Scattering by an infinite elliptic dielectric cylinder coating eccentrically a circular metallic or dielectric cylinder

In this paper, the scattering of a plane electromagnetic wave by an infinite elliptic dielectric cylinder, coating eccentrically a circular metallic or dielectric inner cylinder, is treated. 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. Translational addition theorems for circular cylindrical wave functions are also used. If the solution is specialized to small values of h=k₂c/2, where k ₂ is the wavenumber of the elliptic dielectric cylinder and c its interfocal distance, semianalytical expressions of the form S(h)=S(0)[1+gh²+O(h⁴)] are obtained for the scattered field and the various scattering cross sections of this configuration. The coefficients g are independent of h. Both polarizations are considered for normal incidence. Graphical results for the scattering cross sections are given for various values of the parameters