Autofocus properties of astigmatic chirped symmetric Pearcey Gaussian vortex beams in the fractional Schrödinger equation with parabolic potential.

Described by the fractional Schrödinger equation (FSE) with the parabolic potential, the periodic evolution of the astigmatic chirped symmetric Pearcey Gaussian vortex beams (SPGVBs) is exhibited numerically and some interesting behaviors are found. The beams show stable oscillation and autofocus effect periodically during the propagation for a larger Lévy index (0 < α ≤ 2). With the augment of the α, the focal intensity is enhanced and the focal length becomes shorter when 0 < α ≤ 1. However, for a larger α, the autofocusing effect gets weaker, and the focal length monotonously reduces, when 1 < α ≤ 2. Moreover, the symmetry of the intensity distribution, the shape of the light spot and the focal length of the beams can be controlled by the second-order chirped factor, the potential depth, as well as the order of the topological charge. Finally, the Poynting vector and the angular momentum of the beams prove the autofocusing and diffraction behaviors. These unique properties open more opportunities of developing applications to optical switch and optical manipulation.

Circular Mathieu and Weber autofocusing beams.

In this Letter, the new classes of non-paraxial autofocusing beams are introduced for the first time, to the best of our knowledge. We investigate both numerically and experimentally non-paraxial circular Mathieu and Weber autofocusing beams based on the solutions of the Helmholtz equation in elliptical and parabolic coordinates, respectively. The results show that such beams can significantly shorten the focus distance, and eliminate the intense oscillation effectively after the focusing point. The focal length and the peak intensity can be controlled by tunable parameters. In addition, we further experimentally realize their application of such beams in optical trapping.

Experimental generation of the polycyclic tornado circular swallowtail beam with self-healing and auto-focusing.

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.

Controllable Laguerre Gaussian wave packets along predesigned trajectories.

We introduce controllable Laguerre Gaussian wave packets (LGWPs) with self-accelerating and self-focusing properties along their predesigned parabolic trajectory via phase modulation. Numerically and experimentally recorded intensity patterns of controllable LGWPs with topological charges are obtained, and it is obvious that they agree well with the theoretical model. Furthermore, spatiotemporally controllable LGWPs can propagate stably along predesigned trajectories for many Rayleigh lengths. This paper not only provides a theoretical propagation model for these multi-dimensional controllable LGWPs, but also promotes further development of the basic research into self-bending and autofocusing structured light fields.