Dissipative ring solitons with high values of vorticity

Abstract

Vortices are screw wave front defects that appear in many branches of physics. In recent years, they attracted much attention in optics. Optical vortices in nonlinear media have special properties and they have been dubbed vortex solitons. They can exist both in continuous and periodic media. Vortices can be located on a plane wave which requires an infinite energy to support them. In reality, most of the studies were restricted to optical vortices that are nested in bright beams. The requirement of zero field at the center of the beam converts them into ring structures. These can exist as exact solutions of nonlinear wave equations. Vortex ring solitons with high value of vorticity are of special interest. Their stability in conservative media is a controversial issue. Generally, ring structures in conservative media have been found to be unstable in respect to the modulation instability. The result of such instability is usually the filamentation of the beam. In this respect, we should note that the stability properties of vortex solitons in dissipative media are quite different from those in conservative media. Thus, dissipative soliton structures require separate studies.