Propagation dynamics of vortex airy beams with quadratic phase modulation

We, both theoretically and numerically, investigate dynamic evolutions of vortex Airy beams with quadratic phase modulation (QPM). Different from the conventional Airy vortex beams, where the acceleration velocity of the vortex is twice that of the main lob of the Airy beams, for QPM vortex Airy beams, both the trajectories and velocities of the main beam lobe and initial optical vortex (OV) are dependent on the QPM parameter. Moreover, the reconstructed position and speed of the reappearing OV are related to polarity of QPM parameter. For negative QPM beam, the reconstructed OV reappears in the first quadrant over a sufficiently long distance. In the opposite case of positive QPM, the OV can be quickly reconstructed in the third quadrant within a very short distance. This study shows the possibility of controlling vortex Airy beams by purposely choosing appropriate QPM parameters.