Role of stimulated Raman scattering in spatiotemporal instabilities in dispersive Kerr media

We use the standard linear stability analysis to study the role of stimulated Raman scattering in spatiotemporal instability in dispersive Kerr medium based on an extended (3+1)-dimensional nonlinear Schrodinger equation. We show that the spatiotemporal instability gain spectrum consists of two parts: the conventional spatiotemporal instability gain spectrum and the Raman gain spectrum. Stimulated Raman scattering doesn't affect the conventional spatiotemporal instability gain spectrum; yet it provides additional sidebands which have almost the same gain spectrum in all combinations of the signs of group velocity dispersion and nonlinear refractive index. It is interesting that spatiotemporal instability gain can appear for any spatial frequencies in the presence of stimulated Raman scattering, in sharp contrast to conventional spatiotemporal instability whose gain is located in a limited spatial frequency range.