Spatial correlation properties of tightly focused J₀-correlated

In order to study the spatial correlation properties of tightly focused J₀-correlated radially polarized vortex beam through a high numerical aperture d_NA, the vectorial Debye diffraction theory and the coherence theory were adopted. After theoretical analysis and numerical simulation of the correlation characteristics of focused field on the optical axis and the focal plane, the expression and simulation data of coherence degrees were obtained.The results show that, the longitudinal coherence degrees in the focal region increase as the topological charge n increases, but it decrease as the coherence parameter or the numerical aperture d_NA; The transverse coherence degrees in the focal plane decrease with the increase of the topological charge, coherence parameter or numerical aperture. When n≥5 or d_NA≤0.4, the longitudinal coherence near the focal point approximately equals to 1. Further, the coherence degrees are shown to exhibit phase singularities. The results are of great significance to the application of J₀-correlated vector vortex beams in many fields.