Theory of electromagnetic wave propagation 4188

THEORY OF ELECTROMAGNETIC WAVE PROPAGATION CHARLES HERACH PAPAS PROFESSOR OF ELECTRICAL ENGINEERING CALIFORNIA INSTITUTE OF TECHNOLOGY DOVER PUBLICATIONS, INC., NEW YORK Copyright @ 1965,1988 by Charles Herach Papas All rights reserved under Pan American and International Copyright Conventions Published in Canada by General Publishing Company, Ltd., 30 Lesmill Road, Don Mills, Toronto, Ontario Published in the United Kingdom by Constable and Company, Ltd., 10 Orange Street, London WC2H 7EG This Dover edition, first published in 1988, is an unabridged and corrected republication of the work first published by the McGrawHill Book Company, New York, 1965, in its Physical and Quantum Electronics Series For this Dover edition, the author has written a new preface Manufactured in the United States of America Dover Publications, Inc., 31 East2nd Street, Mineola, N.Y 11501 Library of Congress Cataloging-in-Publication Data Papas, Charles Herach Theory of electromagnetic wave propagation / Charles Herach Papas p em Reprint Originally published: New York : McGraw-Hill, cl965 (McGraw-Hill physical and quantum electronics series) With new pref Includes index ISBN 0-486-65678-0 (pbk.) Electromagnetic waves.~ Title QC661.P29 1988 530.1'41-dcI9 88-12291 CIP "i' To RONOLDWYETH PERCIVAL KING Gordon McKay Professor of Appl1e~ Physics, Harvard University Outstanding Scientist, Inspiring Teacher, and Dear Friend """', ~ ," Preface This book represents the substance of a course of lectures I gave during the winter of 1964 at the California Institute of Technology In these lectures I expounded a number of newly important topics in the theory of electromagnetic wave propagation and antennas, with the purpose of presenting a coherent account of the subject in a way that would reveal the inherent simplicity of the basic ideas and would place in evidence their logical development from the Maxwell field equations So enthusiastically were the lectures received that I was encouraged to put them into book form and thus make them available to a wider audience The scope of the book is as follows: Chapter provides the reader with a brief introduction to Maxwell's field equations and those parts of electromagnetic field theory which he will need to understand the rest of the book Chapter presents the dyadic Green's function and shows how it can be used to compute the radiation from monochromatic sources In Chapter the problem of radiation emitted by wire antennas and by antenna arrays is treated from the viewpoint of analysis and synthesis In Chapter two methods of expanding a radiation field in multipoles are given, one based on the Taylor expansion of the Helmholtz integrals and the other on an expansion in spherical waves Chapter deals with the wave aspects of radio-astronomical antenna theory and explains the Poincare sphere, the Stokes parameters, coherency matrices, the reception of partially polarized radiation, the two-element radio interferometer, and the correlation coefficients in interferometry Chapter gives the theory of electromagnetic wave propagation in a plasma medium and describes, with the aid of the dyadic Green's function, the behavior of an antenna immersed in such a medium Chapter is concerned with the covariance of Maxwell's vii Preface equations in material media and its application to phenomena such as the Doppler effect and aberration in dispersive media The approach of the book is theoretical in the sense that the subject matter is developed step by step from the Maxwell field equations The advantage of such an approach is that it tends to unify the various topics under the single mantle of electromagnetic theory and serves the didactic purpose of making the contents of the book easy to learn and convenient to teach The text contains many results that can be found only in the research literature of the Caltech Antenna Laboratory and similar laboratories in the U.S.A., the U.S.S.R., and Europe Accordingly, the book can be used as a graduate-level textbook or a manual of self-instruction for researchers My grateful thanks are due to Professor W R Smythe of the California Institute of Technology, Professor Z A Kaprielian of the University of Southern California, and Dr K S H Lee of the California Institute of Technology for their advice, encouragement, and generous help I also wish to thank Mrs Ruth Stratton for her unstinting aid in the preparation of the entire typescript Charles Herach Papas Preface to the Dover Edition Except for the correction of minor errors and misprints, this edition of the book is an unchanged reproduction of the original My thanks are due to my graduate students, past and present, for the vigilance they exercised in the compilation of the list of corrections, and to Dover Publications for making the book readily available once again Charles Herach Papas viii Contents Preface vii Preface to the Dover Edition viii The electromagnetic 1.1 Maxwell's Equations in Simple Media 1.2 Duality Energy Relations 14 Radiation from monochromatic sources in unbounded regions 2.1 The Helmholtz Integrals 2.2 Free-space Dyadic Green's Function 2.3 Radiated Power 1.3 Boundary Conditions 1.4 The Field Potentials and Antipotentials 1.5 field 19 19 26 29 Radiation from wire antennas 3.1 Simple Waves of Current 3.2 Radiation from Center-driven Antennas 3.3 Radiation Due to Traveling Waves of Current, 3.4 Cerenkov Radiation 45 Integral Relations between Antenna Current 3.5 and Radiation Pattern 48 Pattern Synthesis by Hermite Polynomials 3.6 General Remarks on Linear Arrays 3.7 Directivity Gain 73 37 56 42 50 37 Multipole expansion of the radiated field 4.1 Dipole and Quadrupole Moments 4.2 Taylor Expansion of Potentials 4.3 Dipole and Quadrupole Radiation 4.4 Expansion of Radiation Field in Spherical Waves 81 81 86 89 97 Radio-astronomical antennas 5.1 Spectral Flux Density 5.2 Spectral Intensity, Brightness, Brightness Temperature, 109 111 Apparent Disk Temperature 115 5.3 Poincare Sphere, Stokes Parameters 118 5.4 Coherency Matrices 5.5 Reception of Partially Polarized Waves 134 140 5.6 Antenna Temperature and Integral Equation for Brightness Temperature 5.7 Radio Interferometer 5.8 148 Elementary Theory of the Two-element 151 Correlation Interferometer 159 Electromagnetic waves in a plasma 6.1 Alternative Descriptions of Continuous Media 6.2 Constitutive Parameters of a Plasma 170 175 6.3 Energy Density in Dispersive Media 6.4 Propagation of Transverse Waves in Homogeneous Isotropic Plasma 183 178 6.5 Dielectric Tensor of Magnetically Biased Plasma 6.6 Plane Wave in Magnetically Biased Plasma 195 6.7 Antenna Radiation in Isotropic Plasma 205 6.8 Dipole Radiation in Anisotropic Plasma 6.9 Reciprocity 212 209 187 169 The Doppler effect 7.1 Covariance of Maxwell's Equations 7.2 Phase Invariance 7.3 Doppler Effect and Aberration 7.4 Doppler Effect in Homogeneous 7.5 Index of Refraetion 7.6 Wave Equation and Wave 4-vector 217 218 223 225 Dispersive Media of a Moving Homogeneous for Moving Homogeneous 227 Medium Isotropie Media Index 230 233 24i A CATALOG OF SELECTED DOVER BOOKS IN ALL FIELDS OF INTEREST DRAWINGS OF REMBRANDT, edited by Seymour 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(3) 19 2 Theory of electromagnetic wave propagation Since the medium is unbounded, q, and A must also satisfy the radiation condition In physical terms this means that q, and A in the far zone must have the form of outwardly traveling spherical (but not necessarily isotropic) waves, the sphericity of the waves being a consequence of the confinement of the sources p and J to a finite part of space Let... for example, S A Schelkunoff, "Electromagnetic D Van Nostrand Company, Inc., Princeton, N.J., 1943 Waves," chap 4, 7 Theory of electromagnetic wave propagation Thus to every electromagnetic field E, H produced by electric current J there is a dual field H', E' produced by a fictive magnetic current J~ 1.3 Boundary Conditions The electromagnetic field at a point on one side of a smooth interface between... paper On the Dynamical Theory of Diffraction, Trans Cambridge Phil Soc., 9: 1 (1849) For a mathematically rigorous proof, see O Blumenthal, Uber die Zerlegung unendlicher Vektorfelder, Math Ann., 61: 235 (1905) 9 Theory of electromagnetic wave propagation V.D=p (46) V.B=O (47) and the constitutive relations for a simple medium D = eE (48) B = ,uH (49) From the solenoidal nature of B, which is displayed... "Electromagnetic Theory, " chap 1, McGraw-Hill Book Company, New York, 1941 1 Theory of electromagnetic wave propagation = electric displacement vector, coulombs per meter2 D(r,t) B(r,t) = magnetic induction vector, webers per meter2 J(r,t) = current-density vector, amperes per meter2 p(r,t) = volume density of charge, coulombs per meter3 r = position vector, meters t = time, seconds The equation of. .. point of view of the theory of differential equations, the solution of Eq (2) consists of not only the particular integral (6) but also a complementary solution In the present instance, however, the radiation condition requires that the complementary solution vanish identically 20 Monochromatic sources in unbounded regions where G(r,r') is a function of the coordinates of the observation point r and of. .. (27) u",E.,(r) In media showing microscopicinertial or relaxation effects, one or more of these parameters may be complex frequency-dependent quantities For the sake of notational simplicity, in most of what follows we shall drop the subscriptw and omit the argument r in the mono5 Theory of electromagnetic wave propagation chromatic case, and we shall suppress the argument r in the timedependent case... made up of charge carriers in motion (discrete case), we must calculate 3 Theory of electromagnetic wave propagation the total force F(r,t) acting on a charge carrier by first integrating the force density f(r,t) throughout the volume occupied by the carrier, i.e., F(r,t) = ff(r + r',t)dV' = q[E(r,t) + v(r,t) X B(r,t)J (17) where q is the total charge, and then equating this force to the force of inertia... meter2• (85) With 15 Theory of electromagnetic wave propagation the aid of expressions (79), the time average of Eq (85) leads to the following expression for the complex Poynting vector: S = ~E (86) X H* If from the scalar product of H* and V' X E = iWJLH the scalar product of E and V' X H* = J* iweE*(e is assumed to be real) is subtracted, and if use is made of the vector identity + V' (E X H*) = H*... A.) (23) which follow from the gradients of the Lorentz conditions V' A = iWEP.!P and V' • A = iwp.!Pm' Thus relations (21) and (22) may be written as follows: E = iw [ A H = ; V' X + b V'(V' • A) ] • ~ V' A + iw [ A + b X A V'(V' • A.) ] (24) (25) 23 Theory of electromagnetic To enable us to cast A wave propagation + ~ V(V A) and A + k V(V A.) into the form of an operator operating on A and A., we...The 1 electromagnetic field In this introductory chapter some basic relations and concepts of the classic electromagnetic field are briefly reviewed for the sake of easy reference and to make clear the significance of the symbols 1.1 Maxwell's Equations in Simple Media In the mks, or Giorgi, system of units, which we shall use throughout this book, Maxwell's ... for example, S A Schelkunoff, "Electromagnetic D Van Nostrand Company, Inc., Princeton, N.J., 1943 Waves," chap 4, Theory of electromagnetic wave propagation Thus to every electromagnetic field... substance of a course of lectures I gave during the winter of 1964 at the California Institute of Technology In these lectures I expounded a number of newly important topics in the theory of electromagnetic. .. due to Professor W R Smythe of the California Institute of Technology, Professor Z A Kaprielian of the University of Southern California, and Dr K S H Lee of the California Institute of Technology