Vortex solitons in a saturable optical medium

Optical vortex solitons in a defocusing saturable medium are analyzed in the framework of the (2 + 1)-dimensional generalized nonlinear Schrödinger equation. Stationary, radially symmetric localized solutions with nonvanishing asymptotics and a phase singularity (vortex solitons) are found numerically for the varying saturation parameter. Relaxation of some localized initial profiles (e.g., vortex-type structures of an elliptic shape) to a vortex soliton is investigated numerically and then compared with the experimentally measured propagation of the vortex solitons created by a laser beam passed through a rubidium vapor, known as a nonlinear medium with strong saturation of the nonlinear refractive index. Reasonably good agreement is found, supporting the validity of the phenomenological model of the saturable nonlinear medium.