Physical Basics of Electromagnetic Wave Scattering

Abstract

In all the foregoing chapters, we have tacitly assumed that the scalar Helmholtz and the vector wave equation are the partial differential equations underlying the scattering problems. In Sect. 7.2, we will provide the justification for this assumption for electromagnetic wave scattering. Starting from Maxwell’s equations, we will discuss the physical constraints resulting in these partial differential equations. This includes a short course in conventional Mie Theory as formulated by Debye. By use of definition (5.79) we will moreover derive a boundary integral equation to calculate the induced surface current at the surface of a three-dimensional, ideal metallic scatterer. This boundary integral equation is already known in the literature. As already mentioned in Sect. 5.4, this equation avoids the strong singularity of the freespace Green function appearing in (5.105) if the dyadic case is considered. It is demonstrated later how one can transfer this solution scheme to calculate the corresponding Green functions. The next section is concerned with the definition of selected scattering quantities we will use in the numerical simulations of Chap. 8. Starting from an appropriate representation of the fields important scattering quantities will be derived. They form the essential link between theory and experiment. In this section, we pursue the goal to emphasize the importance and implications of the far-field region and the plane wave as the primary incident field in the theory of electromagnetic wave scatterings as well as in the related experiments. Using a plane wave as the primary incident field allows us to winnow the scattering problem from the more general diffraction problem. The latter considers any primary incident field generated from a source $\overrightarrow{\rho}({\rm x})$ which is located somewhere in Γ₊ but within a finite distance from the scatterer. Moreover, it does not ask exclusively for the scattered field in the far-field region.