The Propagation Characteristics of Circular Airy Beams with Propagational Fractional-Order Optical Vortices

We investigate the propagation properties of circular Airy beams (CABs) with propagational fractional-order optical vortices (OVs). The superposition of the phase singularity and polarization singularity from a vortex vector beam (VVB) plays a significant role in creating a propagational fractional vortex beam. Propagational fractional vortex beams can be considered as a superposition of left and right circularly polarized vortex beams with different integer topological charges (TCs). We study the propagation characteristics of two kinds of propagational fractional vortex CABs, and the results show that both of the two kinds of beams can stably propagate in free space, and they exhibit an “abruptly auto-focusing” property and “self-healing” property during the propagation. The intensity distribution of the first kind of propagational fractional vortex CAB has an odd number of petals (2m + 1), while the second kind of beam has a crescent-shaped intensity distribution. The influence of turbulence on the beam propagation through atmosphere under different turbulence strengths is also numerically studied in this paper. A fractional vortex CAB with an initial radius r0 = 10 mm can retain its shape after propagating 20 m when the atmospheric refractive-index structure constant CN2=0.2×10−12m−2/3. Our results are expected to broaden the application of CABs.