Bi-stable vortex solitons in the nonlinear fractional Schrödinger equation with Bessel optical lattices

We study the existence and stability of vortex soliton solutions of the nonlinear fractional Schrödinger equation in a competing cubic-quintic medium with an imprinted Bessel optical lattice. Two branches of vortex solitons with a turning point at the threshold of propagation constant were found. Linear stability analysis corroborated by direct propagation simulations reveals that the vortex solitons of the upper branch can be stable in a wide region, while the solitons belonging to the lower branch are always stable above a critical value of the Lévy index. Moreover, the existence area of the vortex solitons can be remarkably suppressed by the increase of Lévy index.