Profile inversion in scattering theory: the TE case

In this paper we discuss an inverse problem in which we try and determine the refractive index corresponding to the scattering of electromagnetic waves by an inhomogeneous medium from far-field data. In particular, we shall extend the dual-space method developed by Colton and Monk (Inverse Problems 10 (1994) 87) for the TM case to the more complicated TE case and consider the case of single frequency. We shall emphasize on the influence of the wave number in the reconstructions. Several examples are presented which illustrate the algorithm.