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 Wave Equation in Classical Optics 3 2.1 Introduction 3 2.2 The Wave Equation 3 2.3 Young's Interference Experiment 11 2.4 Reflection and Transmission of a Wave at an Interface 15 References 19 Chapter 3 The Polarization Ellipse 21 3.1 Introduction 21 3.2 The Instantaneous Optical Field and the Polarization Ellipse 22 3.3 Specialized (Degenerate) Forms of the Polarization Ellipse 25 3.4 Elliptical Parameters of the Polarization Ellipse 27 References 30 Chapter 4 The Stokes Polarization Parameters 31 4.1 Introduction 31 4.2 Derivation of the Stokes Polarization Parameters 32 4.3 The Stokes Vector 37 4.4 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 4.7 Stokes Parameters and Wolf's Coherency Matrix 59 References 63 Chapter 5 The Mueller Matrices for Polarizing Components 65 5.1 Introduction 65 5.2 The Mueller Matrix of a Polarizer 67 5.3 The Mueller Matrix of a Retarder 72 5.4 The Mueller Matrix of a Rotator 75 5.5 Mueller Matrices for Rotated Polarizing Components 77 5.6 Generation of Elliptically Polarized Light 83 References 86 Chapter 6 Methods of Measuring the Stokes Polarization Parameters 87 6.1 Introduction 87 6.2 Classical Measurement Method: The Quarter-Wave Retarder Polarizer Method 87 6.3 Measurement of the Stokes Parameters Using a Circular Polarizer 91 6.4 The Null-Intensity Method 95 6.5 Fourier Analysis Using a Rotating Quarter-Wave Retarder 98 6.6 The Method of Kent and Lawson 102 6.7 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 117 7.1 Introduction 117 7.2 Measurement of Attenuation Coefficients of a Polarizer (Diattenuator) 117 7.3 Measurement of Phase Shift of a Retarder 124 7.4 Measurement of Rotation Angle of a Rotator 130 Reference 132 Chapter 8 Mueller Matrices for Reflection and Transmission 133 8.1 Introduction 133 8.2 Fresnel's Equations for Reflection and Transmission 134 8.3 Mueller Matrices for Reflection and Transmission at an Air-Dielectric Interface 145 8.4 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 Example of Eigenvector Analysis 171 9.5 The Lu-Chipman Decomposition 175 9.6 Summary 185 References 185 Chapter 10 The Mueller Matrices for Dielectric Plates 187 10.1 Introduction 187 10.2 The Diagonal Mueller Matrix and the ABCD Polarization Matrix 187 10.3 Mueller Matrices for Single and Multiple Dielectric Plates 195 References 209 Chapter 11 The Jones Matrix Calculus 211 11.1 Introduction 211 11.2 The Jones Vector 212 11.3 Jones Matrices for the Polarizer, Retarder, and Rotator 216 11.4 Applications of the Jones Vector and Jones Matrices 221 11.5 Jones Matrices for Homogeneous Elliptical Polarizers and Retarders 231 References 239 Chapter 12 The Poincare Sphere 241 12.1 Introduction 241 12.2 Theory of the Poincare Sphere 242 12.3 Projection of the Complex Plane onto a Sphere 258 12.4 Applications of the Poincare Sphere 265 References 273 Chapter 13 The Interference Laws of Fresnel and Arago 275 13.1 Introduction 275 13.2 Mathematical Statements for Unpolarized Light 276 13.3 Young's Interference Experiment with Unpolarized Light 278 13.4 The First Experiment: First and Second Interference Laws 282 13.5 The Second Experiment: Third Interference Law 287 13.6 The Third Experiment: Fourth Interference Law 289 13.7 The Herschel-Stokes Experiment 292 13.8 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 References 298 Chapter 15 Maxwell's Equations for the Electromagnetic Field 301 References 306 Chapter 16 The Classical Radiation Field 307 16.1 Field Components of the Radiation Field 307 16.2 Relation Between the Unit Vector in Spherical Coordinates and Cartesian Coordinates 309 16.3 Relation Between the Poynting Vector and the Stokes Parameters 312 References 317 Chapter 17 Radiation Emitted by Accelerating Charges 319 17.1 Stokes Vector for a Linearly Oscillating Charge 319 17.2 Stokes Vector for an Ensemble of Randomly Oriented Oscillating Charges 322 17.3 Stokes Vector for a Charge Rotating in a Circle 325 17.4 Stokes Vector for a Charge Moving in an Ellipse 328 References 329 Chapter 18 The Radiation of an Accelerating Charge in the Electromagnetic Field 331 18.1 Motion of a Charge in an Electromagnetic Field 331 18.2 Stokes Vectors for Radiation Emitted by Accelerating Charges 345 References 350 Chapter 19 The Classical Zeeman Effect 351 19.1 Historical Introduction 351 19.2 Motion of a Bound Charge in a Constant Magnetic Field 352 19.3 Stokes Vector for the Zeeman Effect 361 References 366 Chapter 20 Further Applications of the Classical Radiation Theory 369 20.1 Relativistic Radiation and the Stokes Vector for a Linear Oscillator 369 20.2 Relativistic Motion of a Charge Moving in a Circle: Synchrotron Radiation 376 20.3 Cerenkov Effect 382 20.4 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 21.3 Faraday Rotation in a Transparent Medium 411 21.4 Faraday Rotation in a Plasma 414 References 416 Chapter 22 The Stokes Parameters for Quantum Systems 417 22.1 Introduction 417 22.2 Relation Between Stokes Polarization Parameters and Quantum Mechanical Density Matrix 419 22.3 Note on Perrin's Introduction of Stokes Parameters, Density Matrix, and Linearity of the Mueller Matrix Elements 427 22.4 Radiation Equations for Quantum Mechanical Systems 432 22.5 Stokes Vectors for Quantum Mechanical Systems 435 References 442 Part III: APPLICATIONS Chapter 23 Introduction 445 Chapter 24 Crystal Optics 447 24.1 Introduction 447 24.2 Review of Concepts from Electromagnetism 448 24.3 Crystalline Materials and Their Properties 450 24.4 Crystals 451 24.5 Application of Electric Fields: Induced Birefringence and Polarization Modulation 463 24.6 Magneto-optics 470 24.7 Liquid Crystals 471 24.8 Modulation of Light 475 24.9 Concluding Remarks 476 References 477 Chapter 25 Optics of Metals 479 25.1 Introduction 479 25.2 Maxwell's Equations for Absorbing Media 480 25.3 Principal Angle of Incidence Measurement of Refractive Index and Extinction Coefficient of Optically Absorbing Materials 489 25.4 Measurement of Refractive Index and Extinction Coefficient at an Incident Angle of 45 496 References 509 Chapter 26 Polarization Optical Elements 511 26.1 Introduction 511 26.2 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 27.3 Oscillating Element Polarimetry 537 27.4 Phase Modulation Polarimetry 543 27.5 Techniques in Simultaneous Measurement of Stokes Vector Elements 545 27.6 Optimization of Polarimeters 554 References 556 Chapter 28 Mueller Matrix Polarimetry 559 28.1 Introduction 559 28.2 Dual Rotating-Retarder Polarimetry 563 28.3 Other Mueller Matrix Polarimetry Methods 578 References 583 Chapter 29 Ellipsometry 585 29.1 Introduction 585 29.2 Fundamental Equation of Classical Ellipsometry 586 29.3 Classical Measurement of the Ellipsometric Parameters Psi {f) and Delta (A) 588 29.4 Solution of the Fundamental Equation of Ellipsometry 597 29.5 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