Approximate boundary conditions in electromagnetics

366 Pages·1995·12.99 MB·English

by  Senior

ELECTROMAGNETIC WAVES SERIES 41
Approximate
boundary
conditions in
electromagnetics
T. B. A. Senior and
J. L. Volakis
The Institution of Electrical Engineers
IEE ELECTROMAGNETIC WAVES SERIES 41
Series Editors: Professor P. J. B. Clarricoats
Professor J. R. Wait
Professor E. V. Jull
Approximate
boundary
conditions in
electromagnetics
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 R. A. Burberry
Volume 36 Propagation, scattering and dissipation of electromagnetic waves
A. S. llyinski, G. Ya. Slepyan and A. Ya. Slepyan
Volume 37 Geometrical theory of diffraction V. A. Borovikov and B. Ye. Kinber
Volume 38 Analysis of metallic antennas and scatterers B. D. Popovic and
B. M. Kolundzija
Volume 39 Microwave horns and feeds A. D. Olver, P. J. B. Clarricoats, A. Kishk
and L. Shafai
Volume 40 Uniform stationary phase method V. A. Borovikov
Approximate
boundary
conditions in
electromagnetics
T. B. A. Senior and
J. L. Volakis
The Institution of Electrical Engineers
Published by: The Institution of Electrical Engineers, London,
United Kingdom
© 1995: 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
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While the authors and the publishers believe that the information and
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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 849 3
Printed in England by Bookcraft, Bath
Contents
Preface ix
1 Introduction 1
2 First order conditions 7
2.1 Basic equations 7
2.2 Classical boundary conditions 9
2.3 First order impedance conditions 12
2.4 First order transition conditions 17
2.5 Accuracy 22
2.6 Surface perturbations 32
2.6.1 Displacement 32
2.6.2 Uniform roughness 33
2.6.3 Corrugations 38
2.7 Uniqueness 41
3 Application to planar structures 47
3.1 Introduction 47
3.2 Wiener-Hopf versus dual integral equation methods 50
3.3 Resistive half-plane (E-polarisation) 53
3.3.1 Dual integral equation solution 53
3.3.2 Uniform diffracted field 60
3.4 Conductive half-plane (E-polarisation) 74
3.5 Resistive and conductive half-planes (H-polarisation) 76
3.6 Impedance half-plane 78
3.7 Sheet and impedance junctions 81
3.7.1 Resistive sheet junction (E-polarisation) 83
3.7.2 Conductive sheet junction (E-polarisation) 87
3.7.3 Resistive and conductive junctions (H-polarisation) 89
3.7.4 Impedance and combination sheet junctions 89
3.8 Skew incidence on junctions 91
3.8.1 Resistive sheet junctions 91
3.9 Tapered impedance junctions 102
vi Contents
4 Application to impedance wedges 107
4.1 Introduction 107
4.2 Normal incidence 108
4.2.1 Formulation and non-uniform diffraction
coefficients 109
4.2.2 Residue computation 113
4.2.3 Special cases 117
4.2.4 Uniform diffraction coefficient 120
4.3 Skew incidence 123
4.3.1 Formulation and solution for special cases 124
4.3.2 Arbitrary wedge angle 129
4.4 PTD for impedance structures 138
4.4.1 Derivation of equivalent currents 143
4.4.2 ILDC for a straight wedge 145
4.4.3 ILDC for a curved wedge 147
5 Second order conditions 155
5.1 Background 155
5.2 Alternative forms 156
5.3 Examples 161
5.3.1 Thin dielectric layer 161
5.3.2 High contrast material 169
5.3.3 Metal-backed layer 169
5.3.4 Wire grid 172
5.4 Uniqueness considerations 175
5.4.1 Scalar GIBC 175
5.4.2 Vector GIBC 180
5.5 Diffraction by half-plane junctions 182
5.5.1 Conductive sheet junction 183
5.5.2 Other related problems 190
5.6 Wedge diffraction 194
5.6.1 Impedance half-plane 195
5.6.2 Right-angled impedance wedge 200
6 Higher order conditions 211
6.1 General forms 211
6.1.1 Scalar conditions 211
6.1.2 Vector conditions 214
6.2 Uniqueness 217
6.3 Generalised Babinet principles 220
6.3.1 Scalar fields 221
6.3.2 Vector fields 223
6.4 Applications 228
Contents vii
7 GIBC applications to cylindrical bodies 231
7.1 Homogeneous circular cylinder 231
7.1.1 Exact eigenfunction solution 231
7.1.2 GIBC simulations 234
7.1.3 Accuracy 237
7.1.4 Skew incidence 238
7.2 Coated metallic cylinder 242
7.2.1 Low and high contrast coatings 242
7.2.2 Accuracy 245
7.3 High frequency solution 247
7.3.1 Lit and deep shadow regions 252
7.3.2 Transition region 254
7.3.3 Near-surface field 255
7.4 Edges and junctions 258
8 Absorbing boundary conditions 261
8.1 Introduction 261
8.2 Two-dimensional ABCs 263
8.2.1 One-way wave equation method 263
8.2.2 Mode annihilation method 272
8.2.3 Method of successive approximations 274
8.2.4 ABCs from GIBCs 277
8.3 Three-dimensional ABCs 279
8.3.1 One-way wave equation method 279
8.3.2 Mode annihilation method 282
8.3.3 Curvilinear coordinates 285
8.3.4 Derivation from GIBCs 291
Appendix A: Generalised Rytov analysis 297
A.I Formulation 297
A.2 Zeroth order solution 298
A.3 First order solution 299
A.4 Second order solution 302
A.5 Special cases 305
A.6 Homogeneous cylinder 308
Appendix B: Special functions 312
B.I Numerical Wiener-Hopf factorisation 312
B.2 Half-plane split function computation 315
B.3 Transition function computation 318
B.4 Maliuzhinets function 321
Appendix C: Steepest descent method 327
viii Contents
Appendix D: PO diffraction coefficient for impedance wedges 340
Appendix E: Determination of constants 345
Author index 348
Subject index 351
Preface
Non-metallic materials and composites are now commonplace in modern vehi-
cle construction and are crucial to the operation of many microwave devices.
It is no longer sufficient to confine attention to metallic surfaces, and the need
to compute scattering and other electromagnetic phenomena in the presence of
material structures has led to the investigation of new simulation and solution
techniques. In most cases it is necessary to introduce some type of simplifica-
tion to make the problem tractable and to achieve a solution simple enough to
use. Approximate boundary conditions have proved effective for simplifying
calculations dealing with material surfaces whose solution would be difficult
or impractical without them. They have been used extensively to generate
analytical solutions to canonical problems and are easily incorporated into nu-
merical codes. In fact, approximate boundary conditions of a special type are
essential in finite element and finite difference codes where they are used to
confine the computational domain to the immediate vicinity of the scattering
or radiating structure.
This book provides the first comprehensive treatment of a variety of ap-
proximate boundary conditions applied to electromagnetics. Methods for de-
riving them are discussed and analytical solutions are developed for a number
of canonical problems involving material interfaces, coatings, layered struc-
tures and perturbed surfaces. These analytical solutions are important in the
development of high-frequency electromagnetic scattering codes and should
therefore be of interest to practicing engineers as well as graduate students con-
cerned with high-frequency diffraction by impedance structures. The chapters
are written in a pedagogical manner with the background material necessary
to make the book suitable for graduate students who have completed a stan-
dard first course in electromagnetic theory. An extensive list of references is
appended to each chapter for further reading from the original sources, but a
substantial amount of the material is new, and has not appeared in the lit-
erature before. Throughout the book, many numerical calculations are given
which should be invaluable to prospective users in demonstrating the accuracy
afforded by the approximate boundary conditions. Overall, the book is in-
tended to provide an up-to-date and comprehensive coverage of the genealogy
and application of standard and higher order impedance boundary conditions,
without overlooking such delicate points as solution uniqueness and accuracy.
IX