Investigating the propagation characteristics of modulated circular Airy vortex beam in free space via angular spectrum method

In this paper, the approximate analytical expression of the Hankel transform of arbitrary order circular Airy vortex beam (CAVB) is derived, which enables researchers to solve the propagation characteristics of the family of CAVB via angular spectrum method. Moreover, based on the approximate analytical expression, the propagation characteristics of Fourier space modulated and azimuthally modulated CAVB are investigated. It is found that by modulating the CAVB via a Fourier space periodic function, multiple focal points can be generated during the propagation; and by modulating the CAVB via azimuthally grafting two spiral phases, the focal point of the beam will deviate from the center of the focal plane. These results provide a simple method for flexible regulation of the number and location of the focal points of the CAVB.