Abstract
In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered electric fields measured on some surface inside the cavity, where such scattered electric fields are due to electric dipoles emitted on the same surface. By making use of a boundary value problem called the exterior transmission problem, we first prove that the measurements can uniquely determine the shape of the cavity. Then we apply the linear sampling method to reconstruct the cavity. Numerical examples are further provided to illustrate the viability of our algorithm.
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