Airy-Gaussian vortex beams in the fractional nonlinear-Schrodinger medium

We address the propagation of vortex beams with the circular Airy-Gaussian shape in a (2 + 1)-dimensional optical waveguide modeled by the fractional nonlinear Schrodinger equation. Systematic analysis of autofocusing of the beams reveals a strongly non-monotonous dependence of peak intensity in the focal plane on the corresponding Levy index alpha, with a strong maximum at alpha similar to 1.4. Effects of the nonlinearity strength, the ratio of wilt hs of the Airy and Gaussian factors in the input, as well as the beams' vorticity on the autofocusing dynamics are explored. In particular, multiple autofocusing events occur if the nonlinearity is strong enough. Under the action of azimuthal mod ulational instability, an axisymmetric beam may split into a set of separating bright spots. In the case of strong fractality (for a dose to one), the nonlinear beams self-trap, after the first instance of autofocusing, into a breathing vortical quasi-soliton. Radiation forces induced by the beams' field are considered too, and a capture position for a probe nanoparticle is thus identified. (C) 2021 Optical Society of America

Automated summary

This study investigates the autofocusing of vortex beams with the circular Airy-Gaussian shape in a (2 + 1)-dimensional optical waveguide modeled by the fractional nonlinear Schrodinger equation. It reveals a strongly non-monotonous dependence of peak intensity on the Levy index alpha, with a strong maximum at alpha around 1.4. The effects of nonlinearity strength, input factors' width ratio, and vorticity of the beams on autofocusing dynamics are explored, with multiple autofocusing events possible under strong nonlinearity.