Application of a class of generalized boundary conditions to scattering by a metal-backed dielectric half-plane

The problem considered is that of a plane wave incident on a perfectly conducting half-plane with a thin dielectric coating on its upper face. The solution is accomplished by introducing a higher order boundary condition to simulate the effect of the dielectric, thereby allowing the structure to be treated as an infinitesimally thin half-plane. Two types of boundary conditions are developed, one applicable to a low-contrast dielectric and the other to a high-contrast one. The problem is then solved using a generalized version of the Maliuzhinets method in which certain additional constants are introduced to assure the correct behavior of the field at the edge. Although these constants play no role in the final solution, they are needed to cancel out inadmissible singularities in the solution of the homogeneous difference equation. The final solution is expressed in a uniform manner and some numerical results are presented