Asymptotic Methods In Electromagnetics

Numerically rigorous techniques for the computation of electromagnetic fields diffracted by an object become computationally intensive, if not impractical to handle, at high frequencies and one must resort to asymptotic methods to solve the scattering problem at short wavelengths. The asymptotic methods provide closed form expansions for the diffracted fields and are also useful for eliciting physical interpretations of the various diffraction phenomena. One of the principal objectives of this book is to discuss the different asymptotic methods in a unified manner. Although the book contains explicit formulas for computing the field diffracted by conducting or dielectric-coated objects, it also provides the mathematical foundations of the different methods and explains how they are interrelated.

Asymptotic methods provide considerable physical insight and understanding of diffraction mechanisms and are very useful in the design of electromagnetic devices such as radar targets and antennas. However, difficulties can arise when trying to solve problems using multipole and asymoptotic methods together, such as in radar crosssection objects. This new book offers a solution to this problem by combining these approaches into hybrid methods, therefore creating high demand for both understanding and learning how to apply asymptotic and hybrid methods to solve diffraction problems.

This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include some recent, direct applications to antennas and computational electromagnetics. Then, specific methods are discussed. These include integration by parts and the Riemann-Lebesgue lemma, the use of contour integration in conjunction with other methods, techniques related to Laplace's method and Watson's lemma, the asymptotic behavior of certain Fourier sine and cosine transforms, and the Poisson summation formula (including its version for finite sums). Often underutilized in the literature are asymptotic techniques based on the Mellin transform; our treatment of this subject complements the techniques presented in our recent Synthesis Lecture on the exact (not asymptotic) evaluation of integrals.

This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include some recent, direct applications to antennas and computational electromagnetics. Then, specific methods are discussed. These include integration by parts and the Riemann-Lebesgue lemma, the use of contour integration in conjunction with other methods, techniques related to Laplace's method and Watson's lemma, the asymptotic behavior of certain Fourier sine and cosine transforms, and the Poisson summation formula (including its version for finite sums). Often underutilized in the literature are asymptotic techniques based on the Mellin transform; our treatment of this subject complements the techniques presented in our recent Synthesis Lecture on the exact (not asymptotic) evaluation of integrals. Throughout, we provide illustrative examples. Some of them are applications to special functions of mathematical physics. Others, taken from our published research, include the application of elementary methods to develop certain simple formulas for transmission lines, examples illustrating the difficulties in solving fundamental integral equations of antenna theory, an examination of the fundamentals of the Method of Auxiliary Sources (MAS), and a study of the near fields of certain unusual types of radiators. Table of Contents: Preface / Introduction: Simple Asymptotic Approximations / Asymptotic Approximations Defined / Concepts from Complex Variables / Laplace's Method and Watson's Lemma / Integration by Parts and Asymptotics of Some Fourier Transforms / Poisson Summation Formula and Applications / Mellin-Transform Method for Asymptotic Evaluation of Integrals / More Applications to Wire Antennas / Authors' Biographies / Index

"Antenna, wireless communication and other electrical engineers use asymptotic techniques for solving electromagnetic problems when the electrical size of a given scenario is large in comparison to the wavelength. This practical book offers in-depth coverage of this area, showing how to apply these techniques to the analysis of complex electromagnetic problems in order to obtain results with an exceptionally high degree of accuracy. Focusing on two highly-effective methods - the uniform theory of diffraction (UTD) and physical optics (PO), this book is unique in that it emphasizes how to solve real-world problems, rather than simply explaining theory like other books on the market. This first-of-its-kind resource show professionals how to apply this knowledge to a wide range of projects in the field, including antenna design, mobile communications, and RCS (radar cross section) computation. This authoritative book is supported with more than 100 illustrations and over 250 equations."

The book reviews developments in the following fields: asymptotic theory; electromagnetic creeping waves; hybrid diffraction coefficients; and asymptotic currents

Electromagnetic wave scattering from random rough surfaces is an active, interdisciplinary area of research with myriad practical applications in fields such as optics, acoustics, geoscience and remote sensing. Focusing on the case of random rough surfaces, this book presents classical asymptotic models used to describe electromagnetic wave scattering. The authors begin by outlining the basic concepts relevant to the topic before moving on to look at the derivation of the scattered field under asymptotic models, based on the Kirchhoff-tangent plane, in order to calculate both the scattered field and the statistical average intensity. More elaborated asymptotic models are also described for dealing with specific cases, and numerical results are presented to illustrate these models. Comparisons with a reference numerical method are made to confirm and refine the theoretical validity domains. The final chapter derives the expressions of the scattering intensities of random rough surfaces under the asymptotic models. Its expressions are given for their incoherent contributions, from statistical calculations. These results are then compared with numerical computations using a Monte-Carlo process, as well as with experimental models, for sea surface backscattering. Contents 1. Electromagnetic Wave Scattering from Random Rough Surfaces: Basics. 2. Derivation of the Scattered Field under Asymptotic Models. 3. Derivation of the Normalized Radar Cross-Section under Asymptotic Models. APPENDIX 1. Far-Field Scattered Fields under the Method of Stationary Phase. APPENDIX 2. Calculation of the Scattering Coefficients under the GO for 3D Problems. About the Authors Nicolas Pinel worked as a Research Engineer at the IETR (Institut d’Electronique et de Télécommunications de Rennes) laboratory at Polytech Nantes (University of Nantes, France) before joining Alyotech Technologies in Rennes, France, in July 2013. His research interests are in the areas of radar and optical remote sensing, scattering and propagation. In particular, he works on asymptotic methods of electromagnetic wave scattering from random rough surfaces and layers. Christophe Bourlier works at the IETR (Institut d’Electronique et de Télécommunications de Rennes) laboratory at Polytech Nantes (University of Nantes, France) and is also a Researcher at the French National Center for Scientific Research (CNRS) on electromagnetic wave scattering from rough surfaces and objects for remote sensing applications and radar signatures. He is the author of more than 160 journal articles and conference papers.