An Integral Equation for Maxwell's Equations if a Layered Medium with an Application to the Factorization Method

In the first part of this paper we study the direct scattering problem for time harmonic electromagnetic fields in a layered medium where arbitrary incident fields are scattered by a medium described by a space dependent permittivity and conductivity.We derive an integral equation and prove a theorem of Riesz-Fredholm type.In the second part we investigate the Factorization Method for the corresponding inverse problem with magnetic dipoles as incident fields.This is the problem to recover the support of the contrast from field measurements.