Inverse scattering for the homogeneous dispersive anisotropic slab using transient electromagnetic fields

An inverse scattering problem for a slab containing a homogeneous dispersive anisotropic medium is investigated. The inverse problem is to recover two three-dimensional dyadic susceptibility kernels from knowledge of the scattering kernels. Time domain techniques involving transient electromagnetic plane waves, wave splitting, invariant imbedding and a Green function technique are used. The inverse problem is separated into two parts: The Dynamics Inverse Problem (DIP) and Retrieval of Interior Parameters (RIP). Furthermore, mirror images and the Mirror Image Pair (MIP) are discussed. The DIP is solved numerically by using an inverse algorithm and scattering data from one MIP. The RIP turns out to be well posed (system of Volterra equations of the second kind) and needs in general two MIPs. In the DIP, the equations for initial values using transmission data have in general not a unique solution. Constraints and simplifications for certain classes of media are pointed out. Numerical examples, including noisy data, illustrate the analysis