In this paper, the polycyclic tornado circular swallowtail beam (PTCSB) with autofocusing and self-healing properties is generated numerically and experimentally and their properties are investigated. Compared with the circular swallowtail beam (CSB), the optical distribution of the PTCSB presents a tornado pattern during the propagation. The number of spiral stripes, as well as the orientation of the rotation, can be adjusted by the number and the sign of the topological charge. The Poynting vectors and the orbital angular momentum are employed to investigate the physical mechanism of beam-rotating. In addition, we also introduce a sector-shaped opaque obstacle to investigate the self-healing property of the PTCSB, passing through it with different center angles and discuss the influence of the scaling factor along the propagation direction. Our results may expand the potential applications in the optical spanner and material processing.
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.
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