Quasi-stable propagation of vortices and soliton clusters in saturable Kerr media with square-root nonlinearity

Analytical and numerical investigation of the propagation of optical beams in Kerr-like saturable photorefractive media is carried out, utilizing a novel model for the local isotropic part of the space-charge field generated in the medium. Using a variational technique, optimal propagation parameters for the most stable propagation of otherwise unstable single Gaussian, single vortex, and optical soliton cluster beams are determined. Analogy between a ring of identical weakly overlapping solitons and a vortex of the same topological charge is explored.