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Theory of Reflection - Reflection and Transmission of Electromagnetic, Particle and Acoustic Waves
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Theory of Reflection - Reflection and Transmission of Electromagnetic, Particle and Acoustic Waves
von: John Lekner
Springer-Verlag, 2016
ISBN: 9783319236278
539 Seiten, Download: 8844 KB
 
Format:  PDF
geeignet für: Apple iPad, Android Tablet PC's Online-Lesen PC, MAC, Laptop

Typ: B (paralleler Zugriff)

 

 
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Inhaltsverzeichnis

  Preface 7  
  Contents 9  
  1 Introducing Reflection 15  
     1.1 The Electromagnetic {\varvec s} Wave 15  
     1.2 The Electromagnetic {\varvec p} Wave 20  
     1.3 Particle Waves 26  
     1.4 Acoustic Waves 30  
     1.5 Scattering and Reflection 34  
     1.6 A Look Ahead 38  
     References 53  
     Further Readings 53  
  2 Exact Results 55  
     2.1 Comparison Identities, and Conservation and Reciprocity Laws 55  
     2.2 General Expressions for {\varvec r}_{{\varvec s}} and {\varvec r}_{{\varvec p}} 60  
     2.3 Reflection at Grazing Incidence, and the Existence of a Principal Angle 66  
     2.4 Reflection by a Homogeneous Layer 69  
     2.5 The Tanh, Exp and Rayleigh Profiles 75  
     References 86  
     Further Readings 87  
  3 Reflection of Long Waves 88  
     3.1 Integral Equation and Perturbation Theory for the s Wave 88  
     3.2 The s Wave to Second Order in the Interface Thickness 92  
     3.3 Integral Invariants 94  
     3.4 \left| {{{\varvec r}}_{{{\varvec p}}} } \right|^{{{\bf 2}}} and {{\varvec r}}_{{{\varvec p}}} {{\varvec /r}}_{{{\varvec s}}} to Second Order 97  
     3.5 Reflection by a Thin Film Between Like Media 101  
     3.6 Six Profiles and Their Integral Invariants 103  
     References 106  
     Further Readings 106  
  4 Variational Theory 107  
     4.1 A Variational Expression for the Reflection Amplitude 107  
     4.2 Variational Estimate for rs in the Long Wave Case 110  
     4.3 Exact, Perturbation and Variational Results for the sech2 Profile 111  
     4.4 Variational Theory for the p Wave 115  
     4.5 Reflection by a Layer Between Like Media 118  
     4.6 The Hulth00E9n-Kohn Variational Method Applied to Reflection 122  
     4.7 Variational Estimates in the Short Wave Case 124  
     References 126  
     Further Readings 126  
  5 Equations for the Reflection Amplitudes 127  
     5.1 A First Order Non-linear Equation for an {\varvec s} Wave Reflection Coefficient 127  
     5.2 An Example: Reflection by the Linear Profile 129  
     5.3 Differential Equation for a {\varvec p} Wave Reflection Coefficient 132  
     5.4 Upper Bounds on {\varvec R}_{{\varvec s}} and on {\varvec R}_{{\varvec p}} 134  
     5.5 Long Wave Expansions 136  
     5.6 Differential Equations for the Reflection Amplitudes 140  
     5.7 Weak Reflection: The Rayleigh Approximation 142  
     5.8 Iteration of the Integral Equation for {\varvec r} 143  
     References 145  
  6 Reflection of Short Waves 147  
     6.1 Short Wave Limiting Forms for Some Solvable Profiles 147  
     6.2 Approximate High-Frequency Waveforms 151  
     6.3 Profiles of Finite Extent with Discontinuities in Slope at the Endpoints 154  
     6.4 Reflection Amplitude Estimates from a Comparison Identity 157  
     6.5 Perturbation Theory for Short Waves 162  
     6.6 Short Wave Results for {\varvec r}_{{\varvec p}} and {\varvec r}_{{\varvec p}} \varvec{/}{\varvec r}_{{\varvec s}} 164  
     6.7 A Single Turning Point: Total Reflection 171  
     6.8 Two Turning Points, and Tunneling 178  
     References 184  
     Further Readings 185  
  7 Simple Anisotropy 186  
     7.1 Anisotropy with Azimuthal Symmetry 186  
     7.2 Ellipsometry of a Thin Film on an Isotropic Substrate 190  
     7.3 Thin Film on an Anisotropic Substrate 193  
     7.4 General Results for Anisotropic Stratifications with Azimuthal Symmetry 195  
     7.5 Differential Equations for the Reflection Amplitudes 196  
     7.6 Reflection from the Ionosphere 198  
     References 200  
     Further Readings 201  
  8 Uniaxial Anisotropy 202  
     8.1 Propagation Within Homogeneous Anisotropic Media 202  
     8.2 Dielectric Tensor and Normal Modes in Uniaxial Crystals 204  
     8.3 Uniaxial Crystal Reflection and Transmission Amplitudes 207  
     8.4 Bounds and Zeros of the Reflection Amplitudes, the Polarizing Angle 210  
     8.5 External Reflection from an Immersed Crystal 212  
     8.6 Normal-Incidence Reflection and Transmission 213  
     8.7 Normal Incidence on a Uniaxial Plate 216  
     8.8 Isotropic Layer on a Uniaxial Substrate 220  
     8.9 Optical Properties of a Uniaxial Layer 222  
     References 223  
  9 Ellipsometry 225  
     9.1 Polarizer--Sample--Analyser 225  
     9.2 Polarizer--Compensator--Sample--Analyser 227  
     9.3 Polarizer--Sample--Compensator--Analyser 228  
     9.4 Polarizer--Modulator--Sample--Analyser 229  
     9.5 Polarizer--Sample--Modulator--Analyser 231  
     9.6 Ellipsometric Measurements: The Principal Angle 231  
     9.7 Transmission Ellipsometry 232  
        9.7.1 Polarizer--Sample--Analyser 233  
        9.7.2 Polarizer--Compensator--Sample--Analyser 233  
        9.7.3 Polarizer--Sample--Compensator--Analyser 234  
        9.7.4 Transmission Ellipsometry with a Polarization Modulator 235  
     9.8 Reflection and Transmission Ellipsometry of a Homogeneous Layer 235  
     9.9 Reflection Ellipsometry of Uniaxial Crystals 238  
     References 240  
  10 Absorption 242  
     10.1 Fresnel Reflection Formulae for an Absorbing Medium 243  
     10.2 General Results for Reflection by Absorbing Media 249  
     10.3 Dielectric Layer on an Absorbing Substrate 250  
     10.4 Absorbing Film on a Non-absorbing Substrate 251  
     10.5 Thin Inhomogeneous Absorbing Films 254  
     10.6 Attenuated Total Reflection, Surface Waves 258  
     10.7 Attenuated Total Reflection: Second Example 265  
     10.8 Reflection by a Diffuse Absorbing Interface: The Tanh Profile 268  
     10.9 Zero Reflection from Dielectric Layer on Absorbing Substrate 271  
     References 271  
  11 Inverse Problems 273  
     11.1 Reflection at a Sharp Boundary 274  
     11.2 Homogeneous Film Between Like Media 277  
     11.3 Inversion of Transmission Ellipsometric Data for a Homogeneous Nonabsorbing Layer 279  
     11.4 Inversion of Reflection Ellipsometric Data for a Homogeneous Nonabsorbing Layer 280  
     11.5 Synthesis of a Profile from r as a Function of Wavenumber 281  
     11.6 Inversion of the Rayleigh Approximation 284  
     11.7 Principal Angle of an Absorber 286  
     References 287  
     Further Readings 288  
  12 Matrix and Numerical Methods 289  
     12.1 Matrices Relating the Coefficients of Linearly Independent Solutions 289  
     12.2 Matrices Relating Fields and Their Derivatives 293  
     12.3 Multilayer Dielectric Mirrors at Normal Incidence 298  
     12.4 Reflection of Long Waves 301  
     12.5 Absorbing Stratified Media: Some General Results 303  
     12.6 High Transparency of an Absorbing Film in a Frustrated Total Reflection Configuration 306  
     12.7 Comparison of Numerical Approaches 308  
     12.8 Numerical Methods Based on the Layer Matrices 309  
     12.9 Variable Step Size, Profile Truncation, Total Reflection and Tunneling, Absorption, and Calculation of Wavefunctions 314  
     References 317  
  13 Periodically Stratified Media 318  
     13.1 Electromagnetic Waves in Stratified Media 319  
     13.2 Periodic Structures, Multilayer Dielectric Mirrors 324  
     13.3 Omnidirectional Reflection by Multilayer Dielectric Mirrors 330  
        13.3.1 Band Edges at Oblique Incidence for a General Stack 332  
        13.3.2 Refractive Indices for Which Omnidirectional Reflection Exists 334  
     13.4 Form Birefringence 336  
     13.5 Absorbing Periodically Stratified Media 339  
        13.5.1 Reflection of s-Polarized Plane Waves 340  
        13.5.2 Reflection of p-Polarized Plane Waves 342  
        13.5.3 Application to an Absorbing Quarter-Wave Stack 344  
     References 345  
  14 Rough or Structured Surfaces 347  
     14.1 Reflection from Rough Surfaces: The Rayleigh Criterion 348  
     14.2 Corrugated Surfaces, Diffraction Gratings 349  
     14.3 Scattering of Light by Liquid Surfaces 355  
     14.4 The Surface Integral Formulation of Scattering by Rough Surfaces 359  
     14.5 Absorbing and Rough Surfaces that Are Wet 362  
     14.6 Coherent Backscattering 364  
     References 365  
     Further Readings 367  
  15 Particle Waves 369  
     15.1 General Results 369  
     15.2 Some Exactly Solvable Profiles 373  
     15.3 Perturbation and Variational Theories 380  
     15.4 Long Waves, Integral Invariants 382  
     15.5 Riccati-Type Equations 384  
     15.6 Reflection of Short Waves 386  
     15.7 Absorption, the Optical Potential 388  
     15.8 Inversion of a Model Reflection Amplitude 391  
     15.9 Time Delay in the Reflection of Wavepackets 393  
     References 396  
  16 Neutron and X-ray Reflection 397  
     16.1 Common Features of X-ray and Neutron Optics 398  
     16.2 Reflection Near the Critical Angle 399  
     16.3 Reflection by Profiles Without Discontinuities 403  
     16.4 Reflection by Profiles with Discontinuities 406  
     16.5 Total Reflection: Extraction of the Phase in Lloyd's Mirror Experiments 411  
     16.6 Reflection of Neutrons by Periodic Stratifications 416  
     16.7 Neutron Reflection by Magnetic Materials 420  
     References 422  
  17 Acoustic Waves 424  
     17.1 General Relations for Stratified Media 424  
        17.1.1 General Results for the Reflection and Transmission Amplitudes 425  
     17.2 Matrix Methods 430  
     17.3 Low-Frequency Reflection and Transmission 436  
     17.4 High-Frequency Limiting Forms 439  
     17.5 Exact Solutions for the exp-lin and exp-exp Stratifications 444  
     17.6 An Upper Bound on the Acoustic Reflectivity 446  
     17.7 Profiles with Discontinuities in Density or Sound Speed 449  
     Appendix: Universal Properties of Acoustic Pulses and Beams 453  
     References 456  
  18 Chiral Isotropic Media 457  
     18.1 Constitutive Relations 458  
     18.2 Reflection and Transmission Amplitudes, Conservation Laws 460  
        18.2.1 Differential Reflectance, Ellipsometry 464  
     18.3 Wave Propagation in Chiral Media 465  
        18.3.1 Eigenstates of Curl 467  
        18.3.2 Boundary Conditions 468  
     18.4 Reflection from an Achiral--Chiral Interface 469  
        18.4.1 Wavefunctions 470  
        18.4.2 Reflection and Transmission Amplitudes 470  
        18.4.3 The Angles {\varvec{\uptheta}}_{{\bf B}} , {\varvec{\uptheta}}_{{\bf pp}}, {{\varvec and}}\,{\varvec{\uptheta}}_{{\bf pol}} 474  
     18.5 Optical Properties of a Chiral Layer 475  
        18.5.1 Normal Incidence 476  
        18.5.2 Optical Properties Near the Critical Angles 478  
     References 479  
  19 Pulses and Wavepackets 480  
     19.1 Reflection of Nearly Monochromatic Pulses: The Time Delay 480  
     19.2 Nonreflection of Wavepackets by a Subset of the sech2 Potentials 484  
        19.2.1 Construction of Reflectionless Wavepackets 485  
     19.3 Exact Solutions of Total and Partial Reflection of Wavepackets 488  
     Appendix: Universal Properties of Electromagnetic Pulses 492  
        Conservation Laws, Energy-Momentum Inequalities 494  
        Angular Momentum, Helicity 496  
        Lorentz Transformation of Pulses 498  
     References 500  
     Further Readings 501  
  20 Finite Beams 502  
     20.1 Universal Properties of Scalar and of Electromagnetic Beams 502  
        20.1.1 Bateman Integral Solution of the Wave Equation 504  
        20.1.2 Conservation Laws and Beam Invariants 505  
        20.1.3 Non-existence Theorems 507  
        20.1.4 Focal Plane Zeros 508  
     20.2 Reflection of Beams: The Lateral Beam Shift 510  
     20.3 Reflection of Gaussian Beams 514  
        20.3.1 Reflection at a Potential Spike (Delta Function) 516  
        20.3.2 Reflection at a Sharp Boundary Between Two Media 517  
     Appendix 1: Total Internal Reflection: The rs, rp Phases and Their Difference 518  
        Total Reflection by the Hyperbolic Tangent Profile 522  
     Appendix 2: Polarization of Electromagnetic Beams 524  
        Examples of Exactly and Approximately Linearly Polarized Beams 526  
        Approximately Circularly Polarized Beams 528  
     References 529  
     Further Readings 530  
  Appendix: Reflection and Transmission Formulae 531  
  Index 536  


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