Dynamic Three-Dimensional Propagation of Light Pulses

Abstract

In this paper we illustrate several characteristics of dynamic three-dimensional nonlinear propagation of light pulses. Recent work has shown that the fully spatio-temporal propagation of a light wave envelope in a cubically nonlinear medium displays, in addition to the usual transverse structures, longitudinal dynamics which play an essential role in the evolution of the wave [1, 2, 3]. It has been suggested that the effect of dispersion coupled with self focusing causes short light pulses having beam waists much larger than their pulse length to display spectral characteristics typical of experimental observations of supercontinuum generation [1]. A recent computational effort has illustrated that the presence of dispersion can inhibit collapse due to two dimensional self focusing in normally dispersive media causing structure in the propagation direction as well as the transverse direction [3]. Finally, analysis of three dimensional propagation of light waves in anomalously dispersive media [4, 5] reveals a set of symmetric solutions which would exist in the intermediate state between collapse and dispersal. The practical stabilization of these light pulses is an open problem.