Polygonal shaping and multi-singularity manipulation of optical vortices via high-order cross-phase

Increasing demand for practical applications is forcing more in-depth research into optical vortices (OVs): from the generation and measurement to the shaping and multi-singularity manipulation of OVs. Herein, we propose a new type of phase structure called the high-order cross-phase (HOCP), which can be employed to modulate OVs to implement polygonal shaping and multi-singularity manipulation simultaneously at far-field. Theoretically, we investigate the propagation characteristics of OVs modulated by a HOCP. In experiments, we achieve the polygonal shaping and multi-singularity manipulation of OVs via HOCPs. On this basis, we discuss the relationship between shapes and the orders of HOCPs, where we find that the order of a HOCP is exactly equal to the number of sides of polygonal OVs. This work provides a novel method to achieve polygonal shaping and multi-singularity manipulation simultaneously, which facilitate applications in optical micro-manipulation and optical communication.