Cellular automaton approach to electromagnetic wave propagation in dispersive media

Extensions of Bia ynicki-Birula's cellular automaton are proposed for studies of the one-dimensional propagation of electromagnetic fields in Drude metals, as well as in both transparent, dispersive and lossy dielectrics. These extensions are obtained by representing the dielectrics with appropriate matter fields, such as polarization together with associated velocity fields. To obtain the different schemes for the integration of the resulting systems of linear partial differential equations, split-operator ideas are employed. Possible further extensions to two-dimensional propagation and for the study of left-handed materials are discussed. The stability properties of the cellular automaton treated as a difference scheme are analysed.