Simultaneous reconstruction of the permittivity and conductivity of an inhomogeneous slab from transient scattered fields due to a point source

The authors consider time-domain electromagnetic scattering from an inhomogeneous slab of finite thickness for a vertical magnetic dipole excitation. In the slab the permittivity and conductivity are functions of the coordinate perpendicular to the slab interfaces, and in the inverse problem both these functions are recovered simultaneously. Equations which can be used to solve both the direct and the inverse scattering problem for this configuration are derived by means of wave splitting and invariant embedding. The solution to the point source excitation case is obtained by means of a formulation that makes it possible to exploit the extensive previous results for a one-dimensional case. Some typical results are presented. Simultaneous reconstructions of permittivity and conductivity as a function of z were obtained using both reflection and transmission data.<>