection and Transmission at an Air–Dielectric Interface

Special Forms for Mueller Matrices for Reflection and Transmission

Emission Polarization

Mathematics of the Mueller Matrix

Constraints on the Mueller Matrix

Eigenvector and Eigenvalue Analysis

Example Eigenvector Analysis

The Lu–Chipman Decomposition

Decomposition Order

Decomposition of Depolarizing Matrices with Depolarization Symmetry

Decomposition Using Matrix Roots


Mueller Matrices for Dielectric Plates

The Diagonal Mueller Matrix and the Abcd Polarization Matrix

Mueller Matrices for Single and Multiple Dielectric Plates

The Jones Matrix Formalism

The Jones Vector

Jones Matrices for the Polarizer, Retarder, and Rotator

Applications of the Jones Vector and Jones Matrices

Jones Matrices for Homogeneous Elliptical Polarizers and Retarders

The Poincare Sphere

Theory of the Poincare Sphere

Projection of the Complex Plane onto a Sphere

Applications of the Poincare Sphere

Fresnel–Arago Interference Laws

Stokes Vector and Unpolarized Light

Young’s Double Slit Experiment

Double Slit with Parallel Polarizers: The First Law

Double Slit with Perpendicular Polarizers: The Second Law

Double Slit and the Third Law

Double Slit and the Fourth Law


Part II: Polarimetry


Methods of Measuring Stokes Polarization Parameters

Classical Measurement Method: Quarter-Wave Retarder and Polarizer Method

Measurement of Stokes Parameters Using a Circular Polarizer

Null-Intensity Method

Fourier Analysis Using a Rotating Quarter-Wave Retarder

Method of Kent and Lawson

Simple Tests to Determine the State of Polarization of an Optical Beam

Measurement of the Characteristics of Polarizing Elements

Measurement of Attenuation Coefficients of a Polarizer (Diattenuator)

Measurement of the Phase Shift of a Retarder

Measurement of Rotation Angle of a Rotator

Stokes Polarimetry

Rotating Element Polarimetry

Oscillating Element Polarimetry

Phase Modulation Polarimetry

Techniques in Simultaneous Measurement of Stokes Vector Elements

Optimization of Polarimeters

Mueller Matrix Polarimetry

Dual Rotating Retarder Polarimetry

Other Mueller Matrix Polarimetry Methods

Techniques in Imaging Polarimetry

Historical Perspective

Measurement Considerations

Measurement Strategies and Data Reduction Techniques

General Measurement Strategies: Imaging Architecture for Integrated Polarimeters

System Considerations


Channeled Polarimetry for Snapshot Measurements

Channeled Polarimetry

Channeled Spectropolarimetry

Channeled Imaging Polarimetry

Sources of Error in Channeled Polarimetry

Mueller Matrix Channeled Spectropolarimeters

Channeled Ellipsometers


Part III: Applications


Crystal Optics

Review of Concepts from Electromagnetism

Crystalline Materials and Their Properties


Application of Electric Fields: Induced Birefringence and Polarization Modulation


Liquid Crystals

Modulation of Light

Photoelastic Modulators

Concluding Remarks

Optics of Metals

Maxwell’s Equations for Absorbing Media

Principal Angle of Incidence Measurement of Refractive Index and Absorption Index of Optically Absorbing Materials

Measurement of Refractive Index and Absorption Index at an Incident Angle of 45°

Polarization Optical Elements






Fundamental Equation of Classical Ellipsometry

Classical Measurement of the Ellipsometric Parameters Psi (ψ) and Delta (Δ)

Solution of the Fundamental Equation of Ellipsometry

Further Developments in Ellipsometry: Mueller Matrix Representation of ψ and Δ

Form Birefringence and Meanderline Retarders

Form Birefringence

Meanderline Elements


Part IV: Classical and Quantum Theory of Radiation by Accelerating Charges

Introduction to Classical and Quantum Theory of Radiation by Accelerating Charges

Maxwell’s Equations for Electromagnetic Fields

The Classical Radiation Field

Field Components of the Radiation Field

Relation between Unit Vector in Spherical Coordinates and Cartesian Coordinates

Relation between Poynting Vector and Stokes Parameters

Radiation Emitted by Accelerating Charges

Stokes Vector for a Linearly Oscillating Charge

Stokes Vector for an Ensemble of Randomly Oriented Oscillating Charges

Stokes Vector for a Charge Rotating in a Circle

Stokes Vector for a Charge Moving in an Ellipse

Radiation of an Accelerating Charge in the Electromagnetic Field

30.1 Motion of a Charge in an Electromagnetic Field

30.2 Stokes Vectors for Radiation Emitted by Accelerating Charges

The Classical Zeeman Effect

Historical Introduction

Motion of a Bound Charge in a Constant Magnetic Field

Stokes Vector for the Zeeman Effect

Further Applications of the Classical Radiation Theory

Relativistic Radiation and the Stokes Vector for a Linear Oscillator

Relativistic Motion of a Charge Moving in a Circle: Synchrotron Radiation

Čerenkov Effect

Thomson and Rayleigh Scattering

The Stokes Parameters and Mueller Matrices for Optical Activity and Faraday Rotation

Optical Activity

Faraday Rotation in a Transparent Medium

Faraday Rotation in a Plasma

Stokes Parameters for Quantum Systems

Relation between Stokes Polarization Parameters and Quantum Mechanical Density Matrix

Note on Perrin’s Introduction of Stokes Parameters, the Density Matrix, and Linearity of Mueller Matrix Elements

Radiation Equations for Quantum Mechanical Systems

Stokes Vectors for Quantum Mechanical Systems



Conventions in Polarized Light

Jones and Stokes Vectors

Jones and Mueller Matrices

Relationships between the Jones and Mueller Matrix Elements

Vector Representation of the Optical Field: Application to Optical Activity

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Dr. Dennis Goldstein is a senior physicist with Polaris Sensor Technologies, Inc., following a 28-year career in electro-optics research at the Air Force Research Laboratory. He is a fellow of SPIE and AFRL, and has served as an adjunct professor at the University of Arizona and University of Florida. He also teaches short courses for the Georgia Institute of Technology. In addition to Polarized Light, Dr. Goldstein has published more than 70 papers and technical reports, and two book chapters. He holds six patents.