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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: ISTE Invoiced
- Sprache: Englisch
This book presents a collection of independent mathematical studies, describing the analytical reduction of complex generic problems in the theory of scattering and propagation of electromagnetic waves in the presence of imperfectly conducting objects.
Their subjects include: a global method for scattering by a multimode plane; diffraction by an impedance curved wedge; scattering by impedance polygons; advanced properties of spectral functions in frequency and time domains; bianisotropic media and related coupling expressions; and exact and asymptotic reductions of surface radiation integrals.
The methods developed here can be qualified as analytical when they lead to exact explicit expressions, or semi-analytical when they drastically reduce the mathematical complexity of studied problems. Therefore, they can be used in mathematical physics and engineering to analyse and model, but also in applied mathematics to calculate the scattered fields in electromagnetism for a low computational cost.
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Seitenzahl: 381
Veröffentlichungsjahr: 2024
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Guide
Cover
Table of Contents
Dedication Page
Title Page
Copyright Page
Introduction
Begin Reading
Index
Other Title
End User License Agreement
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Dedicated to my wife
Waves and Scattering Set
coordinated by
Jean-Michel L. Bernard
Volume 3
Advanced Studies in the Mathematical Theory of Scattering
Jean-Michel L. Bernard
First published 2024 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
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 only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUKwww.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.wiley.com
© ISTE Ltd 2024
The rights of Jean-Michel L. Bernard to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s), contributor(s) or editor(s) and do not necessarily reflect the views of ISTE Group.
Library of Congress Control Number: 2024940000
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-857-3
Introduction
This book is a collection of independent mathematical studies, describing the analytical reduction of complex generic problems in the theory of scattering and propagation of electromagnetic waves in the presence of imperfectly conducting objects. Their subjects are as follows:
a global method for the scattering by a multimode plane;
diffraction by an impedance curved wedge;
scattering by impedance polygons;
advanced properties of spectral functions in frequency and time domains;
bianisotropic media and related coupling expressions;
exact and asymptotic reductions of surface radiation integrals.
Each of our approaches can be qualified as analytical, when it leads to exact explicit expressions, or, as semi-analytical, when it drastically reduces the mathematical complexity of studied problems. Therefore, they can be used in mathematical physics and engineering, to analyze and model, as well as in applied mathematics, to calculate for a low computational cost, the scattered fields in electromagnetism.
All of these works derive from original methods initiated in our publications that we here detail, develop and extend.
The first chapter is devoted to original exact expressions of the diffraction by a multilayered plane that can be partly composed of metamaterials. In whole generality, we then determine the fields as depending on potentials attached to arbitrary passive or active modes whose combination will give the passivity of the complete system. Our expressions directly take account of primary sources composed of electric and magnetic dipoles with arbitrary orientations, and profit of a novel exact development of incomplete Bessel function as an exact series of error functions. This latter characteristic permits a complete uniform analysis for arbitrary complex parameters, contrary to previous known results with error functions that were only approximations. Exact and complete asymptotics (at any order) are described, allowing us to particularly analyze the contribution of guided waves (forward and backward) at any distance.
The second chapter concerns the diffraction of an impedance wedge with curved faces of arbitrary angle that supports distinct surface boundary conditions of impedance type. We then distinguish the domains above and below the tangent planes at the edge. Our method permits an asymptotic evaluation at arbitrary order of curvatures of both faces for arbitrary passive impedance parameters. The uniformity at the crossing of the tangent plane is a characteristic remaining at arbitrary order, permitting us to analyze reflected, guided waves, edge-diffracted waves, but also waves originating from the edge that creep along the faces (creeping waves when faces are convex).
The diffraction in free space of a imperfectly conducting polygons (finite or with semi-infinite faces) is a particularly delicate problem that we study in third chapter, using Sommerfeld–Maliuzhinets integral representation of fields in a novel manner to rigorously consider several discontinuities, without any approximations. Indeed, contrary to common methods which consider large facets to admit asymptotic coupling between edges, we consider a rigorous development valid for arbitrary dimensions of facets, by establishing novel spectral equations that we can solve exactly or asymptotically, from a novel analysis of properties of spectral functions. This is particularly permitted by using their single-face representations, which is perfectly adapted to directly consider boundary conditions on faces with piecewise smooth geometries, as in polygonal cases.
Chapter 4 explores spectral functions in Sommerfeld–Maliuzhinets integral representation, their properties in the complex plane and new developments of them and special functions, attached to the resolution of multiple problems concerning the diffraction by a wedge with impedance boundaries conditions (passive or active). By beginning the study in frequency domain, we also analyze the representation of fields in time domain, in particular for an efficient explicit expression of causality in the case of dispersive (not constant relatively to frequency) multimode faces.
The fifth chapter analyzes the coupling influence between two imperfectly conducting objects in presence of a third one, all constituted by bianisotropic media. After beginning with developments of integral equalities, in particular, a generalized reciprocity one, we derive different properties of fields that will permit a complete analysis of coupling influences. We then give an example of application for an efficient and simple numerical post-process suppression of the influence of one object, that is, its direct but also its coupling contributions, on a second object.
We conclude this book with the determination of explicit contour integral expressions for an efficient evaluation of surface radiation integrals at arbitrary distance. This reduction concerns radiation of plane or curved plates of arbitrary contours, when the fields, highly oscillatory or not, are analytically defined on them, which is particularly the case for physical optics radiation surface integrals, when the surface fields are defined in closed form from geometrical optics.
