3.4 Elliptical Parameters of the Polarization Ellipse References

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1 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 The Wave Equation in Classical Optics 2.1 Introduction 2.2 The Wave Equation 2.3 Young's Interference Experiment 2.4 Reflection and Transmission of a Wave at an Interface The Polarization Ellipse 3.1 Introduction 3.2 The Instantaneous Optical Field and the Polarization Ellipse 3.3 Specialized (Degenera te) Forms of the Polarization Ellipse 3.4 Elliptical Parameters of the Polarization Ellipse The Stokes Polarization Parameters 4.1 Introduction 4.2.Derivation of the Stokes Polarization Parameters 4.3 The Stokes Vector 4.4 Classical Measurement of the Stokes Polarization Parameters vii

2 viii Contents Chapter 5 Chapter 6 Chapter 7 Chapter Stokes Parameters for Unpolarized and Partially Polarized Light 4.6 Additional Properties of the Stokes Polarization Parameters 4.7 Stokes Parameters and Wolf's Coherency Matrix The Mueller Matrices for Polarizing Components 5.1 Introduction 5.2 The Mueller Matrix of a Polarizer 5.3 The Mueller Matrix of a Retarder 5.4 The Mueller Matrix of a Rotator 5.5 Mueller Matrices for Rotated Polarizing Components 5.6 Generation of Elliptically Polarized Light Methods of Measuring the Stokes Polarization Parameters 6.1 Introduction 6.2 Classical Measurement Method: The Quarter-Wave Retarder Polarizer Method 6.3 Measurement of the Stokes Parameters Using a Circular Polarizer 6.4 The Null-Intensity Method 6.5 Fourier Analysis Using a Rotating Quarter-Wave Retarder 6.6 The Method of Kent and Lawson 6.7 Simple Tests to Determine the State of Polarization of an Optical Beam The Measurement of the Characteristics of Polarizing Elements 7.1 Introduction 7.2 Measurement of Attenuation Coefficients of a Polarizer (Diattenuator) 7.3 Measurement of Phase Shift of a Retarder 7.4 Measurement of Rotation Angle of a Rotator Reference Mueller Matrices for Reflection and Transmission 8.1 Introduction 8.2 Fresnel's Equations for Reflection and Transmission 8.3 Mueller Matrices for Reflection and Transmission at an Air-Dielectric Interface 8.4 Special Forms for the Mueller Matrices for Reflection and Transmission

3 Contents Chapter 9 The Mathematics of the Mueller Matrix 9.1 Introduction 9.2 Constraints on the Mueller Matrix 9.3 Eigenvector and Eigenva1ue Ana1ysis 9.4 Examp1e of Eigenvector Analysis 9.5 The Lu-Chipman Decomposition 9.6 Summary ix Chapter 10 The Mueller Matrices for Dielectric Plates 10.1 Introduction 10.2 The Diagonal Mueller Matrix and the ABCD Polarization Matrix 10.3 Mueller Matrices for Single and Multiple Dielectric Plates Chapter 11 The Jones Matrix Calculus 11.1 Introduction 11.2 The Jones Vector 11.3 Jones Matrices for the Polarizer, Retarder, and Rotator 11.4 Applications of the Jones Vector and Jones Matrices 11.5 Jones Matrices for Homogeneous Elliptica1 Polarizers and Retarders Chapter 12 The Poincaré Sphere 12.1 Introduction 12.2 Theory of the Poincaré Sphere 12.3 Projection of the Complex P1ane anta a Sphere 12.4 App1ications of the Poincaré Sphere Chapter 13 The Interference Laws of Fresne1 and Arago 13.1 Introduction 13.2 Mathematica1 Statements for Unpolarized Light 13.3 Young's Interference Experiment with Unpolarized Light 13.4 The First Experiment: First and Second Interference Laws 13.5 The Second Experiment: Third Interference Law 13.6 The Third Experiment: Fourth Interference Law 13.7 The Hersche1-Stokes Experiment 13.8 Summary of the Fresnel-Arago Interference Laws

4 x Contents PART 11: THE CLASSICAL AND QUANTUM THEORY OF RADIATION BY ACCELERATING CHARGES Chapter 14 Introduction to the C1assica1and Quantum Theory of Radiation by Accelerating Charges Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Maxwell's Equations for the Electromagnetic Field The Classical Radiation Fie1d 16.1 Field Components of the Radiation Field 16.2 Relation Between the Unit Vector in Spherical Coordinates and Cartesian Coordinates 16.3 Relation Between the Poynting Vector and the Stokes Parameters Radiation Emitted by Accelerating Charges 17.1 Stokes Vector for a Linearly Oscillating Charge 17.2 Stokes Vector for an Ensemble of Randomly Oriented Oscillating Charges 17.3 Stokes Vector for a Charge Rotating in a Circle 17.4 Stokes Vector for a Charge Moving in an Ellipse The Radiation of an Accelerating Charge in the Electromagnetic Field 18.1 Motion of a Charge in an Electromagnetic Field 18.2 Stokes Vectors for Radiation Emitted by Accelerating Charges The Classical Zeeman Effect 19.1 Historical Introduction 19.2 Motion of a Bound Charge in a Constant Magnetic Field 19.3 Stokes Vector for the Zeeman Effect Further Applications of the Classical Radiation Theory 20.1 Relativistic Radiation and the Stokes Vector for a Linear Oscillator 20.2 Relativistic Motion of a Charge Moving in a Circle: Synchrotron Radiation 20.3 Cerenkov Effect 20.4 Thomson and Rayleigh Scattering

5 Contents Chapter 21 Chapter 22 The Stokes Parameters and Mueller Matrices for Optica1 Activity and Faraday Rotation 21.1 Introduction 21.2 Optica1 Activity 21.3 Faraday Rotation in a Transparent Medium 21.4 Faraday Rotation in a Plasma The Stokes Parameters for Quantum Systems 22.1 Introduction 22.2 Re1ation Between Stokes Po1arization Parameters and Quantum Mechanica1 Density Matrix 22.3 Note on Perrin's Introduction of Stokes Parameters, Density Matrix, and Linearity of the Mueller Matrix E1ements 22.4 Radiation Equations for Quantum Mechanica1 Systems 22.5 Stokes Vectors for Quantum Mechanica1 Systems xi Part III: APPLICATIONS Chapter 23 Chapter 24 Chapter 25 Chapter 26 Introduction Crystal Optics 24.1 Introduction 24.2 Review of Concepts from Electromagnetism 24.3 Crystalline Materials and Their Properties 24.4 Crystals 24.5 Application of Electric Fields: Induced Birefringence and Polarization Modulation 24.6 Magneto-optics 24.7 Liquid Crystals 24.8 Modulation of Light 24.9 Concluding Remarks Optics of Metals 25.1 Introduction 25.2 Maxwell's Equations for Absorbing Media 25.3 Principal Angle of Incidence Measurement of Refractive Index and Extinction Coefficient of Optically Absorbing Materials 25.4 Measurement of Refractive Index and Extinction Coefficient at an Incident Angle of 45 Polarization Optical Elements 26.1 Introduction 26.2 Polarizers

6 xii Contents Chapter 27 Chapter 28 Chapter Retarders 26.4 Rotators 26.5 Depolarizers Stokes Polarimetry 27.1 Introduction 27.2 Rotating Element Polarimetry 27.3 Oscillating Element Polarimetry 27.4 Phase Modulation Polarimetry 27.5 Techniques in Simultaneous Measurement of Stokes Vector Elements 27.6 Optimization of Polarimeters Mueller Matrix Polarimetry 28.1 Introduction 28.2 Dual Rotating-Retarder Polarimetry 28.3 Other Mueller Matrix Polarimetry Methods Ellipsometry 29.1 Introduction 29.2 Fundamental Equation of Classical Ellipsometry 29.3 Classical Measurement of the Ellipsometric Parameters Psi (1/1)and Delta (l:.) 29.4 Solution of the Fundamental Equation of Ellipsometry 29.5 Further Developments in Ellipsometry: The Mueller Matrix Representation of 1/1 and l: Appendix A: Jones and Stokes Vectors Appendix B: Jones and Mueller Matrices Appendix C: Relationships Between the Jones and Mueller Matrix Elements Appendix D: Vector Representation 01 the aptical Field: Application to aptical Activity Bibliography lndex

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

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