Properties of a Controllable Vortex Anomalous Hollow Hermite Beam Propagating in Free Space and Fractional Fourier Transform

A new investigation of controllable vortex anomalous hollow Hermite beam (CVAHHB) as a general form of anomalous hollow beam is introduced. Based on the integral of Huygens-Fresnel, analytical propagation formulas of a CVAHHB in a paraxial ABCD optical system are derived. Our numerical results show that the evolution features of the received intensity pattern upon propagation in free space are affected by controllable beam parameters, Hermite orders and topological charge. Additionally, the intensity and phase distributions of the beam propagating in Fractional Fourier Transform (FRFT) gradually and periodically evolve with respect to the order of the FRFT. The shape of the considered beam depends strongly on the FRFT order and the incident beam parameters. Our results could potentially support the applications of the CVAHHB in optical trapping and laser optics.