Airy–Gaussian vortex beams in the fractional nonlinear-Schrödinger 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 Schrödinger equation. Systematic analysis of autofocusing of the beams reveals a strongly non-monotonous dependence of peak intensity in the focal plane on the corresponding Lévy index α , with a strong maximum at α ∼ 1.4 . Effects of the nonlinearity strength, the ratio of widths 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 modulational instability, an axisymmetric beam may split into a set of separating bright spots. In the case of strong fractality (for α close 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.