# Electromagnetic Waves in Stratified Media

## 1st Edition

### Revised Edition Including Supplemented Material

**Authors:**James R. Wait

**Editors:**A. L. Cullen V. A. Fock J. R. Wait

**eBook ISBN:**9781483184258

**Imprint:**Pergamon

**Published Date:**1st January 1970

**Page Count:**620

## Description

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

Abstract

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

References

III Reflection of Electromagnetic Waves from Inhomogeneous Media with Special Profiles

Abstract

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

References

IV Approximate Methods for Treating Reflections from Inhomogeneous Media

Abstract

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

References

V Propagation along a Spherical Surface

Abstract

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

References

VI Fundamentals of Mode Theory of Wave Propagation

Abstract

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

References

VII Characteristics of the Modes for VLF Propagation

Abstract

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

References

VIII Propagation in Stratified Magneto-Plasma Media

Abstract

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

References

IX VLF Propagation—Theory and Experiment

Abstract

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

References

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

Abstract

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

Appendix

References

XI Asymptotic Development for Guided Wave Propagation

Abstract

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

References

XII Superrefraction and the Theory of Tropospheric Ducting

Abstract

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

References

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

## Details

- No. of pages:
- 620

- Language:
- English

- Copyright:
- © Pergamon 1970

- Published:
- 1st January 1970

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483184258