Electromagnetic scattering from an infinite elliptic metallic cylinder coated by a circular dielectric one

The scattering from an infinite elliptic metallic cylinder coated by a circular dielectric one is considered. The electromagnetic field is expressed in terms of both circular and elliptical cylindrical wave functions, which are connected with one another by well-known expansion formulas. In the special case of small h=ka/2 (a being the interfocal distance of the elliptic conductor and k the wavenumber of the dielectric coating), exact, closed-form expressions of the form S (h)=S(0)[1+g "h²+O(h⁴)] are obtained for the scattered field and the various scattering cross sections of the problem. Both polarizations are considered for normal incidence. Graphical results for various values of the parameters are given