We report, to the best of our knowledge, the first experimental observation of higher-charge vortex solitons and vector vortex solitons in lead glass with strongly thermal nonlocal nonlinearity. A higher-charge vortex soliton with a topological charge of $l=4$ and a vector vortex soliton consisting of two orthogonally polarized vortex components, with charges $l_1=1$ and $l_2=4$, were observed at several times of diffraction length. We show that the ring profiles and the carried topological charges of the two incoherently coupled vortex components can be preserved. We also numerically find that the stability of the higher-charge vortex can be enhanced by co-propagating a stable, single-charge vortex.

We report the experimental observation of the instability suppression of higher-order vortex solitons in cylindrical lead glass with thermal nonlocal nonlinearity. A scalar higher-order vortex soliton with a topological charge $l=10$, which is vulnerable to azimuthal breakup when it is perturbed by an initial noise, is stabilized by a coaxially propagating, mutually incoherent Gaussian beam, forming a Gauss-vortex vector soliton (GVVS). The vortical annular profile and topological charge in the GVVS, and the vortical annular profile in the Gauss-vortex vector breather (GVVB), can be preserved during the propagation. Numerical simulations for unperturbed and perturbed scalar vortex solitons, GVVS, and GVVB demonstrate close agreement with experimental results.

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 ($\left|m\right|\ge 3$) vortex can be suppressed and even eliminated because of the presence of the other lower-order ($\left|m\right|\le 2$) 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 ($m_1=-1$, $m_2\ge 3$) when the two vortex components have equal Gaussian beam widths.