Causality in propagation of a pulse in a nonlinear dispersive medium

Abstract

We investigate the causal propagation of the pulse through dispersive media by very precise numerical solution of the coupled Maxwell-Bloch equations without any approximations about the strength of the input field. We study full nonlinear behaviour of the pulse propagation through solid state media like ruby and alexandrite. We have demonstrated that the information carried by the discontinuity, i.e. front of the pulse, moves inside the media with velocity c even though the peak of the pulse can travel either with sub-luminal or with super-luminal velocity. Our numerical demonstration is subject to the condition that the background refractive index of the medium is unity. We extend the argument of Levi-Civita to prove that the discontinuity would travel with velocity c even in a nonlinear medium.