Scattering on Single Homogeneous and Two-Layered Spheres

Abstract

The first part of this chapter is concerned with the derivation of the T-matrices of sound soft, hard, penetrable, and two-layered spheres. The corresponding boundary conditions the fields have to fulfill along the spherical boundary surfaces are introduced and applied for this purpose. It is demonstrated in a second part, that any rotation and any local shift of these spherical objects have no effect on the scattering behavior in the far field of the laboratory frame. This property can be used to test the correct numerical implementation of the matrix of rotation and the separation matrix, and to estimate the range of applicability of these two quantities. The boundary conditions for the Debye potentials along the surface of an ideal metallic sphere and a homogeneous dielectric sphere for electromagnetic plane wave scattering are discussed in the final part. This provides also a short outlook at the problem of how to derive the T-matrices if nonspherical objects are involved in the scattering process. The chapter ends with a description of the Python programs, which are related to the first two parts. Appendix B provides a complete listing of these programs.