Electromagnetic Waves in Stratified Media. Including Supplemented Material PDF
Preview Electromagnetic Waves in Stratified Media. Including Supplemented Material
OTHER TITLES IN THE SERIES IN ELECTROMAGNETIC WAVES Vol. 1 Electromagnetic Diffraction and Propagation Problems — FOCK Vol. 2 Ionospheric Sporadic-E — SMITH and MATSUSHITA (Editors) Vol. 4 The Scattering of Electromagnetic Waves from Rough Surfaces — BECKMANN and SPIZZICHINO Vol. 5 Electromagnetic Scattering — KERKER Vol. 6 Electromagnetic Theory and Antennas — JORDAN (Editor) Vol. 7 The Propagation of Electromagnetic Waves in Plasmas — GINZBURG Vol. 88 Tropospherìc Radiowave Propagation beyond the Horizon — Du CASTEL Vol. 9 Dipole Radiation in the presence of conducting Half-space — BANOS Vol. 10 Electrical Methods in Geophysical Prospecting — KELLER and FRISCHKNECHT Vol. 11 Electromagnetic Wave Theory — BROWN (Editor) Vol. 12 The Plane Wave Spectrum Representation of Electromagnetic Fields — CLEMMOW Vol. 13 Basic Theory of Waveguide Functions and introductory Microwave - Network Analysis — KERNS and BEATTY Vol. 14 V.L.F. Radio Engineering — WATT Vol. 15 Antennas in Inhomogeneous Media — GALEJS ELECTROMAGNETIC WAVES IN STRATIFIED MEDIA REVISED EDITION INCLUDING SUPPLEMENTED MATERIAL by JAMES R. WAIT, Fellow, I.E.E.E. Professor of Electrical Engineering, University of Colorado, Boulder, Colorado, USA PERGAMON PRESS OXFORD · NEW YORK · TORONTO SYDNEY · BRAUNSCHWEIG Pergamon Press Ltd., Headington Hill Hall, Oxford Pergamon Press Inc., Maxwell House, Fairview Park, Elmsford, New York 10523 Pergamon of Canada Ltd., 207 Queen's Quay West, Toronto 1 Pergamon Press (Aust.) Pty. Ltd., 19a Boundary Street, Rushcutters Bay, N.S.W. 2011, Australia Vieweg & Sohn GmbH, Burgplatz 1, Braunschweig Copyright © 1962 and 1970 Pergamon Press Ltd. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of Pergamon Press Ltd. First edition 1962 Second edition 1970 Library of Congress Catalog Card No. 79-100362 Printed in Great Britain by age Bros. (Norwich) Ltd. 08 0066364 TO GERTRUDE, LAURA AND GEORGE PREFACE TO SECOND EDITION IN this second edition, I have made a number of changes in order to call attention to recent investigations. I am particularly indebted to J. Heading and D. B. Large who brought a number of corrections and typographical errors to my attention. In order to bring the reader up to date, I have added a number of my recent papers (co-authored in some cases). These describe recent work on electro magnetic waves in stratified media. Numerous references to other related investigations are included in the bibliographies of these appended papers. I wish to thank Mrs. Eileen Brackett for her continued assistance and A. J. Steel for his sustained interest in the present series of monographs. Boulder J. R. WAIT PREFACE TO FIRST EDITION THIS book was written primarily to be used as a reference; however, the material was also presented in graduate courses in Wave Propagation at the University of Colorado and the Technical University of Denmark. Although the book is basically of a theoretical nature, numerous numerical examples and references to experimental data are included. Comprehension of the material requires knowledge of electromagnetism and mathematical analysis at the undergraduate level. Much of the subject matter is based on the author's own investigations. Some of these have been published previously in Technical Notes and in the Journal of Research of the National Bureau of Standards over the period 1956-1962. These portions of the work were carried out at the Boulder Laboratories of the National Bureau of Standards with support extended by the Cambridge Research Laboratories of the U.S. Air Force and the Ad vanced Research Projects Agency. It is a pleasure to thank the following individuals: H. Bremmer, K. G. Budden, D. D. Crombie, A. G. Jean, S. Maley, K. A. Norton, W. L. Taylor, A. D. Watt and F. J. Zucker for numerous and helpful discussions; K. P. Spies for extensive assistance in the calculations and critical readings of the manuscript; Mrs. Eileen Brackett for her painstaking care in the typing and preparation of the manuscript, and Mrs. L. C. Walters for helpful editorial comments. I am particularly indebted to my wife, Gertrude Wait who prepared the subject index and helped with proof reading. Finally, I wish to thank the publisher, I. R. Maxwell and his able assistants, J. P. H. Connell and Miss Felicity Slatter for the careful attention they gave to the book during produc tion and printing. Boulder J. R. WAIT xii PREFACE TO SECOND EDITION IN this second edition, I have made a number of changes in order to call attention to recent investigations. I am particularly indebted to J. Heading and D. B. Large who brought a number of corrections and typographical errors to my attention. In order to bring the reader up to date, I have added a number of my recent papers (co-authored in some cases). These describe recent work on electro magnetic waves in stratified media. Numerous references to other related investigations are included in the bibliographies of these appended papers. I wish to thank Mrs. Eileen Brackett for her continued assistance and A. J. Steel for his sustained interest in the present series of monographs. Boulder J. R. WAIT PREFACE TO FIRST EDITION THIS book was written primarily to be used as a reference; however, the material was also presented in graduate courses in Wave Propagation at the University of Colorado and the Technical University of Denmark. Although the book is basically of a theoretical nature, numerous numerical examples and references to experimental data are included. Comprehension of the material requires knowledge of electromagnetism and mathematical analysis at the undergraduate level. Much of the subject matter is based on the author's own investigations. Some of these have been published previously in Technical Notes and in the Journal of Research of the National Bureau of Standards over the period 1956-1962. These portions of the work were carried out at the Boulder Laboratories of the National Bureau of Standards with support extended by the Cambridge Research Laboratories of the U.S. Air Force and the Ad vanced Research Projects Agency. It is a pleasure to thank the following individuals: H. Bremmer, K. G. Budden, D. D. Crombie, A. G. Jean, S. Maley, K. A. Norton, W. L. Taylor, A. D. Watt and F. J. Zucker for numerous and helpful discussions; K. P. Spies for extensive assistance in the calculations and critical readings of the manuscript; Mrs. Eileen Brackett for her painstaking care in the typing and preparation of the manuscript, and Mrs. L. C. Walters for helpful editorial comments. I am particularly indebted to my wife, Gertrude Wait who prepared the subject index and helped with proof reading. Finally, I wish to thank the publisher, I. R. Maxwell and his able assistants, J. P. H. Connell and Miss Felicity Slatter for the careful attention they gave to the book during produc tion and printing. Boulder J. R. WAIT xii Chapter T GENERAL INTRODUCTION 1. SCOPE OF THE SUBJECT This book is concerned with electromagnetic waves in media whose properties vary in one particular direction. The variation may consist of abrupt or continuous changes. In this sense the media may be generally classified as stratified. This is an idealization of many situations which occur in nature. For example, there is a tendency for our terrestrial atmosphere to occur in horizontal layers. Similarly, the properties of the earth's crust do not vary significantly in the horizontal direction. Consequently, a proper understanding of wave phenomena in stratified media is of great practical importance. The major theoretical task is to find solutions of Maxwell's field equations which satisfy the appropriate conditions imposed by the various boundary conditions. Rather than present a sterile and formal treatment couched in the language of the mathematician, a physical approach is adopted. Furthermore, appli cations to the real world are used as illustrations of the theoretical principles. Special emphasis is given to radio waves in the frequency range from 3 to 30 kc/s which is described as v.l.f. (very low frequency). These frequencies correspond to wavelengths ranging from 100 to 10 km. In such cases the ionized layers in the upper atmosphere do indeed behave as stratified media since the scale of the irregularities is usually small compared with the wave length. In addition, many comparisons are made with experimental data on v.l.f. radio transmissions since only in this way can we ascertain if the adopted theoretical model has any real significance. An important feature of these waves is their low attenuation which enables communications at global distances. In addition, they exhibit remarkably stable phase characteristics. To avoid any misconception that the stratified models are only applicable to v.l.f. radio propagation, the results are also applied to e.l.f. (extremely low frequency) which covers the range from 3 kc/s down to about 1.0 c/s. A discussion of the mode theory of tropospheric radio propagation at v.h.f. (very high frequency) is also included. A more detailed summary of the book is given in Section 3 of this chapter. The book contains extensive references to published papers. For conveni ence of the reader each chapter is followed by its own list of references. Also included is a list of "additional" references which are germane to the subject of the chapter, but are not specifically cited. 1 2 Electromagnetic Waves in Stratified Media 2. NOTATION AND SOME BASIC IDEAS Through the book the rationalized MKS system of units is used. Since attention is only confined to linear phenomena, the electrical properties of the medium (or media) can also be defined in terms of the constants e, the dielectric constant (Fm) σ, the conductivity (mho/m) μ, the permeability (H/m) In some cases these "constants" will be functions of the coordinate. Locally, however, they are always considered constant. In later chapters e and σ are regarded as tensors to account for the anisotropie characteristics of magneto-plasmic media. Nearly always the time factor in this book is exp(+*W) when ω is the angu lar frequency and t is the time. Consequently, the actual electric field e{i) is related to the complex phasor E by e(t) = Real part of (Eei(ut). To explain some of the basic notation a very short exposition of plane electromagnetic waves in a homogeneous medium is presented. Ohm's law in the complex form is J = (σ + /€ω)Ε (1) where J is the current density vector and E is the electric field vector. The dimensions of J are A/m2 and those of E are V/m. The analogous relation for magnetic quantities is Β = μΗ (2) where B is the magnetic vector density and H is the magnetic vector intensity. The dimensions of B are wb/m2 and those of H are A/m. In source-free media the above vector quantities are related by curl E = - ψωΆ (3) and curl H = (σ + /€ω)Ε. (4) These are Maxwell's equations. For a homogeneous medium curl curl E = grad div E — div grad E = — ψω{σ + /βω)Ε. (5) General Introduction 3 Since div E = 0, this can be reduced to (V2 _ 2) 0 (6) y E = where V2 = div grad is the Laplacian operator (which operates on the rectangular components of E) and y2 = ίμω(σ + ieœ). The quantity y is defined as the propagation constant. As a simple preliminary problem, the fields are assumed not to vary in either the x or y directions with reference to a conventional coordinate system (*, y, z). Furthermore, the electric field is taken to have only an x component E. Therefore, Eq. (6) reduces to x and the solutions are e+?z and e-?2. Therefore, the general solution is E = Ae?* + B Q-y* (8) x where A and B are constants. The magnetic field component then has only a y component given by 1 dE H = - - -? x = - η-ΐΑ &ζ + η~ιΒ e-yz (9) y Ιμω dz where η = [ΐμω/(σ + ΐ€ω)]* is by definition the characteristic impedance of the medium for plane wave propagation. Remembering that the time factor is eiwi, it can be seen that the term Bt~yz is a wave travelling in the positive z direction with a diminishing amplitude, and the term A&z is a wave travelling in the negative z direction with a diminishing amplitude. The quantity η is thus equal to the complex ratio of the electric and magnetic field components in the x and y directions, respectively, for plane waves in an unbounded homogeneous medium. The quantities defined by y = [ϊμω(σ + 7€ω)]* and η = [/ρ/(σ + lew)]4 are sometimes called the secondary constants. In the case of free space = = 8.854 X IO"12 F/m e €0 μ = = 4π X 10~7 H/m μο σ = 0 4 Electromagnetic Waves in Stratified Media and then y = ik where k = (ε μο)έω = 2π/λ and λ is the wavelength. 0 Furthermore η = ηο = (μο/*ο)έ = 120τ7 Ω. 3. SUMMARY OF SUBJECT MATTER IN FOLLOWING CHAPTERS In Chapter II, a general analysis for the electromagnetic response of a plane stratified medium consisting of any number of parallel homogeneous layers is presented. The solution is first developed for plane-wave incidence and then generalized to both cylindrical and spherical-wave incidence. Numerical results for interesting special cases are presented and discussed. The appli cation of the results to surface-wave propagation over a stratified ground is considered in some detail. In Chapter III, the reflection of electromagnetic waves from planar stratified media is discussed in a relatively concise manner. Attention is confined to special forms of conductivity (or dielectric constant) profiles which lead to solutions in terms of Bessel functions. Most of the results, in equivalent forms, have already appeared in the literature. The chapter is essentially a consolidation of known solutions and their (sometimes novel) applications to the determination of reflection coefficients. In Chapter IV, the oblique reflection of plane electromagnetic waves from a continuously stratified medium is considered. Various approximate pro cedures are employed. For the slowly varying profiles, the WKB method and its extension are most suitable. However, certain modifications must be made when the ray has a turning point. It is shown that under this situation, the phase integral method is applicable. Finally, when the medium is rapidly varying, an alternative approach is adopted which is particularly suitable at low frequencies. In Chapter V, the basic theory of wave propagation around a sphere is given. By utilizing the concept of surface impedance, the derivations are greatly simplified. The formal solution in the form of a slowly convergent series is transformed to a more useful form by following the method of Watson. A further transformation is made in order to obtain a formula which is suitable for very small curvature of the surface. The influence of a concentric in- homogeneous atmosphere, with a smooth and monotonically varying profile, is also considered. In Chapter VI, a self-contained treatment of the waveguide-mode theory of propagation is presented. The model of a flat earth with a sharply bounded homogeneous isotropie ionosphere is treated for both vertical and horizontal dipole excitation. The properties of the modes are discussed in considerable detail. The influence of earth curvature is also considered by reformulating the problem using spherical wave functions of complex order. The modes in such a curved guide are investigated and despite the initial complexity of the
The list of books you might like
