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

We study the spatiotemporal instability in nonlinear self-defocusing dispersive media using a modified (3 + 1)-dimensional nonlinear Schrodinger equation, in which the space-time focusing and self-steepening are considered to describe the spatiotemporal coupling in ultrashort pulsed beam propagation. We find that, in the normal dispersion media, space-time focusing significantly shrinks the instability region by suppressing the growth of the higher frequency components, while in the anomalous dispersion case, in which it is stable in the standard (3 + I)-dimensional nonlinear Schrodinger equation, space-time focusing may lead to the appearance of new instability regions. In addition, the main role played by self-steepening is that it reduces the instability gain and, comparatively, it exerts much more influence on the new instability region resulting from space-time focusing. The numerical simulation of propagation of a cw plane wave in a self-defocusing normal dispersion medium is given to show the break up of the pulse and beam into a pulse train and filament.