A survey of the theory of propagation of transient transverse electromagnetic waves in temporally dispersive, bi-isotropic slabs is given, and a novel wave splitting, which completely separates right-going and left-going waves in the dispersive medium, is proposed. The new approach leads to a simple scattering relation in terms of wave propagators and single-interface scattering operators only. These temporal integral operators are related to the four timedependent susceptibility kernels of the medium through non-linear Volterra equations of the second kind. In a subsequent article, the corresponding inverse scattering problem is addressed on the basis of the new results
