Electromagnetic scattering by spheroidal objects with impedance boundary conditions at axial incidence

An analytic solution of a plane electromagnetic wave scattering by coated and impedance prolate spheroidal bodies is obtained, for axial incidence, by expanding the incident and scattered fields in terms of prolate spheroidal vector wave functions. The unknown expansion coefficients are determined by a doubly infinite system of equations derived using the impedance boundary condition, which relates the tangential components of the electric field to those of the magnetic field through an effective surface impedance of the coating. To solve for the unknown coefficients, the system of equations is truncated by retaining only the first N equations in N unknowns, where N depends on the size of the body and the desired accuracy. Numerical results for the scattering cross section are presented to show the effect of different coatings on the magnitude of the scattered field.