Stabilization of bright optical vortex solitons in nonlocal nonlinear media

An optical vortex is a light beam that carries a phase singularity. Such singular beams can be generated experimentally in different types of linear and nonlinear media [1]. The unique features of vortex fields are expected to lead to many applications including optical data storage, image distribution and processing, optical tweezers, optical trapping and manipulation, etc. However, optical vortices become highly unstable in self-focusing nonlinear media due to the symmetry-breaking azimuthal instability, and they decay into several fundamental solitons (see, e.g., Ref. [2] and references therein). In spite of many theoretical studies suggesting different ways to stabilize optical vortices in nonlinear media, no stable optical vortices were readily observed in experiment. Thus, the important theoretical challenge remains to reveal realistic physical media which would allow the first experimental observation of stable self-trapped vortices in nonlinear media. In this work, we study the light propagation in nonlocal media and demonstrate that the symmetry-breaking azimuthal instability of the vortex beams can be eliminated above a certain threshold in the nonlocal parameter. Our results suggest a simple way to generate experimentally the first stable spatially localized vortices in self-focusing nonlinear media. We consider the evolution of the electric field envelope ? along the z-axis described by the equation i _z?+ _xy?+? ? = 0, where the nonlocal nonlinear response of the media is modeled by the equation ?² ?- _xy? = |?|², ? being the nonlocality parameter. For example, in the case of the wave beam propagation in partially ionized plasmas, ? is the relative electron temperature perturbation; in nematic liquid crystals, ? describes the spatial distribution of the molecular director. We have studied the stationary vortex solutions and their linear stability, and also verified the predictions by direct numerical simulations of the beam propagation. The different evolution scenarios are illustrated by Figs. 1(a,b). We find that, below some critical value ? _cr 0.12 of the nonlocality parameter, the vortex solitons become stable due to nonlocality.