Forerunners and shapes of the signal in the propagation of radiation in structured nonlinear dispersive dielectrics

Propagation of radiation in nonlinear dispersive media has been analyzed numerically without standard assumptions (like the envelope approximation or the rotating wave approximation) in the near-resonant regime in one spatial dimension. The medium has been modeled as an assemblage of two-, three-, or four-level systems. An attempt to include inhomogeneous broadening has been made with the help of random spatial modulation of the frequencies of transitions in those systems. Particular attention has been directed to the propagation in spatially structured media. Non-trivial dynamics of forerunners have been obtained in the cases of "stopped" light and "superluminal" propagation. The shapes of the signal, and, in particular, the propagation of the wings of the signal have been investigated. The time- and parameter-dependence of the group velocity have been studied in detail, and the vagueness of the concept of the group velocity has been stressed.