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This book is an edited volume of nine papers covering the different variants of the generalized multipole techniques (GMT). The papers were presented at the recent 3rd Workshop on Electromagnetics and Light Scattering - Theory and Applications, which focused on current GMT methods. These include the multiple multipole method (MMP), the discrete sources method (DSM), Yasuura's method, method of auxiliary sources and null-field method with discrete sources. Each paper presents a full theoretical description as well as some applications of the method in electrical engineering and optics. It also includes both 2D and 3D methods and other applications developed in the former Soviet Union and Japan.
This book present the lecture notes used in two courses that the late Professor Kasra Barkeshli had offered at Sharif University of Technology, namely, Advanced Electromagnetics and Scattering Theory. The prerequisite for the sequence is vector calculus and electromagnetic fields and waves. Some familiarity with Green's functions and integral equations is desirable but not necessary. The book provides a brief but concise introduction to classical topics in the field. It is divided into three parts including annexes. Part I covers principle of electromagnetic theory. The discussion starts with a review of the Maxwell's equations in differential and integral forms and basic boundary conditions. The solution of inhomogeneous wave equation and various field representations including Lorentz's potential functions and the Green's function method are discussed next. The solution of Helmholtz equation and wave harmonics follow. Next, the book presents plane wave propagation in dielectric and lossy media and various wave velocities. This part concludes with a general discussion of planar and circular waveguides. Part II presents basic concepts of electromagnetic scattering theory. After a brief discussion of radar equation and scattering cross section, the author reviews the canonical problems in scattering. These include the cylinder, the wedge and the sphere. The edge condition for the electromagnetic fields in the vicinity of geometric discontinuities are discussed. The author also presents the low frequency Rayleigh and Born approximations. The integral equation method for the formulation of scattering problems is presented next, followed by an introduction to scattering from periodic structures. Part III is devoted to numerical methods. It begins with finite-difference methods to solve elliptic equations, and introduces the finite-difference time-domain method for the solution of hyperbolic and parabolic equations. Next, the part turns to the method of moments for the solution of integral equations. This part ends with a short introduction to the finite-element method.
In this thesis, the motivation was to study the applicability and test the limits of analytical formulations using surface equivalence, in dealing with the scattering problem of a thin dielectric slab of finite extent. In this application of the surface equivalence principle, the unknowns, equivalent surface electric and magnetic currents, are established using the method of moments. Described herein, in order to solve for the unknowns, are four new numerical techniques called LSM, CLSM, CLSM+RCA and CWLSM+RCA, employed to deal with the radar cross section (RCS) of electromagnetic wave scattering from thin dielectric slabs, for different thicknesses in three dimensions. The designations, LSM, CLSM, CLSM+RCA and CWLSM+RCA stand for least squares method, constrained least squares method, constrained least squares method plus ring current approximation and constrained weighted least squares method plus ring current approximation, respectively. The least squares method is utilized in the new numerical techniques, providing a better solution in the null region of the RCS than the combined field integral equation (CFIE). The new numerical techniques employ surface distributions of equivalent currents, thus in principle requiring less computer memory than those employing volume distributions of current density. Moreover, there is no need to worry about how nearly perfect should be the absorbing boundary condition (ABC) that is used in the finite difference time domain technique (FDTD). Further, in this work, the importance of the equivalent surface currents flowing on the edge of a thin slab (which are referred to as 'ring currents') has been identified. The new techniques also show fast convergence for the particularly challenging case of edge-on wave incidence, even when the slab is as thin as 0.001 [lambda]0 ([lambda]0 is wavelength in free space). In particular, the CLSM+RCA and CWLSM+RCA analyses have been validated by experiments for the case of backward RCS, these experiments showing good agreement with the analyses. For edge-on incidence, the bistatic RCS predicted by CLSM+RCA is also compared with a simulation from a simple approximation: the simulation shows qualitative similarity to CLSM+RCA, but the quantitative differences of up to 10 dB indicate that use of the new methods can be significantly beneficial.