Stable azimuthal stationary state in quintic nonlinear optical media

We analyze the structure of the first azimuthal stationary state for a nonlinear medium presenting simultaneously a cubic (focusing) and a quintic (defocusing) dependence with the light intensity in the refractive index. This solution takes the form of a dark vortex of light hosted in a compact light beam. The existence of these modes is guaranteed if the flux exceeds a certain minimum threshold and if the modes are extremely stable for fluxes larger than a critical value that we calculated. We verified the robust nature of this solution inducing internal oscillations by an initial phase chirp. Using the variational method, we obtain an approximate picture for the beam internal dynamics. We also studied numerically the interactions between two near-vortex solutions, finding that for a wide combination of beam parameters they show elastic collisions.