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

In this paper the inverse problem of the determination of the dielectric pr ofile of a slab embedded into a homogeneous half space starting from the kn owledge of the scattered field for different illumination angles is conside red. A comparison between the features of a linear and a quadratic distorte d approximation of the scattering problem is carried out, in order to deter mine the kind of profiles that can be reconstructed. In particular, the inv estigation of the direct problem reveals that, under the linear approximati on, only a limited number of Fourier harmonics of the profile give: contrib ution 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 dep endence of the results on the dielectric permittivity of the host medium is also highlighted. Numerical examples support the theoretical consideration s.