Airy–Gaussian vortex beams in the fractional nonlinear-Schrödinger medium

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