One dimensional inverse dielectric profiling of embedded slabs by a quadratic approximation

In this paper the inverse problem of the determination of the dielectric profile of a slab embedded into a homogeneous half space starting from the knowledge of the scattered field for different illumination angles is considered. A comparison between the features of a linear and a quadratic distorted approximation of the scattering problem is carried out, in order to determine the kind of profiles that can be reconstructed. In particular, the investigation of the direct problem reveals that, under the linear approximation, only a limited number of Fourier harmonics of the profile give: contribution to the scattered field. The use of the quadratic approximation allows to change the number and order of the harmonic that can be imaged. The dependence of the results on the dielectric permittivity of the host medium is also highlighted. Numerical examples support the theoretical considerations.