Analysis of the scattering map of a linearized inverse medium problem for electromagnetic waves

The main goal of this paper is to study the linearization of an inverse medium problem for Maxwell's equations. Regularity and stability results are established for the near-field scattering map which maps the scatterer to the scattered field. Properties on continuity and Frechet differentiability of the scattering map are examined. A lower bound of the linearized scattering map is obtained, which in particular characterizes the stability properties of the scattering map, These results are useful in the analysis and computation of the nonlinear inverse scattering problem for Maxwell's equations.