A uniqueness result for the inverse electromagnetic scattering problem in a two-layered medium

This paper is concerned with the inverse problem of scattering of time-harmonic electromagnetic waves by an impenetrable obstacle buried in the lower half-space of a two-layered background medium. We prove that the buried obstacle and its physical property can be uniquely determined from a knowledge of the tangential component of the electric field on some two-dimensional device in the upper half-space corresponding to all incident electric dipoles located on another two-dimensional device in the upper half-space with two different polarizations. The key ingredient of our proof is a novel reciprocity relation established in this paper for the solution of the scattering problem of the electric dipole located at two different source points.