Stable two-dimensional spinning solitons in a bimodal cubic-quintic model with four-wave mixing

We show the formation of stable two-dimensional spinning solitons in a bimodal system described by coupled cubic-quintic nonlinear Schrödinger equations. The cubic part of the model includes the self-phase modulation, cross-phase modulation, and four-wave mixing. Thresholds for the formation of both spinning and non-spinning solitons are found. Instability growth rates of perturbation eigenmodes with different azimuthal indices are calculated as functions of the solitons' propagation constant. As a result, existence and stability domains are identified for the solitons with vorticity s = 0, 1, and 2 in the model's parameter plane. The vortex solitons are found to be stable if their energy flux exceeds a certain critical value, so that, in typical cases, the stability domain of the s = 1 solitons occupies about 18% of their existence region, whereas that of the s = 2 solitons occupies 10% of the corresponding existence region. Direct simulations of the full nonlinear system are in perfect agreement with the linear-stability analysis: stable solitons easily self-trap from arbitrary initial pulses with embedded vorticity, while unstable vortex solitons split into a set of separating zero-spin fragments whose number is exactly equal to the azimuthal index of the strongest unstable perturbation eigenmode.