Scattering of Electromagnetic Waves Numerical Simulations

, by Tsang, Leung; Kong, Jin Au; Ding, Kung-Hau; Ao, Chi On

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ISBN: 9780471388005 | 0471388009
Cover: Hardcover
Copyright: 6/1/2001

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Summary

Author Biography

Supplemental Materials

This volume is devoted to the mathematical solution of problems using MATLAB.

Preface

xix

Monte Carlo Simulations of Layered Media

(12)

One-Dimensional Layered Media with Permittivity Fluctuations

(6)

Continuous Random Medium

(2)

Generation of One-Dimensional Continuous Gaussian Random Medium

(1)

Numerical Results and Applications to Antarctica

(3)

Random Discrete Layering and Applications

(5)

References and Additional Readings

(1)

Integral Equation Formulations and Basic Numerical Methods

(48)

Integral Equation Formulation for Scattering Problems

(9)

Surface Integral Equations

(3)

Volume Integral Equations

(2)

Dyadic Green's Function Singularity and Electrostatics

(4)

Method of Moments

(4)

Discrete Dipole Approximation (DDA)

(10)

Small Cubes

(1)

Radiative Corrections

(2)

Other Shapes

(6)

Product of Toeplitz Matrix and Column Vector

(9)

Discrete Fourier Transform and Convolutions

(4)

FFT for Product of Toeplitz Matrix and Column Vector

(4)

Conjugate Gradient Method

(15)

Steepest Descent Method

(2)

Real Symmetric Positive Definite Matrix

(4)

General Real Matrix and Complex Matrix

(5)

References and Additional Readings

(4)

Scattering and Emission by a Periodic Rough Surface

(50)

Dirichlet Boundary Conditions

(6)

Surface Integral Equation

(1)

Floquet's Theorem and Bloch Condition

(1)

2-D Green's Function in 1-D Lattice

(3)

Bistatic Scattering Coefficients

(1)

Dielectric Periodic Surface: T-Matrix Method

(17)

Formulation in Longitudinal Field Components

(5)

Surface Field Integral Equations and Coupled Matrix Equations

(7)

Emissivity and Comparison with Experiments

(4)

Scattering of Waves Obliquely Incident on Periodic Rough Surfaces: Integral Equation Approach

(8)

Formulation

(4)

Polarimetric Brightness Temperatures

(4)

Ewald's Method

(18)

Preliminaries

(5)

3-D Green's Function in 3-D Lattices

(4)

3-D Green's Function in 2-D Lattices

102

(3)

Numerical Results

105

(5)

References and Additional Readings

110

(1)

Random Rough Surface Simulations

111

(66)

Perfect Electric Conductor (Non-Pentrable Surface)

114

(23)

Integral Equation

114

(2)

Matrix Equation: Dirichlet Boundary Condition (EFIE for TE Case)

116

(2)

Tapering of Incident Waves and Calculation of Scattered Waves

118

(6)

Random Rough Surface Generation

124

(1)

Gaussian Rough Surface

124

(8)

Fractal Rough Surface

132

(2)

Neumann Boundary Condition (MFIE for TM Case)

134

(3)

Two-Media Problem

137

(17)

TE and TM Waves

139

(2)

Absorptivity, Emissivity and Reflectivity

141

(2)

Impedance Matrix Elements: Numerical Integrations

143

(2)

Simulation Results

145

(1)

Gaussian Surface and Comparisons with Analytical Methods

145

(5)

Dirichlet Case of Gaussian Surface with Ocean Spectrum and Fractal Surface

150

(1)

Bistatic Scattering for Two Media Problem with Ocean Spectrum

151

(3)

Topics of Numerical Simulations

154

(9)

Periodic Boundary Condition

154

(4)

MFIE for TE Case of PEC

158

(3)

Impedance Boundary Condition

161

(2)

Microwave Emission of Rough Ocean Surfaces

163

(3)

Waves Scattering from Real-Life Rough Surface Profiles

166

(11)

Introduction

166

(1)

Rough Surface Generated by Three Methods

167

(2)

Numerical Results of the Three Methods

169

(6)

References and Additional Readings

175

(2)

Fast Computational Methods for Solving Rough Surface Scattering Problems

177

(90)

Banded Matrix Canonical Grid Method for Two-Dimensional Scattering for PEC Case

179

(17)

Introduction

179

(1)

Formulation and Computational Procedure

180

(7)

Product of a Weak Matrix and a Surface Unknown Column Vector

187

(1)

Convergence and Neighborhood Distance

188

(1)

Results of Composite Surfaces and Grazing Angle Problems

189

(7)

Physics-Based Two-Grid Method for Lossy Dielectric Surfaces

196

(16)

Introduction

196

(2)

Formulation and Single-Grid Implementation

198

(2)

Physics-Based Two-Grid Method Combined with Banded Matrix Iterative Approach/Canonical Grid Method

200

(3)

Bistatic Scattering Coefficient and Emissivity

203

(9)

Steepest Descent Fast Multipole Method

212

(30)

Steepest Descent Path for Green's Function

213

(3)

Multi-Level Impedance Matrix Decomposition and Grouping

216

(6)

Multi-Level Discretization of Angles and Interpolation

222

(4)

Steepest Descent Expression of Multi-Level Impedance Matrix Elements

226

(9)

SDFMM Algorithm

235

(7)

Numerical Results

242

(1)

Method of Ordered Multiple Interactions (MOMI)

242

(7)

Matrix Equations Based on MFIE for TE and TM Waves for PEC

242

(3)

Iterative Approach

245

(2)

Numerical Results

247

(2)

Physics-Based Two-Grid Method Combined with the Multilevel Fast Multipole Method

249

(18)

Single Grid and PBTG

249

(3)

Computational Complexity of the Combined Algorithm of the PBTG with the MLFMM

252

(2)

Gaussian Rough Surfaces and CPU Comparison

254

(3)

Non-Gaussian Surfaces

257

(6)

References and Additional Readings

263

(4)

Three-Dimensional Wave Scattering from Two-Dimensional Rough Surfaces

267

(104)

Scattering by Non-Penetrable Media

270

(23)

Scalar Wave Scattering

270

(1)

Formulation and Numerical Method

270

(3)

Results and Discussion

273

(4)

Convergence of SMFSIA

277

(1)

Electromagnetic Wave Scattering by Perfectly Conducting Surfaces

278

(1)

Surface Integral Equation

278

(2)

Surface Integral Equation for Rough Surface Scattering

280

(1)

Computation Methods

281

(5)

Numerical Simulation Results

286

(7)

Integral Equations for Dielectric Surfaces

293

(11)

Electromagnetic Fields with Electric and Magnetic Sources

293

(3)

Physical Problem and Equivalent Exterior and Interior Problems

296

(1)

Equivalent Exterior Problem, Equivalent Currents and Integral Equations

296

(2)

Equivalent Interior Problem, Equivalent Currents and Integral Equations

298

(2)

Surface Integral Equations for Equivalent Surface Currents, Tangential and Normal Components of Fields

300

(4)

Two-Dimensional Rough Dielectric Surfaces with Sparse Matrix Canonical Grid Method

304

(22)

Integral Equation and SMCG Method

304

(14)

Numerical Results of Bistatic Scattering Coefficient

318

(8)

Scattering by Lossy Dielectric Surfaces with PBTG Method

326

(24)

Introduction

326

(2)

Formulation and Single Grid Implementation

328

(1)

Physics-Based Two-Grid Method

329

(5)

Numerical Results and Comparison with Second Order Perturbation Method

334

(9)

Numerical Simulations of Emissivity of Soils with Rough Surfaces at Microwave Frequencies

343

(7)

Four Stokes Parameters Based on Tangential Surface Fields

350

(4)

Parallel Implementation of SMCG on Low Cost Beowulf System

354

(17)

Introduction

354

(1)

Low-Cost Beowulf Cluster

355

(1)

Parallel Implementation of the SMCG Method and the PBTG Method

356

(4)

Numerical Results

360

(6)

References and Additional Readings

366

(5)

Volume Scattering Simulations

371

(32)

Combining Simulations of Collective Volume Scattering Effects with Radiative Transfer Theory

373

(3)

Foldy-Lax Self-Consistent Multiple Scattering Equations

376

(6)

Final Exciting Field and Multiple Scattering Equation

376

(3)

Foldy-Lax Equations for Point Scatterers

379

(3)

The N-Particle Scattering Amplitude

382

(1)

Analytical Solutions of Point Scatterers

382

(10)

Phase Function and Extinction Coefficient for Uniformly Distributed Point Scatterers

382

(7)

Scattering by Collection of Clusters

389

(3)

Monte Carlo Simulation Results of Point Scatterers

392

(11)

References and Additional Readings

401

(2)

Particle Positions for Dense Media Characterizations and Simulations

403

(50)

Pair Distribution Functions and Structure Factors

404

(7)

Introduction

404

(2)

Percus-Yevick Equation and Pair Distribution Function for Hard Spheres

406

(3)

Calculation of Structure Factor and Pair Distribution Function

409

(2)

Percus-Yevick Pair Distribution Functions for Multiple Sizes

411

(3)

Monte Carlo Simulations of Particle Positions

414

(10)

Metropolis Monte Carlo Technique

415

(3)

Sequential Addition Method

418

(1)

Numerical Results

418

(6)

Sticky Particles

424

(20)

Percus-Yevick Pair Distribution Function for Sticky Spheres

424

(5)

Pair Distribution Function of Adhesive Sphere Mixture

429

(5)

Monte Carlo Simulation of Adhesive Spheres

434

(10)

Particle Placement Algorithm for Spheroids

444

(9)

Contact Functions of Two Ellipsoids

445

(1)

Illustrations of Contact Functions

446

(4)

References and Additional Readings

450

(3)

Simulations of Two-Dimensional Dense Media

453

(42)

Introduction

454

(4)

Extinction as a Function of Concentration

454

(2)

Extinction as a Function of Frequency

456

(2)

Random Positions of Cylinders

458

(11)

Monte Carlo Simulations of Positions of Hard Cylinders

458

(2)

Simulations of Pair Distribution Functions

460

(1)

Percus-Yevick Approximation of Pair Distribution Functions

461

(2)

Results of Simulations

463

(1)

Monte Carlo Simulations of Sticky Disks

463

(6)

Monte Carlo Simulations of Scattering by Cylinders

469

(17)

Scattering by a Single Cylinder

469

(7)

Foldy-Lax Multiple Scattering Equations for Cylinders

476

(4)

Coherent Field, Incoherent Field, and Scattering Coefficient

480

(1)

Scattered Field and Internal Field Formulations

481

(1)

Low Frequency Formulas

482

(2)

Independent Scattering

484

(1)

Simulation Results for Sticky and Non-Sticky Cylinders

485

(1)

Sparse-Matrix Canonical-Grid Method for Scattering by Many Cylinders

486

(9)

Introduction

486

(3)

The Two-Dimensional Scattering Problem of Many Dielectric Cylinders

489

(1)

Numerical Results of Scattering and CPU Comparisons

490

(3)

References and Additional Readings

493

(2)

Dense Media Models and Three-Dimensional Simulations

495

(56)

Introduction

496

(1)

Simple Analytical Models For Scattering From a Dense Medium

496

(16)

Effective Permittivity

496

(4)

Scattering Attenuation and Coherent Propagation Constant

500

(5)

Coherent Reflection and Incoherent Scattering From a Half-Space of Scatterers

505

(5)

A Simple Dense Media Radiative Transfer Theory

510

(2)

Simulations Using Volume Integral Equations

512

(21)

Volume Integral Equation

512

(2)

Simulation of Densely Packed Dielectric Spheres

514

(4)

Densely Packed Spheroids

518

(15)

Numerical Simulations Using T-Matrix Formalism

533

(18)

Multiple Scattering Equations

533

(8)

Computational Considerations

541

(4)

Results and Comparisons with Analytic Theory

545

(2)

Simulation of Absorption Coefficient

547

(1)

References and Additional Readings

548

(3)

Angular Correlation Function and Detection of Buried Object

551

(42)

Introduction

552

(1)

Two-Dimensional Simulations of Angular Memory Effect and Detection of Buried Object

553

(11)

Introduction

553

(1)

Simple and General Derivation of Memory Effect

553

(2)

ACF of Random Rough Surfaces with Different Averaging Methods

555

(2)

Scattering by a Buried Object Under a Rough Surface

557

(7)

Angular Correlation Function of Scattering by a Buried Object Under a 2-D Random Rough Surface (3-D Scattering)

564

(11)

Introduction

564

(1)

Formulation of Integral Equations

565

(5)

Statistics of Scattered Fields

570

(1)

Numerical Illustrations of ACF and PACF

571

(4)

Angular Correlation Function Applied to Correlation Imaging in Target Detection

575

(18)

Introduction

575

(3)

Formulation of Imaging

578

(2)

Simulations of SAR Data and ACF Processing

580

(11)

References and Additional Readings

591

(2)

Multiple Scattering by Cylinders in the Presence of Boundaries

593

(48)

Introduction

594

(1)

Scattering by Dielectric Cylinders Above a Dielectric Half-Space

594

(28)

Scattering from a Layer of Vertical Cylinders: First-Order Solution

594

(9)

First- and Second-Order Solutions

603

(10)

Results of Monte Carlo Simulations

613

(9)

Scattering by Cylinders in the Presence of Two Reflective Boundaries

622

(19)

Vector Cylindrical Wave Expansion of Dyadic Green's Function Between Two Perfect Conductors

622

(7)

Dyadic Green's Function of a Cylindrical Scatterer Between Two PEC

629

(2)

Dyadic Green's Function with Multiple Cylinders

631

(4)

Excitation of Magnetic Ring Currents

635

(2)

First Order Solution

637

(1)

Numerical Results

638

(2)

References and Additional Readings

640

(1)

Electromagnetic Waves Scattering by Vegetation

641

(52)

Introduction

642

(2)

Plant Modeling by Using L-Systems

644

(10)

Lindenmayer Systems

644

(2)

Turtle Interpretation of L-Systems

646

(3)

Computer Simulations of Stochastic L-Systems and Input Files

649

(5)

Scattering from Trees Generated by L-Systems Based on Coherent Addition Approximation

654

(13)

Single Scattering by a Particle in the Presence of Reflective Boundary

655

(1)

Electric Field and Dyadic Green's Function

655

(1)

Scattering by a Single Particle

656

(3)

Scattering by Trees

659

(8)

Coherent Addition Approximation with Attenuation

667

(2)

Scattering from Plants Generated by L-Systems Based on Discrete Dipole Approximation

669

(16)

Formulation of Discrete Dipole Approximation (DDA) Method

670

(2)

Scattering by Simple Trees

672

(5)

Scattering by Honda Trees

677

(8)

Rice Canopy Scattering Model

685

(8)

Model Description

685

(4)

Model Simulation

689

(2)

References and Additional Readings

691

(2)

Index

693

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Scattering of Electromagnetic Waves Numerical Simulations

Summary

Author Biography

Table of Contents

Supplemental Materials