Scattering by Two Infinitely Long Dielectric-Coated Confocal Conducting Elliptic Cylinders

Abstract

Analytical solution of the problem of a plane electromagnetic wave scattering by two infinitely long dielectric coated confocal conducting elliptic cylinders is derived. The incident, scattered and transmitted fields in every region are expressed in terms of Mathieu functions. To impose the boundary conditions, the translation addition theorem for Mathieu functions is implemented to express the scattered field by one cylinder in terms of the elliptic coordinate system of the other cylinder. The resulting system of equations is written in matrix form while the scattered and transmitted field coefficients are obtained by using matrix inversion. Numerical results are obtained for the scattered field in the far zone for different axial ratios, electrical separations, relative dielectric constants, and angles of incidence.