Spatiotemporal instability in nonlinear dispersive media in the presence of space-time focusing effect

Abstract

Spatiotemporal instability in nonlinear dispersive media is investigated on the basis of the nonlinear envelope equation. A general expression for instability gain which includes the effects of space-time focusing, arbitrarily higher-order dispersions and self-steepening is obtained. It is found that, for both normal and anomalous group-velocity dispersions, space-time focusing may lead to the appearance of new instability regions and influence the original instability gain spectra mainly by shrinking their regions. The region of the original instability gain spectrum shrinks much more in normal dispersion case than in anomalous one. In the former case, space-time focusing completely suppresses the growing of higher frequency components. In addition, we find that all the oddth-order dispersions contribute none to instability, while all the eventh-order dispersions influence instability region and do not influence the maximum instability gain, therein the fourth-order dispersion plays the same role as space-time focusing in spatiotemporal instability. The main role played by self-steepening in spatiotemporal instability is that it reduces the instability gain and exerts much more significant influence on the new instability regions resulting from space-time focusing.