Electromagnetic interaction with a magnetic coated elliptic cylinder

A solution for scattering of plane electromagnetic waves from a permeable elliptic cylinder with a confocal coating material is considered. The solution is formulated in terms of infinite series of Mathieu and modified Mathieu functions with unknown expansion coefficients. These coefficients are determined by enforcing exact boundary conditions on the total fields at the core and the coating surfaces. Numerical calculations are carried out for different cases including, as limiting cases, perfectly conducting objects and homogeneous objects as well as objects with circular cross sections and thin objects.