Table Of ContentOTHER TITLES IN THE SERIES ON
ELECTROMAGNETIC WAVES
Vol. 1 Diffraction by Convex Surface - FOCK
Vol. 2 Ionospheric Sporadic E - SMITH AND MATSUSHITA (Editors)
Vol. 3 Electromagnetic Waves in Stratified Media - WAIT
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
Vol. 7 The Propagation of Electromagnetic Waves in Plasmas - GINZBURG
Vol. 8 Tropospheric Radiowave Propagation beyond the Horizon - DU CASTEL
Vol. 9 Dipole Radiation in the Presence of a Conducting Half-space - BANOS
Vol. 10 Electrical Methods in Geophysical Prospecting - KELLER AND
FRISCH KNECHT
ELECTROMAGNETIC
WAVE THEORY
Parti
Proceedings of a Symposium held at
Delft, The Netherlands, September 1965
Edited by
J. BROWN
SYMPOSIUM PUBLICATIONS DIVISION
PERGAMON PRESS
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Copyright © 1967
Pergamon Press Ltd.
First edition 1967
Library of Congress Catalog Card No. 66-17928
(2890/67)
SYMPOSIUM COMMITTEE
(Organizing and Technical Committees)
F.L.H.M.STUMPERS, the Netherlands, Chairman
H.M.BARLOW, U.K.
H.BREMMER, the Netherlands
H.A.W.GOOSSENS, the Netherlands, Treasurer
A.T. DE HOOP, the Netherlands
O.E.H.RYDBECK, Sweden
J. P. SCHOUTEN, the Netherlands
K.M.SIEGEL, U.S.A.
V.I.SIFOROV, U.S.S.R.
B.D.H.TELLEGEN, the Netherlands
R. TIMMAN, the Netherlands, Secretary
G. TORALDO DI FRANCIA, Italy
INTRODUCTION
AN U.R.S.I. Symposium on Electromagnetic Wave Theory was held in Delft
from September 6 to 11, 1966. It was sponsored by the International Scientific
Radio Union (U.R.S.I.) and its Netherlands National Committee, by the Tech
nological University of Delft, and by the Netherlands Electronic and Radio
Society (N.E.R.G.).
It was during a visit of Professor Timman to the University of Michigan, that
Professor Siegel, president of the Symposium Committee of U.R.S.I. Commis
sion VI, suggested that it would be in line with the great Dutch scientific
tradition to organize this Symposium. Professor Timman got the approval of
the Board of his University, the National Committee of U.R.S.I. also agreed
to sponsor the invitation, and during the Plenary Assembly of U.R.S.I. in
Tokyo 1963, the invitation was accepted.
The pioneer of the Dutch tradition in this sector of physics certainly was
Christiaan Huygens 1629-95. Three hundred years before the date of our Sym
posium we find in his works references to the wave propagation of light. He
discussed spheroidal waves in 1677, and his famous "Traite de la lumiere" was
prepared in 1678. It was printed in 1690. Huygens' principle still finds fruitful
application in modern calculations on electromagnetic wave theory. The full
title of his treatise: "Traite de la lumiere ou sont expliquoes les causes de ce
qui luy arrive dans le reflexion et dans le refraction et particulierement dans
l'etrange refraction du cristal d'islande" is also remarkable because of its strong
relation to the title of a thesis of about 200 years later: "On the theory of
reflection and refraction of light", 1875. In this work (in Dutch) the then 22 year-
old H. A.Lorentz gave the first sign of his great talents by calculations based on
the electromagnetic theory of light, proposed by Clerk Maxwell in 1865. About
1880 he derived the Lorentz-Lorenz relation between the macroscopical optical
properties of the medium and the properties of the scattering particles. The
second Lorenz is the famous Danish physicist L.V. Lorenz, who found the
relation independently at about the same time. In later years the coherence
theory of light, lately so much in the forefront because of laser develoments,
was developed by van Cittert (1934) and Zernike (1938) at the universities of
Utrecht and Groningen in our country. Zernike's many ideas and developments
in the application of the theory of light won him a Nobel prize. The study of
electromagnetic wave propagation for radio purposes owes much to the great
talents of another Dutch physicist, so well known in U.R.S.I., Professor Balth
van der Pol. His paper "On the propagation of radiowaves over a finitely con
ducting spherical earth" (with H.Bremmer) is a classic. His last paper (with
xin
XIV INTRODUCTION
A.Levelt) published posthumously, was still devoted to this branch of science:
'On the propagation of a discontinuous electromagnetic wave" (1960).
If there is a long and strong tradition in the Netherlands in the study of
wave propagation there is also the tradition in U.R.S.L on which we could
build forth. The U.R.S.L Symposia form a distinguished list: McGill University,
Montreal 1953, Michigan University, Ann Arbor, 1955, University of Toronto,
1959, Technical University of Denmark, Copenhague 1962. To organize the
next Symposium in this series was not only a question of effort but also of
money. The Committee received substantial donations from the "International
Scientific Radio Union", the Netherlands National Committee of U.R.S.L,
the Philips Industries in the Netherlands, the Netherlands Radar Research
Station. The following Netherlands companies, firms and foundations also con
tributed by donations to the success of the Symposium: Van der Heem N.V.,
I.B.M. Nederland, P. J. Kipp and Sons, Netherlands Cable factories, Neth.
Standard Electric Cy, N.V. Radium, the Dutch P.T.T., Dutch Mathematical
Society. It is a great pleasure to thank the Minister of Education and the Boards
of Curators of the Technological University, Delft, for their approval to hold the
symposium in the Main Building of the Technological University. The Minister
also gave a substantial financial guarantee for which we were very thankful,
although it proved unnecessary to make use of it. The Technological University
assisted the organizing committee in very many ways. The congress bureau of
the city of the Hague, where most participants were lodged, also gave much
assistance and support.
An organizing and technical committee was formed, many members of which
could only help us by correspondence. We wish to mention especially that
Professor Barlow drafted the first programme, and that we had many useful
additions and names through a U.S. Committee under Professor Siegel. Pro
fessor Siforov helped in organizing the participation from U.S.S.R. scientists.
For most of the practical organization problems Professor Timman, Mr. Goos-
sens and the chairman formed a small executive committe.
The opening ceremony of the Symposium on Monday, September 6, 1965,
was attended by a representative of the Minister of Science and Education, the
Mayor of Delft, the Secretary of the College of Curators of the University, the
chairmen of the Delft Departments of Electrical Engineering and General
Science and by many participants of the Symposium. After a word of welcome
by the chairman, Professor Kuypers, acting rector, gave an address on the history
of the University and its future. He then officially opened the Symposium. Pro
fessor Manneback for U.R.S.L thanked the University for its cooperation and
wished the Symposium every success. After a coffee break, Professor Barlow
gave his as-usual clear lecture on "Millimetre Waves and Optical Waves for
Long Distance Telecommunications", and Mr. Kampinsky spoke on: "Ex
perimental Evaluation of the results of the passive Communication Satellite,
Echo II."
In the afternoon the symposium split into a section on Antenna Theory,
chaired by Professor Knudsen and Professor Roubine and a section on Pro-
INTRODUCTION XV
pagation in Inhomogeneous Media chaired by Dr. Stumpers. Invited papers
were given by Professor Felsen (on "Lateral waves"—even among the good
invited papers an excellent one) and by Professor Karbowiak (on "Aspects of
Propagation in Inhomogeneous Media").
In the evening the acting Rector gave a reception to the participants and their
ladies.
On Tuesday the section on antennas continued. In addition, we had a section
on Propagation in Plasmas, chaired by Professor Cloutier, with an invited paper
by Professor Rydbeck (some wave propagation phenomena in ionized media),
and a section on Underground Waves and Space Waves, chaired by Professor
de Hoop, with an invited paper Dr. J. Wait (Terrestrial Waveguides).
Wednesday was devoted to a very interesting excursion to the Delta project.
The plans of closing the sea arms were discussed, and some dykes and sluices
were visited. The long boat trip from Hellevoetsluis to Rotterdam gave an
opportunity to renew old friendships and to discuss mutual problems.
On Thursday Professor Timman chaired a session on Boundary Value Prob
lems (invited paper: Professor S.Karp). Professor Siforov chaired a session on
Millimetre Waves and Optical Waves. (The invited paper was that given by
Professor Barlow on Monday). D. Kay chaired the session on Coherence Prob
lems and Modern Optics. In this session Professor Marechal gave an invited
paper on Wavefront Optics, and Professor Picinbono one on Statistical Optics.
Some of these sections continued on Friday.
New sections then started on Surface Waves and Wave Beams, chairman
Professor Barzilay, with invited papers by Professor Oliner (Guided complex
waves on slow wave periodic structures) and Dr.Zucker (Aspects of the theory
of surface waves). Another section was devoted to Propagation in Nonlinear
Media, chairman Professor Siegel, and had quite a number of contributions
from Russian scientists.
Saturday was divided between Multiple Scattering and Scattering on
Rough Boundaries, in one hall and Deterministic Scattering in the other hall
of the University. The first session was chaired by Professor van de Hülst, and
invited papers were given by Dr. Twersky (Multiple scattering of waves by
N-bodies) and by Professor Saxon (Propagation in random and periodic lat
tices). The second session was chaired by Professor Marcuvitz, and the invited
paper was given by Dr. Weston (Recent highlights in Diffraction Theory).
Shortly before 2 o'clock Dr. Stumpers thanked the chairmen, speakers and
participants and closed the Symposium.
On Friday night a banquet was organized in the Kurhaus Hotel, attended by
many participants and their ladies. Professor Siegel presided and Professor
Casimir gave the after-dinner speech; in a parable he slightly teased the theore
ticians about their prolonged discussions on unit systems. Professor Silver
addressed the participants on behalf of the Board of U.R.S.I. Professors
Marechal, Knudsen and Siforov spoke on behalf of the foreign participants
and Dr. Stumpers for the organizers.
Apart from the invited lectures, 117 contributions were presented at the Sym-
XVI INTRODUCTION
posium. For this reason there were always two sessions simultaneously, but
those who so desired could follow all the papers on any subject. The number of
registered participants was 264; 64 from the United States, 46 from the Nether
lands, 25 from France, 24 from the United Kingdom, 20 from Danmark, 18 from
Italy, 14 from Sweden, and 14 from U.S.S.R.—Canada, Poland, Norway,
Greece, D.D.R., Switzerland, Hungary, Yougo-Slavia, Australia and Finland
were also represented.
During the Symposium the main burden of organisatorial activities fell on
Mr. Goossens (Rear-Admiral, retired). Mrs. Timman, chairman of the Ladies
Committee, and Mrs. de Hoop organized daily trips to picturesque parts of the
country for the ladies and children of the participants.
From a scientific point of view the classical subjects; inhomogeneous media,
antenna theory, boundary value problems and surface waves had most attention.
We had hoped for more contributions on millimetre waves and optical waves,
coherence problems, modern optics and scattering problems, but apparently
the attention in universities and research institutes shifts only slowly. Many
international contacts were renewed and new contacts laid. The state of the art
and the still open problems in our domain were clearly exposed. In this way
this Symposium fulfilled the main task given to the Symposia of the International
Scientific Radio Union. I hope it was a worthy successor to Copenhague, etc.
After the Symposium, Professor John Brown accepted an invitation to edit the
Transactions. On behalf of all readers we thank him and Pergamon Press, the
publishers, for their work.
Dr. F. L. STUMPERS
Chairman Commission VI
International Scientific Radio Union
SECTION A
WAVE PROPAGATION
WAVE PROPAGATION
IN INHOMOGENEOUS MEDIA
A.E.KARBOWIAK
University of New South Wales, Kensington, N.S.W.
1. INTRODUCTION
Wave propagation problems in inhomogeneous and anisotropic media are
of very frequent occurrence; in fact it is the phenomenon of wave propagation
in homogeneous and anisotropic structures that occurs rather infrequently in
nature.
We recognize at the outset that wave propagation problems under the most
general, unrestricted inhomogeneous and anisotropic conditions neither have
explicit (and useful analytical solutions) nor can such problems be within our
conceptual control (and adequate grasp). It is because of the complexity of the
real problem that we find it necessary to restrict the class of problems to which
our solutions apply. In the course of trying to simplify the characterization of
our physical processes we tend to isolate different classes of problems and to
study certain limiting conditions of real physical situations. It is in this process
of reasoning that various patterns begin to emerge. But it is precisely at this
point that we should question our process of thinking and wonder whether the
patterns thus revealed—by painstaking analysis—are really projections of the
physically undergoing phenomena or perhaps they are simply reflections of the
patterns of our way of thinking, with little relation to physics.
Necessarily, we find ourselves simplifying our physical models to a manageable
level, to permit the use of known mathematical methods. Yet many a simplifica
tion hides a clue to the solution of the real physical problem, thus taking us no
nearer our final goal. Moreover, what appears to be a useful model may take
us on a long chase of what may be a fascinating, but irrelevant class of problems.
What do we need to help us in the growing complexity of problems? Until
recently it was the time-consuming numerical evaluation of many problems
that was the main stumbling block; but now, equipped with powerful computers,
this is no longer the case.
We need new and more powerful analytical tools and alongside of this a
wider and deeper conceptual grasp of physics.
Let us now examine the nature and breadth of the problems and perhaps
then we will be in a better position to assess our needs.
EWTI 1
1
2 A.E.KARBOWIAK
2. PARTICULAR ANALYTICAL APPROACHES
2.1. "Exact Solutions"
The most successful analytical solutions are invariably based on some
"judicious approach" and this is particularly true of various synthesis problems,
where we recognize that certain particular configurations lead to a clearly
defined class of problems, which, subsequently, can be tackled by well estab
lished mathematical methods. In such cases explicit closed form solutions can be
obtained. Such cases are, however, rare.
2.2. Approximate Solutions
All other analytical approaches are based on approximations. Their successes
are therefore limited by the explicit, and sometimes even implicit, approxima
tions. The more successful approximate methods include:
(1) variational methods,
(2) perturbation calculus,
(3) asymptotic evaluations,
(4) WKB method,
(5) Rayleigh-Ritz method,
(6) statistical approach.
2.3. New Concepts
New concepts are sometimes of assistance in analysis, but more frequently
they are a help in understanding the physical processes. Often, new concepts
are born out of an attempt of trying to gain a better understanding of physics.
In theory of wave propagation new concepts embrace waves such as, for
example:
(a) surface waves,
(b) leaky waves,
(c) quasi-modes,
(d) backward waves,
(e) longitudinal section waves,
(f) equivalent circuits,
(g) rays and geometrical optics, etc.
3. PARTICULAR "PHYSICAL" CONFIGURATIONS
3.1. Plane Waves along a Plane Interface Separating two Dissimilar Media
The class of problems encountered in wave propagation in the presence of a
plane interface is now well understood. Here plane waves of types (a), (b) and (c)
are found depending on circumstances, but because planes of infinite extent
