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Index

Index

A

  • ABCD parameters, 102, 178
    • advantage, 96
    • equivalent network, 96
    • incident voltage, 98
    • lossless transmission line, 97
    • matrix definition, 96
    • networks in cascade, 96
    • N transmission lines in tandem, 98
    • reflection coefficient, 98–99
    • series impedance, 97
    • transmission coefficient, 98–99
  • Acoustic velocity, 188, 291, 493
  • AC resistance
    • electric, magnetic, and current density phasors, 20
    • equivalent resistance, 21–22
    • round wire, 22–23
      • actual and approximate distribution, cylindrical wire, 362
      • approximation, 361
      • Ber(x) and Bei(x) functions, 362
      • Bessel equation, 361
      • current distribution, cylindrical wire, 362
      • internal impedance per unit length, 363
      • magnetic field, 363
      • propagation constant, 361
      • solid wire skin effect quantities, 364
      • wave equation, current density, 361
    • semi-infinite good conductor, 20
    • time-averaged power density, 21
  • Adiabatic invariants, 261–262
  • Adiabatic process, 188
  • Air–plasma–air cold plasma case, 458
  • Airy functions, 175
  • Ampere–Maxwell equation, 279
  • Ampere’s law
    • circular contour, 37
    • of direct current, 142
  • Associate Legendre polynomials, 65–67
  • Average incident power, 365
  • Average reflected power, 366

B

  • Babinet’s principle of complementary screens, 123
  • Backscatter width, 116
  • Bergeron diagram
    • for linear load, 231–232
    • nonlinear resistive load, 242
  • Bernstein waves, 300
  • Bessel function
    • Bessel equation, 36–37
    • first and second kind, 39–40
    • first kind, 54
    • modified Bessel functions, 39–40
    • power series, 37–38
    • zeros, 37, 40
  • Biaxial crystal, wave propagation
    • dispersion relation, 216
    • linear polarization, 216–217
    • phase of wave, 217
    • refractive index, 216
    • uniform plane wave, 215
    • z-direction, 216
  • Bistatic width, 116
  • Boltzmann equation
    • Boltzmann–Vlasov equation, 298
    • density function, 295
    • fluid theory, 297
    • isotropic dielectric constant of plasma, 299–300
    • isotropic distribution function, 296
    • kinetic theory, 297
    • Krook model for collisions, 298
    • Landau damping, 300
    • Maxwellian distribution, 296–297
    • phase space, 295
    • plasma dispersion function, 300
    • temperature, kinetic definition of, 296
  • Boltzmann–Vlasov equation, 298
  • Boundary conditions, 5
    • circular cylindrical coordinates, 83–84
    • dielectric–dielectric interface, 377–378
    • left-handed materials, 427
    • PEC, 19–20
    • p wave, 31
    • s wave, 33
  • Boundary value problem, 32
  • Brewster angle, 32
    • dielectric medium, 563
    • maximum signal strength, 563
    • medium velocities, 567
    • parallel motion, 563
    • plane of incidence, 563
    • plasma half-space, 565–567
    • power reflection coefficient, 563–564
    • relative permittivity, 564
    • root of dispersion equation, 564
    • variation, 565
  • Building-up magnetoplasma, 288–289

C

  • Cartesian coordinates
    • and cylindrical coordinates, 37, 39
    • one-dimensional solutions, 74
    • system, 254
    • three-dimensional solutions, 85
    • two-dimensional solutions, 43–45
      • Fourier coefficients, 75–76
      • geometry, 74–75
      • periodic continuation, Fourier series, 76–77
      • potential determination, field region, 77–79
      • superposition, 78–79
  • Centripetal acceleration, 256
  • Charged particle dynamics
    • conservation of particle energy, 256
    • constant electric and magnetic fields, 256–259
    • constant gravitational field and magnetic field, 259
    • electromagnetic momentum, 253
    • equations of motion
      • Hamiltonian formulation, 264–265
      • Lagrange formulation, 263–264
      • photon ray theory, 265–270
    • Maxwell stress tensor, 253
    • Newton’s second law, 253–254
    • nonuniform B field, drift velocity in, 260–261
    • position vector, velocity and acceleration, 254–256
    • time-varying fields and adiabatic invariants, 261–262
  • Circuit theory, 355
  • Circular cylindrical coordinates
    • boundary condition, 83–84
    • commutator problem, 80–82
    • Laplace equation, 82–83
    • potential, 79
    • two ordinary differential equations, 80
  • Coaxial cable, 23–24
  • Cold plasma, 278
  • Collapsing magnetoplasma, 290–291
  • Collision frequency, 131
  • Commutator problem, 80–82
  • Comparison identities, 292
  • Compton scattering, 271–273
  • Continuity equation, 188
  • Coriolis acceleration, 256
  • Critical angle, 34–35, 460
  • Curl of gradient, 345
  • Curvature drift, 261
  • Cyclotron damping, 300
  • Cylindrical coordinates, 254
    • and Cartesian coordinates, 37, 39
    • radial coordinate, 36
  • Cylindrical to rectangular transformation, 337–339
  • Cylindrical waveguide
    • dielectric cylindrical waveguide
      • eigenvalue equation, 56–57
      • hybrid modes, 57
      • step index optical fiber, 55
      • tangential electric and magnetic fields, 55
      • transcendental equation, 56–57
    • TE modes, 53
    • TM modes, 52–53

D

  • D’Alembert’s principle, 263
  • DC conductivity, 132
  • Debye shielding phenomenon, 198
  • Dielectric–conductor medium, 397
  • Dielectric constant
    • frequency-dependent dielectric constant, 130–132
    • mixing formula, 138–139
  • Dielectric cylindrical waveguide, see Optical fiber
  • Dielectric–dielectric interface, 33
    • boundary conditions, 377–378
    • boundary, two dielectrics, 376–377
    • incident wave, 376
    • reflected and transmitted wave, 377
    • reflection and transmission coefficient, 377
  • Dielectric–PEC interface, 30–31
  • Diffraction
    • by circular hole, 121–123
    • electric vector potential, 118–119
    • elemental plane wave source and radiation intensity, 120–121
    • far-zone fields and radiation intensity, 119–120
    • geometrical optics approximation, 117
    • magnetic charge density, 117
    • magnetic current density, 117–119
    • magnetic vector potential, 118
    • spherical wave front, 117
  • Dirichlet boundary conditions, 403, 413–414
    • rectangular waveguide, 45–47
    • sector waveguide, 54
  • Distortionless transmission line, 245
  • Divergence of curl, 345
  • Double-negative (DNG) medium, 419
  • Drift velocity, 257, 259–261

E

  • Echo area, 115
  • Electric stress tensor, 505
  • Electric susceptibility, 131
  • Electromagnetic modeling
    • chiral medium
      • artificial chiral material, 155–156
      • chirality parameter vs. frequency, 156
      • electric dipole moment, 154
      • emf, 153
      • helix model approximation, 153
      • magnetic and electric dipole moment, 154
      • magnetic dipole moment, 154
      • magnetic excitation, 155
    • dielectric constant
      • frequency-dependent dielectric constant, 130–132
      • mixing formula, 138–139
    • dielectric polarization
      • Clausius–Mossotti relation, 136–137
      • complex permittivity, 137
      • dispersion, 137
      • electric field, 135–136
      • electronic and ionic components, 137
      • frequency response of hypothetical dielectric, 138
      • interfacial polarization, 138
      • Kramer–Kronig relations, 137
      • molecular polarizability and local field, 135–136
    • good conductors
      • collision frequency, 140
      • conductivity, electron mobility, 140
      • electrical resistivity, 140
      • free electrons, 139
      • mean free path, 140
      • power dissipation per unit volume, 140
      • relaxation time, 140
      • temperature dependence, 140
    • magnetic materials
      • cyclotron frequency, 152
      • equivalence of magnetic dipole, 148, 150
      • ferrimagnetic materials, 153
      • frequency of circulation, 152
      • Larmor frequency, 152
      • Lorentz force equation, 151
      • magnetization vector, 148
      • net dipole moment per unit volume, 148, 152
      • orbital magnetic dipole moment, 152
      • paramagnetism, 152
      • planar loop, 149
      • relative permeability, 152
      • surface current of density, 150
      • torque, 150–151
      • vector potential, 148
      • volume current of density, 150
      • volume of magnetic dipoles, 149–150
    • metals
      • high-frequency region, 133–134
      • intermediate-frequency region, 133
      • low-frequency region, 132
      • low-loss plasma, 132
    • metamaterials, 156–157
    • perfect conductors and superconductors
      • Ampere’s law of direct current, 142
      • analogy, 145
      • Bmax and Tmax limits, 142
      • current density, 142–143
      • empirical law, 141
      • London penetration depth, 143
      • magnetic field, 146
      • Maxwell’s equations, 146
      • Meissner effect, 142, 147
      • paired electrons, 144
      • perfect diamagnet, 142, 144
      • resistivity vs. temperature, 141–142
      • semi-infinite superconductor, 143
      • surface impedance, 147–148
      • surface resistance, 147
      • time-harmonic field, 144
      • total momentum, 143
      • two-fluid model, 144–145
      • wave equation, 146
    • plasma medium
      • angular plasma frequency, 133
      • Coulomb forces, 134
      • electronic charge layer oscillation, 134
      • force balance equation, 135
      • plasma state, 133
    • plasmonics, 156–157
    • semiconductors
    • volume of electric dipoles
      • dipole moment, 127–128
      • dipole moment density, 129
      • electric field, 127
      • electric susceptibility, 130
      • elementary electric dipole, 127–128
      • equivalence, 129
      • Gauss’s law in free space, 129
      • polarization vector, 128
      • potential fields, 127
      • relative permittivity, 130
  • Electromagnetic momentum density, 253, 505–506
  • Electromagnetic potentials, 4
  • Electromagnetics
    • AC resistance
      • electric, magnetic, and current density phasors, 20
      • equivalent resistance, 21–22
      • of round wires, 22–23
      • semi-infinite good conductor, 20
      • time-averaged power density, 21
    • Bessel functions
      • Bessel equation, 36–37
      • first and second kind, 39–40
      • modified Bessel functions, 39–40
      • power series, 37–38
      • zeros, 37, 40
    • continuity equation, 3
    • cylindrical and Cartesian coordinates, 37, 39
    • cylindrical radial coordinate, 36
    • electromagnetic potentials, 4
    • force equation, 3
    • good-conductor
      • approximation, 18
      • skin effect, 18–19
    • Maxwell’s equations, 3
      • integral form and circuit parameters, 12–16
      • quasistatic approximation, 11
      • static approximation, 11
    • one-dimensional cylindrical wave, 39, 41
    • PEC boundary conditions, 19–20
    • p wave, 31–32
    • simple medium
      • boundary conditions, 5
      • material idealization, 4–5
      • scalar constants, 4
      • time-domain electromagnetics, 5–9
    • s wave, 33
    • time-harmonic fields, 9–11
    • transmission lines
      • bounded transmission line, 26–28
      • characteristic impedance, 26
      • coaxial cable, 23–24
      • distributed circuit theory, 23
      • first-order coupled partial differential equations, 24
      • propagation constant, 26
      • TEM wave, 23, 25
      • two-port network, 24
      • wave equation, 25
    • uniform plane waves
      • skin effect, 18–19
      • in sourceless medium, 17–18
    • wave propagation
      • angle of transmission, 34
      • arbitrary direction, 29–30
      • critical angle, 34–35
      • elliptic polarization, 29
      • instantaneous vector electric field, 28
      • L and R waves, 29
      • linearly polarized wave, 28–29
      • refractive index, 33
      • surface wave, 35–36
    • wave reflection, 30–31
  • Electromagnetic wave interaction, bounded plasma
    • basic equations
      • exponential variation, 531
      • parallel polarization, 532
      • perpendicular polarization, 533
      • power reflection and transmission coefficients, 532
      • root of dispersion equation, 532
    • critical slab velocity, 531
    • dielectric medium, 573
    • dispersive medium, 573
    • isotropic dielectric half-space, 573
    • laboratory frame, 573
    • numerical results and discussion
      • angle of incidence and reflection, 533, 535
      • energy balance analysis, 536
      • incident wave interaction, 535–537
      • phase velocity vs. slab velocity, 535
      • power reflection coefficient vs. normalized slab velocity, 533–534
      • transcendental equation, 538
      • uni-x plasma with β, 580–581
      • uni-y plasma with β, 580
      • uni-z plasma with β, 580–582
      • variation of ρ, 580
    • power reflection and transmission coefficients, 577–579
    • power transmission mechanism, 579
    • problem formulation
      • arbitrary plane of incidence, 574
      • E- and H-plane waves, 577
      • eigenvector method, 575
      • electric field, 575–576
      • exponential variation, 574
      • isotropic plasma, 574
      • state-variable form, 575
      • uni-x plasma, 575
      • uni-y and uni-z plasma, 575
    • stationary plasma, 573
  • Electromagnetic wave propagation, 28–29; see Wave propagation
  • Electroquasistatic equations, 11
  • Electrostatics, 11, 345–346
  • Elliptic polarization, 29
  • Energy conservation, 353–354
  • Energy conservation law, 256
  • Evanescent wave, 35–36, 167
  • Extraordinary wave (X wave), 285

F

  • Fano mode, 183
  • Faraday equation, 280
  • Faraday rotation, 205–206
    • electric field at z = d, 480–481
    • linearly polarized wave, 480
    • longitudinal propagation, 479–480
    • vs. natural rotation, 481–482
    • net rotation angle, 481
    • wave propagation, 479
    • x-polarized (linear) wave, 479
  • Faraday’s law, 262
  • Far-radiated field, 442
  • Fermi velocity, 187, 197, 448, 493
  • Ferrimagnetic materials, 153
  • Ferrites
    • magnetic materials, 153
    • and permeability tensor
      • anisotropic magnetic material, 483
      • equation of angular motion, 483
      • external magnetic field, 484
      • Faraday rotation, 485
      • magnetization vector, 483–484
      • matrix elements, 484
      • precession (Larmor) motion, 483
      • torque, 483
  • First-order Lorentz transformations (FOLT), 309
  • Floquet’s theorem, 294
  • Fluid theory, 297
  • Force density, 253, 505
  • Forced resonance, 294–295
  • Fourier series expansion
    • boundary conditions, 399
    • function x(t) vs. time interval, 399–400
    • Laplace equation, 399
    • periodic continuation, 400–402
    • periodic function, 399
  • Four-vector wave number, 319
  • Fraunhoffer diffraction, 123
  • Free electron laser (FEL), 281
  • Frequency and polarization transformer
    • black box description, 511–512
    • collapsing magnetoplasma medium
    • electron cyclotron frequency, 512
    • extraordinary wave, 512
    • k-conservation property, 511
    • longitudinal propagation
      • basic field equations, 514–515
      • collapsing plasma profile, 515–516
      • constitutive relationship, collapsing magnetoplasma, 515
      • ω–k diagram, 514
      • output frequencies, collapsing magnetoplasma, 516–517
      • polarization state, 513
      • relative permittivity, 513
      • waveguide mode, 514
      • whistler mode, 514
    • one-dimensional FDTD simulation
      • collapsing plasma, 1-D cavity, 518–519
      • exponential time stepping, 519
    • space-invariant medium, 511
    • whistler-to-waveguide mode frequency transformation
      • absorption, 527
      • FDTD results, 525–526
      • frequency and amplitude, three modes, 525, 527
      • spectrogram, 527
      • switching angle, 527
    • whistler-to-whistler mode frequency transformation
      • FDTD results, 523–524
      • frequencies and amplitudes, three modes, 523–524
      • plasma collapse profile, 516, 523
      • polarization, 523
      • spectrogram, x-component, 523, 525
  • Frequency transformers 10–1000 GHz, 291–292
  • Fresnel diffraction, 123
  • Frozen field condition, 276
  • Full wave theory, 270

G

  • Galilean transformation (GT)
    • Faraday’s law, 308–309
    • form invariance, Ampere’s law, 309
    • motional emf, 308
    • nonrelativistic velocities, 310
    • surface integrals, 308
    • transformer emf, 308
    • two frames of reference, 307–308
  • Gamma rays, 271
  • Garnets, 153
  • Gauss’s law, 15
  • Goos–Hanschen shift, 36
  • Gradient of a scalar, 345
  • Green’s first identity, 413
  • Green’s function
    • clamped string under tension, 94
    • construction procedure, 95
    • and derivatives, 94
    • impulse function, 93
    • impulse input, 92
    • one-dimensional Helmholtz equation, 95
    • properties, 95
  • Green’s second identity, 413
  • Gross parameter representation, 357
  • Group velocity, 91–92

H

  • Half-integral Bessel functions
    • scalar Helmholtz equation, 63–67
    • vector Helmholtz equation, 67
    • zeros, 64
  • Hamiltonian formulation, 264–265
  • Hankel function, 37
  • Heaviside step function, 9
  • Helicon mode, 286
  • Helmholtz equation, 73
  • High altitude electromagnetic pulse, early-time (HEMP-E1), 270
    • Compton scattering, 271–273
    • destructive effect, 271
    • electrical circuit analogy, 273
    • electric field, 272–273
    • generic waveform of, 273
    • peak value, 273
    • planar geometry model, 271–272
    • saturation, 272–273
  • Hill’s equation, 292
  • Hybrid electric and magnetic (HEM) modes, 57
  • Hydrodynamic equation, 188
  • Hypotenuse, 327

I

  • Impulse current source, 7–9
  • Incident power, 559
  • Incident s-wave
    • electric field, free space, 320
    • phase of reflected wave, 322
    • results for case, 322–323
    • transformation, 321
    • wave vector and frequency, 321
  • Inhomogeneous warm magnetoplasmas
    • characteristic equation, 471
    • first-order linear coupled differential equations, 470
    • free-space wave, arbitrary polarization, 470
    • plasma parameters, 469
    • Runge–Kutta method, 469
    • small-signal theory, 469
  • Input impedance, 365
  • Instantaneous angular acceleration, 256
  • Instantaneous angular velocity, 256
  • Isotropic cold plasma
    • basic equations
      • dielectric constant, 160
      • field variables, 159
      • frequency vs. dielectric constant, 161
      • intrinsic impedance, medium, 162
      • scalar one-dimensional equations, 160–161
      • TEM, 162
      • typical real dielectric, 162–163
      • uniform plane waves, 162
      • vector wave equations, 160
      • velocity of phase propagation, 161
    • dielectric–dielectric spatial boundary
      • boundary condition, tangential component, 164–165
      • conservation of frequency, 164–165
      • problem, 163
      • reflected wave, 164
      • reflection and transmission coefficient, 165
      • source wave, 163
      • time-averaged power density, 165–166
      • transmitted wave, 164
    • force, 159
    • inhomogeneous slab problem, 175
    • perfect dispersive medium, 184–185
    • periodic layers
      • Bloch wave condition, 176
      • complex constant, 176
      • continuity, 177
      • dielectric function, 175
      • dispersion relation, 178–179
      • electric field, 177
      • ω–β diagram, dielectric layers, 179
      • refractive index, 177
      • stop band, 179
      • unbounded, unit cell, 176–177
      • wave propagation, 176
    • plasma current density, 159
    • plasma half-space
    • plasma slab
    • solitons, 185
    • surface waves, 180–183
  • Isotropic plasma; see Isotropic cold plasma; see Warm isotropic plasma slab
    • dielectric constant, 160
    • half-space s wave, 184–185
    • slab (parallel polarization), 172, 174
    • time-varying medium
      • Ampere–Maxwell equation, 279
      • cold plasma, 278
      • current density, 279
      • cutoff frequency, 278
      • electromagnetic wave, propagation of, 280
      • electron density, 279
      • Faraday equation, 280
      • ionization front, 278–279
      • Lorentz plasma, 278
      • plasma slab, sudden creation of, 282–283
      • radio approximation, 279
      • sudden-change approximation, 278
      • unbounded plasma medium, sudden creation of, 280–282
      • velocity at time, 279–280
      • velocity of electrons, 279

K

  • Klein–Gordon equation, 247–249
  • Korteweg-de-Vries (KdV) equation, 250–253
  • Kronecker delta, 415
  • Krook model for collisions, 298

L

  • Lagrange formulation, 263–264
  • Landau damping, 300
  • Laplace equation, 23
    • Fourier series expansion, 399
    • one-dimensional solutions, 74
    • rectangular coordinates
      • formulation and closed form solution, 409–411
      • series form (bilateral) solution, 411–412
    • static/low-frequency problems, 73
    • three-dimensional solutions
      • Cartesian coordinates, 85
      • cylindrical coordinates, 85
      • spherical coordinates, 85–89
      • time-harmonic equation, 73
    • two-dimensional solutions
      • Cartesian coordinates, 74–79
      • circular cylindrical coordinates, 79–84
  • Laplace transform technique, 240–241
    • exponential time stepping, 519
    • lossy transmission lines
      • distortion constant, 245
      • distortionless line, 245
      • Laplace inverse of exp[-k(s)z], 245–246
      • loss-free line, 245
      • peak value, 246
      • wake behind the undistorted wave, 246
      • zero initial energy, 244
    • time-domain solutions, 227
  • Larmor radius, 261–262
  • Left-hand circular polarization (LHC) polarization, 28–29
  • Left-handed materials
    • artificial
      • effective electron density, 430
      • effective value for mass, 430
      • negative -μ resonant structure, 430–431
      • plasma frequency, 430
      • plasmonic-type permeability frequency, 430
      • split–ring resonate structure, 431–432
      • thin-wire plasmonic structure, 429
    • artificial transmission line, 419–420
    • balanced transmission line, 421–424
    • boundary conditions, 427
    • diffraction limit, 429
    • dispersion relation, 420, 423
    • DNG medium, 419
    • electromagnetic properties
      • dispersive medium, 424, 426
      • features, 425–426
      • frequency variation, 425
      • refractive index, 425–426
      • relative permittivity and permeability, 425
      • TEM harmonic wave, 424
    • intrinsic impedances, 428
    • NPV medium, 419
    • ω–k diagram, 421–422
    • PDE, 419
    • PRH system, 421
    • transmission line analogy, 421–422
    • transmission through interface, two media, 427–428
    • two symmetrical rays, 428
    • “Veselago” medium, 419
  • Legendre functions, see Legendre polynomials
  • Legendre polynomials, 65–67
  • Legendre transformation, 264
  • Linearly polarized wave, 28–29
  • London penetration depth, 143
  • Longitudinal propagation, 285
    • basic field equations, 514–515
    • collapsing plasma profile, 515–516
    • constitutive relationship, collapsing magnetoplasma, 515
    • ω–k diagram, 514
    • output frequencies, collapsing magnetoplasma, 516–517
    • polarization state, 513
    • relative permittivity, 513
    • waveguide mode, 514
    • whistler mode, 514
  • Lorentz plasma, 278
  • Lorentz transformation (LT)
    • electromagnetic fields, 319
    • first-order, 330
    • four-dimensional space, 311
    • length contraction, 312
    • relative velocity, 312
    • special relativity theory, 311
    • time dilation, 312–313
    • velocity of light, 308, 311
  • Lossy transmission lines, 243–246
  • Low-frequency approximation; see Laplace equation
    • lumped-parameter circuit theory, 12
    • Maxwell’s equations
      • circuit parameters R, L, and C, 357
      • memristor, 357–360
      • time-rate parameter, 355–357
  • Low-frequency wave propagation, 279
  • Lumped-parameter circuit theory, 12

M

  • Magnetic dipole antenna, 112
  • Magnetic materials
    • cyclotron frequency, 152
    • equivalence of magnetic dipole, 148, 150
    • ferrimagnetic materials, 153
    • frequency of circulation, 152
    • Larmor frequency, 152
    • Lorentz force equation, 151
    • magnetization vector, 148
    • net dipole moment per unit volume, 148, 152
    • orbital magnetic dipole moment, 152
    • paramagnetism, 152
    • planar loop, 149
    • relative permeability, 152
    • surface current of density, 150
    • torque, 150–151
    • vector potential, 148
    • volume current of density, 150
    • volume of magnetic dipoles, 149–150
  • Magnetohydrodynamics (MHD)
    • B field, evolution of, 274–276
    • definition, 274
    • hydrodynamic and electromagnetic variables, 274
    • Ohm’s law, 274
  • Magnetoionic theory, 201, 284, 286
  • Magnetoplasma
    • cold anisotropic plasma medium, 201–202
    • longitudinal propagation, one-dimensional equations
      • basic equations, 203
      • characteristic waves, 204
      • circular polarization, 203
      • cutoff frequencies, 204
      • dielectric constant, L wave, 204, 206
      • dielectric constant, R wave, 204–205
      • dispersion relation, 204
      • Faraday rotation, 205
      • fusion plasmas, 207
      • ω–k diagram, L wave, 204, 206
      • ω–k diagram, R wave, 204–205
      • plane of polarization, 206
      • plane wave solutions, 203–204
      • R wave resonance, 207
      • static magnetic field, 203
      • whistler mode, 205
      • z-coordinate, 203
    • lossy medium, dielectric tensor, 212–213
    • periodic layers, 213
    • permeability tensor, 213
    • reflection, 214
    • surface magnetoplasmons, 213
    • time-varying medium
      • basic field equations, 284
      • building-up plasma, 288–289
      • characteristic waves, 284–285
      • cold magnetoplasma, 282
      • collapsing magnetoplasma, 290–291
      • cutoff frequency, 282
      • frequency shifting of R waves, 287–288
      • resonant frequency, 282, 284
      • R-wave propagation, 285–286
      • unbounded magnetoplasma medium, sudden creation of, 286–287
    • transverse propagation
  • Magnetoquasistatic equations, 11
  • Magnetostatics, 11, 345–346
  • Mass of electron, 326
  • Mathieu equation, 293–295
  • Maxwell–Ampere law, 13
  • Maxwell–Garnet mixing formula, 139
  • Maxwell’s equations, 8, 37, 47, 353, 417
    • electromagnetic phenomena, 3
    • integral form and circuit parameters
      • capacitance circuit parameter, 13–14
      • circuit element inductance, 12
      • conductance, 14
      • conduction current, 15
      • displacement current, 13, 15
      • lumped-parameter circuit theory, 12
      • magnetic flux, 16
      • principle of conservation of charge, 16
      • volt–ampere (V–I) relationship, 12, 14
    • quasistatic and static approximations, 11
    • for superconductors, 146
    • time domain solutions, see Time domain solutions
    • transverse components, 57
  • Maxwell stress tensor, 253, 505–506
  • Meissner effect, 142, 147
  • Memristor
    • approximate conditions, 358
    • charge-controlled memristor, 358
    • HP memristor, mathematical model, 359
    • incremental memristance, 358
    • linear resistor, 359
    • nonlinear relationships, 358
    • Φm vs. q curve, 359
    • physical device, 358
    • regime of operation, 360
    • resistance, 360
    • state equation, 359
    • two-terminal device, 357–358
  • Metamaterials, 156–157, 419
  • Microstrip lines, 23
  • Minkowsky theory, 325
  • Modified Bessel function
    • optical fiber guide, 56
    • second kind, 39–40
  • Modified Maxwell equations, 117
  • Monostatic width, 116
  • Moving media
    • Brewster angle, plasma medium, 329; see Brewster angle
    • constitutive relations, moving dielectric, 325–326
    • critical angle, 329; see Total reflection, electromagnetic wave
    • four-dimensional space
      • continuity equation, 315–316
      • excitation tensor, 318
      • field strength tensor, 317–318
      • four divergence, 316
      • four-vector differential operator, 316
      • four-vector potential, 316
      • Lienard–Wiechert potentials, 317
      • Lorentz space, 318
      • Maxwell equations, 318
      • quantity, italic symbol, 315
      • second-rank tensor, 318
      • wave equation, free space, 316–317
    • frequency transformation and phase invariance, 319–320
    • Galilean transformation
      • Faraday’s law, 308–309
      • form invariance, Ampere’s law, 309
      • motional emf, 308
      • nonrelativistic velocities, 310
      • surface integrals, 308
      • transformer emf, 308
      • two frames of reference, 307–308
    • impulse response, 330
    • Lorentz scalars, vectors, and tensors
      • derivative, four-gradient, 314
      • four-vector, 314–315
      • geometry of rotation, 313–314
      • inverse transformation, 314
      • Lorentz invariant operator, 315
      • orthogonal transformation, 313
      • second-rank tensor, 315
      • transformation matrix, 313
    • Lorentz transformation
      • electromagnetic fields, 319
      • first-order, 330
      • four-dimensional space, 311
      • length contraction, 312
      • relative velocity, 312
      • special relativity theory, 311
      • time dilation, 312–313
      • velocity of light, 308, 311
    • plane of incidence, 330; see Electromagnetic wave interaction, bounded plasma
    • plasma parameter transformation, 328
    • position four-vector, 331–332
    • reflection
      • field transformations, 323
      • incident s-wave, 320–323
      • plasma slab, 328–329
      • power reflection coefficient, s-wave incidence, 323–325
    • relativistic particle dynamics, 326–327
    • Snell’s law
      • boundary condition, 305–306
      • frequency difference, Doppler radar, 307
      • reflection, moving mirror, 305–306
      • tangential component, 306
    • waveguide modes, 330
  • Moving point charge
    • electric and B fields, 584
    • extended particle concept, 584–585
    • generalized Coulomb field, 584
    • Lienard–Wiechert potentials, 583–584
    • radiation field, 584
    • retarded time concept, 583
    • scalar potential, 583
    • space and time differentiation, 585–586

N

  • Navier–Stokes equation, 188
  • Negative phase velocity (NPV) medium, 419
  • Neuman boundary value problem, 49
  • Newton’s second law, 253–254, 263
  • Newton’s third law
    • definition, 507
    • differential vector magnetic force, 507
    • Lorentz force equation, 508–509
    • moving point charge, 509
    • repulsive force, 508
    • validity check, electric and magnetic forces, 507–508
  • Nonlinear resistive load, 242
  • Nonlinear transmission line (NLTL)
    • differential length, circuit representation of, 249
    • dispersion relation, sketch of, 250
    • KdV equation, “soliton” solution of, 250–253
    • nonlinear PDE, 249
    • “TODA” model of, 250
  • Nonuniform transmission line
    • arbitrary load, 394–395
    • exponential transmission line
      • characteristic impedances, 393
      • harmonic variation, space and time, 390
      • inductance and capacitance, 390
      • positive and negative traveling wave, 392
      • time-harmonic solution, 392
      • uniform line, 393
    • first-order coupled differential equations, 389
    • input impedance, 394
    • phase velocity, 389
    • phasor form, 389–390
    • series inductance value, 389
    • shunt capacitance value, 389
  • Nuclear electromagnetic pulse, 270–273

O

  • Oblique incidence
    • equivalent transmission lines, 385
    • incident wave freespace wavelength, 383
    • length in wavelengths, 385
    • perpendicular polarization, 383–384
    • reflection coefficient, 387
    • solution of plane wave reflection, 386
    • vs. transmission line analogy, 383–384
  • Ohmic power loss, 354
  • Ohm’s law, 271, 274
  • One-dimensional cylindrical wave, 39, 41
  • Optical fiber
    • admissible function, 56
    • boundary value problem, 55
    • eigenvalue equation, 56
    • first three surface-wave modes, polystyrene rod, 57
    • HEM modes, 57
    • step index, 55
    • tangential electric and magnetic fields, 55
    • transcendental equation, 56
  • Optical waves, anisotropic crystals
    • k-Surface, 220–221
    • polar angle
      • definition, 221
      • magnitude of group velocity, 222
      • quartz, 224
      • various angles, extraordinary wave, 223
    • principal refractive indices, 215
    • propagation, arbitrary direction
      • determination of transformation matrix, 218
      • dispersion relation, 219
      • impermittivity tensor, 218
      • orthogonal coordinate system, 217
      • transformation determination, 218
      • uniaxial crystal, 219–220
    • reflection, anisotropic half-space, 224–225
    • wave propagation, biaxial crystal
      • dispersion relation, 216
      • linear polarization, 216–217
      • phase of wave, 217
      • refractive index, 216
      • uniform plane wave, 215
      • z-direction, 216
    • zero off-diagonal elements, 215
  • Ordinary differential equations (ODEs), 44
  • Ordinary wave (O wave), 207, 285
  • Orthonormal matrix, 339–341

P

  • Parallel plate transmission line, 23
  • Parallel-polarized wave, 31–32
  • Parametric pendulum, 293–295
  • Parametric resonance, 293–295
  • Partial differential equation (PDE), 44, 419
  • PEC boundary conditions
    • circular waveguide, 52
    • rectangular waveguide
      • Dirichlet boundary condition, 45–47
      • Neuman problem, 49
    • sector waveguide, 54
    • spherical cavity, 69–70
  • Perfect conductor
    • interface, 375–376
    • perfect dielectric medium, 14
    • and superconductors
      • Ampere’s law of direct current, 142
      • analogy, 145
      • Bmax and Tmax limits, 142
      • current density, 142–143
      • empirical law, 141
      • London penetration depth, 143
      • magnetic field, 146
      • Maxwell’s equations, 146
      • Meissner effect, 142, 147
      • paired electrons, 144
      • perfect diamagnet, 142, 144
      • resistivity vs. temperature, 141–142
      • semi-infinite superconductor, 143
      • surface impedance, 147–148
      • surface resistance, 147
      • time-harmonic field, 144
      • total momentum, 143
      • two-fluid model, 144–145
      • wave equation, 146
    • wave reflection, 30
  • Perfect electric conductor (PEC), 19–20, 30–31, 54, 69, 114, 306, 324, 397, 520
  • Perpendicular-polarized wave, 33
  • Phasor–vector field, 9
  • Photon ray theory
    • electric field, 265
    • Hamiltonian canonical pair, 266–267
    • Lagrange equation, 267
    • local dispersion relation, 266
    • ponderomotive force, 267
    • propagating wave packet, group velocity of, 266–267
    • space–time refraction
      • dielectric medium, 268
      • direction of wave propagation, 268
      • Hamiltonian pair, 268
      • Snell’s law, 269
      • spatial discontinuity, 268–269
      • temporal discontinuity, 268, 270
    • zero mass and charge, 267
  • Planar geometry model, 271–272
  • Plasma density, 198
  • Plasma dispersion function, 300
  • Plasma frequency, 328
  • Plasma plume
    • back scatter, 442
    • collision frequency, 433–434
    • effect of frequency, 444
    • effect of L, 444
    • effect of polarization, 444
    • electron density, 433–434
    • numerical method, dispersion relation, 441
    • problem classification, parameters, 433, 435
    • sample calculation
      • attenuation and phase constant, 443
      • propagation velocity, 444
      • square of plasma frequency, 442
      • turbulent layer, 443
    • surface waves
      • dispersion characteristic, 437
      • excitation, 440–441
      • free space-plasma interface, 437, 439
      • surface plasmon, 437
      • turbulent layer, 437, 439
    • TM wave absorption
      • equation, time-harmonic fields, 436
      • first-order-coupled differential equations, 436
      • frequency dependence, various power coefficients, 437–438
      • magnetoionic theory notations, 436
      • mathematical model, inhomogeneity, 435
      • numerical method, 436–437
      • power reflection coefficient vs. angle of incidence, 437, 439
      • turbulence, 437
  • Plasma slab
    • power tunneling
      • electric and magnetic field interaction, 172
      • evanescent waves, 172
      • plasma frequency/slab width, 175
      • power flow, 172
      • q1 imaginary, 173
      • q1 real, 173
      • transcendental equation, 175
      • transmitted power, isotropic plasma, 174
      • z-component calculation, Poynting vector, 173
    • reflection
      • boundary conditions, tangential components, 169
      • Brewster angle, plasma medium, 171
      • exponential factor, 168
      • field amplitudes, free space, 168–169
      • free space wavelength, 170
      • incident wave, 168
      • power reflection coefficient, 170
      • power transmission coefficient, 171
      • problem, 167
      • reflected wave, 168
      • ρ vs. Ω parallel polarization, 172
      • transmitted wave, 168
      • wave number, 169
  • Plasmonics, 156–157, 447, 487
  • Polar angle
    • definition, 221
    • magnitude of group velocity, 222
    • quartz, 224
    • various angles, extraordinary wave, 223
  • Ponderomotive force, 267
  • Power loss per meter square, 397
  • Power reflection coefficient
    • characteristic roots, 456–457
    • critical points, 456–457
    • normalized film thickness, 455–456
    • region 1 and power tunneling effect, 457–459
    • region 1 and surface plasmons, 459–460
    • region 2 and approximation, 461–463
    • region 2 and film thickness, 463–465
    • sodium thin film, 465–466
    • transverse vs. longitudinal modes, 456
  • Poynting theorem, 6–7, 353–354, 506
  • Principle of conservation of charge, 13, 15
  • Pure right-handed (PRH) system, 421

Q

  • Quality factor (Q), 62

R

  • Radar cross section (RCS), 115
  • Radiation pressure
    • Brewster angle, dielectric medium, 539
    • calculation, 541
    • characteristic root, 541
    • conducting surface, 542–543
    • exponential variation, 541
    • laboratory system, 541
    • Maxwell stress tensor, 539
    • normalized mechanical power, 540–542
    • reflection coefficient, 541
    • surface stress tensor, 539
  • Radiation, waves
    • antenna problem, 110
    • arbitrary length dipoles, 110
    • boundary value problem, 107, 110
    • Cerenkov radiation, 111
    • continuity equation, 105
    • electric dipole moment, 106
    • in far zone, 104
    • field region classification, 104
    • filamentary current, 105
    • in free space, 104
    • half-wave dipole
      • approximations, 108–109
      • center-fed wire antenna, 107–108
      • monopole antenna, 110
      • normalized radiation intensity, 109
      • radiated electric field, 108
      • radiation pattern, 109–110
      • time-averaged power density, 109
    • Hertzian dipole, 106–107
    • pattern shaping, 110
    • practical radiating systems, 113
    • small circular loop antenna, 111–113
    • traveling wave antenna, 110–111
  • Radiative surface plasmon, 181–182
  • Radio approximation, 279
  • Radio wave propagation, 279
  • Rectangular cavity
    • TE modes
      • losses, 61
      • quality factor, 62
      • resonant frequency, 60–61
      • surface currents, 61
      • total energy, 62
    • TM modes, 59–60
  • Rectangular waveguide
    • TE modes
      • attenuation, 51
      • boundary condition, 48–49
      • cross section, 49
      • dominant mode, 49–50
      • power flow, 51
    • TM modes
      • cross section, 45–46
      • Dirichlet boundary condition, 45–47
      • field components, 47
      • lowest cutoff frequency, 47
      • wave impedance, 47
      • wavelength, 48
  • Reductive perturbation method, 252
  • Reflection and transmission
    • coefficients, 549
    • dispersion relation, 548–549
    • isotropic plasma slab, 545
    • numerical results and discussion
      • oscillatory and nonoscillatory function, 550
      • slab motion normal to interface, 556–561
      • slab motion parallel to interface, 554–556
      • variation with β, 553–554
      • variation with Ω, 550–552
    • parallel-polarized electromagnetic waves, 545
    • problem formulation
      • angle of reflection, 548
      • exponential variation, 546
      • geometry, 545–546
      • harmonic time variation, 545
      • magnetostatic field, 546
      • slab motion cases, 547–548
      • stationary system, 547
  • Refractive index, 33
  • Relativistic Doppler effect, 319
  • Relativistic force, 326
  • Relativistic momentum of mass, 326
  • Relaxation time, 140
  • Retarded potentials
    • electrostatics, 345–346
    • magnetostatics, 345–346
    • one-dimensional solution, wave equation, 350–351
    • time-varying case
      • charge density, 348
      • electric potential, 347
      • Hertzian dipole, 349–350
      • Lorentz condition, 348
      • point charge, 348–349
      • static vs. dynamic cases, 348–349
      • uncoupled equations, 347–348
      • wave equations, 348
  • Reynolds number, 275
  • Right-hand circular polarization, 29
  • R-wave propagation
    • ω–k diagram, 285–286
    • relative permittivity for, 285

S

  • Saturation, 272–273
  • Scalar constants, simple medium, 4–5
  • Scalar Helmholtz equation, 64
    • associate Legendre polynomials, 65–67
    • differential equation, 63
    • half–integral Bessel functions, 65
    • separation of variables, 65
    • spherical Bessel function, 65
  • Scalar magnetic potential, 88
  • Scalar wave number, 220
  • Scattering parameters
    • forward transmission coefficient, 101
    • normalized voltages, 99
    • one-port network, 99
    • output reflection coefficient, 101
    • propagation constant, 101
    • reverse transmission coefficient, 101
    • S–ABCD–S parameters transformation, 101
    • two-port network, 100
  • Scattering width, 115–116
  • Sector waveguide
    • TE modes, 54
    • TM modes, 54
  • Semiconductors
  • Smith chart
    • analysis, 373–374
    • constant resistance (r) and reactance (x) contours, 370–372
    • construction, reflection coefficient, 369
    • design, 369
    • family of circles, 370–371
    • final scale, 371–372
    • graduated line segments, 373
    • load impedance, 369
    • normalized input impedance, 372
    • oblique incidence
      • equivalent transmission lines, 385
      • incident wave freespace wavelength, 383
      • length in wavelengths, 385
      • perpendicular polarization, 383–384
      • reflection coefficient, 387
      • solution of plane wave reflection, 386
      • vs. transmission line analogy, 383–384
    • polar coordinates, 369–370
    • scenario, 373–374
    • vs. transmission line problem
      • dielectric–dielectric interface, 376–378
      • dielectric interface problem solving, 379–380
      • equivalent load, 378–379
      • equivalent transmission line circuit, 379–380
      • problem geometry, 379
      • radome analysis geometry, 381
      • radome equivalent transmission line circuit, 381–382
      • solution of radome problem, 382–383
      • transmission line interface, 378
    • uniform plane wave reflection, 375–376
    • voltage and current, transmission line, 372
  • Snell’s law, 32, 224, 269
  • Space–charge polarization, 138
  • Space-time modulation, 300
  • S parameters, see Scattering parameters
  • Spatial discontinuity, 268–269
  • Spherical Bessel function, 63, 65, 70
  • Spherical coordinates
    • half-integral Bessel functions
      • scalar Helmholtz equation, 63–67
      • vector Helmholtz equation, 67
      • zeros, 64
    • spherical cavity, 69–71
    • TEr modes, 68–69
    • TMr modes, 68
  • Spherical to cylindrical transformation, 338–340
  • Spherical to rectangular transformation, 338, 340–341
  • State of polarization, 201, 285, 417, 513
  • Step index optical fiber, 55
  • Stokes’ theorem, 13
  • Strip lines, 23
  • Subcycle time-varying medium, 292
  • Superconductors
    • Ampere’s law of direct current, 142
    • analogy, 145
    • Bmax and Tmax limits, 142
    • current density, 142–143
    • empirical law, 141
    • London penetration depth, 143
    • magnetic field, 146
    • Maxwell’s equations, 146
    • Meissner effect, 142, 147
    • paired electrons, 144
    • perfect diamagnet, 142, 144
    • resistivity vs. temperature, 141–142
    • semi-infinite superconductor, 143
    • surface impedance, 147–148
    • surface resistance, 147
    • time-harmonic field, 144
    • total momentum, 143
    • two-fluid model, 144–145
  • Surface current
    • calculation, 61
    • cylinder surface, 115
    • density, 5, 19, 150
  • Surface plasmon resonance, 447, 460
  • Surface plasmons, 183, 437, 439–440
  • Surface resistance (RS), 397
  • Surface waves, 35–36
    • dispersion characteristic, 437
    • excitation, 440–441
    • free space-plasma interface, 437, 439
    • surface plasmon, 437
    • turbulent layer, 437, 439
  • Surfatron, 183

T

  • Temperate plasma, see Cold plasma
  • Temporal discontinuity, 268, 270
  • Thevenin’s theorem, 230
  • Three-dimensional solutions
    • TE modes, rectangular cavity, 60–62
    • TM modes, rectangular cavity, 59–60
  • Time-averaged reactive power density, 35
  • Time-domain electromagnetics
    • conservation of energy, 7
    • field and source point, 6
    • Lorentz condition, 6
    • Poynting theorem, 6–7
    • radiation by impulse current source, 7–9
    • wave equations, 5
  • Time-domain magnetic field, 8
  • Time-domain reflectometer, 243
  • Time domain solutions
    • bounded ideal transmission lines
      • internal impedance, 227
      • Laplace transform, 240–241
      • linear load, Bergeron diagram for, 231–232
      • load end, 227, 229
      • load resistance, 227
      • load voltage, sketch of, 240–241
      • negative-going wave, 228–229
      • nonlinear terminations, response to, 241–242
      • parasitic capacitance, effect of, 239–241
      • positive-going wave, 229
      • rectangular pulse, response to, 238
      • reflection coefficients, 229–231
      • rise and fall time, pulse with, 239
      • sketches V(0, t) and I(0, t), 236–237
      • sketches V(0.25l, t) and I(0.25l, t), 233–235
      • source, 227–228
      • successive reflected waves, bounce diagram for, 229–230
      • Thevenin’s theorem, 230
      • time-domain reflectometer, 243
      • transient waves, propagation of, 228
      • voltage–current relationship, 229, 231–232
      • voltage V(0, t), sketch of, 238
      • voltage V(0.25l, t), sketch of, 232
      • wave equation for voltage V(z, t), 228
    • charged particles, see Charged particle dynamics
    • Klein–Gordon equation, 247–249
    • lossy transmission lines, 243–246
    • magnetohydrodynamics, 274–276
    • NLTL equation
      • differential length, circuit representation of, 249
      • dispersion relation, sketch of, 250
      • KdV equation, “soliton” solution of, 250–253
      • nonlinear PDE, 249
      • “TODA” model of, 250
    • nuclear electromagnetic pulse, 270–273
    • one-dimensional scalar wave equation, 227
    • scalar potential, 227
    • second-order partial differential equation, 227
    • statistical mechanics and Boltzmann equation, see Boltzmann equation
    • time-varying medium, see Time-varying electromagnetic medium
  • Time-rate parameter
    • higher-order sets of equations, 356–357
    • Maxwell’s equations, 355–356
    • power-series expressions, 356
    • series of equations, 356
  • Time-varying electromagnetic medium
    • frequency transformers 10–1000 GHz, 291–292
    • isotropic plasma medium
      • Ampere–Maxwell equation, 279
      • cold plasma, 278
      • current density, 279
      • cutoff frequency, 278
      • electromagnetic wave, propagation of, 280
      • electron density, 279
      • Faraday equation, 280
      • ionization front, 278–279
      • Lorentz plasma, 278
      • plasma slab, sudden creation of, 282–283
      • radio approximation, 279
      • sudden-change approximation, 278
      • unbounded plasma medium, sudden creation of, 280–282
      • velocity at time, 279–280
      • velocity of electrons, 279
    • magnetoplasma medium
      • basic field equations, 284
      • building-up plasma, 288–289
      • characteristic waves, 284–285
      • cold magnetoplasma, 282
      • collapsing magnetoplasma, 290–291
      • cutoff frequency, 282
      • frequency shifting of R waves, 287–288
      • resonant frequency, 282, 284
      • R-wave propagation, 285–286
      • unbounded magnetoplasma medium, sudden creation of, 286–287
    • Mathieu equation and parametric resonance, 293–295
    • periodically time-varying parameter, 292–295
    • spatial vs. temporal discontinuities, 276–277
    • subcycle time-varying medium, 292
  • TM wave absorption
    • equation, time-harmonic fields, 436
    • first-order-coupled differential equations, 436
    • frequency dependence, various power coefficients, 437–438
    • magnetoionic theory notations, 436
    • mathematical model, inhomogeneity, 435
    • numerical method, 436–437
    • power reflection coefficient vs. angle of incidence, 437, 439
    • turbulence, 437
  • Total reflection, electromagnetic wave
    • critical angle, 569
    • definition, 572
    • exponential variation, 569
    • frequency range, total reflection, 570–571
    • isotropic/uniaxially anisotropic medium, 569
    • laboratory frame, 569
    • normalized incident wave frequency, 570
    • oblique incidence, 569
    • parallel-polarized wave, 570
    • plasma half-space moving normal, 571–572
    • plasma half-space moving parallel, 570
  • Transformation matrix, 218, 313, 339
  • Transmission lines
    • bounded transmission line, 26–28
    • characteristic impedance, 26
    • coaxial cable, 23–24
    • distributed circuit theory, 23
    • first-order coupled partial differential equations, 24
    • parallel-polarized wave, 31–32
    • perpendicular-polarized wave, 33
    • power calculation, 365–366
    • propagation constant, 26
    • special case Zg = Z0, 367
    • TEM wave, 23, 25
    • two-port network, 24
    • wave equation, 25
  • Transverse electric and magnetic waves (TEM), 162
  • Transverse electric (TE) modes
    • cylindrical waveguide, 53
    • rectangular cavity, 60–62
    • rectangular waveguide
      • attenuation, 51
      • boundary condition, 48–49
      • cross section, 49
      • dominant mode, 49–50
      • power flow, 51
    • sector waveguide, 54
  • Transverse magnetic (TM) modes
    • cylindrical waveguide, 52–53
    • rectangular cavity, 59–60
    • rectangular waveguide
      • cross section, 45–46
      • Dirichlet boundary condition, 45–47
      • field components, 47
      • lowest cutoff frequency, 47
      • wave impedance, 47
      • wavelength, 48
    • sector waveguide, 54
  • Transverse propagation, 285
    • O wave, 207
    • X wave
      • basic equations, 208
      • dielectric constant, 209–210
      • dielectric modeling of plasma, 210
      • dielectric tensor, 210
      • direction of phase propagation, 207–208
      • dispersion relation, 209
      • geometrical sketch, directions of various components, 211
      • ω–k diagram, 209–210
      • plane wave solution, 208
  • Transverse wave number, 220
  • Two- and three-dimensional Green’s functions
    • differential equation, 403
    • Dirichlet boundary conditions, 403
    • generalized method, 413–414
    • Green’s dyadic, 414–415
    • infinite series, 405–406
    • one-dimensional Helmholtz equation, 404
    • rectangular coordinates
      • Helmholtz equation, 412
      • Laplace equation, 409–412
    • Sturm–Liouville operator, 406–408
  • Two-dimensional solutions
    • Cartesian coordinates, 43–45
    • TE modes
      • cylindrical waveguide, 53, 55–57
      • rectangular waveguide, 48–51
      • sector waveguide, 54
    • TM modes
      • cylindrical waveguide, 52–53, 55–57
      • rectangular waveguide, 45–48
      • sector waveguide, 54

U

  • Upper hybrid frequency, 490

V

  • Vector differential operators
    • cylindrical coordinates, 342
    • rectangular coordinates, 341
    • spherical coordinates, 342
  • Vector Helmholtz equation, 67
  • Vector identities
    • addition and multiplication, 343
    • differentiation, 343–344
    • integration, 344
  • Vector transformations
    • cylindrical to spherical transformation, 338–340
    • rectangular to cylindrical transformation, 337–339
    • rectangular to spherical transformation, 338, 340–341
  • Voltage and current harmonic waves, see Transmission lines

W

  • Warm drifting uniaxial electron plasma
    • dielectric medium, 473
    • dispersion relation, TM modes, 474
    • drift velocity, 474
    • fourth-degree curve, 476
    • fourth-degree polynomial equation, 474
    • guided wave propagation, 473
    • infinite static magnetic field, 473–474
    • Maxwell equations, 473
    • Ω–B diagram, 475–476
    • ω–β diagram, 474–476
    • phase characteristics, waveguide wave, 476–477
    • wave equation, 474
  • Warm isotropic plasma slab
    • longitudinal characteristic roots, 448
    • oblique incidence, 448–449
    • oscillations, 447
    • power reflection coefficient
      • characteristic roots, 456–457
      • critical points, 456–457
      • normalized film thickness, 455–456
      • region 2 and approximation, 461–463
      • region 2 and film thickness, 463–465
      • region 1 and power tunneling effect, 457–459
      • region 1 and surface plasmons, 459–460
      • sodium thin film, 465–466
      • transverse vs. longitudinal modes, 456
    • state–space methods, 447
    • thin-film gratings, 447
    • thin film reflection properties, 447
    • transverse wave, 447
    • two different dielectric media
      • boundary conditions, 453–454
      • collisionless plasma equations, 453
      • complex reflection coefficient, 454–455
      • longitudinal component of waveform, 454
    • wave equation, 447
    • waves inside slab
      • characteristic roots, 452
      • conservation of energy, 450
      • conservation of momentum, 450
      • dimensionless parameter, 451
      • electric and magnetic field intensities, 451
      • electric field-dependent electron velocity, 453
      • equation of state, 450
      • Maxwell’s equations, 450
      • phase of fields, 451
      • ratio of magnetic to electric tangential components, 453
      • TM and acoustic wave, 451
    • waves outside slab
      • electric and magnetic fields, 448–450
      • phase factor, 449
      • phase reference of waveform, 448
      • Snell’s law, 449
      • wave vector geometry, 448–449
  • Warm magnetoplasma slab
    • characteristic roots and power reflection coefficient
    • extraordinary wave, 488
    • normal incidence, 487–489
    • oblique incidence, 487
    • parameters, 487–488
    • waves inside slab
    • waves outside slab, 488
  • Warm plasma
    • conservation of energy, 490
    • conservation of momentum, 490
    • dispersion relation, 492
    • electric and magnetic field intensities, 491
    • equation of state, 491
    • hydrodynamic approach, 492
    • loss-free, dielectric model, 195
    • lossy
      • conductor model, 195–196
      • constitutive relation, 193–194
    • Maxwell’s curl equations, 492
    • normalized velocity variable, 491
    • parameters, 490–491
    • permittivity, 187
    • phase of fields, 492
    • power reflection coefficient, 492
    • spatial dispersion and nonlocal metal optics, 196–197
    • technical definition
      • Debye length, 198
      • one-dimensional electron–proton plasma, 197
      • temperate plasma, 197
      • unneutralized plasma, 198
    • wave equation, 491
    • waves
      • compressible gas, 187–188
      • electron plasma wave, 191–192
      • equation for pressure, 189–190
      • force equation, 189
      • hydrodynamic equation, 188–189
      • parallel component, 191
      • plasma oscillation, 192
      • propagation, 192
  • Wave number
    • conserved, temporal discontinuity, 270, 286
    • cutoff, 53
    • instantaneous value, 266
    • L wave, 418
    • in plasma, 169
    • R wave, 285, 418
    • scalar and transverse, 220
    • surface waves, 181
  • Wave propagation
    • angle of transmission, 34
    • arbitrary direction, 29–30
    • chiral media, 417–418
    • critical angle, 34–35
    • elliptic polarization, 29
    • instantaneous vector electric field, 28
    • L and R waves, 29
    • linearly polarized wave, 28–29
    • refractive index, 33
    • surface wave, 35–36
  • Waves
    • diffraction
      • by circular hole, 121–123
      • electric vector potential, 118–119
      • elemental plane wave source and radiation intensity, 120–121
      • far-zone fields and radiation intensity, 119–120
      • geometrical optics approximation, 117
      • magnetic charge density, 117
      • magnetic current density, 117–119
      • magnetic vector potential, 118
      • spherical wave front, 117
    • Green’s function
      • clamped string under tension, 94
      • construction procedure, 95
      • and derivatives, 94
      • impulse function, 93
      • impulse input, 92
      • one-dimensional Helmholtz equation, 95
      • properties, 95
    • group velocity, 91–92
    • network formulation
      • ABCD parameters, 96–99
      • classical network theory, 95–96
      • S parameters, 99–101
      • two-port network, 96
    • radiation
      • antenna problem, 110
      • arbitrary length dipoles, 110
      • boundary value problem, 107, 110
      • Cerenkov radiation, 111
      • continuity equation, 105
      • electric dipole moment, 106
      • in far zone, 104
      • field region classification, 104
      • filamentary current, 105
      • in free space, 104
      • half-wave dipole, 107–110
      • Hertzian dipole, 106–107
      • pattern shaping, 110
      • practical radiating systems, 113
      • small circular loop antenna, 111–113
      • traveling wave antenna, 110–111
    • scattering
      • cylindrical wave transformations, 113–114
      • induced current, 114–115
      • time-harmonic electromagnetic wave, 113
      • total fields, 113
      • width, 115–116
    • stop bands, periodic media
      • dispersion relation, 101
      • eigenvalue, 102–103
      • first stop band, 103–104
      • first transmission line, 102
      • reciprocal network, 103
      • second transmission line, 102
      • stop and pass bands, 104
      • unit cell, 101–102
  • Whistler mode
    • collapsing magnetoplasma, 517
    • C1 region, 521–522
    • frequency transformation
      • FDTD results, 523–524
      • frequencies and amplitudes, three modes, 523–524
      • plasma collapse profile, 516, 523
      • polarization, 523
      • spectrogram, x-component, 523, 525
    • longitudinal propagation, 205, 514
    • R-wave propagation, 286
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