Spheroidal wave functions in electromagnetic theory / Le-Wei Li, Xiao-Kang Kang, Mook-Seng Leong.

Format:

Book

Author/Creator:

Li, Le-Wei.

Contributor:

Kang, Xiao-Kang.

Leong, Mook-Seng.

Series:

Wiley series in microwave and optical engineering

Language:

English

Subjects (All):

Electromagnetic theory.

Spheroidal functions.

Physical Description:

xiii, 295 pages : illustrations ; 25 cm.

Place of Publication:

New York : Wiley, [2002]

Summary:

"Spheroidal Wave Functions in Electromagnetic Theory" is a fundamental reference for scientists, engineers, and graduate students practicing modern computational electromagnetics or applied physics.

Contents:

1.2 EM Scattering by Spheroids 4

1.3 Spheroidal Antenna 5

1.4 EM Radiation in Dielectric Spheroids 7

1.5 Oblate Spheroidal Models 8

1.6 Spheroidal Cavity System 9

1.7 Spheroidal Harmonics and Mathematica Software 10

2 Spheroidal Coordinates and Wave Functions 13

2.1 Spheroidal Coordinate Systems 13

2.2 Spheroidal Scalar Wave Functions 17

2.3 Spheroidal Angular Harmonics 18

2.3.1 Series Representation in Terms of Associated Legendre Functions 18

2.3.2 Power Series Representation 20

2.4 Eigenvalues [lambda subscript mn] and Expansion Coefficients d[superscript mn subscript r] 22

2.4.1 Case I: / |[superscript 2] [less than or equal] 1000 23

2.4.2 Case II: / |[superscript 2] > 1000 26

2.5 Spheroidal Radial Harmonics 27

2.5.1 Series Representation in Terms of Spherical Bessel Functions 27

2.5.2 Proportional Relations of Angular and Radial Functions 29

2.5.3 Power and Legendre Functional Series Representations 30

2.6 Derivatives of Spheroidal Functions 35

2.6.1 Derivatives of Angular Functions 35

2.6.2 Derivatives of Radial Functions 35

2.7 Numerical Calculations and Discussion 36

2.7.1 Mathematica Source Codes 36

2.7.2 Geometrical Features of Spheroidal Functions 37

2.7.3 Tabulated Numerical Data: New Results and Comparison 37

2.8 Spheroidal Vector Wave Functions 44

3 Dyadic Green's Functions in Spheroidal Systems 61

3.1 Dyadic Green's Functions 61

3.2 Fundamental Formulation 63

3.3 Unbounded Dyadic Green's Functions 66

3.3.1 Method of Separation of Variables 66

3.3.2 Unbounded Scalar Green's Function 67

3.3.3 Appropriate Spheroidal Vector Wave Functions for Construction of DGFs 68

3.3.4 Unbounded Green's Dyadics 69

3.4 Scattering Green's Dyadics 70

3.4.1 Scattering Green's Dyadics in the Inner Region (f = 1) 71

3.4.2 Scattering Green's Dyadics in the Intermediate Regions (2 [less than or equal] f [less than or equal] N - 1) 71

3.4.3 Scattering Green's Dyadics in the Outer Region (f = N) 72

3.5 Determination of Scattering Coefficients 73

3.5.1 Nonorthogonality and Functional Expansion 73

3.5.2 Matrix Equation Systems 76

3.6 Convergence of the Solution 86

4 EM Scattering by a Conducting Spheroid 89

4.1 Geometry of the Problem 89

4.2 Incident and Scattered Fields 89

4.3 Transformation of Incident Fields to Scattered Fields 92

4.3.1 Imposing the Boundary Conditions 92

4.3.2 TE Polarization for Oblique Incidence 93

4.3.3 TM Polarization for Oblique Incidence 99

4.3.4 Fields at Axial Incidence 101

4.3.5 TE Fields with Incidence Angle 90[degree] 102

4.4 Far-Field Expressions 103

4.5 Numerical Computation and Mathematica Source Codes 106

5 EM Scattering by a Coated Dielectric Spheroid 115

5.1 Geometry of the Problem 115

5.2 Incident, Transmitted and Scattered Fields 117

5.3 Relationship between Incident and Scattered Fields 119

5.3.1 Boundary Conditions 119

5.3.2 TE Polarization for Nonaxial Incidence 119

5.3.3 TM Polarization for Nonaxial Incidence 128

5.3.4 Fields at Axial Incidence 130

5.4 Numerical Computation and Mathematica Source Code 130

6 Spheroidal Antennas 145

6.2 Prolate Spheroidal Antenna 146

6.2.1 Antenna Geometry 146

6.2.2 Maxwell's Equations for the Spheroidal Antenna 146

6.2.3 Auxiliary Scalar Wave Function 148

6.2.4 Imposing the Boundary Conditions 149

6.2.5 Far-Field Expressions 150

6.2.6 Numerical Computations and Mathematica Code 150

6.3 Dielectric-coated Prolate Spheroidal Antenna 152

6.3.1 Coated Dielectric Antenna Geometry 152

6.3.2 Obtaining the Auxiliary Wave Functions 158

6.3.3 Imposing the Boundary Conditions 161

6.3.4 Numerical Computations 162

6.3.5 Mathematica Code 163

6.4 Prolate Spheroidal Antenna enclosed in a Confocal Radome 168

6.4.1 Geometry of the Antenna with Radome 168

6.4.2 Obtaining the Auxiliary Wave Functions 174

6.4.3 Imposing the Boundary Conditions 174

6.4.4 Numerical Computations 176

6.4.5 Mathematica Code 177

6.4.6 Results and Discussion 179

7 SAR Distributions in a Spheroidal Head Model 191

7.2 Multilayered Prolate Spheroidal Head Model 192

7.3 Formulation of the Problem 194

7.3.1 Expansions of EM Fields Using Spheroidal Wave Functions 194

7.3.2 EM Boundary Conditions for Multispheroidal Interfaces 195

7.3.3 Specific Absorption Rate 195

7.4 Numerical Computation 196

7.6 Effects on Wire Antennas Due to the Presence of the Multilayered Spheroid 209

7.7 Numerical Results and Discussion 218

8 Analysis of Rainfall Attenuation Using Oblate Raindrops 227

8.1.1 Rainfall Attenuation 227

8.1.2 Raindrop Models in Different Sizes 228

8.1.3 Oblate Spheroidal Raindrops 229

8.2 Problem Formulation 230

8.2.1 Geometry of the Problem 230

8.2.2 Definition of the EM Field 230

8.2.3 Boundary Conditions and Solution of Unknowns 234

8.2.4 Total Cross Section 237

8.3 Size Parameters of Raindrops 238

8.3.1 Radius-Independent Oblate Spheroid Raindrop 238

8.3.2 Radius-Dependent Oblate Spheroid Raindrop 238

8.4 Numerical Calculation and Results 239

9 EM Eigenfrequencies in a Spheroidal Cavity 245

9.2 Theory and Formulation 246

9.2.2 Derivation 247

9.3 Numerical Results for TE Modes 249

9.3.1 Numerical Calculation 249

9.4 Numerical Results for TM Modes 252

9.4.1 Numerical Calculation 252

9.4.2 Results and Comparison 252

Appendix A Expressions of Spheroidal Vector Wave Functions 255

Appendix B Intermediates I[superscript mn subscript t,e](c) in Closed Form 263

B.1 The Case where m [greater than or equal] 1 264

B.2 The Case where m = 0 269

Appendix C U[superscript q(i),t] and V[superscript q(i),t] Used in the Matrix Equation System 273.

Notes:

"A Wiley-Interscience publication."

Includes bibliographical references (pages 277-291) and index.

ISBN:

0471031704

OCLC:

47297702

Online:

Table of Contents