Transient external 3D excitation of a dispersive and anisotropic slab

Propagation of a transient electromagnetic field in a stratified, dispersive and anisotropic slab, and related direct and inverse problems, are investigated. The field is generated by a transient external three-dimensional (3D) source. The analysis relies on the wave splitting concept and a two-dimensional Fourier transformation in the transverse spatial coordinates. An investigation of the physical properties of the split fields is made. To solve the direct and inverse scattering problems, wave propagators are used. This method is a generalization and a unification of the previously used imbedding and Green functions methods. The wave propagator approach provides an exact solution of the transmission operator. From this solution it is possible to extract the first precursor (the Sommerfeld forerunner). These results also hold for a bi-anisotropic slab. An inverse problem is outlined using reflection and transmission data corresponding to four, two-dimensional Fourier parameters. Due to the stratification of the medium, the inverse Fourier transformation is not needed in the inverse problem