Hybrid Formulation of Wave Propagation and Scattering

429 Pages·1984·16.391 MB·English

by  L. B. Felsen (auth.), L. B. Felsen (eds.)

Hybrid Formulation of
Wave Propagation and Scattering
NATO ASI Series
Advanced Science Institutes Series
A Series presenting the results of activities sponsored by the NATO Science
Committee, which aims at the dissemination of advanced scientific and technological
knowledge, with a view to strengthening links between scientific communities.
The Series is published by an international board of publishers in conjunction with the
NATO Scientific Affairs Division
A Life Sciences Plenum Publishing Corporation
B Physics London and New York
C Mathematical and D. Reidel Publishing Company
Physical Sciences Dordrecht and Boston
0 Behavioural and Martinus Nijhoff Publishers
Social Sciences Dordrecht/Boston/Lancaster
E Applied Sciences
F Computer and Springer-Verlag
Systems Sciences Berlin/Heidelberg/New York
G Ecological Sciences
Series E: Applied Sciences - No. 86
Hybrid Formulation of
Wave Propagation and Scattering
edited by
L.B. Felsen
Department of Electrical Engineering and Computer Science
Polytechnic Institute of New York
Farmingdale, NY 11735
USA
1984 Martinus Nijhoff Publishers
Dordrecht I Boston I Lancaster
Published in cooperation with NATO Scientific Affairs Division
Proceedings of the NATO Advanced Research Workshop on Hybrid Formulation of
Wave Propagation and Scattering, IAFE, Castel Gandolfo (Rome), Italy, August 30-
September 3, 1983
Library of Congress Cataloging in Publication Data
NATO Advanced Resrarch Workshop on Ilybrid Formulation
of Wave Propa~ation nnll Scattering (1981 : Castel
Gandolfo, Italy)
Jlybrid formulation of wave propagation and sC.rl.ttering.
(NATO AS! series. Series E. Applied sciences;
no. 86)
"Proceedings of the NATO Advanced Research Workshop
on llybrid Formulation of Wave Propagation and
Scattering, IAFE, Castel Grtndolfo. (Rome), Italy,
.~ugust "lO-September 3. rQ83"--T.p. verso.
"Published in cooperation with NATO Scientific
Affairs Division.1t
Includes bibliographical references.
1. Beam optics--Congresscs. 2. Electromagnetic
waves--Transmission--Congrcsses. 1. Electromagnetic
waves--Scattering--Congrcssps. 4. Waves--Congresses.
I. Felsen, Leonard B. II. North Atlantic Treaty
Organization. Scipntific Affairs Division. TIl. Title.
IV. Serif's.
QC3S9.N"lR lQS1 535'.'32 84-20651
ISBN -13: 978-94-009-6221-7 e-ISBN -13:978-94-009-6219-4
DOl: 10.1007/978-94-009-6219-4
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Copyright © 1984 by Martinus Nijhoff Publishers, Dordrecht
Softcover reprint of the hardcover I st edition 1984
v
Preface
The Workshop on Hybrid Formulations of Wave Propagat~on and
Scattering underwent a sequence of iterations before emerging in
the format recorded here. These iterations were caused by various
administrative and logistical problems which need not be detailed.
However, its direction being set initially, the iterations led to
modifications of the original concept so that the final form was
arrived at through an indirect approach. This circumstance may ex
plain some possible deficiencies which might have been removed, had
the final concept been implemented directly.
The motivation arose from a perception that the newly restored
interest, coupled with new developments, in hybrid methods employ
ing progressing wave fields and oscillatory wave fields for time
harmonic and transient guided propagation in manmade or general geo
physical environments, and for scattering by targets and irregulari
ties, merits exposure to the wider scientific community. Accord
ingly, a meeting with highly tutorial content was envisaged. For
administrative reasons, related to sponsorship and organizational
structure, this objective could not be realized but, eventually,
there emerged the possibility of convening an Advanced Research
Workshop (ARW) under the auspices of the NATO Advanced Study Insti
tute Series. The original concept was then modified to accommodate
a Workshop, wherein state-of-the-art science is discussed by a
relatively small group of specialists, instead of tutorial presenta
tions of more basic material. Moreover, the concept was broadened
to provide interaction between researchers in different disciplines
for the purpose of exposing specialists in one area to the methods
and techniques employed for similar problems by workers in other
areas. The designation "hybrid" was now interpreted more hroadly
to encompass an approach to difficult wave problems that involvesvar-
ious combinations of techniques leading to a more effective solu
cion. Much of the discussion at the Workshop centered in fact on
what is meant by "effective". Here, the constraints imposed by
differing requirements and objectives in various research organiza
tions (academic, governmental and industrial) turned out to nlay
an essential role. A major accomplishment of the Workshop Fas to
impress upon groups motivated by one objective the different view
points of groupR motivated by other objectives.
A prerequisite for establishing interaction among specialists
from different disciplines is the ability of each to understand the
lanfuage of the other. Although no formal mechanism was employed
to achieve this goal, it turned out that the "language barrier"
was overcome rather quickly so that intensive interplay character
ized the discussions after the first day of presentations. Here,
the informality of a Workshop, where speakers are interrupted for
on-the-spot clarification, sets an effective framework. At the
conclusion of the Workshop, there was agreement that everyone had
leartled to listen to everyone else. While this may not lead to a
VI
change of the modus operandi of those who already feel to be oper
ating in the most "effective" manner, it will at least have helped
them to understand the operational procedure of others having differ
ent requirements and constraints.
The disciplines included in the Workshop were colored by the
background of the Director who, from personal knowledge, attempted
to select areas (and individuals representing them) so as to opti
mize the likelihood of interdisciplinary dialogue. A special effort
was made to include in each discipline an emphasis on analysis as
well as numerical implementation. The analysis-computer interface
was, in fact,a principal item for lively debate. Deliberately ex
cluded were statistical phenomena in the propagation environment
as well as the consideration of inverse problems. The scope of
these unquestionably important problem areas was regarded to be so
broad as to dilute the concentration on the other topical themes.
Invitations were extended to workers in e1ectromagnetics. optics,
tropospheric propagation, underwater acoustics, elasticity and
seismology. The final program had gaps in some of these areas be
cause of last minute perturbations caused by the inability of sev
eral invitees to attend. Nevertheless, the strong representation
in e1ectromagnetics, guided optics, elasticity and underwater acous
tics included enough diversity to demonstrate that a Workshop with
strong interdisciplinary f1avo~ can be an enriching experience.
Should the exercise be repeated in the future, one may draw on the
present experience to broaden and improve.
The papers included in this volume are based on preprints sub
mitted by participants at the time of the Workshop and were solic
ited by the Director who also made suggestions concerning their
length and contents. By an informal internal review scheme, most
papers were subjected to a reading by at least one of the other con
tributors. Thereafter, only a minimal attempt was made to edit
the final submitted manuscripts and to standardize the notation.
This route was followed to expedite the processing of this volume,
but it resulted in a lack of uniformity and in certain linguistic
transgressions. On the other hand, this style preserved some of
the spontaneity and international flavor that characterized a Work
shop attended by participants from many countries.
The contributions are grouped into four sections: 1. Rays
and modes; 2. Rays and beams; 3. Transient propagation and scatter
ing; and 4. Numerical modeling. The hybrid viewpoint is exploited
most specifically in section 1, which contains several contributions
emphasizing the interplay between time-harmonic ray fields and
modal fields in guiding configurations, the role of adiabatic in
variants and of spectral considerations in defining local modes in
waveguides with wea:: longitudinal and lateral variation, and, via
two introductory papers, the hybrid mix of progressing (ray) and
oscillatory (mode) fields. Section 2 begins with ray methods for
time-harmonic diffraction problems involving edges on planar and
VII
curved boundaries, and with the uniformization of conventional ray
techniques required there. Also illustrated is the use of ray
methods for propagation in complicated inhomogeneous media and for
propagation in tapered guiding structures. Conventional ray theory
is then generalized to include complex rays and their utilization
for the description of beam type fields. This is followed by sev
eral examples of beam tracing in different propagation and diffrac
tionconfigurations. The construction of transient field solutions
in terms of progressing (wavefront) and oscillatory (resonance)
constituents is taken up in section 3 and is applied there to
t
diffraction problems and to propagation in weakly and strongly dis
persive environments. Here the requirement of causality leads to
t
formulations that effectively employ hybrid wavefront-resonance
combinations. While numerical implementation is of concern through
out these presentations, the contributions in section 4 focus atten
tion on various algorithms that have been devised for solution of
time-harmonic and transient propagation under quite general condi
tions. Here, one may gain an appreciation of the accuracy, complex
ity and efficiency of computer codes derived from models based on
rays, modes and beams, and on layered approximations for inhomo
geneous environments.
The contributions in each section demonstrate both the diver
sity of wave problems in different disciplines and the COMMonality
of techniques to cope with them. While a specialist in one disci
pline may not be familiar with the terminology in another discipline,
he should recognize the relevance of what is done elsewhere by the
similarity of the mathematical formulation and by the physical con
tent. Cross fertilization was achieved rather well by direct con
tact at the Workshop, and it is hoped that this feature has not
been lost through the more formal structure of papers in this vol
ume. Especially those readers unfamiliar with propagation in elas
tic media and its application to seismology should not be discouraged
by the complicated structure of the basic equations since the tech
niques employed in the seismological examples here deserve to be
carefully explored in electromagnetics, optics and underwater acous
tics. Conversely, electromagnetic diffraction, both time-harmonic
and transient, has been developed to a degree not yet incorDorated
into other types of fields.
As noted earlier, much time at the Workshop was spent in dis
cussion periods. Although the discussions were taped, it was im
practical either to incorporate the voluminous verbatim transcripts,
or to have the Director edit them, subject to approval of the parti
cipants. The possible gains obtained by these options would have
been offset by substantial delays in publication. It is hoped that
the included Summary, based on the reports from the Working Groups,
will provide the principal perspectives and assessments that emerged
from the exchanges of views during the Workshop.
VIll
The Workshop would not have been possible without the assist
ance of the Organizing Committee, which carried the burden of cop
ing with logistical and organizational problems in Italy and coor
dinating these problems with a non-resident, the Director. I ex
press my sincere gratitude especially to Professors Laura Ronchi
Abbozzo and Annamaria Scheggi at the Institute for Electromagnetic
Wave Research (IROE) in Florence for their dedication. My appre
ciation is also extended to Professor V. Cappellini, Director of
IROE, for his generous support in making available administrative
services for typing, preparation of preprints and other conference
materials. A generous financial contribution from SELENIA, Rome,
is also gratefully acknowledged. Finally, it has been a pleasure
to interact with Dr. M. DiLullo, the Director of the NATO ARW Pro
gram, who has extended friendly advice on a host of administrative
details.
Leopold B. Felsen
Workshop Director
IX
TABLE OF CONTENTS
PREFACE V
PART I: RAYS AND MODES
1. L. B. Felsen
Progressing Fields, Oscillatory Fields, and
Hybrid Combinations 3
2. E. C. Shang
Transform Relations between Rays and Modes 23
3. J.M. Arnold
Spectral Synthesis and Adiabatic Invariants for
Non-Uniform Waveguides 33
4. D.E. Weston
Rays, Modes and Flux 4?
5. C.H. Harrison
Ray/Mode Trajectories and Shadows in the
Horizontal Plane by Ray Invariants 61
6. M. J. Buckingham
Acoustic Propagation in A Wedge-Shaped Ocean
with Perfectly Reflecting Boundaries ??
Part II: RAYS AND BEAMS
1. R. Tiberio
A Spectral Extended Ray Method for Edge
Diffraction 109
2. M. Idemen
Modal Edge-Diffraction Coefficients for
Cylindrically and spherically Curved Concave
Surfaces 131
x
3. A.M. Scheggi~ R. Falciai~ P. Cavigli~ S. Mezza
Rays in Tapered Waveguides 139
4. A. Hanyga
Numerical Computation of Elastic Wavefields in
Anisotropic Elastic Media in the Presence of
Caustics 153
5. G. Ghione~ I. Montrosset~ R. Orta
Complex Rays 169
6. E.F. Kuester and D.C. Chang
Imaging and Propagation of Beams in Metallic
or Dielectric Waveguides 185
7. J. Jacob and H.G. Unger
Gaussian Beam Transformation through Lenses
and by Curved Gratings 195
8. A. Hanyga
Gaussian Beams in Anisotropic Elastic Media
and Applications 215
Part III: TRANSIENT PROPAGATION AND DIFFRACTION
1. L.W. Pearson
The Singularity Expansion Representation of
Surface Current on A Perfectly Conducting
Scatterer 229
2. E. Heyman and L.B. Felsen
Wavefront Interpretation of SEM Resonances~
Turn-On Times~ and Entire Functions 253
3. E. Heyraan and L. B. Fe lsen
Non-Dispersive Approximations for Transient
Ray Fields in An Inhomogeneous Medium 269
4. E.F. Kuester and A.G. TiJhuis
Time-Domain Weyl Plane-Wave Representation for
Wave Functions 285
Part IV: NUMERICAL MODELING
1. F.B. Jensen
Numerical Models in Underwater Acoustics 295