Generation and measurement of irregular polygonal perfect vortex optical beam based on all-dielectric geometric metasurface

The perfect optical vortex (POV) beam carrying orbital angular momentum with topological charge-independent radial intensity distribution possesses ubiquitous applications in optical communication, particle manipulation, and quantum optics. But the mode distribution of conventional POV beam is relatively single, limiting the modulation of the particles. Here, we originally introduce the high-order cross-phase (HOCP) and ellipticity γ into the POV beam and construct all-dielectric geometric metasurfaces to generate irregular polygonal perfect optical vortex (IPPOV) beams following the trend of miniaturization and integration of optical systems. By controlling the order of the HOCP, conversion rate u, and ellipticity factor γ, various shapes of IPPOV beams with different electric field intensity distributions can be realized. In addition, we analyze the propagation characteristics of IPPOV beams in free-space, and the number and rotation direction of bright spots at the focal plane give the magnitude and sign of the topological charge carried by the beam. The method does not require cumbersome devices or complex calculation process, and provides a simple and effective method for simultaneous polygon shaping and topological charge measurement. This work further improves the beam manipulation ability while maintaining the characteristics of the POV beam, enriches the mode distribution of the POV beam, and provides more possibilities for particle manipulation.