Spatiotemporal Instability of Ultrashort Pulses in Dispersive Self-Focusing Media

Spatiotemporal instability in dispersive self-focusing media is
investigated on the basis of a modified nonlinear Schrödinger equation (NLSE) beyond the 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 space-time coupling related to the fourth-order dispersion. Furthermore, space-time focusing shrinks the instability regions and slightly reduces the maximum growth rates of the original spatiotemporal instability gain spectra obtained from the standard NLSE.