Spatiotemporal dissipative solitons and vortices in a multi-transverse-mode fiber laser

We introduce a model for spatiotemporal modelocking in multimode fiber lasers, which is based on the (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation (cGLE) with conservative and dissipative nonlinearities and a 2-dimensional transverse trapping potential. Systematic numerical analysis reveals a variety of stable nonlinear modes, including stable fundamental solitons and breathers, as well as solitary vortices with winding number $n=1$, while vortices with $n=2$ are unstable, splitting into persistently rotating bound states of two unitary vortices. A characteristic feature of the system is bistability between the fundamental and vortex spatiotemporal solitons.