Transient wave propagation in a finite bi-isotropic slab is treated. The incident field impinges normally on the slab, which can be inhomogeneous wrt depth. Dispersion and bi-isotropy are modeled by time convolutions in the constitutive relations. Outside the slab the medium is assumed to be homogeneous, non-dispersive and isotropic, and such that there is no phase velocity mismatch at the boundaries of the slab. Two alternative methods of solution to the propagation problem are given—the imbedding method and the Green function approach. The second method is used to solve the inverse problem and the first to generate synthetic data. The inverse scattering problem is to reconstruct the four susceptibility kernels of the medium using a set of finite time trace of reflection and transmission data
