Spheroidal Wave Functions in Electromagnetic Theory (Wiley Series in Microwave and Optical Engineering)

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Spheroidal Wave Functions in Electromagnetic Theory (Wiley Series in Microwave and Optical Engineering)

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  • 製本 Hardcover:ハードカバー版/ページ数 295 p.
  • 言語 ENG
  • 商品コード 9780471031703
  • DDC分類 530.141

Full Description


The flagship monograph addressing the spheroidal wave function and its pertinence to computational electromagnetics Spheroidal Wave Functions in Electromagnetic Theory presents in detail the theory of spheroidal wave functions, its applications to the analysis of electromagnetic fields in various spheroidal structures, and provides comprehensive programming codes for those computations. The topics covered in this monograph include: Spheroidal coordinates and wave functions Dyadic Green's functions in spheroidal systems EM scattering by a conducting spheroid EM scattering by a coated dielectric spheroid Spheroid antennas SAR distributions in a spheroidal head model The programming codes and their applications are provided online and are written in Mathematica 3.0 or 4.0. Readers can also develop their own codes according to the theory or routine described in the book to find subsequent solutions of complicated structures. Spheroidal Wave Functions in Electromagnetic Theory is a fundamental reference for scientists, engineers, and graduate students practicing modern computational electromagnetics or applied physics.

Table of Contents

Preface                                            v
Acknowledgments vii
Introduction 1 (12)
Overview 1 (3)
EM Scattering by Spheroids 4 (1)
Spheroidal Antenna 5 (2)
EM Radiation in Dielectric Spheroids 7 (1)
Oblate Spheroidal Models 8 (1)
Spheroidal Cavity System 9 (1)
Spheroidal Harmonics and Mathematica 10 (3)
Software
Spheroidal Coordinates and Wave Functions 13 (48)
Spheroidal Coordinate Systems 13 (4)
Spheroidal Scalar Wave Functions 17 (1)
Spheroidal Angular Harmonics 18 (4)
Series Representation in Terms of 18 (2)
Associated Legendre Functions
Power Series Representation 20 (2)
Eigenvalues λmn and Expansion 22 (5)
Coefficients drmn
Case I:|c|2 ≤ 1000 23 (3)
Case II:|c|2 > 1000 26 (1)
Spheroidal Radial Harmonics 27 (8)
Series Representation in Terms of 27 (2)
Spherical Bessel Functions
Proportional Relations of Angular and 29 (1)
Radial Functions
Power and Legendre Functional Series 30 (5)
Representations
Derivatives of Spheroidal Functions 35 (1)
Derivatives of Angular Functions 35 (1)
Derivatives of Radial Functions 35 (1)
Numerical Calculations and Discussion 36 (8)
Mathematica Source Codes 36 (1)
Geometrical Features of Spheroidal 37 (1)
Functions
Tabulated Numerical Data: New Results and 37 (7)
Comparison
Spheroidal Vector Wave Functions 44 (17)
Dyadic Green's Functions in Spheroidal Systems 61 (28)
Dyadic Green's Functions 61 (2)
Fundamental Formulation 63 (3)
Unbounded Dyadic Green's Functions 66 (4)
Method of Separation of Variables 66 (1)
Unbounded Scalar Green's Function 67 (1)
Appropriate Spheroidal Vector Wave 68 (1)
Functions for Construction of DGFs
Unbounded Green's Dyadics 69 (1)
Scattering Green's Dyadics 70 (3)
Scattering Green's Dyadics in the Inner 71 (1)
Region (f = 1)
Scattering Green's Dyadics in the 71 (1)
Intermediate Regions (2 ≤ f ≤ N -1)
Scattering Green's Dyadics in the Outer 72 (1)
Region (f = N)
Determination of Scattering Coefficients 73 (13)
Nonorthogonality and Functional Expansion 73 (3)
Matrix Equation Systems 76 (10)
Convergence of the Solution 86 (3)
EM Scattering by a Conducting Spheroid 89 (26)
Geometry of the Problem 89 (1)
Incident and Scattered Fields 89 (3)
Transformation of Incident Fields to 92 (11)
Scattered Fields
Imposing the Boundary Conditions 92 (1)
TE Polarization for Oblique Incidence 93 (6)
TM Polarization for Oblique Incidence 99 (2)
Fields at Axial Incidence 101(1)
TE Fields with Incidence Angle 90° 102(1)
Far-Field Expressions 103(3)
Numerical Computation and Mathematica 106(2)
Source Codes
Results and Discussion 108(7)
EM Scattering by a Coated Dielectric Spheroid 115(30)
Geometry of the Problem 115(2)
Incident, Transmitted and Scattered Fields 117(2)
Relationship between Incident and Scattered 119(11)
Fields
Boundary Conditions 119(1)
TE Polarization for Nonaxial Incidence 119(9)
TM Polarization for Nonaxial Incidence 128(2)
Fields at Axial Incidence 130(1)
Numerical Computation and Mathematica 130(2)
Source Code
Results and Discussion 132(13)
Spheroidal Antennas 145(46)
Introduction 145(1)
Prolate Spheroidal Antenna 146(6)
Antenna Geometry 146(1)
Maxwell's Equations for the Spheroidal 146(2)
Antenna
Auxiliary Scalar Wave Function 148(1)
Imposing the Boundary Conditions 149(1)
Far-Field Expressions 150(1)
Numerical Computations and Mathematica 150(1)
Code
Results and Discussion 151(1)
Dielectric-coated Prolate Spheroidal Antenna 152(16)
Coated Dielectric Antenna Geometry 152(6)
Obtaining the Auxiliary Wave Functions 158(3)
Imposing the Boundary Conditions 161(1)
Numerical Computations 162(1)
Mathematica Code 163(2)
Results and Discussion 165(3)
Prolate Spheroidal Antenna enclosed in a 168(23)
Confocal Radome
Geometry of the Antenna with Radome 168(6)
Obtaining the Auxiliary Wave Functions 174(1)
Imposing the Boundary Conditions 174(2)
Numerical Computations 176(1)
Mathematica Code 177(2)
Results and Discussion 179(12)
SAR Distributions in a Spheroidal Head Model 191(36)
Introduction 191(1)
Multilayered Prolate Spheroidal Head Model 192(2)
Formulation of the Problem 194(2)
Expansions of EM Fields Using Spheroidal 194(1)
Wave Functions
EM Boundary Conditions for 195(1)
Multispheroidal Interfaces
Specific Absorption Rate 195(1)
Numerical Computation 196(1)
Results and Discussion 197(12)
Effects on Wire Antennas Due to the 209(9)
Presence of the Multilayered Spheroid
Numerical Results and Discussion 218(9)
Analysis of Rainfall Attenuation Using Oblate 227(18)
Raindrops
Introduction 227(3)
Rainfall Attenuation 227(1)
Raindrop Models in Different Sizes 228(1)
Oblate Spheroidal Raindrops 229(1)
Problem Formulation 230(8)
Geometry of the Problem 230(1)
Definition of the EM Field 230(4)
Boundary Conditions and Solution of 234(3)
Unknowns
Total Cross Section 237(1)
Size Parameters of Raindrops 238(1)
Radius-Independent Oblate Spheroid 238(1)
Raindrop
Radius-Dependent Oblate Spheroid Raindrop 238(1)
Numerical Calculation and Results 239(6)
EM Eigenfrequencies in a Spheroidal Cavity 245(10)
Introduction 245(1)
Theory and Formulation 246(3)
Background Theory 246(1)
Derivation 247(2)
Numerical Results for TE Modes 249(3)
Numerical Calculation 249(1)
Results and Comparison 250(2)
Numerical Results for TM Modes 252(2)
Numerical Calculation 252(1)
Results and Comparison 252(2)
Discussion 254(1)
Appendix A Expressions of Spheroidal Vector 255(8)
Wave Functions
Appendix B Intermediates Imnt,l (C) in Closed 263(10)
Form
B.1 The Case where m ≥ 1 264(5)
B.2 The Case where m = 0 269(4)
Appendix C uq(i),t and vq(i),t Used in the 273(4)
Matrix Equation System
References 277(15)
Index 292