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Closed-form solution to the scattering by an infinite lossless or lossy elliptic cylinder coating a circular metallic core.

An analytical, closed-form solution to the scattering problem from an infinite lossless or lossy elliptical cylinder coating a circular metal core is treated in this work. The problem is solved by expressing the electromagnetic field in both elliptical and circular wave functions, connected with one another by well-known expansion formulas. The procedure for solving the problem is cumbersome because of the nonexistence of orthogonality relations for Mathieu functions across the dielectric elliptical boundary. The solution obtained, which is free of Mathieu functions, is given in closed form, and it 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, permitting an immediate calculation for the scattering cross sections. The proposed method is an alternative one, for small h, to the standard exact numerical solution obtained after the truncation of the system matrices, composed after the satisfaction of the boundary conditions. Both polarizations are considered for normal incidence. The results are validated against the exact solution, and numerical results are given for various values of the parameters.