Nonlinear vortex light beams supported and stabilized by dissipation

We describe nonlinear Bessel vortex beams as localized and stationary solutions with embedded vorticity to the nonlinear Schr\"odinger equation with a dissipative term that accounts for the multi-photon absorption processes taking place at high enough powers in common optical media. In these beams, power and orbital angular momentum are permanently transferred to matter in the inner, nonlinear rings, at the same time that they are refueled by spiral inward currents of energy and angular momentum coming from the outer linear rings, acting as an intrinsic reservoir. Unlike vortex solitons and dissipative vortex solitons, the existence of these vortex beams does not critically depend on the precise form of the dispersive nonlinearities, as Kerr self-focusing or self-defocusing, and do not require a balancing gain. They have been shown to play a prominent role in "tubular" filamentation experiments with powerful, vortex-carrying Bessel beams, where they act as attractors in the beam propagation dynamics. Nonlinear Bessel vortex beams provide indeed a new solution to the problem of the stable propagation of ring-shaped vortex light beams in homogeneous self-focusing Kerr media. A stability analysis demonstrates that there exist nonlinear Bessel vortex beams with single or multiple vorticity that are stable against azimuthal breakup and collapse, and that the mechanism that renders these vortexes stable is dissipation. The stability properties of nonlinear Bessel vortex beams explain the experimental observations in the tubular filamentation experiments.
Comment: Chapter of book