Scattering of Electromagnetic Waves

Leung Tsang is the author of Scattering of Electromagnetic Waves: Numerical Simulations, published by Wiley. Jin Au Kong was an American expert in applied electromagnetics. He was a 74th-generation lineal descendent of the famous Chinese philosopher Confucius.

• PREFACE xixCHAPTER 1 MONTE CARLO SIMULATIONS OF LAYERED MEDIA 11 One-Dimensional Layered Media with Permittivity Fluctuations 21.1 Continuous Random Medium 21.2 Generation of One-Dimensional Continuous Gaussian Random Medium 41.3 Numerical Results and Applications to Antarctica 52 Random Discrete Layering and Applications 8References and Additional Readings 12CHAPTER 2 INTEGRAL EQUATION FORMULATIONS AND BASIC NUMERICAL METHODS 131 Integral Equation Formulation for Scattering Problems 141.1 Surface Integral Equations 141.2 Volume Integral Equations 171.3 Dyadic Green's Function Singularity and Electrostatics 192 Method of Moments 233 Discrete Dipole Approximation (DDA) 273.1 Small Cubes 283.2 Radiative Corrections 293.3 Other Shapes 314 Product of Toeplitz Matrix and Column Vector 374.1 Discrete Fourier Transform and Convolutions 384.2 FFT for Product of Toeplitz Matrix and Column Vector 425 Conjugate Gradient Method 465.1 Steepest Descent Method 465.2 Real Symmetric Positive Definite Matrix 485.3 General Real Matrix and Complex Matrix 52References and Additional Readings 57CHAPTER 3 SCATTERING AND EMISSION BY A PERIODIC ROUGH SURFACE 611 Dirichlet Boundary Conditions 621.1 Surface Integral Equation 621.2 Floquet's Theorem and Bloch Condition 631.3 2-D Green's Function in 1-D Lattice 641.4 Bistatic Scattering Coefficients 672 Dielectric Periodic Surface: T-Matrix Method 682.1 Formulation in Longitudinal Field Components 692.2 Surface Field Integral Equations and Coupled Matrix Equations 742.3 Emissivity and Comparison with Experiments 813 Scattering of Waves Obliquely Incident on Periodic Rough Surfaces: Integral Equation Approach 853.1 Formulation 853.2 Polarimetric Brightness Temperatures 894 Ewald's Method 934.1 Preliminaries 934.2 3-D Green's Function in 3-D Lattices 984.3 3-D Green's Function in 2-D Lattices 1024.4 Numerical Results 105References and Additional Readings 110CHAPTER 4 RANDOM ROUGH SURFACE SIMULATIONS 1111 Perfect Electric Conductor (Non-Penetrable Surface) 1141.1 Integral Equation 1141.2 Matrix Equation: Dirichlet Boundary Condition (EFIE for TE Case) 1161.3 Tapering of Incident Waves and Calculation of Scattered Waves 1181.4 Random Rough Surface Generation 1241.4.1 Gaussian Rough Surface 1241.4.2 Fractal Rough Surface 1321.5 Neumann Boundary Condition (MFIE for TM Case) 1342 Two-Media Problem 1372.1 TE and TM Waves 1392.2 Absorptivity, Emissivity and Reflectivity 1412.3 Impedance Matrix Elements: Numerical Integrations 1432.4 Simulation Results 1452.4.1 Gaussian Surface and Comparisons with Analytical Methods 1452.4.2 Dirichlet Case of Gaussian Surface with Ocean Spectrum and Fractal Surface 1502.4.3 Bistatic Scattering for Two Media Problem with Ocean Spectrum 1513 Topics of Numerical Simulations 1543.1 Periodic Boundary Condition 1543.2 MFIE for TE Case of PEC 1583.3 Impedance Boundary Condition 1614 Microwave Emission of Rough Ocean Surfaces 1635 Waves Scattering from Real-Life Rough Surface Profiles 1665.1 Introduction 1665.2 Rough Surface Generated by Three Methods 1675.3 Numerical Results of the Three Methods 169References and Additional Readings 175CHAPTER 5 FAST COMPUTATIONAL METHODS FOR SOLVING ROUGH SURFACE SCATTERING PROBLEMS 1771 Banded Matrix Canonical Grid Method for Two-Dimensional Scattering for PEC Case 1791.1 Introduction 1791.2 Formulation and Computational Procedure 1801.3 Product of a Weak Matrix and a Surface Unknown Column Vector 1871.4 Convergence and Neighborhood Distance 1881.5 Results of Composite Surfaces and Grazing Angle Problems 1892 Physics-Based Two-Grid Method for Lossy Dielectric Surfaces 1962.1 Introduction 1962.2 Formulation and Single-Grid Implementation 1982.3 Physics-Based Two-Grid Method Combined with Banded Matrix Iterative Approach/Canonical Grid Method 2002.4 Bistatic Scattering Coefficient and Emissivity 2033 Steepest Descent Fast Multipole Method 2123.1 Steepest Descent Path for Green's Function 2133.2 Multi-Level Impedance Matrix Decomposition and Grouping 2163.3 Multi-Level Discretization of Angles and Interpolation 2223.4 Steepest Descent Expression of Multi-Level Impedance Matrix Elements 2263.5 SDFMM Algorithm 2353.6 Numerical Results 2424 Method of Ordered Multiple Interactions (MOMI) 2424.1 Matrix Equations Based on MFIE for TE and TM Waves for PEC 2424.2 Iterative Approach 2454.3 Numerical Results 2475 Physics-Based Two-Grid Method Combined with the Multilevel Fast Multipole Method 2495.1 Single Grid and PBTG 2495.2 Computational Complexity of the Combined Algorithm of the PBTG with the MLFMM 2525.3 Gaussian Rough Surfaces and CPU Comparison 2545.4 Non-Gaussian Surfaces 257References and Additional Readings 263CHAPTER 6 THREE-DIMENSIONAL WAVE SCATTERING FROM TWO-DIMENSIONAL ROUGH SURFACES 2671 Scattering by Non-Penetrable Media 2701.1 Scalar Wave Scattering 2701.1.1 Formulation and Numerical Method 2701.1.2 Results and Discussion 2731.1.3 Convergence of SMFSIA 2771.2 Electromagnetic Wave Scattering by Perfectly Conducting Surfaces 2781.2.1 Surface Integral Equation 2781.2.2 Surface Integral Equation for Rough Surface Scattering 2801.2.3 Computation Methods 2811.2.4 Numerical Simulation Results 2862 Integral Equations for Dielectric Surfaces 2932.1 Electromagnetic Fields with Electric and Magnetic Sources 2932.2 Physical Problem and Equivalent Exterior and Interior Problems 2962.2.1 Equivalent Exterior Problem, Equivalent Currents and Integral Equations 2962.2.2 Equivalent Interior Problem, Equivalent Currents and Integral Equations 2982.3 Surface Integral Equations for Equivalent Surface Currents, Tangential and Normal Components of Fields 3003 Two-Dimensional Rough Dielectric Surfaces with Sparse Matrix Canonical Grid Method 3043.1 Integral Equation and SMCG Method 3043.2 Numerical Results of Bistatic Scattering Coefficient 3184 Scattering by Lossy Dielectric Surfaces with PBTG Method 3264.1 Introduction 3264.2 Formulation and Single Grid Implementation 3284.3 Physics-Based Two-Grid Method 3294.4 Numerical Results and Comparison with Second Order Perturbation Method 3344.5 Numerical Simulations of Emissivity of Soils with Rough Surfaces at Microwave Frequencies 3435 Four Stokes Parameters Based on Tangential Surface Fields 3506 Parallel Implementation of SMCG on Low Cost Beowulf System 3546.1 Introduction 3546.2 Low-Cost Beowulf Cluster 3556.3 Parallel Implementation of the SMCG Method and the PBTG Method 3566.4 Numerical Results 360References and Additional Readings 366CHAPTER 7 VOLUME SCATTERING SIMULATIONS 3711 Combining Simulations of Collective Volume Scattering Effects with Radiative Transfer Theory 3732 Foldy-Lax Self-Consistent Multiple Scattering Equations 3762.1 Final Exciting Field and Multiple Scattering Equation 3762.2 Foldy-Lax Equations for Point Scatterers 3792.3 The JV-Particle Scattering Amplitude 3823 Analytical Solutions of Point Scatterers 3823.1 Phase Function and Extinction Coefficient for Uniformly Distributed Point Scatterers 3823.2 Scattering by Collection of Clusters 3894 Monte Carlo Simulation Results of Point Scatterers 392References and Additional Readings 401CHAPTER 8 PARTICLE POSITIONS FOR DENSE MEDIA CHARACTERIZATIONS AND SIMULATIONS 4031 Pair Distribution Functions and Structure Factors 4041.1 Introduction 4041.2 Percus Yevick Equation and Pair Distribution Function for Hard Spheres 4061.3 Calculation of Structure Factor and Pair Distribution Function 4092 Percus—Yevick Pair Distribution Functions for Multiple Sizes 4113 Monte Carlo Simulations of Particle Positions 4143.1 Metropolis Monte Carlo Technique 4153.2 Sequential Addition Method 4183.3 Numerical Results 4184 Sticky Particles 4244.1 Percus-Yevick Pair Distribution Function for Sticky Spheres 4244.2 Pair Distribution Function of Adhesive Sphere Mixture 4294.3 Monte Carlo Simulation of Adhesive Spheres 4345 Particle Placement Algorithm for Spheroids 4445.1 Contact Functions of Two Ellipsoids 4455.2 Illustrations of Contact Functions 446References and Additional Readings 450CHAPTER 9 SIMULATIONS OF TWO-DIMENSIONAL DENSE MEDIA 4531 Introduction 4541.1 Extinction as a Function of Concentration 4541.2 Extinction as a Function of Frequency 4562 Random Positions of Cylinders 4582.1 Monte Carlo Simulations of Positions of Hard Cylinders 4582.2 Simulations of Pair Distribution Functions 4602.3 Percus-Yevick Approximation of Pair Distribution Functions 4612.4 Results of Simulations 4632.5 Monte Carlo Simulations of Sticky Disks 4633 Monte Carlo Simulations of Scattering by Cylinders 4693.1 Scattering by a Single Cylinder 4693.2 Foldy-Lax Multiple Scattering Equations for Cylinders 4763.3 Coherent Field, Incoherent Field, and Scattering Coefficient 4803.4 Scattered Field and Internal Field Formulations 4813.5 Low Frequency Formulas 4823.6 Independent Scattering 4843.7 Simulation Results for Sticky and Non-Sticky Cylinders 4854 Sparse-Matrix Canonical-Grid Method for Scattering by Many Cylinders 4864.1 Introduction 4864.2 The Two-Dimensional Scattering Problem of Many Dielectric Cylinders 4894.3 Numerical Results of Scattering and CPU Comparisons 490References and Additional Readings 493CHAPTER 10 DENSE MEDIA MODELS AND THREE-DIMENSIONAL SIMULATIONS 4951 Introduction 4962 Simple Analytical Models For Scattering From a Dense Medium 4962.1 Effective Permittivity 4962.2 Scattering Attenuation and Coherent Propagation Constant 5002.3 Coherent Reflection and Incoherent Scattering From a Half-Space of Scatterers 5052.4 A Simple Dense Media Radiative Transfer Theory 5103 Simulations Using Volume Integral Equations 5123.1 Volume Integral Equation 5123.2 Simulation of Densely Packed Dielectric Spheres 5143.3 Densely Packed Spheroids 5184 Numerical Simulations Using T-Matrix Formalism 5334.1 Multiple Scattering Equations 5334.2 Computational Considerations 5414.3 Results and Comparisons with Analytic Theory 5454.4 Simulation of Absorption Coefficient 547References and Additional Readings 548CHAPTER 11 ANGULAR CORRELATION FUNCTION AND DETECTION OF BURIED OBJECT 5511 Introduction 5522 Two-Dimensional Simulations of Angular Memory Effect and Detection of Buried Object 5532.1 Introduction 5532.2 Simple and General Derivation of Memory Effect 5532.3 ACF of Random Rough Surfaces with Different Averaging Methods 5552.4 Scattering by a Buried Object Under a Rough Surface 5573 Angular Correlation Function of Scattering by a Buried Object Under a 2-D Random Rough Surface (3-D Scattering) 5643.1 Introduction 5643.2 Formulation of Integral Equations 5653.3 Statistics of Scattered Fields 5703.4 Numerical Illustrations of ACF and PACF 5714 Angular Correlation Function Applied to Correlation Imaging in Target Detection 5754.1 Introduction 5754.2 Formulation of Imaging 5784.3 Simulations of SAR Data and ACF Processing 580References and Additional Readings 591CHAPTER 12 MULTIPLE SCATTERING BY CYLINDERS IN THE PRESENCE OF BOUNDARIES 5931 Introduction 5942 Scattering by Dielectric Cylinders Above a Dielectric Half-Space 5942.1 Scattering from a Layer of Vertical Cylinders: First-Order Solution 5942.2 First- and Second-Order Solutions 6032.3 Results of Monte Carlo Simulations 6133 Scattering by Cylinders in the Presence of Two Reflective Boundaries 6223.1 Vector Cylindrical Wave Expansion of Dyadic Green's Function Between Two Perfect Conductors 6223.2 Dyadic Green's Function of a Cylindrical Scatterer Between Two PEC 6293.3 Dyadic Green's Function with Multiple Cylinders 6313.4 Excitation of Magnetic Ring Currents 6353.4.1 First Order Solution 6373.4.2 Numerical Results 638References and Additional Readings 640CHAPTER 13 ELECTROMAGNETIC WAVES SCATTERING BY VEGETATION 6411 Introduction 6422 Plant Modeling by Using L-Systems 6442.1 Lindenmayer Systems 6442.2 Turtle Interpretation of L-Systems 6462.3 Computer Simulations of Stochastic L-Systems and Input Files 6493 Scattering from Trees Generated by L-Systems Based on Coherent Addition Approximation 6543.1 Single Scattering by a Particle in the Presence of Reflective Boundary 6553.1.1 Electric Field and Dyadic Green's Function 6553.1.2 Scattering by a Single Particle 6563.2 Scattering by Trees 6594 Coherent Addition Approximation with Attenuation 6675 Scattering from Plants Generated by L-Systems Based on Discrete Dipole Approximation 6695.1 Formulation of Discrete Dipole Approximation (DDA) Method 6705.2 Scattering by Simple Trees 6725.3 Scattering by Honda Trees 6776 Rice Canopy Scattering Model 6856.1 Model Description 6856.2 Model Simulation 689References and Additional Readings 691INDEX 693

"this graduate textbook presents numerical simulation techniques and results for electromagnetic wave scattering in random media and rough surfaces..." (SciTech Book News, Vol. 25, No. 3, September 2001)