Stability of vortex solitons under competing local and nonlocal cubic nonlinearities

We investigate systematically the stability of two-dimensional vortex solitons in nonlinear media under competing local and nonlocal cubic nonlinearities. We obtain the analytical results to describe the relations between the parameters of the vortex solitons. When the local cubic nonlinearity is self-focusing, the formation power of the vortex solitons will approach a constant in the limit of strong nonlocality. The long-lived stable vortex solitons can be obtained with moderate degree of nonlocality when the nonlocal cubic nonlinearity is self-focusing. Otherwise, the vortex solitons will suffer from the unstable dynamics, such as splitting, diffraction enhancement, and catastrophic collapse. In the limit of strong degree of nonlocality, the vortex solitons are always unstable which is different from the previous results that the vortex solitons can be stabilized completely. The stability and the dynamics of the vortex solitons are also demonstrated numerically with the split-step Fourier transform method.