Spatiotemporal instability of ultrashort pulses in dispersive self-focusing media

Spatiotemporal instability in dispersive self-focusing media is investigate d on the basis of a modified nonlinear Schrodinger equation (NLSE) beyond t he slowly varying envelope approximation. It is found that, for both normal and anomalous dispersions, space-time focusing may lead to the appearance of new temporal instability regions for some range of spatial frequencies. The physical origin of the new instability regions lies in the part of spac etime coupling related to the fourth-order dispersion. Furthermore, space-t ime focusing shrinks the instability regions and slightly reduces the maxim um growth rates of the original spatiotemporal instability gain spectra obt ained from the standard NLSE.