Polarized Light

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.

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.

Part I: Introduction to Polarized Light

Introduction

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
Summary

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

Introduction

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
Summary

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

Introduction

Crystal Optics
Review of Concepts from Electromagnetism
Crystalline Materials and Their Properties
Crystals
Application of Electric Fields: Induced Birefringence and Polarization Modulation
Magneto-Optics
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
Polarizers
Retarders
Rotators
Depolarizers

Ellipsometry
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


Appendices:
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