Global caustic and phase chirality reversal of the focused vortex beam

We predict the reversal of the phase chirality before and after the focal plane during propagation based on ray tracing. The interference patterns of a focused vortex beam (FVB) and a plane beam during propagation verify the fact of phase chirality reversal through diffraction theoretical simulations and experiments. Also, we deduce an analytical expression for the caustic based on the ray equation, which effectively represents the change of the hollow light field during propagation. Simulation and experimental results demonstrate the effectiveness of the caustic in describing the variation of the global hollow dark spot radius. Furthermore, based on the caustic results at the focal plane, we customize FVBs with the same dark spot radii but different topological charges. Our research results reveal the characteristics of the light field and phase distribution of the FVB during propagation, which will expand our understanding of the properties of the FVB and provide a reference value for applications such as chiral particle manipulation and topological charge recognition.