Plane wave scattering by a material coated parabolic cylinder

An eigenfunction solution to the problem of transverse magnetic (TM) or transverse electric (TE) scattering by a coated parabolic cylinder is presented. Paralleling the well-known solution for the coated circular cylinder, eigenfunction expansions involving parabolic cylinder functions are obtained for the fields in the exterior and coating regions. Next, boundary conditions are enforced to obtain a pair of coupled equations for the unknown coefficients in the eigenfunction expansions for the fields. Unlike the corresponding solution for the coated circular cylinder, the eigenfunctions in the exterior and coating regions are not orthogonal, and an exact term-by-term solutions of these equations is not possible. Instead, the equations are solved by the method of moments. For thin coatings both an uncoupled-mode approximation and a surface-impedance model are described. In particular, for the TM polarization it is shown that a thin coating can be modeled by a specific nonuniform surface impedance for which an exact term-by-term solution is possible. Numerical data are presented, showing the convergence of the solution and comparing the solutions for the uncoupled-mode and surface-impedance models