Uniqueness and numerical resolution via iterated sensitivity equation of an inverse electromagnetic coefficient problem with partial boundary data

In this paper we study an inverse boundary value problem for Maxwell's equations. The goal is to reconstruct perturbations in the refractive index of the medium inside an object from the knowledge of the tangential trace of an electric field on a part of the boundary of the domain. We first provide a uniqueness result for this inverse problem. Then, we propose a new approach to reconstruct numerically the perturbations. This complete procedure is based on the minimization of a cost functional involving an iterated sensitivity equation.