Stable vortex solitons in a vectorial cubic-quintic model

We investigate the stability of vectorial (two-component) vortex solitons of two types. Their stationary shapes are identical, but their stability (which is the most important issue for spinning solitons) is drastically different. These are solitons with vorticities (S,S) and (S,-S) in the two components. The analysis is performed in a vectorial cubic-quintic model, with the two components nonlinearly coupled by the incoherent cross-phase-modulation interaction, but we expect that the results are quite generic. The stability was investigated by means of computing eigenvalues of perturbations around the stationary solitons, as well as in direct simulations. We also report new analytical results for the well-known problem of the description of the stationary form of scalar solitons in media of this type. The analytical results explain the shape of the spinning solitons, and the strong dependence of their norm (power) on the vorticity, in both the 2D and 3D cases. In this paper we also give the first estimate of the physical characteristics (power and radius) of the stable solitons with different values of S, making use of recently measured values of the necessary nonlinear parameters. All the two-component solitons of type (S,-S) are unstable. In contrast, those of type (S,S) have their stability regions, the size of which strongly depends on S. An unstable soliton always splits into a set of separating zero-spin ones, in precise compliance with the azimuthal index of the most unstable perturbation eigenmode. Direct simulations demonstrate that stable solitons readily self-trap from arbitrary initial pulses which belong to their topological class