Exact solution to the scattering by infinitely long composite elliptical dielectric cylinders under oblique illumination

In the present work an exact solution to the electromagnetic scattering by a dielectric elliptical cylinder which is coated eccentrically by a nonconfocal dielectric elliptical cylinder is studied, under oblique illumination, with the use of the separation of variables method. The addition theorem for Mathieu functions is used to express the fields in different regions. The process of the solution is complicated because of the nonexistence of orthogonality relations for Mathieu functions due to the different constitutive parameters between the two cylinders and the background medium, because of the hybrid waves that appear due to the oblique incidence, and due to the complicated form of the addition theorem which introduces a cross relation between even and odd terms. The solution of the present method is validated compared with other published data from the literature. Both polarizations are studied and numerical results are given for the scattering cross sections.