Generation of multiple rotationally-symmetric power-exponent-phase vortex beams on a spatial arbitrary distribution by using holographic phase control techniques

In this paper, a method for generating multiple rotationally-symmetric power-exponent-phase vortex beams (RPVBs) on a spatial arbitrary distribution was demonstrated. The properties of a single RPVB were studied experimentally and theoretically with good agreement. Then, the flexibilities of user-defined spatial arbitrary distribution of multiple RPVBs were illustrated by applying an appropriated computer-generated hologram (CGH) on a spatial light modulator (SLM). This CGH was generated by superposing the interference pattern of a single RPVB, which derived from a phase mask of Laguerre-Gaussian (LG) beam and RPVB, and the phase shift calculated by the lenses and gratings (L&G) algorithm. As a result, the user-defined beam number, radial exponent (p), topological charge (TC), and power exponent (n) of the RPVBs can be controlled. Compared with the results of a single RPVB, the properties of individual spatial arbitrary distribution RPVBs were still kept the same as the CGH generated by the L&G algorithm, which would only bring a phase shift and would not involve additional phase transformations. The propagation properties of the multiple RPVBs were also studied. These results will extend the applications of RPVBs in optical trapping and may provide a new method to generate complex patterns like chiral structures.