Scattering by an infinite circular metallic cylinder coated by a lossless or lossy elliptical cylinder: Closed-form solutions

A closed-form solution to the scattering by an infinite lossless or lossy elliptical cylinder coating a circular metal core is studied in this work. The obtained solution, free of Mathieu functions, is given in closed-form and is valid for small values of the eccentricity h of the elliptical cylinder. Analytical expressions of the form S(h) = S(0)[1+g⁽²⁾h²+g⁽⁴⁾h⁴+O(h⁶)] are obtained, enabling an immediate calculation for the fields and scattering cross sections. Both polarizations are considered and numerical results are given for lossless/lossy materials.