Cellular automaton approach to light propagation in dispersive periodic and disordered media

The propagation of electromagnetic waves in one-dimensional photonic crystals and random media is studied and compared with the help of extensions of a cellular automaton introduced by Bialynicki-Birula. The dielectric elements, which form spatially regular or random structures, are assumed to possess dispersion. The behaviour of forerunners is investigated numerically. Their dependence on the applied signal and on the topology of dispersive medium is shown. Peculiarities of propagation in pumped media with negative effective static polarizability are pointed out.