Scattering of Electromagnetic Waves: Advanced Topics

PREFACE xiii

CHAPTER 1 TWO-DIMENSIONAL RANDOM ROUGH SURFACE SCATTERING BASED ON SMALL PERTURBATION METHOD 1

1 Electromagnetic Wave Scattering by a Perfect Electric Conductor 2

1.1 Zeroth- and First-Order Solutions 7

1.2 Second-Order Solutions 11

2 Electromagnetic Wave Scattering by a Dielectric Rough Surface 18

2.1 Zeroth- and First-Order Solutions 27

2.2 Second-Order Solutions 36

3 Coherent Reflection, Emissivities, and Bistatic Scattering Coefficients of Random Dielectric Surfaces 47

3.1 Coherent Reflection 48

3.2 Emissivities of Four Stokes Parameters 51

3.3 Bistatic Scattering Coefficients 58

References and Additional Readings 61

CHAPTER 2 KIRCHHOFF APPROACH AND RELATED METHODS FOR ROUGH SURFACE SCATTERING 65

1 Kirchhoff Approach 66

1.1 Perfectly Conducting Rough Surface 66

1.2 Dielectric Rough Surfaces 72

1.3 Second-Order Slope Corrections 94

2 Phase Perturbation Method 101

3 Emissivity Based on Composite Surface Model 108

References and Additional Readings 118

CHAPTER 3 VOLUME SCATTERING: CASCADE OF LAYERS 121

1 Single Scattering Solution of a Thin Layer, Coherent Wave, and Effective Propagation Constant 122

2 Transition Operator 128

3 Electromagnetic Wave Case of a Thin Layer and Extinction Matrix 130

4 First- and Second-Order Solutions: Incoherent Waves 135

5 Cascading of Layers: From First- and Second-Order Wave Solutions to Radiative Transfer Equation 143

6 Effects of Clustering 150

References and Additional Readings 160

CHAPTER 4 ANALYTIC WAVE THEORY FOR A MEDIUM WITH PERMITTIVITY FLUCTUATIONS 161

1 Dyson's Equation for the Mean Field 162

1.1 Bilocal Approximation 167

1.2 Nonlinear Approximation 170

2 Second Moment of the Field 171

2.1 Bethe-Salpeter Equation 171

2.2 Energy Conservation 175

3 Strong Permittivity Fluctuations 178

3.1 Random Medium with Spherically Symmetric Correlation Function 179

3.2 Very Low Frequency Effective Permittivity 181

3.3 Effective Permittivity Under the Bilocal Approximation 182

3.4 Backscattering Coefficients 185

3.5 Results of Effective Permittivity and Bistatic Coefficients 187

References and Additional Readings 194

CHAPTER 5 MULTIPLE SCATTERING THEORY FOR DISCRETE SCATTERERS 197

1 Transition Operator 198

2 Multiple Scattering Equations 203

3 Approximations of Multiple Scattering Equations 204

3.1 Configurational Average of Multiple Scattering Equations 205

3.2 Effective Field Approximation (EFA, Foldy's Approximation) 207

3.3 Quasi-crystalline Approximation (QCA) 210

3.4 Coherent Potential (CP) 213

3.5 Quasi-crystalline Approximation with Coherent Potential (QCA-CP) 216

3.6 Low-Frequency Solutions 219

3.7 QCA-CP for Multiple Species of Particles 224

4 Ward's Identity and Energy Conservation 226

5 Derivation of Radiative Transfer Equation from Ladder Approximation 232

References and Additional Readings 241

CHAPTER 6 QUASI-CRYSTALLINE APPROXIMATION IN DENSE MEDIA SCATTERING 245

1 Scattering of Electromagnetic Waves from a Half-Space of Dielectric Scatterers— Normal Incidence 246

1.1 Coherent Wave Propagation 247

1.2 Effective Phase Velocity and Attenuation Rate in the Low-Frequency Limit 257

1.3 Dispersion Relations at Higher Frequencies 259

2 Scattering of Electromagnetic Waves from a Half-Space of Dielectric Scatterers—Oblique Incidence 266

2.1 Dispersion Relation and Coherent Reflected Wave 266

2.2 Vertically and Horizontally Polarized Incidence 275

3 Cases with Size Distributions 280

3.1 Coherent Field 281

3.2 Incoherent Field Using Distorted Born Approximation 287

4 Dense Media Radiative Transfer Theory Based on Quasi-crystalline Approximation 300

4.1 Phase Matrix, Extinction, Scattering, and Absorption Coefficients 301

4.2 Brightness Temperature Computed with QCA-based DMRT 307

4.3 Numerical Results for Sticky and Non-Sticky Particles 309

References and Additional Readings 319

CHAPTER 7 DENSE MEDIA SCATTERING 323

1 Introduction 324

2 Effective Propagation Constants, Mean Green's Function, and Mean Field for Half-Space DiscreteRandom Medium of Multiple Species 325

3 Derivation of Dense Media Radiative Transfer Equation (DMRT) 329

4 Dense Media Radiative Transfer Equations for Active Remote Sensing 340

5 General Relation between Active and Passive Remote Sensing with Temperature Distribution 344

6 Dense Media Radiative Transfer Equations for Passive Remote Sensing 349

7 Numerical Illustrations of Active and Passive Remote Sensing 351

References and Additional Readings 357

CHAPTER 8 BACKSCATTERING ENHANCEMENT 359

1 Introduction 360

1.1 Volume Scattering 361

1.2 Volume Scattering in the Presence of Reflective Boundary 362

2 Second-Order Volume Scattering Theory of Isotropic Point Scatterers 366

3 Summation of Ladder Terms and Cyclical Terms for Isotropic Point Scatterers 374

3.1 Formulation 375

3.2 Numerical Illustrations 380

4 Anisotropic Scatterers and Diffusion Approximation 385

4.1 Summation of Ladder Terms and Cyclical Terms 386

4.2 Unidirectional Point Source Green's Function 391

4.3 Second-Order Multiple-Scattering Theory 393

4.4 Diffusion Approximation 395

4.5 Numerical Results 399

References and Additional Readings 403

INDEX 407