Spatiotemporal instability and space-time focusing in nonlinear self-defocusing dispersive media

Abstract

We study the spatiotemporal instability in nonlinearself-defocusing dispersive media using a modified(3+1)-dimensional nonlinear Schrödinger equation, in which thespace-time focusing and self-steepening are considered to describethe spatiotemporal coupling in ultrashort pulsed beam propagation.We find that, in the normal dispersion media, space-time focusingsignificantly shrinks the instability region by suppressing thegrowth of the higher frequency components, while in the anomalousdispersion case, in which it is stable in the standard(3+1)-dimensional nonlinear Schrödinger equation, space-timefocusing may lead to the appearance of new instability regions. Inaddition, the main role played by self-steepening is that itreduces the instability gain and, comparatively, it exerts muchmore influence on the new instability region resulting fromspace-time focusing. The numerical simulation of propagation of acw plane wave in a self-defocusing normal dispersion medium isgiven to show the break up of the pulse and beam into a pulse train andfilament.