Scattering by systems of spheroids in arbitrary configurations

Abstract

By expanding the incident, scattered, and transmitted electromagnetic fields in terms of appropriate vector spheroidal wave functions, an analytic solution is obtained to the problem of electromagnetic scattering by n dielectric spheroids of arbitrary orientation. The incident wave is considered to be a monochromatic uniform plane electromagnetic wave of arbitrary polarization and angle of incidence. The boundary conditions at the surface of a given spheroid are imposed by expressing the electromagnetic fields scattered by all the other n-1 spheroids in terms of the spheroidal coordinates attached to the spheroid considered, using the rotational-translational addition theorems for vector spheroidal wave functions. The solution of the associated set of algebraic equations yields the column matrix of the unknown scattered and transmitted field expansion coefficients expressed as the product of a system matrix and the column matrix of the known incident field expansion coefficients. The numerical evaluation of various matrix elements and spheroidal wave functions is presented in detail. Even though the formulation is general, the numerical results in the form of far-field scattering cross-sections are presented only for two spheroids of arbitrary orientation with various axial ratios, orientations, and center-to-center distances.