Stabilization of spatiotemporal solitons in second-harmonic-generating media

We report the results of a systematic analysis of the existence and stability of spatiotemporal (two-dimensional) solitons (STSs) in the model of a planar waveguide with the intrinsic χ⁽²⁾ nonlinearity. Fundamental obstacles to the creation of STSs under physically realistic conditions are the normal sign of the group-velocity dispersion (GVD) at the second harmonic (SH), and the significant group-velocity mismatch (GVM) between the SH and fundamental-frequency (FF) components. To construct STS solutions in a numerical form, we adjust the iterative method, which was recently used for finding temporal (one-dimensional) χ⁽²⁾ solitons in a similar setting. We identify effective existence borders for the STSs, within which the energy loss to the generation of extended "tails" in the SH component (due to the normal sign of the GVD) is negligible. It is demonstrated that the existence region can be made much broader by means of the GVD-management and GVM-management techniques. We also explore interactions between the STSs, and find robust two-soliton bound states, with a moderate separation in the longitudinal (temporal) direction. Head-on collisions between the STSs are always destructive.