Electromagnetic Waves, Materials, and Computation with MATLAB

Electromagnetic Waves, Materials, and Computation with MATLAB
اسم المؤلف
Dikshitulu K. Kalluri
التاريخ
8 أكتوبر 2021
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Electromagnetic Waves, Materials, and Computation with MATLAB
Dikshitulu K. Kalluri
Contents
Preface xiii
Acknowledgments . xix
Author xxi
Selected.List.of.Symbols xxiii
List.of.Book.Sources xxv
Part I Electromagnetics of Bounded Simple Media
1 Electromagnetics of Simple Media 3
1.1. Introduction 3
1.2. Simple.Medium 4
1.3. Time-Domain.Electromagnetics 5
1.3.1. Radiation.by.an.Impulse.Current.Source 7
1.4. Time-Harmonic.Fields .9
1.5. Quasistatic.and.Static.Approximations 11
2 Electromagnetics of Simple Media: One-Dimensional Solution 13
2.1. Uniform.Plane.Waves.in.Sourceless.Medium.(ρV.=.0,.Jsource.=.0) . 13
2.2. Good.Conductor.Approximation 14
2.3. Uniform.Plane.Wave.in.a.Good.Conductor:.Skin.Effect 15
2.4. Boundary.Conditions.at.the.Interface.of.a.Perfect.Electric.
Conductor with a Dielectric . 15
2.5. AC.Resistance . 16
2.6. AC.Resistance.of.Round.Wires 18
2.7. Voltage.and.Current.Harmonic.Waves:.Transmission.Lines . 19
2.8. Bounded.Transmission.Line .23
2.9. Electromagnetic.Wave.Polarization 25
2.10. Arbitrary.Direction.of.Propagation .26
2.11. Wave.Reflection 27
2.12. Incidence.of.p.Wave:.Parallel-Polarized 28
2.13. Incidence.of.s.Wave:.Perpendicular-Polarized 30
2.14. Critical.Angle.and.Surface.Wave . 31
2.15. One-Dimensional.Cylindrical.Wave.and.Bessel.Functions .33
References 39
3 Two-Dimensional Problems and Waveguides 41
3.1. Two-Dimensional.Solutions.in.Cartesian.Coordinates 41
3.2. TM
mn.Modes.in.a.Rectangular.Waveguide .43
3.3. TE
mn.Modes.in.a.Rectangular.Waveguide 46
3.4. Dominant.Mode.in.a.Rectangular.Waveguide:.TE10.Mode .48
3.5. Power.Flow.in.a.Waveguide:.TE10.Mode .49
3.6. Attenuation.of.TE10.Mode.due.to.Imperfect.Conductors.and
. Dielectric Medium .49
3.7. Cylindrical.Waveguide:.TM.Modes 50vi Contents
3.8. Cylindrical.Waveguide:.TE.Modes 51
3.9. Sector.Waveguide . 52
3.10. Dielectric.Cylindrical.Waveguide—Optical.Fiber 53
References 56
4 Three-Dimensional Solutions 57
4.1. Rectangular.Cavity.with.PEC.Boundaries:.TM.Modes 57
4.2. Rectangular.Cavity.with.PEC.Boundaries:.TE.Modes .58
4.3. Q.of.a.Cavity .59
Reference 60
5 Spherical Waves and Applications . 61
5.1. Half-Integral.Bessel.Functions . 61
5.2. Solutions.of.Scalar.Helmholtz.Equation . 62
5.3. Vector.Helmholtz.Equation 64
5.4. TMr.Modes 65
5.5. TEr.Modes 66
5.6. Spherical.Cavity . 67
6 Laplace Equation: Static and Low-Frequency Approximations .71
6.1. One-Dimensional.Solutions .72
6.2. Two-Dimensional.Solutions .72
6.2.1. Cartesian.Coordinates 72
6.2.2. Circular.Cylindrical.Coordinates .78
6.3. Three-Dimensional.Solution 83
6.3.1. Cartesian.Coordinates 83
6.3.2. Cylindrical.Coordinates .84
6.3.3. Spherical.Coordinates 84
References 87
7 Miscellaneous Topics on Waves .89
7.1. Group.Velocity.vg .89
7.2. Green’s.Function .90
7.3. Network.Formulation 94
7.3.1. ABCD.Parameters .94
7.3.2. S.Parameters 97
7.4. Stop.Bands.of.a.Periodic.Media .99
7.5. Radiation . 102
7.5.1. Hertzian.Dipole . 105
7.5.2. Half-Wave.Dipole 106
7.5.3. Dipoles.of.Arbitrary.Length 108
7.5.4. Shaping.the.Radiation.Pattern 108
7.5.5. Antenna.Problem.as.a.Boundary.Value.Problem 109
7.5.6. Traveling.Wave.Antenna.and.Cerenkov.Radiation . 109
7.5.7. Small.Circular.Loop.Antenna . 110
7.5.8. Other.Practical.Radiating.Systems . 111
7.6. Scattering . 111
7.6.1. Cylindrical.Wave.Transformations 112
7.6.2. Calculation.of.Current.Induced.on.the.Cylinder . 112Contents vii
7.6.3. Scattering.Width . 114
7.7. Diffraction . 115
7.7.1. Magnetic.Current.and.Electric.Vector.Potential . 115
7.7.2. Far-Zone.Fields.and.Radiation.Intensity . 118
7.7.3. Elemental.Plane.Wave.Source.and.Radiation.Intensity 119
7.7.4. Diffraction.by.the.Circular.Hole . 120
References 122
Part II Electromagnetic Equations of Complex Media
8 Electromagnetic Modeling of Complex Materials 125
8.1. Volume.of.Electric.Dipoles 125
8.2. Frequency-Dependent.Dielectric.Constant 128
8.3. Modeling.of.Metals 130
8.4. Plasma.Medium . 131
8.5. Polarizability.of.Dielectrics 133
8.6. Mixing.Formula . 137
8.7. Good.Conductors.and.Semiconductors 138
8.8. Perfect.Conductors.and.Superconductors 140
8.9. Magnetic.Materials 147
References 152
9 Artificial Electromagnetic Materials . 153
9.1. Artificial.Dielectrics.and.Plasma.Simulation . 153
9.1.1. One-Dimensional.Artificial.Dielectric . 154
9.1.2. Experimental.Simulation.of.Loss-Free.Plasma.Medium 157
9.1.3. Experimental.Simulation.of.Lossy.Plasma.Medium . 158
9.1.4. Experimental.Simulation.of.Plasma.Using.Strip.Medium . 159
9.1.5. Experimental.Simulation.of.a.Warm.Plasma.Medium . 159
9.1.6. Comprehensive.Theory.of.Artificial.Dielectrics 160
9.2. Left-Handed.Materials 160
9.2.1. Electromagnetic.Properties.of.a.Left-Handed.Material 166
9.2.2. Boundary.Conditions,.Reflection,.and.Transmission 168
9.2.3. Artificial.Left-Handed.Materials 170
9.3. Chiral.Medium . 174
References 177
10 Waves in Isotropic Cold Plasma: Dispersive Medium 179
10.1. Basic.Equations . 179
10.2. Dielectric–Dielectric.Spatial.Boundary 182
10.3. Reflection.by.a.Plasma.Half-Space 185
10.4. Reflection.by.a.Plasma.Slab 187
10.5. Tunneling.of.Power.through.a.Plasma.Slab . 192
10.6. Inhomogeneous.Slab.Problem . 195
10.7. Periodic.Layers.of.Plasma . 196
10.8. Surface.Waves .200
10.9. Transient.Response.of.a.Plasma.Half-Space 204viii Contents
10.9.1. Isotropic.Plasma.Half-Space.s.Wave 204
10.9.2. Impulse.Response.of.Several.Other.Cases.
. Including.Plasma.Slab 206
10.10. Solitons 206
References 206
11 Spatial Dispersion and Warm Plasma .209
11.1. Waves.in.a.Compressible.Gas .209
11.2. Waves.in.Warm.Plasma . 211
11.3. Constitutive.Relation.for.a.Lossy.Warm.Plasma . 215
11.4. Dielectric.Model.of.Warm.Loss-Free.Plasma . 217
11.5. Conductor.Model.of.Warm.Lossy.Plasma 218
11.6. Spatial.Dispersion.and.Nonlocal.Metal.Optics . 219
11.7. Technical.Definition.of.Plasma.State .220
11.7.1. Temperate.plasma .220
11.7.2. Debye.Length,.Collective.Behavior,.and.
. Overall.Charge.Neutrality .220
11.7.3. Unneutralized.Plasma 221
References 221
12 Wave in Anisotropic Media and Magnetoplasma 223
12.1. Introduction 223
12.2. Basic.Field.Equations.for.a.Cold.Anisotropic.Plasma.Medium 223
12.3. One-Dimensional.Equations:.Longitudinal.Propagation.and.
. L and R Waves 224
12.4. One-Dimensional.Equations:.Transverse.Propagation:.O.Wave 229
12.5. One-Dimensional.Solution:.Transverse.Propagation:.X.Wave 229
12.6. Dielectric.Tensor.of.a.Lossy.Magnetoplasma.Medium 234
12.7. Periodic.Layers.of.Magnetoplasma .235
12.8. Surface.Magnetoplasmons 235
12.9. Surface.Magnetoplasmons.in.Periodic.Media .236
12.10. Permeability.Tensor .236
References 236
13 Optical Waves in Anisotropic Crystals . 239
13.1. Wave.Propagation.in.a.Biaxial.Crystal.along.the.Principal.Axes . 239
13.2. Propagation.in.an.Arbitrary.Direction . 241
13.3. Propagation.in.an.Arbitrary.Direction:.Uniaxial.Crystal 243
13.4. k-Surface 244
13.5. Group.Velocity.as.a.Function.of.Polar.Angle . 246
13.6. Reflection.by.an.Anisotropic.Half-Space 249
References 250
14 Electromagnetics of Moving Media 251
14.1. Introduction 251
14.2. Snell’s.Law . 251
14.3. Galilean.Transformation .253
14.4. Lorentz.Transformation 257
14.5. Lorentz.Scalars,.Vectors,.and.Tensors .259Contents ix
14.6. Electromagnetic.Equations.in.Four-Dimensional.Space 262
14.7. Lorentz.Transformation.of.the.Electromagnetic.Fields 266
14.8. Frequency.Transformation.and.Phase.Invariance 266
14.9. Reflection.from.a.Moving.Mirror 267
14.10. Constitutive.Relations.for.a.Moving.Dielectric .272
14.11. Relativistic.Particle.Dynamics . 273
14.12. Transformation.of.Plasma.Parameters 275
14.13. Reflection.by.a.Moving.Plasma.Slab . 276
14.14. Brewster.Angle.and.Critical.Angle.for.Moving.Plasma.Medium 277
14.15. Bounded.Plasmas.Moving.Perpendicular.to.the.Plane.
of.Incidence .277
14.16. Waveguide.Modes.of.Moving.Plasmas .277
14.17. Impulse.Response.of.a.Moving.Plasma.Medium . 278
References 278
Part III Electromagnetic Computation
15 Introduction and One-Dimensional Problems .283
15.1. Electromagnetic.Field.Problem:.Formulation.as.Differential.
and Integral Equations 283
15.2. Discretization.and.Algebraic.Equations .286
15.3. One-Dimensional.Problems .286
15.3.1. Finite.Differences 287
15.3.2. Method.of.Weighted.Residuals .290
15.3.2.1. Collocation.(Point.Matching) . 291
15.3.2.2. Subdomain.Method 292
15.3.2.3. Galerkin’s.Method . 292
15.3.2.4. Method.of.Least.Squares 292
15.3.3. Moment.Method . 296
15.3.4. Finite-Element.Method 301
15.3.5. Variational.Principle .302
References 310
16 Two-Dimensional Problem . 311
16.1. Finite-Difference.Method . 311
16.2. Iterative.Solution 315
16.3. Finite-Element.Method 317
16.3.1. Two.Elements . 323
16.3.2. Global.and.Local.Nodes . 326
16.3.3. Standard.Area.Integral 330
16.4. FEM.for.Poisson’s.Equation.in.Two.Dimensions . 332
16.5. FEM.for.Homogeneous.Waveguide.Problem 336
16.5.1. Second-Order.Node-Based.Method .343
16.5.2. Vector.Finite.Elements 350
16.5.3. Fundamental.Matrices.for.Vector.Finite.Elements 355
16.5.4. Application.of.Vector.Finite.Elements.to.Homogeneous.
Waveguide Problem .359
16.6. Characteristic.Impedance.of.a.Transmission.Line:.FEM . 362x Contents
16.7. Moment.Method:.Two-Dimensional.Problems .365
16.8. Moment.Method:.Scattering.Problem . 374
16.8.1. Formulation . 374
16.8.2. Solution . 376
References 380
17 Advanced Topics on Finite-Element Method 381
17.1. Node-.and.Edge-Based.FEM 381
17.2. Weak.Formulation.and.Weighted.Residual.Method 386
17.2.1. Weak.Form.of.the.Differential.Equation . 387
17.2.2. Galerkin.Formulation.of.the.WRM.Method:.Homogeneous.
Waveguide Problem . 387
17.3. Inhomogeneous.Waveguide.Problem .390
17.3.1. Example.of.Inhomogeneous.Waveguide.Problem . 391
17.4. Open.Boundary,.Absorbing.Boundary,.Conditions,.
. and Scattering Problem . 392
17.4.1. Boundary.Condition.of.the.Third.Kind 396
17.4.1.1. A.Simple.Example . 397
17.4.2. Example.of.Electromagnetic.Problems.with.Mixed.BC 400
17.5. The.3D.Problem 406
17.5.1. Volume.Coordinates .406
17.5.2. Functional 409
17.5.3. S,.T,.and.g.Matrices .409
17.5.4. 3D.Edge.Elements . 411
17.5.5. Higher-Order.Edge.Elements 411
References 412
18 Case Study Ridged Waveguide with Many Elements . 413
18.1. Homogenous.Ridged.Waveguide 413
18.1.1. Node-Based.FEM 415
18.1.2. Edge-Based.FEM . 417
18.1.3. Second-Order.Node-Based.FEM 419
18.1.4. HFSS.Simulation . 419
18.2. Inhomogeneous.Waveguide . 421
18.2.1. Loaded.Square.Waveguide 421
18.2.2. Inhomogeneous.Ridged.WG .423
19 Finite-Difference Time-Domain Method .429
19.1. Air-Transmission.Line .429
19.2. Finite-Difference.Time-Domain.Solution .430
19.3. Numerical.Dispersion .435
19.4. Waves.in.Inhomogeneous,.Nondispersive.Media:.FDTD.Solution 438
19.5. Waves.in.Inhomogeneous,.Dispersive.Media 441
19.6. Waves.in.Debye.Material:.FDTD.Solution 444
19.7. Stability.Limit.and.Courant.Condition .444
19.8. Open.Boundaries .445
19.9. Source.Excitation 446
19.10. Frequency.Response 446
References 448Contents xi
20 Finite-Difference Time-Domain Method Simulation of Electromagnetic
Pulse Interaction with a Switched Plasma Slab 449
20.1. Introduction 449
20.2. Development.of.FDTD.equations 450
20.2.1. Total-Field.and.Scattered-Field.Formulation 451
20.2.2. Lattice.Truncation:.PML 453
20.2.3. FDTD.Formulation.for.an.R.Wave.in.a.Switched.Plasma.Slab 453
20.3. Interaction.of.a.Continuous.Wave.with.a.Switched.Plasma.Slab 454
20.4. Interaction.of.a.Pulsed.Wave.with.a.Switched.Plasma.Slab 455
References 460
21 Approximate Analytical Methods Based on Perturbation and
Variational Techniques 461
21.1. Perturbation.of.a.Cavity 461
21.1.1. Theory.for.Cavity.Wall.Perturbations . 461
21.1.2. Cavity.Material.Perturbation 466
21.2. Variational.Techniques.and.Stationary.Formulas . 469
21.2.1. Rayleigh.Quotient .469
21.2.2. Variational.Formulation:.Scalar.Helmholtz.Equation . 470
21.2.3. Variational.Formulation:.Vector.Helmholtz.Equation 473
References 477
Part IV Appendices
Appendix 1A: Vector Formulas and Coordinate Systems . 481
Appendix 1B: Retarded Potentials and Review of Potentials for the Static Cases 491
Appendix 1C: Poynting Theorem .499
Appendix 1D: Low-Frequency Approximation of Maxwell’s Equations R, L, C,
and Memristor M . 501
Appendix 2A: AC Resistance of a Round Wire When the Skin Depth δ Is
Comparable to the Radius a of the Wire .507
Appendix 2B: Transmission Lines: Power Calculation 511
Appendix 2C: Introduction to the Smith Chart . 515
Appendix 2D: Nonuniform Transmission lines 535
Appendix 4A: Calculation of Losses in a Good Conductor at High
Frequencies: Surface Resistance RS .543
Appendix 6A: On Restricted Fourier Series Expansion 545
Appendix 7A: Two- and Three-Dimensional Green’s Functions .549
Appendix 9A: Experimental Simulation of a Warm-Plasma Medium .563
Appendix 9B: Wave Propagation in Chiral Media 571
Appendix 10A: Backscatter from a Plasma Plume due to Excitation of
Surface Waves . 573xii Contents
Appendix 10B: Classical Photon Theory of Electromagnetic Radiation 585
Appendix 10C: Photon Acceleration in a Time-Varying Medium . 591
Appendix 11A: Thin Film Reflection Properties of a Warm Isotropic Plasma
Slab between Two Half-Space Dielectric Media . 613
Appendix 11B: The First-Order Coupled Differential Equations for Waves
in Inhomogeneous Warm Magnetoplasmas 635
Appendix 11C: Waveguide Modes of a Warm Drifting Uniaxial Electron Plasma . 639
Appendix 12A: Faraday Rotation versus Natural Rotation 645
Appendix 12B: Ferrites and Permeability Tensor .649
Appendix 14A: Electromagnetic Wave Interaction with Moving Bounded Plasmas .653
Appendix 14B: Radiation Pressure Due to Plane Electromagnetic Waves
Obliquely Incident on Moving Media 661
Appendix 14C: Reflection and Transmission of Electromagnetic Waves
Obliquely Incident on a Relativistically Moving Uniaxial Plasma Slab . 667
Appendix 14D: Brewster Angle for a Plasma Medium Moving at a
Relativistic Speed . 685
Appendix 14E: On Total Reflection of Electromagnetic Waves from
Moving Plasmas 691
Appendix 14F: Interaction of Electromagnetic Waves with Bounded Plasmas
Moving Perpendicular to the Plane of Incidence . 695
Appendix 16A: MATLAB® Programs 705
Appendix 16B: Cotangent Formula 715
Appendix 16C: Neumann Boundary Conditions: FEM Method . 719
Appendix 16D: Standard Area Integral 727
Appendix 16E: Numerical Techniques in the Solution of Field Problems 733
Appendix 17A: The Problem of Field Singularities 747
Appendix 18A: Input Data .753
Appendix 18B: Main Programs . 769
Appendix 18C: Function Programs 773
Appendix 21A: Complex Poynting Theorem . 787
Part V Problems
Problems

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