A survey of the theory of propagation of transient transverse electrom
agnetic waves in temporally dispersive, bi-isotropic slabs is given, a
nd a novel wave splitting, which completely separates right-going and
left-going waves in the dispersive medium, is proposed. The new approa
ch leads to a simple scattering relation in terms of wave propagators
and single-interface scattering operators only. These temporal integra
l operators are related to the four time-dependent susceptibility kern
els of the medium through non-linear Volterra equations of the second
kind. In a subsequent paper, the corresponding inverse scattering prob
lem is addressed on the basis of the new results. (C) 1999 Elsevier Sc
ience B.V. All rights reserved.