Preface xiii 8

1 Maxwell's Equations    1

1.1 Maxwell's Equations, 1
1.2 Lorentz Force, 2
1.3 Constitutive Relations, 3
1.4 Boundary Conditions, 7 5
1.5 Currents, Fluxes, and Conservation Laws, 9
1.6 Charge Conservation, 10
1.7 Energy Flux and Energy Conservation, 11
1.8 Harmonic Time Dependence, 13
1.9 Simple Models of Dielectrics, Conductors, and Plasmas, 16
1.10 Kramers-Kronig Dispersion Relations, 26
1.11 Group Velocity, Energy Velocity, 29
1.12 Problems, 31

2 Uniform Plane Waves   36

2.1 Uniform Plane Waves in Lossless Media, 36 6
2.2 Monochromatic Waves, 42
2.3 Energy Density and Flux, 45
2.4 Wave Impedance, 46
2.5 Polarization, 46
2.6 Uniform Plane Waves in Lossy Media, 52
2.7 Propagation in Weakly Lossy Dielectrics, 58
2.8 Propagation in Good Conductors, 59
2.9 Propagation in Oblique Directions, 61
2.10 Complex or Inhomogeneous Waves, 63
2.11 Doppler Effect, 66
2.12 Propagation in Negative-Index Media, 70
2.13 Problems, 73

3 Pulse Propagation in Dispersive Media   80

3.1 Propagation Filter, 80
3.2 Front Velocity and Causality, 82
3.3 Exact Impulse Response Examples, 85
3.4 Transient and Steady-State Behavior, 88
3.5 Pulse Propagation and Group Velocity, 92
3.6 Group Velocity Dispersion and Pulse Spreading, 95
3.7 Propagation and Chirping, 100
3.8 Dispersion Compensation, 101
3.9 Slow, Fast, and Negative Group Velocities, 103
3.10 Chirp Radar and Pulse Compression, 110
3.11 Further Reading, 120
3.12 Problems, 120

4 Propagation in Birefringent Media    129

4.1 Linear and Circular Birefringence, 129
4.2 Uniaxial and Biaxial Media, 130
4.3 Chiral Media, 132
4.4 Gyrotropic Media, 135
4.5 Linear and Circular Dichroism, 136
4.6 Oblique Propagation in Birefringent Media, 137
4.7 Problems, 144

5 Reflection and Transmission    150

5.1 Propagation Matrices, 150
5.2 Matching Matrices, 154
5.3 Reflected and Transmitted Power, 157
5.4 Single Dielectric Slab, 160
5.5 Reflectionless Slab, 163
5.6 Time-Domain Reflection Response, 171
5.7 Two Dielectric Slabs, 173
5.8 Reflection by a Moving Boundary, 175
5.9 Problems, 178

6 Multilayer Structures   183

6.1 Multiple Dielectric Slabs, 183
6.2 Antireflection Coatings, 185
6.3 Dielectric Mirrors, 190
6.4 Propagation Bandgaps, 201
6.5 Narrow-Band Transmission Filters, 201
6.6 Equal Travel-Time Multilayer Structures, 206
6.7 Applications of Layered Structures, 220
6.8 Chebyshev Design of Reflectionless Multilayers, 223
6.9 Problems, 231

7 Oblique Incidence   238

7.1 Oblique Incidence and Snel's Laws, 238
7.2 Transverse Impedance, 240
7.3 Propagation and Matching of Transverse Fields, 243
7.4 Fresnel Reflection Coefficients, 245
7.5 Maximum Angle and Critical Angle, 247
7.6 Brewster Angle, 256
7.7 Complex Waves, 258
7.8 Total Internal Reflection, 261
7.9 Oblique Incidence on a Lossy Medium, 262
7.10 Zenneck Surface Wave, 267
7.11 Surface Plasmons, 269
7.12 Oblique Reflection from a Moving Boundary, 272
7.13 Geometrical Optics, 276
7.14 Fermat's Principle, 279
7.15 Ray Tracing, 281
7.16 Snel's Law in Negative-Index Media, 292
7.17 Problems, 295

8 Multilayer Film Applications   300

8.1 Multilayer Dielectric Structures at Oblique Incidence, 300
8.2 Lossy Multilayer Structures, 302
8.3 Single Dielectric Slab, 304
8.4 Frustrated Total Internal Reflection, 306
8.5 Surface Plasmon Resonance, 310
8.6 Perfect Lens in Negative-Index Media, 319
8.7 Antireflection Coatings at Oblique Incidence, 327
8.8 Omnidirectional Dielectric Mirrors, 330
8.9 Polarizing Beam Splitters, 341
8.10 Reflection and Refraction in Birefringent Media, 343
8.11 Brewster and Critical Angles in Birefringent Media, 347
8.12 Multilayer Birefringent Structures, 350
8.13 Giant Birefringent Optics, 352
8.14 Problems, 357

9 Waveguides   359

9.1 Longitudinal-Transverse Decompositions, 360
9.2 Power Transfer and Attenuation, 365
9.3 TEM, TE, and TM modes, 367
9.4 Rectangular Waveguides, 370
9.5 Higher TE and TM modes, 372
9.6 Operating Bandwidth, 374
9.7 Power Transfer, Energy Density, and Group Velocity, 375
9.8 Power Attenuation, 377
9.9 Reflection Model of Waveguide Propagation, 380
9.10 Resonant Cavities, 382
9.11 Dielectric Slab Waveguides, 384
9.12 Problems, 392

10 Transmission Lines   394

10.1 General Properties of TEM Transmission Lines, 394
10.2 Parallel Plate Lines, 400
10.3 Microstrip Lines, 401
10.4 Coaxial Lines, 405
10.5 Two-Wire Lines, 410
10.6 Distributed Circuit Model of a Transmission Line, 412
10.7 Wave Impedance and Reflection Response, 414
10.8 Two-Port Equivalent Circuit, 416
10.9 Terminated Transmission Lines, 417
10.10 Power Transfer from Generator to Load, 420
10.11 Open- and Short-Circuited Transmission Lines, 422
10.12 Standing Wave Ratio, 425
10.13 Determining an Unknown Load Impedance, 427
10.14 Smith Chart, 431
10.15 Time-Domain Response of Transmission Lines, 435
10.16 Problems, 442

11 Coupled Lines   453

11.1 Coupled Transmission Lines, 453
11.2 Crosstalk Between Lines, 459
11.3 Weakly Coupled Lines with Arbitrary Terminations, 462
11.4 Coupled-Mode Theory, 464
11.5 Fiber Bragg Gratings, 466
11.6 Diffuse Reflection and Transmission, 469
11.7 Problems, 471

12 Impedance Matching   473

12.1 Conjugate and Reflectionless Matching, 473
12.2 Multisection Transmission Lines, 475
12.3 Quarter-Wavelength Chebyshev Transformers, 476
12.4 Two-Section Dual-Band Chebyshev Transformers, 482
12.5 Quarter-Wavelength Transformer With Series Section, 488
12.6 Quarter-Wavelength Transformer With Shunt Stub, 491
12.7 Two-Section Series Impedance Transformer, 493
12.8 Single Stub Matching, 498
12.9 Balanced Stubs, 502
12.10 Double and Triple Stub Matching, 504
12.11 L-Section Lumped Reactive Matching Networks, 506
12.12 Pi-Section Lumped Reactive Matching Networks, 509
12.13 Reversed Matching Networks, 516
12.14 Problems, 518

13 S-Parameters   522

13.1 Scattering Parameters, 522
13.2 Power Flow, 526
13.3 Parameter Conversions, 527
13.4 Input and Output Reflection Coefficients, 528
13.5 Stability Circles, 530
13.6 Power Gains, 536
13.7 Generalized S-Parameters and Power Waves, 542
13.8 Simultaneous Conjugate Matching, 546
13.9 Power Gain Circles, 551
13.10 Unilateral Gain Circles, 552
13.11 Operating and Available Power Gain Circles, 554
13.12 Noise Figure Circles, 560
13.13 Problems, 565

14 Radiation Fields   568

14.1 Currents and Charges as Sources of Fields, 568
14.2 Retarded Potentials, 570
14.3 Harmonic Time Dependence, 573
14.4 Fields of a Linear Wire Antenna, 575
14.5 Fields of Electric and Magnetic Dipoles, 577
14.6 Ewald-Oseen Extinction Theorem, 582
14.7 Radiation Fields, 587
14.8 Radial Coordinates, 590
14.9 Radiation Field Approximation, 592
14.10 Computing the Radiation Fields, 593
14.11 Problems, 595

15 Transmitting and Receiving Antennas   598

15.1 Energy Flux and Radiation Intensity, 598
15.2 Directivity, Gain, and Beamwidth, 599
15.3 Effective Area, 604
15.4 Antenna Equivalent Circuits, 608
15.5 Effective Length, 610
15.6 Communicating Antennas, 612
15.7 Antenna Noise Temperature, 614
15.8 System Noise Temperature, 618
15.9 Data Rate Limits, 624
15.10 Satellite Links, 626
15.11 Radar Equation, 629
15.12 Problems, 631

16 Linear and Loop Antennas   634

16.1 Linear Antennas, 634
16.2 Hertzian Dipole, 636
16.3 Standing-Wave Antennas, 638
16.4 Half-Wave Dipole, 642
16.5 Monopole Antennas, 643
16.6 Traveling-Wave Antennas, 645
16.7 Vee and Rhombic Antennas, 647
16.8 Loop Antennas, 650
16.9 Circular Loops, 652
16.10 Square Loops, 654
16.11 Dipole and Quadrupole Radiation, 655
16.12 Problems, 657

17 Radiation from Apertures   658

17.1 Field Equivalence Principle, 658
17.2 Magnetic Currents and Duality, 660
17.3 Radiation Fields from Magnetic Currents, 662
17.4 Radiation Fields from Apertures, 663
17.5 Huygens Source, 666
17.6 Directivity and Effective Area of Apertures, 668
17.7 Uniform Apertures, 670
17.8 Rectangular Apertures, 670
17.9 Circular Apertures, 672
17.10 Vector Diffraction Theory, 675
17.11 Extinction Theorem, 679
17.12 Vector Diffraction for Apertures, 681
17.13 Fresnel Diffraction, 682
17.14 Knife-Edge Diffraction, 686
17.15 Geometrical Theory of Diffraction, 694
17.16 Rayleigh-Sommerfeld Diffraction Theory, 700
17.17 Plane-Wave Spectrum Representation, 703
17.18 Fresnel Diffraction and Fourier Optics, 708
17.19 Problems, 719

18 Aperture Antennas    723

18.1 Open-Ended Waveguides, 723
18.2 Horn Antennas, 727
18.3 Horn Radiation Fields, 729
18.4 Horn Directivity, 734
18.5 Horn Design, 737
18.6 Microstrip Antennas, 740
18.7 Parabolic Reflector Antennas, 746
18.8 Gain and Beamwidth of Reflector Antennas, 748
18.9 Aperture-Field and Current-Distribution Methods, 751
18.10 Radiation Patterns of Reflector Antennas, 754
18.11 Dual-Reflector Antennas, 763
18.12 Lens Antennas, 766

19 Antenna Arrays    768

19.1 Antenna Arrays, 768
19.2 Translational Phase Shift, 768
19.3 Array Pattern Multiplication, 770
19.4 One-Dimensional Arrays, 780
19.5 Visible Region, 782
19.6 Grating Lobes, 784
19.7 Uniform Arrays, 786
19.8 Array Directivity, 790
19.9 Array Steering, 791
19.10 Array Beamwidth, 794
19.11 Problems, 796

20 Array Design Methods    799

20.1 Array Design Methods, 799
20.2 Schelkunoff's Zero Placement Method, 802
20.3 Fourier Series Method with Windowing, 804
20.4 Sector Beam Array Design, 805
20.5 Woodward-Lawson Frequency-Sampling Design, 809
20.6 Discretization of Continuous Line Sources, 814
20.7 Narrow-Beam Low-Sidelobe Designs, 818
20.8 Binomial Arrays, 822
20.9 Dolph-Chebyshev Arrays, 823
20.10 Taylor One-Parameter Source, 836
20.11 Prolate Array, 840
20.12 Taylor Line Source, 842
20.13 Villeneuve Arrays, 846
20.14 Multibeam Arrays, 847
20.15 Problems, 850

21 Currents on Linear Antennas   852

21.1 Hallen and Pocklington Integral Equations, 852
21.2 Delta-Gap, Frill Generator, and Plane-Wave Sources, 855
21.3 Solving Hallen's Equation, 856
21.4 Sinusoidal Current Approximation, 858
21.5 Reflecting and Center-Loaded Receiving Antennas, 859
21.6 King's Three-Term Approximation, 862
21.7 Evaluation of the Exact Kernel, 869
21.8 Method of Moments, 874
21.9 Delta-Function Basis, 877
21.10 Pulse Basis, 881
21.11 Triangular Basis, 886
21.12 NEC Sinusoidal Basis, 888
21.13 Hallen's Equationfor Arbitrary Incident Field, 891
21.14 Solving Pocklington's Equation, 896
21.15 Problems, 900

22 Coupled Antennas   902

22.1 Near Fields of Linear Antennas, 902
22.2 Self and Mutual Impedance, 905
22.3 Coupled Two-Element Arrays, 911
22.4 Arrays of Parallel Dipoles, 914
22.5 Yagi-Uda Antennas, 923
22.6 Hallen Equations for Coupled Antennas, 929
22.7 Problems, 936

A Appendices   938

A Physical Constants, 938
B Electromagnetic Frequency Bands, 939
C Vector Identities and Integral Theorems, 941
D Green's Functions, 944
E Coordinate Systems, 947
F Fresnel, Exponential, Sine, and Cosine Integrals, 949
G Gauss-Legendre Quadrature, 955
H Lorentz Transformations, 961
I MATLAB Functions, 969 References 974

Index 1021

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Electromagnetic Waves and Antennas

Sophocles J. Orfanidis

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