Study on the propagation properties of controllable vortex anomalous hollow beams

The evolution of a controllable vortex anomalous hollow beam (CVAHB) in free space is studied theoretically and numerically. Based on the Collins integral, the analytical formula of its propagation under free space paraxial approximation is derived. The corresponding beams with different parameters are simulated numerically, and the influence of each beam parameter on the beam type and intensity distribution during beam propagation is studied. Through the parameter control, the CVAHB can present a variety of intensity modes, such as hollow, three-segment, boat, etc. It is obvious that the evolution of CVAHB is different from that of the controllable anomalous hollow beam (CAHB). By changing the value of the topological charge (TC), the role of the orbital angular momentum (OAM) in the transverse distribution and propagation of light intensity is studied in detail.