Theoretical study of vortex beam generation based on geometric coordinate transformation

By performing a conformal optical mapping of an input beam from Cartesian to log-polar coordinates, we propose a method to generate vortex beam. By tilting the incident beam, a phase gradient is attached and evolves into a vortex phase due to the optical transformation. Thus, the topological charge of the generated vortex beam is continuously adjustable. With this method, vortex beams with integer and fractional orders are generated. The purity of the generated vortex beam is theoretically analyzed, as well as the possible effects of phase misalignment on the output vortex. The continuously tunable vortex beam achieved by this method is expected to be used in information processing and optical routing in optical communications.