Lateral Electromagnetic Waves

1 Historical and Technical Overview of Electromagnetic Surface Waves; Introduction to Lateral Waves.- 1.1 Electromagnetic Waves.- 1.2 Electromagnetic Waves Along Surfaces.- 1.3 Surface Waves in the Field of a Vertical Electric Dipole over the Earth; The Formula of Norton.- 1.4 General Integrals and Approximate Formulas.- 1.5 Numerical Methods with High-Speed Computers.- 1.6 Lateral Waves.- 1.7 Lateral Waves and the Geoelectromagnetic Investigation of the Earth's Crust and Upper Mantle.- 2 Electromagnetic Preliminaries.- 2.1 Maxwell's Equations; Parameters.- 2.2 The Vector and Scalar Potentials; The Electromagnetic Field of a Unit Electric Dipole.- 2.3 The Electromagnetic Field of a Unit Magnetic Dipole.- 2.4 The Reflection and Transmission of Plane Waves at the Plane Boundary Between Electrically Different Media.- 2.5 The Reflection and Transmission of Plane Waves at the Boundary Between Two Lossless Half-Spaces (Case A).- 2.6 The Reflection and Transmission of Plane Waves at the Boundary of a Dissipative Half-Space (Case B).- 2.7 The Reflection and Transmission of Plane Waves Incident from a Lossy Half-Space (Cases C and D).- 3 The Electromagnetic Field of a Unit Vertical Electric Dipole in the Presence of a Plane Boundary.- 3.1 Maxwell's Equations and Their Transforms.- 3.2 Solution of the Transformed Equations.- 3.3 General Integrals for the Field When the Dipole Is in Region 1.- 3.4 Integrated Formulas for the Electromagnetic Field of a Vertical Electric Dipole at the Depth d in Region 1.- 3.5 The Polarization of the Electromagnetic Field of a Vertical Electric Dipole on the Boundary in Region 1; Wave Tilt.- 3.6 The Complete Electromagnetic Field in Region 1 of the Vertical Electric Dipole in Region 1.- 3.7 The Field in Region 2 for the Vertical Electric Dipole in Region 1.- 3.8 Alternative Derivation of the Field in Region 2 for the Vertical Electric Dipole in Region 1.- 3.9 Generalization of the Field in Region 2.- 4 Applications of the Theory of the Vertical Dipole Near The Boundary Between Two Half-Spaces.- 4.1 Limitations of the Theory.- 4.2 Radio Communication over the Surface of the Earth; Electromagnetic Field in Air Due to a Vertical Electric Dipole at Height d in Air.- 4.3 Division of Radiated Power Between Air and Earth Half-Spaces.- 4.4 Communication with Submarines-Unit Vertical Dipole.- 4.5 Communication with Submarines-A Practical Antenna.- 4.6 The Measurement of the Conductivity of the Oceanic Crust with a Vertical Electric Dipole as the Source-Theory.- 4.7 The Measurement of the Conductivity of the Oceanic Crust Using a Vertical Dipole-Comparison of Theory with Measurement.- 4.8 A Note on the Effective Length of the Antenna.- 5 The Electromagnetic Field of a Horizontal Electric Dipole in the Presence of a Plane Boundary.- 5.1 Introduction.- 5.2 Maxwell's Equations and Their Transforms.- 5.3 Solution of the Differential Equations for ?x and B x.- 5.4 The Components of the Electromagnetic Field of the Horizontal Dipole as General Integrals.- 5.5 Integrated Formulas for the Electromagnetic Field in Regions 1 and 2 of the Horizontal Electric Dipole at the Depth d in Region 1.- 5.6 Evaluation of the Integrals for the Electromagnetic Field in Region 1 of the Horizontal Electric Dipole at the Depth d in Region 1.- 5.7 Evaluation of the Integrals of the Field in Region 2 of the Horizontal Electric Dipole at the Depth d in Region 1.- 5.8 Alternative Derivation of the Field in Region 2 of the Horizontal Electric Dipole at the Depth d in Region 1.- 5.9 The Locus of the Poynting Vector and the Depth of Penetration of the Lateral Wave in Region 2.- 5.10 Generalization of the Field in Region 2.- 6 Interference Patterns; Comparison of Approximate Formulas with General Integrals and Measurements.- 6.1 Introduction.- 6.2 Radial Electric Field and Interference Patterns.- 6.3 The Complete Electric and Magnetic Fields.- 6.4 Comparison of Theory with Measurements.- 7 Applications of the Theory of the Horizontal Dipole Near the Boundary Between Air and Earth or Sea.- 7.1 Comparison with the Vertical Dipole.- 7.2 Lateral-Wave Propagation over the Surface of the Earth and into the Ocean-Unit Horizontal Dipoles.- 7.3 The Wave Antenna for Communication over the Earth.- 7.4 Communicating with Submarines with Horizontal Antennas.- 7.5 Lateral Waves from a Horizontal Antenna for Remote Sensing in the Earth or Water.- 7.6 Lateral Electromagnetic Waves from a Horizontal Antenna for Remote Sensing in the Ocean.- 7.7 On the Detection of Submerged Submarines with Lateral Electromagnetic Waves.- 7.8 Detection of Magnetic Field Instead of Electric Field.- 7.9 Determination of the Permittivity and Conductivity of the Earth from Measurement of the Admittance of a Horizontal Antenna.- 7.10 Field of a Horizontal Electric Dipole in the Air over Earth or Sea; Application to FM Communication and Television.- 8 The Measurement of the Conductivity of the Oceanic Lithosphere with a Horizontal Antenna as the Source.- 8.1 The Homogeneous Isotropic Half-Space Model of the Oceanic Lithosphere-Theory.- 8.2 The Measurement of ?2.- 8.3 The Measurement of ?2.- 8.4 Comparison with Measurements.- 8.5 Reflections from an Ideal Reflecting Layer.- 8.6 Interpretation of Measured Data.- 9 Lateral Waves in a One-Dimensionally Anisotropie Half-Space.- 9.1 Introduction.- 9.2 Transform of Maxwell's Equations; Equations for ?x and B x.- 9.3 Solutions of the Differential Equations for ?x and B x.- 9.4 Approximate Integrated Formulas for the Complete Field in Region 1.- 9.5 Comparison with Measurements.- 9.6 Evaluation of the Integrals for the Field in Region 1 over a Homogeneous Anisotropic Region 2.- 9.7 Evaluation of H?1(?, 0), Ho1( ?, 0), and Hz1 (?, 0).- 9.8 Three-Dimensionally Anisotropic Region 2.- 10 The Propagation of Lateral Electromagnetic Waves in Air over Vertical Discontinuities.- 10.1 Review of Formulas for the Field in Homogeneous Isotropic Half-Spaces.- 10.2 Formulation of the Problem When the Properties of Region 1 Are Discontinuous.- 10.3 The Scattered Field in Regions 1 and 3.- 10.4 Numerical Evaluation of the Scattered Field; The Total Field.- 10.5 Propagation in the Presence of a Metal Wall in the Air; Induced Current and Scattered Field.- 10.6 Experiments on the Reflection of Lateral Electromagnetic Waves.- 11 The Horizontally Layered Half-Space.- 11.1 Description and Notation; Reflection Coefficients.- 11.2 The n-Layered Half-Space.- 11.3 The Surface Impedance and Reflection Coefficient for an n-Layered Region: Electric Type.- 11.4 The Surface Admittance and Reflection Coefficient for an n-Layered Region: Magnetic Type.- 11.5 The Electromagnetic Field in Region 1 over an n-Layered Half-Space.- 11.6 The Three-Layered Region; General Formulas.- 12 The Three-Layer Problem for Sediment on the Oceanic Crust.- 12.1 Introduction.- 12.2 Integrals for the Components of the Field of a Horizontal Electric Dipole.- 12.3 Approximate Formulas for the Quantity (?1/2)(Q3 -1).- 12.4 Approximate Formulas for the Quantity (?1/2?1)(P3 + 1).- 12.5 Evaluation of F?1 (?, z + d) and Fo1 (?, z + d).- 12.6 Evaluation of F z1(?, z + d); Formulas for the Electric Field.- 12.7 Evaluation of G?1 (?, z + d) and G o1 (?, z + d).- 12.8 Evaluation of Gz1(?, z + d); Formulas for the Magnetic Field.- 12.9 The Lateral-Wave Field; Comparison of Theoretical and Numerical Results.- 12.10 Application of the Three-Layer Formula to the Sea Floor.- 12.11 Integrals for the Components of the Field of a Vertical Electric Dipole.- 13 Exact Formulas for the Lateral Electromagnetic Pulses Generated by Vertical Dipoles.- 13.1 Introduction.- 13.2 The Time-Independent Field of a Unit Vertical Electric Dipole on the Boundary Between Electrically Different Half-Spaces.- 13.3 The Time-Dependent Component E2z(?,t) with a ?-Function Excitation.- 13.4 Evaluation of the Integrals for E2z(?,t).- 13.5 Evaluation of E2z(?,t).- 13.6 The Time-Dependent Component B2o(?,t) with a ?-Function Excitation.- 13.7 The Time-Dependent Component E2?(?,t) with a ?-Function Excitation.- 13.8 The Hertz Potential with ?-Function Excitation.- 14 Approximate Formulas for Lateral Electromagnetic Pulses Generated by Vertical and Horizontal Electric Dipoles.- 14.1 Integrals for the Approximate Time-Dependent Field of a Vertical Dipole; ?-Function Excitation.- 14.2 Evaluation of Integrals.- 14.3 The Approximate Time-Dependent Electromagnetic Field of the Vertical Dipole with ?-Function Excitation; Comparison with Exact Field.- 14.4 Generalization to the Field When the Source and Point of Observation Are in the Dielectric Region 1.- 14.5 Approximate Time-Domain Formulas for the Field of a Horizontal Electric Dipole; ?-Function Excitation.- 14.6 The Approximate Transient Field of a Vertical Dipole Excited by a Gaussian Pulse.- 14.7 The Exact Transient Field of a Vertical Dipole Excited by a Gaussian Pulse.- 14.8 The Approximate Transient Field of a Horizontal Dipole Excited by a Gaussian Pulse.- 15 The Propagation of Signals Along a Three-Layered Region: Open Microstrip.- 15.1 Introduction.- 15.2 The Horizontal Electric Dipole on or above the Air-Dielectric Boundary.- 15.3 Evaluation of the Integrals for the Field of the Horizontal Dipole over Microstrip.- 15.4 Integrated Formulas for the Components of the Electromagnetic Field.- 15.5 Comparison of the Electromagnetic Field of the Horizontal Dipole in Three Related Environments.- 15.6 The Propagation of Pulses on Microstrip.- 15.7 The Propagation of a Gaussian Pulse Along the Boundary Between Air and a Dielectric.- 15.8 The Transient Electric Field Generated in Open Microstrip by a Horizontal Dipole Excited by a Gaussian Pulse.- 15.9 Microstrip Transmission Lines.- 15.10 Gaussian Pulse Propagation on an Open Microstrip Transmission Line.- 15.11 Radiation from a Unit Dipole on a Dielectric Substrate.- 15.12 Microstrip Antennas.- 15.13 Generalization of the Theory; Application to Surface-Wave Propagation over the Arctic Ice.- 16 Antennas in Material Media Near Boundaries: The Bare Metal Dipole.- 16.1 Introduction.- 16.2 The Bare Cylindrical Antenna in a Dissipative Medium.- 16.3 The Effective Length and Figure of Merit of the Bare Antenna.- 16.4 The Bare Cylindrical Antenna in a Dissipative Medium Near a Boundary.- 16.5 Summary and Conclusions.- 17 Antennas in Material Media Near Boundaries: The Terminated Insulated Antenna.- 17.1 Circuit Properties of Insulated Antennas.- 17.2 The Effective Length of the Insulated Antenna.- 17.3 Antennas for Special Purposes: An Underground Antenna.- 17.4 Antennas for Special Purposes: An Antenna for the Sea Floor at f = 1 kHz.- 17.5 Antennas for Special Purposes: An Antenna for the Sea Floor at Very Low Frequencies.- 17.6 Conclusion and Summary.- 18 The Wave Antenna.- 18.1 Introduction.- 18.2 Description of the Wave Antenna and Its Surroundings.- 18.3 The Electric Field Due to Dipoles with Unit Electric Moment.- 18.4 The Electric Field of the Vertical Elements of the Beverage Antenna.- 18.5 The Electric Field of the Horizontal Elements of the Beverage and Horizontal-Wire Antennas.- 18.6 The Electric Field of the Beverage Antenna.- 18.7 The Electric Field of the Horizontal-Wire Antenna.- 18.8 Summary: The Beverage and Horizontal-Wire Antennas for Transmission.- 18.9 The Beverage and Horizontal-Wire Antennas for Reception-The Current in the Main Horizontal Wire.- 18.10 The Beverage and Horizontal-Wire Antennas for Reception-The Current Due to the Terminations, in the Load, and in the Entire Antenna.- 18.11 Generalization of the Field of the Wave Antenna for Application to Over-the-Horizon Radar Using Ionospheric Reflections.- Appendix A: Tabulation of Integrals.- Appendix B: Evaluation of Integrals with Radicals in the Integrand.- Appendix C: Evaluation of Integrals of Bessel Functions.- Appendix D: Evaluation of Integrals with Products and Quotients of Radicals.- Appendix G: Evaluation of Integrals for the Power in the Air and in the Earth Radiated by a Vertical Dipole in the Air above a Dielectric Earth.