Instability suppression of vector vortex solitons in nonlocal nonlinear media

We studied the instability suppression of vector vortex solitons (VVS), comprised of two incoherently coupled vortices with different topological charges $m$ in thermal nonlocal nonlinear media with cylindrical symmetry. Using linear stability analysis, we found that the azimuthal instability of the higher-order ($|m|\ensuremath{\ge}3$) vortex can be suppressed and even eliminated because of the presence of the other lower-order ($|m|\ensuremath{\le}2$) vortex, including the fundamental beam. The VVS will be stable when the power ratio of the lower-order vortex exceeds a threshold. We also found that stable VVS exists in some combinational states with opposite-sign charges (${m}_{1}=\ensuremath{-}1$, ${m}_{2}\ensuremath{\ge}3$) when the two vortex components have equal Gaussian beam widths.