Propagation dynamics of radially polarized symmetric Airy beams in the fractional Schr\"odinger equation

TL;DR

This paper investigates the propagation behavior of radially polarized symmetric Airy beams within a fractional Schrödinger framework, revealing autofocusing effects, vortex influences, and particle capture capabilities in complex optical systems.

Contribution

It introduces a detailed analysis of R-SABs in fractional diffraction systems, highlighting autofocusing, vortex effects, and particle trapping, which are novel in the context of fractional Schrödinger equations.

Findings

Autofocusing becomes stronger with increased Levy index.

Vorticity influences autofocusing dynamics.

R-SABs can trap nano-particles at multiple positions.

Abstract

We analyze the propagation dynamics of radially polarized symmetric Airy beams (R-SABs) in a (2+1)-dimensional optical system with fractional diffraction, modeled by the fractional Schr\"odinger equation (FSE) characterized by the L\'evy index. The autofocusing effect featured by such beams becomes stronger, while the focal length becomes shorter, with the increase of . The effect of the intrinsic vorticity on the autofocusing dynamics of the beams is considered too. Then, the ability of R-SABs to capture nano-particles by means of radiation forces is explored, and multiple capture positions emerging in the course of the propagation are identified. Finally, we find that the propagation of the vortical R-SABs with an off-axis shift leads to rupture of the ring-shaped pattern of the power-density distribution.