Abruptly autofocusing of polycyclic tornado symmetric Pearcey vortex beams in the fractional Schrödinger equation

In this paper, we study polycyclic tornado symmetric Pearcey (PTSP) vortex beam induced by superimposing spiral phase and vortex, and its propagation dynamics in the fractional Schrödinger equation (FSE). We find that the autofocusing of the symmetric Pearcey beam is enhanced and the autofocus length is shorten with the increase of Lévy index α. Polycyclic tornado phase will form a dark tornado ring (DTR) on the basis of PTSP vortex beam, and the radius of the DTR will also change with the increase of the propagation distance. Finally, the divergence force and gradient force of the PTSP vortex beam in FSE are displayed during transmission. The development of these special properties in FSE has important implications for optical tweezers, medical and military applications.