Off-site and on-site vortex solitons in space-fractional photonic lattices.

We address the existence and stability of off-site and on-site vortex solitons with a unit topological charge in space-fractional Kerr lattices. In contrast to the reported ordinary Kerr lattices, vortex solitons in the proposed space-fractional lattices are stable only in the intermediate region of propagation constant, and this region widens rapidly with the increase of a Lévy index. Under the same Lévy index, the stability range of on-site vortices is larger than that of off-site ones. In particular, for on-site vortex solitons, the upper edge of the stability range appears where the maximum of soliton power is located, which provides an effective way to identify the stability range of on-site vortices. Our results extend the study of vortex solitons into space-fractional systems and deepen the understanding of Kerr lattices in fractional dimensions.