Analysis Methods for Electromagnetic Wave Problems

v. 1

By: Eikichi Yamashita (Editor)

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Hardcover | 1 June 1990

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432 Pages

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23.5 x 15.88 x 3.18

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Instructs advanced and important analysis methods which are frequently used for researchers, engineers and students who work on applications of electromagnetic waves to microwave devices and antennas. The book also includes various numerical techniques.

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Non-Fiction Engineering & Technology Energy Technology & Engineering Electrical Engineering Science Physics Electricity Electronics & Communications Engineering Communications Engineering & Telecommunications Electronics Engineering Microwave Technology

Preface	p. xiii
The Authors	p. xv
The Finite-Element Method	p. 1
Historical Background	p. 1
The Range of Applications	p. 2
Elementary Ideas of the Finite-Element Method	p. 4
Outline of Finite-Element Calculations	p. 5
Elements	p. 8
Applications to Waveguide Problems	p. 10
Vectorial Wave Analysis by the One-Dimensional, Finite-Element Method	p. 12
Vectorial Wave Analysis by the Two-Dimensional, Finite-Element Method	p. 13
Treatment of Infinite Regions	p. 27
Some Precautions for Programming	p. 29
References	p. 30
The Boundary-Element Method	p. 33
Introduction	p. 33
Historical Background	p. 33
Limitations of the Method	p. 34
Integral Representations	p. 35
Two-Dimensional Problems	p. 35
Fields Due to Source Distributions	p. 39
General Vector-Field Problems	p. 40
Integral Equations	p. 45
Expressions with the Observation Point Taken on the Boundary	p. 46
Fundamental Integral Equations	p. 52
Notes on the Involvement of Resonant Solutions	p. 60
Numerical Calculation of Integral Equations	p. 62
Discretization Methods of the Boundary-Element Method	p. 62
Discretization of Integral Equations and Derivation of Matrix Equations	p. 63
Numerical Calculation of Elements of Coefficient Matrices	p. 69
Some Precautions for Programming and Numerical Calculation	p. 74
References	p. 76
The Point-Matching Method	p. 79
Historical Background	p. 79
Characteristics of the Method and Range of Application	p. 80
Homogeneous Dielectric Waveguides Having the Cross Section of Arbitrary Boundary	p. 81
Basic Equations	p. 81
Electromagnetic Fields of Dielectric Waveguides	p. 82
Symmetry in the Waveguide Cross Section	p. 84
Application of the Point-Matching Method	p. 85
Boundary Condition Matrices	p. 86
Designation of Propagation Modes	p. 88
Numerical Analysis of Dielectric Waveguides Having the Cross Section of a Chipped Circle Boundary	p. 89
Composite Dielectric Waveguides	p. 95
Composite Dielectric Waveguides with Cross Sections Composed of Fan-Shaped Boundaries	p. 95
Composite Dielectric Waveguides with Cross Sections Composed of Elliptical Boundaries	p. 98
Coupled Dielectric Waveguides	p. 100
Coupled Dielectric Waveguides Composed of Two Waveguides	p. 100
Coupled Dielectric Waveguides Composed of Multiple Waveguides	p. 102
Some Precautions for Programming	p. 103
Conclusion	p. 105
References	p. 105
The Mode-Matching Method	p. 107
Introduction	p. 107
Formulation of Scattering by Cylindrical Obstacles	p. 108
Two-Dimensional Scattering Problems	p. 108
Scattered Far Fields	p. 111
A Conventional Mode-Matching Method	p. 112
Modal Functions and Approximate Wave Function	p. 112
Method of Solution: E-Wave Case	p. 113
Definition of Errors	p. 114
Some Precautions for Numerical Computation	p. 116
Method of Solution: H-Wave Case	p. 117
A Smoothing Procedure	p. 117
Approximation of [characters not producible]	p. 118
Smoothing Procedure	p. 118
Definition of Errors	p. 120
Some Precautions on Using the MMM with the SP	p. 121
Computing the Near Field	p. 121
Method of Solution: H-Wave Case	p. 121
A Singular-Smoothing Procedure	p. 122
E-Wave Scattering by an Edged Scatterer	p. 122
Singular-Smoothing Procedure	p. 123
Some Precautions on Numerical Computations	p. 125
Numerical Examples	p. 125
Scattering by a Periodic Deformed Cylinder	p. 125
Diffraction by a Fourier Grating	p. 127
Diffraction by an Echelette Grating	p. 132
Conclusion	p. 132
A General Expression and Some Examples of Modal Functions	p. 133
Derivation of Equation (4.55)	p. 134
Iterated Kernel K[subscript p](s,t)	p. 135
Application of the Orthogonal Decomposition Methods	p. 135
References	p. 137
The Spatial Network Method	p. 139
Introduction	p. 139
The Range of Applications	p. 141
Spatial Network for Three-Dimensional Maxwell's Equation	p. 142
The Bergeron Method	p. 152
Bergeron's Expression in the Three-Dimensional Spatial Network	p. 160
Analyzed Results and Discussion	p. 165
The Boundary Condition of the conductor System	p. 165
Treatment of Dielectric Materials	p. 167
Treatment of the Free Boundary	p. 167
Analyzed Results	p. 169
Some Precautions for Programming	p. 174
References	p. 175
The Equivalent Source Method	p. 177
Historical Background and Applications	p. 177
Basic Theory of the Equivalent Source Method	p. 180
Approximated Wave Function for the Equivalent Source Method	p. 181
Boundary Conditions and Scattered Field	p. 186
Error Estimation of the Scattered Field	p. 188
Optimum Arrangement of Equivalent Sources	p. 189
Application to Analyses of an Electromagnetic Field Scattered by Perfect-Conducting Cylinders	p. 191
Numerical Examples by the Linear-Search Method	p. 191
Numerical Examples Obtained by Nonlinear Optimization	p. 195
Practical Analyses of the Scattered Field from Dielectric Cylinders	p. 199
Approximate Wave Functions for Dielectric Region and Boundary Conditions	p. 199
Numerical Examples of the Scattered Field from Lossless Dielectric Cylinders	p. 201
Numerical Examples of the Scattered Field from Lossy Dielectric Cylinders	p. 203
Some Precautions for Programming	p. 208
References	p. 211
The Geometrical Theory of Diffraction	p. 213
High-Frequency Approximation of Electromagnetic Field and Geometrical Theory of Diffraction	p. 213
Historical Background	p. 213
The Range of Applications	p. 214
Geometrical Optics	p. 214
Canonical Problems	p. 217
Keller's GTD	p. 223
Application of GTD and Its Defects	p. 227
GTD for Diffraction from a Circular Disk	p. 227
Diffraction from a Sphere	p. 230
Defects of GTD	p. 232
Improvements for Keller's GTD	p. 233
Improvements to Diffraction Coefficients	p. 233
Method of Equivalent Edge Currents	p. 235
Modified Physical Theory of Diffraction	p. 239
Radiation Pattern Analysis of Reflector Antennas	p. 241
Some Precautions for Programming	p. 242
References	p. 243
The Wiener-Hopf and Modified Residue Calculus Techniques	p. 245
Introduction	p. 245
Historical Background	p. 245
Range of Applications	p. 247
Mathematical Preliminaries from the Theory of Fourier Integrals and Functions of a Complex Variable	p. 249
Complex Fourier Integrals	p. 249
Asymptotic Behavior of the Complex Fourier Integrals	p. 251
Decomposition and Factorization of Functions	p. 253
Saddle-Point Method	p. 255
Wiener-Hopf Technique	p. 257
Diffraction by a Semiinfinite Plate	p. 259
Radiation Condition and Edge Condition	p. 259
Formulation of the Problem	p. 261
Exact Solution of the Wiener-Hopf Equation	p. 265
Scattered-Field Representations	p. 266
Diffraction by a Strip	p. 271
Formulation of the Problem	p. 272
Formal Solution of the Wiener-Hopf Equation	p. 274
High-Frequency Asymptotic Solution	p. 277
Scattered Far Field	p. 280
Diffraction by a Thick Semiinfinite Plate	p. 282
Transformed-Wave Equations	p. 283
Simultaneous Wiener-Hopf Equations	p. 284
Factorization of Kernel Functions	p. 287
Formal Solutions	p. 288
Application of the Modified Residue-Calculus Technique	p. 290
Determination of Zeros	p. 293
Scattered Far Field	p. 295
Concluding Remarks	p. 297
References	p. 298
Asymptotic Expansion Methods	p. 303
Historical Background	p. 303
Mathematical Foundations of Asymptotic Expansions	p. 304
Definition of Asymptotic Expansions	p. 304
Liouville-Green Asymptotic Expansions	p. 306
The Airy Function	p. 307
The Method of Matching by Gans	p. 311
Formalism by Wentzel, Kramers, and Brillouin (WKB Method)	p. 313
Higher-Order Asymptotic Solutions	p. 315
Langer Transformation	p. 315
Froman-Froman Method	p. 316
Uniform Asymptotic Solutions	p. 318
Eigenvalue Problems	p. 319
Wentzel-Dunham Quantum Condition	p. 319
Froman-Froman Quantum Condition	p. 321
Maslov-Argyres Regularization	p. 322
Uniform Asymptotic-Perturbational Method	p. 323
Felsen Series	p. 324
Multiple Scattering Expansions	p. 325
Solutions of Coupled Equations	p. 325
Multilayer Solutions	p. 329
The Invariant Imbedding Approach	p. 331
Asymptotic Expansions in an Optical Waveguide System	p. 332
Significance of Expansions and the Range of Applications	p. 338
References and Bibliography	p. 339
The Beam Propagation Method	p. 341
Introduction	p. 341
Historical Background	p. 341
Features of BPM	p. 341
Computing Technology	p. 342
Construction of this Chapter	p. 342
Basis of the Beam Propagation Method	p. 342
Optical Planar Circuits	p. 342
Principle of BPM	p. 347
BPM in Three-Dimensional Media and Fresnel-Type Approximation	p. 351
BPM Formulation of Three-Dimensional Helmholtz Equation	p. 351
BPM Formula Based on the Fresnel Equation	p. 354
Propagation Constants Obtained From Fresnel and Hemholz Equations	p. 356
BPM in Anisotropic Media	p. 357
Basic Equations	p. 357
Basic Variables and Assumptions	p. 358
Formulation for BPM	p. 358
Cases When Refractive-Index Variations in x- and y-Directions are Different	p. 361
Examples of Calculation Results	p. 361
Cases in Isotropic Media	p. 361
Cases in Anisotropic Media	p. 363
Conclusion	p. 368
References and Bibliography	p. 368
The Spectral Domain Method	p. 371
Historical Background	p. 371
Characteristics of the Method and the Range of Applications	p. 372
Spectral Domain Method Based on the Electromagnetic-Field Expansions	p. 373
Galerkin's Method of Solution	p. 380
Characteristic Impedance	p. 383
Immitance Method	p. 386
Some Precautions for Programming	p. 396
Symmetry	p. 396
Convergence	p. 397
Other Precautions	p. 397
Conclusions	p. 397
References	p. 398
Bibliography	p. 399
Index	p. 411
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Analysis Methods for Electromagnetic Wave Problems

v. 1

At a Glance

Hardcover

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