Evolution of the Phase Singularity of an Orbital Angular Momentum Beam with an Astigmatism Phase

In this study, we explore the impact of the astigmatism phase on the evolution of the phase singularity of an orbital angular momentum (OAM) beam propagating through free space. The results demonstrate that the high-order phase singularity dispersed into a cluster of individual unit phase singularities owing to the astigmatism phase. The number of singularities equaled the topological charge of the OAM beam. By adjusting the astigmatism phase, we could manipulate and control the evolution of the phase singularities, including their displacements and rotation angles. These findings offer significant prospects for customizing 3D vortex lines, optical topologies, and applications involving topological charge measurement, information encoding, and transfer.