Polarized Light. Second Edition, Revised and Expanded. Dennis Goldstein Air Force Research Laboratory Eglin Air Force Base, Florida, U.S.A.

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1 Polarized Light Second Edition, Revised and Expanded Dennis Goldstein Air Force Research Laboratory Eglin Air Force Base, Florida, U.S.A. ш DEK KER MARCEL DEKKER, INC. NEW YORK BASEL

Contents Preface to the Second Edition Hi Preface to the First Edition v A Historical Note Edward Collett xiii PART I: THE CLASSICAL OPTICAL FIELD Chapter 1 Introduction 1 References 2 Chapter 2 The

2 Contents Preface to the Second Edition Hi Preface to the First Edition v A Historical Note Edward Collett xiii PART I: THE CLASSICAL OPTICAL FIELD Chapter 1 Introduction 1 References 2 Chapter 2 The Wave Equation in Classical Optics Introduction The Wave Equation Young's Interference Experiment Reflection and Transmission of a Wave at an Interface 15 References 19 Chapter 3 The Polarization Ellipse Introduction The Instantaneous Optical Field and the Polarization Ellipse Specialized (Degenerate) Forms of the Polarization Ellipse Elliptical Parameters of the Polarization Ellipse 27 References 30 Chapter 4 The Stokes Polarization Parameters Introduction Derivation of the Stokes Polarization Parameters The Stokes Vector Classical Measurement of the Stokes Polarization Parameters 43 VII

viii Contents 4.5 Stokes Parameters for Unpolarized and Partially Polarized Light 47 4.6 Additional Properties of the Stokes Polarization Parameters 49 4.

3 viii Contents 4.5 Stokes Parameters for Unpolarized and Partially Polarized Light Additional Properties of the Stokes Polarization Parameters Stokes Parameters and Wolf's Coherency Matrix 59 References 63 Chapter 5 The Mueller Matrices for Polarizing Components Introduction The Mueller Matrix of a Polarizer The Mueller Matrix of a Retarder The Mueller Matrix of a Rotator Mueller Matrices for Rotated Polarizing Components Generation of Elliptically Polarized Light 83 References 86 Chapter 6 Methods of Measuring the Stokes Polarization Parameters Introduction Classical Measurement Method: The Quarter-Wave Retarder Polarizer Method Measurement of the Stokes Parameters Using a Circular Polarizer The Null-Intensity Method Fourier Analysis Using a Rotating Quarter-Wave Retarder The Method of Kent and Lawson Simple Tests to Determine the State of Polarization of an Optical Beam 108 References 115 Chapter 7 The Measurement of the Characteristics of Polarizing Elements Introduction Measurement of Attenuation Coefficients of a Polarizer (Diattenuator) Measurement of Phase Shift of a Retarder Measurement of Rotation Angle of a Rotator 130 Reference 132 Chapter 8 Mueller Matrices for Reflection and Transmission Introduction Fresnel's Equations for Reflection and Transmission Mueller Matrices for Reflection and Transmission at an Air-Dielectric Interface Special Forms for the Mueller Matrices for Reflection and Transmission 152 References 163

Contents Chapter 9 The Mathematics of the Mueller Matrix 165 9.1 Introduction 165 9.2 Constraints on the Mueller Matrix 167 9.3 Eigenvector and Eigenvalue Analysis 168 9.

4 Contents Chapter 9 The Mathematics of the Mueller Matrix Introduction Constraints on the Mueller Matrix Eigenvector and Eigenvalue Analysis Example of Eigenvector Analysis The Lu-Chipman Decomposition Summary 185 References 185 Chapter 10 The Mueller Matrices for Dielectric Plates Introduction The Diagonal Mueller Matrix and the ABCD Polarization Matrix Mueller Matrices for Single and Multiple Dielectric Plates 195 References 209 Chapter 11 The Jones Matrix Calculus Introduction 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 231 References 239 Chapter 12 The Poincare Sphere Introduction Theory of the Poincare Sphere Projection of the Complex Plane onto a Sphere Applications of the Poincare Sphere 265 References 273 Chapter 13 The Interference Laws of Fresnel and Arago Introduction Mathematical Statements for Unpolarized Light Young's Interference Experiment with Unpolarized Light The First Experiment: First and Second Interference Laws The Second Experiment: Third Interference Law The Third Experiment: Fourth Interference Law The Herschel-Stokes Experiment Summary of the FresneL-Arago Interference Laws 294 References 296

X Contents PART II: THE CLASSICAL AND QUANTUM THEORY OF RADIATION BY ACCELERATING CHARGES Chapter 14 Introduction to the Classical and Quantum Theory of Radiation by Accelerating Charges 297

5 X Contents PART II: THE CLASSICAL AND QUANTUM THEORY OF RADIATION BY ACCELERATING CHARGES Chapter 14 Introduction to the Classical and Quantum Theory of Radiation by Accelerating Charges 297 References 298 Chapter 15 Maxwell's Equations for the Electromagnetic Field 301 References 306 Chapter 16 The Classical Radiation Field Field Components of the Radiation Field Relation Between the Unit Vector in Spherical Coordinates and Cartesian Coordinates Relation Between the Poynting Vector and the Stokes Parameters 312 References 317 Chapter 17 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 328 References 329 Chapter 18 The Radiation of an Accelerating Charge in the Electromagnetic Field Motion of a Charge in an Electromagnetic Field Stokes Vectors for Radiation Emitted by Accelerating Charges 345 References 350 Chapter 19 The Classical Zeeman Effect Historical Introduction Motion of a Bound Charge in a Constant Magnetic Field Stokes Vector for the Zeeman Effect 361 References 366 Chapter 20 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 Cerenkov Effect Thomson and Rayleigh Scattering 393 References 401

Contents XI Chapter 21 The Stokes Parameters and Mueller Matrices for Optical Activity and Faraday Rotation 403 21.1 Introduction 403 21.2 Optical Activity 405 21.

6 Contents XI Chapter 21 The Stokes Parameters and Mueller Matrices for Optical Activity and Faraday Rotation Introduction Optical Activity Faraday Rotation in a Transparent Medium Faraday Rotation in a Plasma 414 References 416 Chapter 22 The Stokes Parameters for Quantum Systems Introduction Relation Between Stokes Polarization Parameters and Quantum Mechanical Density Matrix Note on Perrin's Introduction of Stokes Parameters, Density Matrix, and Linearity of the Mueller Matrix Elements Radiation Equations for Quantum Mechanical Systems Stokes Vectors for Quantum Mechanical Systems 435 References 442 Part III: APPLICATIONS Chapter 23 Introduction 445 Chapter 24 Crystal Optics Introduction 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 Concluding Remarks 476 References 477 Chapter 25 Optics of Metals Introduction Maxwell's Equations for Absorbing Media Principal Angle of Incidence Measurement of Refractive Index and Extinction Coefficient of Optically Absorbing Materials Measurement of Refractive Index and Extinction Coefficient at an Incident Angle of References 509 Chapter 26 Polarization Optical Elements Introduction Polarizers 511

xii Contents 26.3 Retarders 522 26.4 Rotators 529 26.5 Depolarizers 531 References 532 Chapter 27 Stokes Polarimetry 533 27.1 Introduction 533 27.2 Rotating Element Polarimetry 534 27.

7 xii Contents 26.3 Retarders Rotators Depolarizers 531 References 532 Chapter 27 Stokes Polarimetry Introduction Rotating Element Polarimetry Oscillating Element Polarimetry Phase Modulation Polarimetry Techniques in Simultaneous Measurement of Stokes Vector Elements Optimization of Polarimeters 554 References 556 Chapter 28 Mueller Matrix Polarimetry Introduction Dual Rotating-Retarder Polarimetry Other Mueller Matrix Polarimetry Methods 578 References 583 Chapter 29 Ellipsometry Introduction Fundamental Equation of Classical Ellipsometry Classical Measurement of the Ellipsometric Parameters Psi {f) and Delta (A) Solution of the Fundamental Equation of Ellipsometry Further Developments in Ellipsometry: The Mueller Matrix Representation of ф and A 616 References 623 Appendix A: Jones and Stokes Vectors 625 Appendix B: Jones and Mueller Matrices 627 Appendix C: Relationships Between the Jones and Mueller Matrix Elements 631 Appendix D: Vector Representation of the Optical Field: Application to Optical Activity 633 Bibliography 645 Index 647

3.4 Elliptical Parameters of the Polarization Ellipse References

3.4 Elliptical Parameters of the Polarization Ellipse References Contents Preface to the Second Edition Preface to the First Edition A Historical Note Edward Collett iii v xiii PART 1: THE CLASSICAL OPTICAL FIELD Chapter 1 Chapter 2 Chapter 3 Chapter 4 Introduction