A uniqueness result for the inverse electromagnetic scattering problem in a piecewise homogeneous medium

The scattering of time-harmonic electromagnetic plane waves by an impenetrable obstacle in a piecewise homogeneous medium is considered. The well-posedness of the direct problem is proved by the variational method. Under the condition that the wave numbers in the innermost and outermost homogeneous layers coincide, we then establish a uniqueness result for the inverse problem, that is, the unique determination of the obstacle and its boundary condition from a knowledge of the electric far field pattern for incident plane waves. The proof is based on a generalization of the mixed reciprocity relation.