Bistatic scattering and backscattering of electromagnetic waves by conducting and coated dielectric spheroids: A new analysis using mathematica package

Abstract

Solutions to electromagnetic scattering at any angle of incidence by a perfectly conducting spheroid and a homogeneous dielectric spheroid coated with a dielectric layer are obtained by solving Maxwell's equations together with boundary conditions. The method used is that of expanding electric and magnetic fields in the spheroidal coordinates in terms of the spheroidal vector wave functions and matching their respective boundary conditions at spheroidal interfaces. In this formulation, the column vector of the series expansion coefficients of the scattered field is obtained from that of the incident field by means of a matrix transformation, which is in turn obtained from a system of equations derived from boundary conditions. The matrix depends only on the scatterer's properties; hence the scattered field at a different direction of incidence is obtained without repeatedly solving a new set of simultaneous equations. Different from the previous work, the present work developed an accurate and efficient Mathematica source code for more accurate solution to the problem. Normalized bistatic and backscattering cross sections are obtained for conducting (for verification purpose), homogeneous dielectric (for verification purpose), and coated dielectric prolate (for some new results) spheroids, with real and complex permittivities. Numerically exact results for the coated dielectric prolate spheroids are newly obtained and are not found in existing literature.