Plane wave scattering by two dielectric coated conducting strips

A plane electromagnetic wave scattered by two dielectric coated conducting strips is addressed here. Two methods of solutions are introduced. The first is based on solving the Helmholtez wave equation in terms of elliptical coordinates. As a result a Fourier series of radial and angular Mathieu functions of unknown coefficients in each region is obtained. The unknown coefficients can be obtained by enforcing the boundary conditions. The application of the boundary condition requires the use of the addition theorem of Mathieu function. The second method is based on an asymptotic approximate technique introduced by Karp and Russek for solving scattering by wide slit. Numerical examples are calculated using both methods and they are compared with each other. Excellent agreement between both cases is found.