Electromagnetic Waves in Stratified Media

Electromagnetic Waves in Stratified Media

Revised Edition Including Supplemented Material

1st Edition - January 1, 1970

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  • Author: James R. Wait
  • eBook ISBN: 9781483184258

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International Series of Monographs in Electromagnetic Waves, Volume 3: Electromagnetic Waves in Stratified Media provides information pertinent to the electromagnetic waves in media whose properties differ in one particular direction. This book discusses the important feature of the waves that enables communications at global distances. Organized into 13 chapters, this volume begins with an overview of the general analysis for the electromagnetic response of a plane stratified medium comprising of any number of parallel homogeneous layers. This text then explains the reflection of electromagnetic waves from planar stratified media. Other chapters consider the oblique reflection of plane electromagnetic waves from a continuously stratified medium. This book discusses as well the fundamental theory of wave propagation around a sphere. The final chapter deals with the theory of propagation in a spherically stratified medium. This book is a valuable resource for electrical engineers, scientists, and research workers.

Table of Contents

  • Preface to Second Edition

    Preface to First Edition

    I General Introduction

    1. Scope of the Subject

    2. Notation and Some Basic Ideas

    3. Summary of Subject Matter in following Chapters

    General References

    II Reflection of Electromagnetic Waves from Horizontally Stratified Media


    1. Introduction

    2. Plane Wave Incidence

    3. Extension to Perpendicular Incidence

    4. Impedance Matching and Natural Oscillations in Stratified Media

    5. Line Source Excitation

    6. Line Source on a Homogeneous Medium

    7. Line Source over a Thin Layer

    8. The Radiation Field of the Line Source for Any Number of Layers

    9. Magnetic Line Source over a Stratified Medium

    10. Magnetic Line Source over a Dielectric Coated Conductor

    11. The Fields of a Vertical Electric Dipole over a Stratified Half-Space

    12. Some Experimental Measurements

    Appendix A Evaluation of the Integral P

    Appendix B Numerical Results for Surface Impedance of a Stratified Conductor


    III Reflection of Electromagnetic Waves from Inhomogeneous Media with Special Profiles


    1. Introduction

    2. General Considerations

    3. Inverse Square Profile

    4. Profile with an Exponential Transition

    5. Other Exponential Profiles

    6. Linear Profile

    7. Extension to Vertical Polarization

    8. Exponential Profile with Vertical Polarization

    9. Power Law Profile for Normal Incidence


    IV Approximate Methods for Treating Reflections from Inhomogeneous Media


    1. Introduction and the Conventional WKB Method

    2. WKB Method for Oblique Incidence

    3. Generalization of WKB Method

    4. Generalized WKB Method for Vertical Polarization

    5. Relation to Geometrical Optics

    6. Application to Tropospheric Propagation

    7. The Phase Integral Approach

    8. A Generalization of the Phase Integral Method

    9. Phase Integral for Vertical Polarization

    10. Rapidly Varying Transition Region

    10.1 Introduction

    10.2 Differential Equation for the Reflection Coefficient

    10.3 Iterative Solution

    10.4 Some Simple Extensions of the Solution

    10.5 Discussion of the Form of the Solution


    V Propagation along a Spherical Surface


    1. Basic Formulation

    2. The Watson Transformation

    3. Formula for Small Curvature

    4. Influence of an Inhomogeneous Atmosphere

    5. Equivalent Earth Radius Concept

    6. Extension to Non-Linear Atmosphere

    7. Asymptotic Form of the Solution

    8. Distance to the Horizon

    9. Concluding Remarks


    VI Fundamentals of Mode Theory of Wave Propagation


    1. Introduction

    2. Basic Concepts

    3. Formulation for Flat Earth Case

    3.1 Vertical Dipole Excitation

    3.2 Horizontal Dipole Excitation

    4. Properties of the Modes for Flat Earth Case

    4.1 Vertical Polarization

    4.2 Horizontal Polarization

    5. Influence of Earth Curvature

    6. Mode Series for a Curved Earth

    7. Antipodal Effects

    8. Resonator-Type Oscillations between Earth and the Ionosphere

    9. Excitation by Horizontal Dipoles for the Curved Earth

    10. Higher Approximations to the Curved Earth Theory

    11. Influence of Stratification at the Lower Edge of the Ionosphere

    12. Average Decay Laws

    13. Appendix


    VII Characteristics of the Modes for VLF Propagation


    1. Introduction

    2. The Ground Wave

    3. The Sky Waves

    4. The Roots of the Modal Equation

    5. Comments on a More Accurate Form of the Mode Equation

    6. The Height-Gain Functions

    7. The Excitation of VLF Modes

    8. Discussion of the Earth Detached Mode


    VIII Propagation in Stratified Magneto-Plasma Media


    1. Introduction

    2. The Dielectric Properties of a Plasma

    3. The Field Equations

    4. Reflection Coefficient for a Plane Boundary between Free Space and Plasma

    5. Reflection from a Stratified Plasma

    6. Arbitrary Inclination of Magnetic Field

    7. Reflection from a Homogeneous Plasma with Arbitrary Magnetic Field

    8. Derivation of Approximate Reflection Coefficients

    9. The Mode Series for an Anisotropic Ionosphere

    10. Effect of Earth Curvature

    Appendix A

    Appendix B A Note on the Energy Dependence of the Collision Frequency

    Appendix C Application of the Booker Quartic to Calculation of Reflection Coefficients


    IX VLF Propagation—Theory and Experiment


    1. Introduction

    2. Approximate Solutions of the Mode Equation

    2.1 Alternate Expansion for the Reflection Coefficient

    2.2 Application of the Q.L. Approximation

    2.3 Application of the Transverse Condition

    2.4 Extension to Arbitrary Dipping Magnetic Field

    2.5 Inclusion of Earth Curvature in the Analysis

    3. Measured Field Strength vs. Distance Data at VLF

    4. Measured Phase Characteristics of VLF Carriers

    5. Measurements of Diurnal Phase Shifts at VLF

    6. Sferics and Mode Theory


    X ELF (Extremely Low Frequency) Propagation—Theory and Experiment


    1. Introduction

    2. Basic Theoretical Model

    3. Antipodal Effects

    4. Earth-Flattening Approximation

    5. Distance and Frequency Dependence

    6. Near-Field Behavior

    7. Effect of the Earth's Magnetic Field

    8. Effect of an Inhomogeneous Atmosphere

    9. Propagation of ELF Pulses

    10. Interpretation of Hepburn's Experimental Data

    11. Influence of Horizontal Currents



    XI Asymptotic Development for Guided Wave Propagation


    1. Introduction

    2. Formulation of Problem

    3. The Complex Integral Representation

    4. The Mode Representation

    5. Ray Theory and Saddle Point Approximations

    6. Relation to Geometrical Optics

    7. Treatment at the Caustic

    8. Applications to Tropospheric Propagation

    9. Concluding Remarks


    XII Superrefraction and the Theory of Tropospheric Ducting


    1. Introduction

    2. Formulation

    3. The Asymptotic Solution

    4. The Special Case of a Normal Atmosphere

    5. Reduction to Ray Theory for "Normal" Atmosphere

    6. Extension of Theory to Include Superrefraction

    7. Refinements to the Asymptotic Approximations

    8. A Few Quantitative Results for Tropospheric Ducting

    9. Reduction to the Phase Integral Form

    10. The Modified Index of Refraction Method


    XIII Appendix-Supplementary Material

    1. Influence of the Lower Ionosphere on Propagation of VLF Waves to Great Distances

    2. Height-Gain for VLF Radio Waves 379

    3. Concerning Solutions of the VLF Mode Problem for an Anisotropic Curved Ionosphere

    4. Reflection of VLF Radio Waves from an Inhomogeneous Ionosphere

    Part I. Exponentially Varying Isotropic Model

    5. Reflection of VLF Radio Waves from an Inhomogeneous Ionosphere

    Part II. Perturbed Exponential Model

    6. Reflection of VLF Radio Waves from an Inhomogeneous Ionosphere

    Part III. Exponential Model with Hyperbolic Transition

    7. Some Remarks on Mode and Ray Theories of VLF Radio Propagation

    8. Two-Dimensional Treatment of Mode Theory of the Propagation of VLF Radio Waves

    9. Reflection of Electromagnetic Waves from a Lossy Magnetoplasma

    10. A Note on Vhf Reflection from a Tropospheric Layer

    11. Concerning the Mechanism of Reflection of Electromagnetic Waves from an Inhomogeneous Lossy Plasma

    12. Influence of an Inhomogeneous Ground on the Propagation of VLF Radio Waves in the Earth-Ionosphere Waveguide

    13. Propagation in a Model Terrestrial Waveguide of Nonuniform Height: Theory and Experiment

    14. Transverse Propagation of Waveguide Modes in a Cylindrically Stratified Magnetoplasma

    15. Cavity Resonator Modes in a Cylindrically Stratified Magnetoplasma

    16. Electromagnetic Propagation in an Idealized Earth Crust Waveguide

    17. Illumination of an Inhomogeneous Spherical Earth by an LF Plane Electromagnetic Wave

    18. Radiation from Dipoles in an Idealized Jungle Environment

    19. Comments on a Paper "a Numerical Investigation of Classical Approximations Used in VLF Propagation" by Pappert, Gossard, Rothmuller

    20. On the Calculation of Mode Conversion at a Graded Height Change in the Earth-Ionosphere Waveguide at VLF

    Errata and Addenda

    Author Index

    Subject Index

Product details

  • No. of pages: 620
  • Language: English
  • Copyright: © Pergamon 1970
  • Published: January 1, 1970
  • Imprint: Pergamon
  • eBook ISBN: 9781483184258

About the Author

James R. Wait

About the Editors

A. L. Cullen

V. A. Fock

J. R. Wait

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