TM scattering by a homogeneous elliptic cylinder with dielectric or magnetic coating

An analytical solution for electromagnetic scattering by a dielectric or magnetic coated homogeneous elliptic cylinder is outlined. This problem has wide-ranging applications in areas such as reduction of radar cross section using different coating materials, interaction of electromagnetic waves with the human body, and verification of newly developed numerical and approximation techniques. The analysis presented is exact and based on the eigenfunction technique, where the total fields inside the homogeneous cylinder, the dielectric (magnetic) coating, and the exterior regions are expanded in terms of elliptical harmonics, i.e., Mathieu and modified Mathieu functions, with unknown expansion coefficients which are determined by imposing appropriate boundary conditions.<>