Paraxial propagation characteristics of a controllable anomalous hollow vortex beam in free space

Abstract Propagation of a recently proposed controllable anomalous hollow vortex (CAHV) beam is investigated. Based on the integral formula of generalized Huygens–Fresnel diffraction, analytical expression for the CAHV beam through a paraxial ABCD optical system is derived. The factors that affect the intensity pattern are determined by the beam’s controllable parameters a , c x , c y , and the topological charge m . Results show that the Gaussian distribution features are controlled by parameter a , and the horizontal and vertical stretching deformations of the beam are adjusted by parameters c x and c y , respectively. For a controllable anomalous hollow (CAH) beam, when propagating in free space, it could initially maintain anomalous hollow property and the size of the spot increases with the increase of the propagation distance. Due to the CAHV beam carries the optical vortex, a dark hollow channel appears in the center of the beam during propagation, and the channel structure changes with the increase of topological charge. Additionally, the Poynting vector of CAHV beam proves the direction of energy flow corresponding to the intensity distribution. Results obtained in this paper could have potential applications in particle trapping and optical control.