Geometrical theory of diffraction

402 Pages·1994·21.039 MB·English, Russian

by  Kinber, Boris Evseevich, Borovikov, Vladimir Andreevich

ElEctromagnEtic wavEs sEriEs 37
Geometrical theory
of diffraction
v. a. Borovikov
and B. Ye. Kinber
The Institution of Electrical Engineers
IEE ELECTROMAGNETIC WAVES SERIES 37
Series Editors: Professor P. J. B. Clarricoats
Professor Y. Rah mat-Sam ii
Professor J. R. Wait
Geometrical theory
of diffraction
Other volumes in this series:
Volume 1 Geometrical theory of diffraction for electromagnetic waves
G. L James
Volume 2 Electromagnetic waves and curved structures L. Lewin,
D. C. Chang and E. F. Kuester
Volume 3 Microwave homodyne systems R. J. King
Volume 4 Radio direction-finding P. J. D. Gething
Volume 5 ELF communications antennas M. L. Burrows
Volume 6 Waveguide tapers, transitions and couplers F. Sporleder and
H. G. Unger
Volume 7 Reflector antenna analysis and design P. J. Wood
Volume 8 Effects of the troposphere on radio communications
M. P. M. Hall
Volume 9 Schumann resonances in the earth-ionosphere cavity
P. V. Bliokh, A. P. Nikolaenko and Y. F. Flippov
Volume 10 Aperture antennas and diffraction theory E. V. Jull
Volume 11 Adaptive array principles J. E. Hudson
Volume 12 Microstrip antenna theory and design J. R. James, P. S. Hall
and C. Wood
Volume 13 Energy in electromagnetism H. G. Booker
Volume 14 Leaky feeders and subsurface radio communications
P. Delogne
Volume 15 The handbook of antenna design, Volume 1 A. W. Rudge,
K. Milne, A. D. Olver, P. Knight (Editors)
Volume 16 The handbook of antenna design, Volume 2 A. W. Rudge,
K. Milne, A. D. Olver, P. Knight (Editors)
Volume 17 Surveillance radar performance prediction P. Rohan
Volume 18 Corrugated horns for microwave antennas P. J. B. Clarricoats
and A. D. Olver
Volume 19 Microwave antenna theory and design S. Silver (Editor)
Volume 20 Advances in radar techniques J. Clarke (Editor)
Volume 21 Waveguide handbook N. Marcuvitz
Volume 22 Target adaptive matched illumination radar D. T. Gjessing
Volume 23 Ferrites at microwave frequencies A. J. Baden Fuller
Volume 24 Propagation of short radio waves D. E. Kerr (Editor)
Volume 25 Principles of microwave circuits C. G. Montgomery,
R. H. Dicke, E. M. Purcell (Editors)
Volume 26 Spherical near-field antenna measurements J. E. Hansen
(Editor)
Volume 27 Electromagnetic radiation from cylindrical structures
J. R. Wait
Volume 28 Handbook of microstrip antennas J. R. James and P. S. Hall
(Editors)
Volume 29 Satellite-to-ground radiowave propagation J. E. Allnutt
Volume 30 Radiowave propagation M. P. M. Hall and L. W. Barclay
(Editors)
Volume 31 Ionospheric radio K. Davies
Volume 32 Electromagnetic waveguides: theory and application S. F. Mahmoud
Volume 33 Radio direction finding and superresolution P. J. D. Gething
Volume 34 Electrodynamic theory of superconductors S.-A. Zhou
Volume 35 VHF and UHF antennas Burberry
Volume 36 Propagation, scattering and dissipation of electromagnetic waves
A. S. llyinski, G. Ya. Slepyan and A. Ya. Slepyan
Geometrical theory
of diffraction
V. A. Borovikov
and B. Ye. Kinber
The Institution of Electrical Engineers
Published by: The Institution of Electrical Engineers,
London, United Kingdom
© 1994: The Institution of Electrical Engineers
This publication is copyright under the Berne Convention and the
Universal Copyright Convention. All rights reserved.
Apart from any fair dealing for the purposes of research or private study,
or criticism or review, as permitted under the Copyright, Designs and
Patents Act, 1988, this publication may be reproduced, stored or
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sent to the publishers at the undermentioned address:
The Institution of Electrical Engineers,
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Herts. SG1 2AY, United Kingdom
While the authors and the publishers believe that the information and
guidance given in this work is correct, all parties must rely upon their own
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publishers assume any liability to anyone for any loss or damage caused
by any error or omission in the work, whether such error or omission is
the result of negligence or any other cause. Any and all such liability is
disclaimed.
The moral right of the authors to be identified as author of this work has
been asserted by them in accordance with the Copyright, Designs and
Patents Act 1988.
British Library Cataloguing in Publication Data
A CIP catalogue record for this book
is available from the British Library
ISBN 0 85296 830 2
Printed in England by Bookcraft, Bath
Contents
Editorial preface viii
Preface ix
1 Introduction 1
2 Fundamendals of the geometrical theory of diffraction 7
2.1 Laws of geometrical optics 7
2.2 Postulates of the geometrical theory of diffraction 9
2.3 Diffraction by slit: representation of edge waves in terms of
diffraction coefficients 13
2.4 Diffraction by slit: explicit expressions for edge diffracted
waves 17
2.5 Reconstruction of antenna radiation pattern by its near-
field measurements 21
2.6 Compensation of diffraction effects in antenna synthesis 24
2.7 GTD applicability limits 28
3 Ray fields and reflections from smooth bodies 29
3.1 Ray expansions 29
3.2 Eikonal equation and transport equations 30
3.3 Applicability limits for ray expansions: crossing caustics 35
3.4 Ray expansions of simple fields 35
3.5 Asymptotic solutions of reflection problems 44
3.6 Transformation of ray fields by smoothly curved diffraction
gratings 49
3.7 Ray fields in irregular flaring waveguides 54
3.8 Smooth junction between regular waveguides 59
4 Caustic and focal expansions 69
4.1 Uniform asymptotic expansions 69
4.2 Relationships between wavefronts and caustics 70
4.3 Systems of co-ordinates near caustics 73
4.4 Caustic expansions 75
4.5 Field near asymptote of a caustic 78
vi Contents
4.6 Focal expansions 80
4.7 Diffraction integral 83
5 Diffracted waves 92
5.1 Classification 92
5.2 Diffraction of plane wave by halfplane: penumbra fields 95
5.3 Cylindrical wave diffraction by halfplane; diffraction by
wedge 101
5.4 Penumbra fields in slit diffraction 108
5.5 2-D diffraction of arbitrary wave by curved wedge 112
5.6 3-D edge diffraction 120
5.7 Diffraction of toroidal wave by bicone 123
5.8 Canonic wave expansions 129
5.9 Reflection of penumbra field from smooth surface 132
5.10 Diffraction of penumbra field by wedge 137
5.11 Radiation pattern of slotted-guide antenna 142
5.12 Wedge diffraction of field with caustic in inhomogeneous
medium 148
6 GTD or physical optics methods? 155
6.1 Approximations of Kirchhoff and physical theory of
diffraction 155
6.2 High-frequency asymptotics in Kirchhoff approximation
and physical theory of diffraction 159
6.3 Radiation of reflector antenna 168
6.4 Diffraction by corner point of edge 177
6.5 Diffraction by arbitrary aperture 181
6.6 Side radiation of parabolic antenna with noncircular edge 199
6.7 Applicability limits of GTD formulations: Fresnel zones 207
6.8 Field-forming region and applicability criterion of
geometrical optics 217
7 Diffraction by bodies of complex geometry 224
7.1 Phase structure of solutions 224
7.2 Successive diffraction method 230
7.3 Diffraction by strip: recursion expressions for edge
diffracted waves 231
7.4 Method of self-consistent field 237
7.5 Accuracy of successive diffraction and self consistent field
methods 245
8 Diffraction at open end of waveguide 264
8.1 Waveguide penumbra fields 264
8.2 Open-ended waveguide: nonuniform asymptotic 268
8.3 Waveguiding problems: slotted waveguide, reflector in
waveguide bend 277
8.4 Open-ended waveguide: asymptotic uniform over
observation angle 289
8.5 Open-ended waveguide: asymptotic uniform over angles of
incidence and observation 298
Contents vii
8.6 Mode conversion in waveguide-horn junction 304
8.7 Asymptotic of excitation and reflection coefficients of horn
modes in a waveguide-horn junction 314
9 Methods and results of asympotic diffraction theory 325
9.1 Sommerfeld integral method 325
9.2 Method of canonical waves 331
9.3 Boundary layer method: edge diffraction by bicone 337
9.4 Nonstationary problems 349
9.5 Diffraction by cone 355
10 Appendix 364
10.1 Generalised Fresnel integral 364
10.2 Expressions for radiation pattern of reflector antenna 365
10.3 Calculation of sums of integrals 369
10.4 Field of system of equidistant sources 374
11 References 377
Index 388
Editorial preface
Volume 1 in this series, entitled 'Geometrical theory of diffraction for
electromagnetic waves', was written by Graeme James mainly during his stay in
the Electromagnetics Group at Queen Mary College in the 1970s and it was my
privilege to encourage him in that project. Much later, on the occasion of an URSI
Electromagnetic Symposium in Budapest in 1986, Professor Borovikov showed
me the Russian treatise covering the same subject. There seemed to be a place
for both texts in our Series, a view which was confirmed by Graeme James. Now
that the Russian text has appeared, that judgement has been vindicated and the
Series Editors are confident that the two works will complement each other into
the distant future.
Peter Clarricoats
Queen Mary and Westfield College,
University of London, 1992
Preface
In the 15 years since the publication of this book in Russian, the geometrical theory
of diffraction (GTD) has gained ever wider use and acceptance. Today there is
no need to take pains convincing the reader, as we did 15 years ago, that this
theory is useful for, and applicable to, wave field evaluation. Nevertheless, as far
as I know, there is no English monograph which gives a systematic and detailed
exposition of the system of ideas underlying GTD, expounds on the state of the
art, and delineates the limits and relationships with other popular asymptotic
theories (physical optics and edge wave methods). This book fills this gap.
We updated the Russian original of the book by including pertinent results
obtained in recent years. New material has been specially written for the western
reader poorly versed in the works of Russian authors. A natural course of events
in GTD research has brought about parallel efforts in different countries and often
the publications of the Russian authors lead their counterparts in the USA and
elsewhere by 10-15 years. By way of example we refer to work devoted to
diffraction by polygons. Had these publications been immediately known to
western researchers the theory could have advanced at a faster pace. Unfortunately,
the situation with the literature persists and, as before, some effective ideas and
methods developed in our country remain unknown to readers at large. Therefore,
in updating the book we paid particular attention to the results of Russian authors
that are practically unknown elsewhere.
The geometrical theory of diffraction is based on the solutions of model problems
obtained with exact or asymptotic methods of diffraction theory beyond GTD.
In the Russian book we gave these solutions without derivations and placed the
centre of gravity on their qualitative analysis. To balance the presentation in this
English edition we have added a chapter devoted to the solution techniques of
model problems.
The modifications have enlarged the English volume 1.5 times over its Russian
original. Sections 5.12, 6.8, 7.3, 8.4, 8.5, Chapter 9, and Sections 10.3 and 10.4
were written by V. A. Borovikov; Section 3.6 was written by B. YE. Kinber, and
the remaining materials are the result of co-authorship.
Unfortunately, B. YE. Kinber died of a heart attack last autumn at an early
stage in the preparation of this edition. Therefore the responsibility for all the
mistakes remaining in this volume is entirely mine.
V. A. Borovikov
Moscow
September 1992