Observation of higher-order deterministic optical vortices from random vortex beams
Yonglei Liu, Siyu Xu, Peipei Peng, Yongtao Zhang, Siting Dai, Yahong Chen, Yangjian Cai, Fei Wang
Abstract
Optical vortices in coherent beams have been identified as spiral phases with intensity nulls at singularities, while in random beams, they appear as coherence vortices in correlation functions, often not matching intensity nulls. Observing deterministic optical vortices in random beams is challenging due to their randomness. In this work, we propose a scheme relying on spatial coherence engineering and fractional Fourier transform to design a partially coherent light source capable of generating deterministic optical vortices at specific propagation distances in free space. At other propagation distances (including the source plane), the beam may exhibit coherence vortices characterized by spatially coupled two-point correlations, while deterministic vortices emerge only at designated distances. We show that both the topological charge and the axial position of the deterministic vortex are determined by the coherence parameters of the light source. Using a random-mode superposition approach, we experimentally synthesize such partially coherent light sources and characterize both coherence vortices and deterministic phase vortex through measurements of the four-dimensional correlation function at different propagation distances. In addition, we study the coherence phase orbital angular momentum (OAM) spectrum of the random beam both theoretically and experimentally. Our results reveal that the phase OAM spectrum is pure when the random beam carries a deterministic vortex, whereas for coherence vortices, the phase OAM spectrum is non-pure. This study provides a pathway for understanding and controlling the transition between deterministic phase vortices and coherence vortices, with potential applications in optical communication and metrology.