Chapter 4 - Models of Electromagnetic Scattering Problems Based on Discrete Sources Method

Abstract

This chapter reviews the Discrete Sources Method (DSM) as a basis for constructing mathematical models of electromagnetic wave scattering problems. The chapter concentrates on numerical schemes for investigating polarized scattering by a penetrable obstacle. Computer simulation of results associated with discrimination of smooth substrate defects is discussed. The analysis of scattering of electromagnetic waves by local obstacles and structures has a wide variety of applications in electromagnetics, optics, computerized tomography, and metrology. Mathematical modeling, operating with Boundary Value Scattering Problem (BVSPs), is a common tool for such an advanced analysis. From mathematical viewpoint BVSPs are classical problems of mathematical physics. The essential feature of BVSP under consideration is that the obstacle is far away from both the primary field sources and the region of the scattered field measurement. This allows the Quasi-Solution (QS) concept to be employed that enables one to avoid methods requiring the boundary conditions at the obstacle surface to be satisfied exactly, which obviously increases computational costs. The Discrete Sources Method (DSM) seems to be one of the most effective and flexible tools for QS construction. In the frame of DSM, the approximate solution is constructed as a finite linear combination of the fields of dipoles and multipoles.