电磁场的理论与计算 IEEE Jin, Jian-Ming.pdf

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CONTENTS
Preface xv
Acknowledgments xxi
PART I Electromagnetic Field Theory 1
1 Basic Electromagnetic Theory 3
1.1 Review of Vector Analysis, 3
1.1.1 Vector Operations and Integral Theorems, 4
1.1.2 Symbolic Vector Method, 6
1.1.3 Helmholtz Decomposition Theorem, 9
1.1.4 Green’s Theorems, 9
1.2 Maxwell’s Equations in Terms of Total Charges and Currents, 11
1.2.1 Maxwell’s Equations in Integral Form, 12
1.2.2 Maxwell’s Equations in Differential Form, 17
1.2.3 Current Continuity Equation, 17
1.2.4 The Lorentz Force Law, 18
1.3 Constitutive Relations, 18
1.3.1 Electric Polarization, 19
1.3.2 Magnetization, 21
1.3.3 Electric Conduction, 22
1.3.4 Classification of Media, 23
1.4 Maxwell’s Equations in Terms of Free Charges and Currents, 25
vi CONTENTS
1.5 Boundary Conditions, 27
1.6 Energy, Power, and Poynting’s Theorem, 31
1.7 Time-Harmonic Fields, 33
1.7.1 Time-Harmonic Fields, 33
1.7.2 Fourier Transforms, 35
1.7.3 Complex Power, 37
1.7.4 Complex Permittivity and Permeability, 42
References, 46
Problems, 46
2 Electromagnetic Radiation in Free Space 53
2.1 Scalar and Vector Potentials, 53
2.1.1 Static Fields, 54
2.1.2 Time-Harmonic Fields and the Lorenz Gauge Condition, 58
2.2 Solution of Vector Potentials in Free Space, 61
2.2.1 Delta Function and Green’s Function, 61
2.2.2 Green’s Function in Free Space, 62
2.2.3 Field–Source Relations in Free Space, 63
2.2.4 Why Use Auxiliary Potential Functions, 64
2.2.5 Free-Space Dyadic Green’s Functions, 66
2.3 Electromagnetic Radiation in Free Space, 69
2.3.1 Infinitesimal Electric Dipole, 69
2.3.2 Finite Electric Dipole, 72
2.3.3 Far-Field Approximation and the Sommerfeld Radiation
Condition, 73
2.3.4 Circular Current Loop and Magnetic Dipole, 76
2.4 Radiation by Surface Currents and Phased Arrays, 78
2.4.1 Radiation by a Surface Current, 78
2.4.2 Radiation by a Phased Array, 81
References, 84
Problems, 85
3 Electromagnetic Theorems and Principles 89
3.1 Uniqueness Theorem, 90
3.2 Image Theory, 94
3.2.1 Basic Image Theory, 94
3.2.2 Half-Space Field–Source Relations, 99
3.3 Reciprocity Theorems, 101
3.3.1 General Reciprocity Theorem, 101
3.3.2 Lorentz Reciprocity Theorem, 102
3.3.3 Rayleigh–Carson Reciprocity Theorem, 103
3.4 Equivalence Principles, 107
3.4.1 Surface Equivalence Principle, 107
3.4.2 Application to Scattering by a Conducting Object, 109
3.4.3 Application to Scattering by a Dielectric Object, 114
3.4.4 Volume Equivalence Principle, 116
CONTENTS vii
3.5 Duality Principle, 120
3.6 Aperture Radiation and Scattering, 121
3.6.1 Equivalent Problems, 121
3.6.2 Babinet’s Principle, 124
3.6.3 Complementary Antennas, 127
References, 128
Problems, 129
4 Transmission Lines and Plane Waves 135
4.1 Transmission Line Theory, 135
4.1.1 Governing Differential Equations and General Solutions, 135
4.1.2 Reflection and Transmission, 138
4.1.3 Green’s Function and Eigenfunction Expansion, 140
4.2 Wave Equations and General Solutions, 144
4.2.1 Wave Equations and Solution by Separation of Variables, 144
4.2.2 Characteristics of a Plane Wave, 146
4.2.3 Wave Velocities and Attenuation, 147
4.2.4 Linear, Circular, and Elliptical Polarizations, 151
4.2.5 Wave Propagation in Metamaterials, 154
4.3 Plane Waves Generated by a Current Sheet, 156
4.4 Reflection and Transmission, 159
4.4.1 Reflection and Transmission at Normal Incidence, 159
4.4.2 Reflection and Transmission at Oblique Incidence, 161
4.4.3 Total Transmission and Total Reflection, 164
4.4.4 Transmission into a Left-Handed Medium, 168
4.4.5 Plane Waves Versus Transmission Lines, 170
4.5 Plane Waves in Anisotropic and Bi-Isotropic Media, 174
4.5.1 Plane Waves in Uniaxial Media, 174
4.5.2 Plane Waves in Gyrotropic Media, 179
4.5.3 Plane Waves in Chiral Media, 183
References, 190
Problems, 191
5 Fields and Waves in Rectangular Coordinates 199
5.1 Uniform Waveguides, 199
5.1.1 General Analysis, 200
5.1.2 General Characteristics, 204
5.1.3 Uniform Rectangular Waveguide, 208
5.1.4 Losses in Waveguides and Attenuation Constant, 215
5.2 Uniform Cavities, 220
5.2.1 General Theory, 221
5.2.2 Rectangular Cavity, 223
5.2.3 Material and Geometry Perturbations, 226
5.3 Partially Filled Waveguides and Dielectric Slab Waveguides, 229
5.3.1 General Theory, 229
5.3.2 Partially Filled Rectangular Waveguide, 231
5.3.3 Dielectric Slab Waveguide on a Ground Plane, 236
viii CONTENTS
5.4 Field Excitation in Waveguides, 241
5.4.1 Excitation by Planar Surface Currents, 242
5.4.2 Excitation by General Volumetric Currents, 243
5.5 Fields in Planar Layered Media, 245
5.5.1 Spectral Green’s Function and Sommerfeld Identity, 245
5.5.2 Vertical Electric Dipole above a Layered Medium, 247
5.5.3 Horizontal Electric Dipole above a Layered Medium, 249
5.5.4 Dipoles on a Grounded Dielectric Slab, 251
References, 257
Problems, 257
6 Fields and Waves in Cylindrical Coordinates 261
6.1 Solution of Wave Equation, 261
6.1.1 Solution by Separation of Variables, 262
6.1.2 Cylindrical Wave Functions, 263
6.2 Circular and Coaxial Waveguides and Cavities, 266
6.2.1 Circular Waveguide, 267
6.2.2 Coaxial Waveguide, 273
6.2.3 Cylindrical Cavity, 276
6.3 Circular Dielectric Waveguide, 279
6.3.1 Analysis of Hybrid Modes, 279
6.3.2 Characteristics of Hybrid Modes, 283
6.4 Wave Transformation and Scattering Analysis, 287
6.4.1 Wave Transformation, 288
6.4.2 Scattering by a Circular Conducting Cylinder, 289
6.4.3 Scattering by a Circular Dielectric Cylinder, 293
6.4.4 Scattering by a Circular Multilayer Dielectric Cylinder, 296
6.5 Radiation by Infinitely Long Currents, 300
6.5.1 Line Current Radiation in Free Space, 300
6.5.2 Radiation by a Cylindrical Surface Current, 304
6.5.3 Radiation in the Presence of a Circular Conducting Cylinder, 306
6.5.4 Radiation in the Presence of a Conducting Wedge, 309
6.5.5 Radiation by a Finite Current, 312
References, 319
Problems, 320
7 Fields and Waves in Spherical Coordinates 325
7.1 Solution of Wave Equation, 325
7.1.1 Solution by Separation of Variables, 325
7.1.2 Spherical Wave Functions, 328
7.1.3 TEr and TMr Modes, 329
7.2 Spherical Cavity, 331
7.3 Biconical Antenna, 335
7.3.1 Infinitely Long Model, 335
7.3.2 Finite Biconical Antenna, 339
7.4 Wave Transformation and Scattering Analysis, 341
7.4.1 Wave Transformation, 342
CONTENTS ix
7.4.2 Expansion of a Plane Wave, 344
7.4.3 Scattering by a Conducting Sphere, 347
7.4.4 Scattering by a Dielectric Sphere, 352
7.4.5 Scattering by a Multilayer Dielectric Sphere, 357
7.5 Addition Theorem and Radiation Analysis, 360
7.5.1 Addition Theorem for Spherical Wave Functions, 360
7.5.2 Radiation of a Spherical Surface Current, 362
7.5.3 Radiation in the Presence of a Sphere, 368
7.5.4 Radiation in the Presence of a Conducting Cone, 370
References, 377
Problems, 377
PART II Electromagnetic Field Computation 383
8 The Finite Difference Method 385
8.1 Finite Differencing Formulas, 385
8.2 One-Dimensional Analysis, 387
8.2.1 Solution of the Diffusion Equation, 387
8.2.2 Solution of the Wave Equation, 389
8.2.3 Stability Analysis, 390
8.2.4 Numerical Dispersion Analysis, 392
8.3 Two-Dimensional Analysis, 393
8.3.1 Analysis in the Time Domain, 393
8.3.2 Analysis in the Frequency Domain, 395
8.4 Yee’s FDTD Scheme, 397
8.4.1 Two-Dimensional Analysis, 397
8.4.2 Three-Dimensional Analysis, 399
8.5 Absorbing Boundary Conditions, 402
8.5.1 One-Dimensional ABC, 403
8.5.2 Two-Dimensional ABCs, 404
8.5.3 Perfectly Matched Layers, 406
8.6 Modeling of Dispersive Media, 417
8.6.1 Recursive Convolution Approach, 417
8.6.2 Auxiliary Differential Equation Approach, 420
8.7 Wave Excitation and Far-Field Calculation, 422
8.7.1 Modeling of Wave Excitation, 422
8.7.2 Near-to-Far-Field Transformation, 426
8.8 Summary, 427
References, 428
Problems, 429
9 The Finite Element Method 433
9.1 Introduction to the Finite Element Method, 434
9.1.1 The General Principle, 434
9.1.2 One-Dimensional Example, 435
x CONTENTS
9.2 Finite Element Analysis of Scalar Fields, 439
9.2.1 The Boundary-Value Problem, 439
9.2.2 Finite Element Formulation, 440
9.2.3 Application Examples, 446
9.3 Finite Element Analysis of Vector Fields, 450
9.3.1 The Boundary-Value Problem, 450
9.3.2 Finite Element Formulation, 452
9.3.3 Application Examples, 456
9.4 Finite Element Analysis in the Time Domain, 465
9.4.1 The Boundary-Value Problem, 465
9.4.2 Finite Element Formulation, 466
9.4.3 Application Examples, 470
9.5 Discontinuous Galerkin Time-Domain Method, 472
9.5.1 Basic Idea, 473
9.5.2 Central-Flux DGTD Method, 475
9.5.3 Upwind-Flux DGTD Method, 478
9.5.4 Application Example, 481
9.6 Absorbing Boundary Conditions, 483
9.6.1 Two-Dimensional ABCs, 483
9.6.2 Three-Dimensional ABCs, 486
9.6.3 Perfectly Matched Layers, 488
9.7 Some Numerical Aspects, 494
9.7.1 Mesh Generation, 494
9.7.2 Matrix Solvers, 494
9.7.3 Higher-Order Elements, 495
9.7.4 Curvilinear Elements, 496
9.7.5 Adaptive Finite Element Analysis, 496
9.8 Summary, 497
References, 497
Problems, 499
10 The Method of Moments 505
10.1 Introduction to the Method of Moments, 506
10.2 Two-Dimensional Analysis, 510
10.2.1 Formulation of Integral Equations, 510
10.2.2 Scattering by a Conducting Cylinder, 514
10.2.3 Scattering by a Conducting Strip, 518
10.2.4 Scattering by a Homogeneous Dielectric Cylinder, 522
10.3 Three-Dimensional Analysis, 523
10.3.1 Formulation of Integral Equations, 523
10.3.2 Scattering and Radiation by a Conducting Wire, 528
10.3.3 Scattering by a Conducting Body, 532
10.3.4 Scattering by a Homogeneous Dielectric Body, 538
10.3.5 Scattering by an Inhomogeneous Dielectric Body, 542
10.4 Analysis of Periodic Structures, 544
10.4.1 Scattering by a Planar Periodic Conducting Patch Array, 544
10.4.2 Scattering by a Discrete Body-of-Revolution Object, 549
CONTENTS xi
10.5 Analysis of Microstrip Antennas and Circuits, 551
10.5.1 Formulation of Integral Equations, 552
10.5.2 The Moment-Method Solution, 556
10.5.3 Evaluation of Green’s Functions, 556
10.5.4 Far-Field Calculation and Application Examples, 561
10.6 The Moment Method in the Time Domain, 561
10.6.1 Time-Domain Integral Equations, 563
10.6.2 Marching-On-in-Time Solution, 564
10.7 Summary, 568
References, 568
Problems, 571
11 Fast Algorithms and Hybrid Techniques 575
11.1 Introduction to Fast Algorithms, 576
11.2 Conjugate Gradient–FFT Method, 578
11.2.1 Scattering by a Conducting Strip or Wire, 578
11.2.2 Scattering by a Conducting Plate, 579
11.2.3 Scattering by a Dielectric Object, 585
11.3 Adaptive Integral Method, 591
11.3.1 Planar Structures, 592
11.3.2 Three-Dimensional Objects, 596
11.4 Fast Multipole Method, 602
11.4.1 Two-Dimensional Analysis, 602
11.4.2 Three-Dimensional Analysis, 606
11.4.3 Multilevel Fast Multipole Algorithm, 610
11.5 Adaptive Cross-Approximation Algorithm, 614
11.5.1 Low-Rank Matrix, 615
11.5.2 Adaptive Cross-Approximation, 617
11.5.3 Application to the Moment-Method Solution, 619
11.6 Introduction to Hybrid Techniques, 623
11.7 Hybrid Finite Difference–Finite Element Method, 624
11.7.1 Relation Between FETD and FDTD, 625
11.7.2 Hybridization of FETD and FDTD, 627
11.7.3 Application Example, 629
11.8 Hybrid Finite Element–Boundary Integral Method, 630
11.8.1 Traditional Formulation, 631
11.8.2 Symmetric Formulation, 635
11.8.3 Numerical Examples, 638
11.9 Summary, 642
References, 643
Problems, 649
12 Concluding Remarks on Computational Electromagnetics 651
12.1 Overview of Computational Electromagnetics, 651
12.1.1 Frequency- Versus Time-Domain Analysis, 651
12.1.2 High-Frequency Asymptotic Techniques, 653
12.1.3 First-Principle Numerical Methods, 654
xii CONTENTS
12.1.4 Time-Domain Simulation Methods, 656
12.1.5 Hybrid Techniques, 658
12.2 Applications of Computational Electromagnetics, 659
12.3 Challenges in Computational Electromagnetics, 670
References, 671
Appendix A Vector Identities, Integral Theorems, and Coordinate
Transformation 681
A.1 Vector Identities, 681
A.2 Integral Theorems, 682
A.3 Coordinate Transformation, 682
Appendix B Bessel Functions 683
B.1 Definition, 683
B.2 Series Expressions, 683
B.3 Integral Representation, 685
B.4 Asymptotic Expressions, 685
B.5 Recurrence and Derivative Relations, 685
B.6 Symmetry Relations, 686
B.7 Wronskian Relation, 686
B.8 Useful Integrals, 686
Appendix C Modified Bessel Functions 687
C.1 Definition, 687
C.2 Series Expressions, 687
C.3 Integral Representations, 688
C.4 Asymptotic Expressions, 688
C.5 Recurrence and Derivative Relations, 689
C.6 Symmetry Relations, 690
C.7 Wronskian Relation, 690
C.8 Useful Integrals, 690
Appendix D Spherical Bessel Functions 691
D.1 Definition, 691
D.2 Series Expressions, 692
D.3 Asymptotic Expressions, 693
D.4 Recurrence and Derivative Relations, 693
D.5 Symmetry Relations, 694
D.6 Wronskian Relation, 695
D.7 Riccati–Bessel Functions, 695
D.8 Modified Spherical Bessel Functions, 695
Appendix E Associated Legendre Polynomials 697
E.1 Definition, 697
E.2 Series Expression, 698
CONTENTS xiii
E.3 Special Values, 700
E.4 Symmetry Relations, 701
E.5 Recurrence and Derivative Relations, 701
E.6 Orthogonal Relations, 702
E.7 Fourier–Legendre Series, 702
Index 703