Scattering by an infinite circular dielectric cylinder coating eccentrically an elliptic dielectric one

The scattering of a plane electromagnetic wave from an infinite circular dielectric cylinder, coating eccentrically an elliptic dielectric one, is examined. Both E and H polarizations are treated for normal incidence. The electromagnetic field is expressed in terms of both circular and elliptical cylindrical wave functions. Using transformation theorems between the field expressions in different coordinate systems, for the satisfaction of the boundary conditions, we obtain two infinite sets of linear nonhomogeneous equations for the expansion coefficients of the field. For small values of h=k(2)c/2, where k(2) is the wavenumber of the dielectric coating and c is the interfocal distance of the elliptic cylinder, we conclude with semianalytical expressions of the form S(h)-S(0)[1+gh(2)+O(h(4))] for the scattered field and the scattering cross sections. The coefficients g are independent of h while S(0) corresponds to the eccentric circular problem. Numerical results are given for various values of the parameters.