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.

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.

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.

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.