Numerical integration of Maxwell’s full-vector equations in nonlinear focusing media

In this paper, we present results of parallel numerical simulations on Maxwell’s equations. The parallel code is used to study the effect of the instantaneous focusing nonlinearity upon dispersionless pulse propagation in bulk dielectric. Indications are given of the development of shocks on the optical carrier wave and upon the pulse envelope. We then use the code to study focusing and collapse of optical pulses at anomalously dispersive frequencies. We examine the effect of varying the focusing of the light by varying the intensity as a way to compensate linear dispersion. We demonstrate blow up of sufficiently intense short pulses at finite propagation distances, and we show numerically that the location of blow up depends nontrivially upon the intensity of the light.