Self-Trapping of “Necklace” Beams in Self-Focusing Kerr Media

Abstract

We show that an azimuthally periodically modulated bright ring ``necklace'' beam can self-trap in self-focusing Kerr media and can exhibit stable propagation for very large distances. These are the first bright $(2+1)\mathrm{D}$ beams to exhibit stable self-trapping in a system described by the cubic $(2+1)\mathrm{D}$ nonlinear Schr\"odinger equation.