Spatial Correlation Properties of Tightly Focused J₀-Correlated Azimuthally Polarized Vortex Beams

Based on vectorial Debye diffraction theory, the spatial correlation properties in the focal region of a J₀-correlated azimuthally polarized vortex beam through a high numerical aperture (NA) are analyzed. The expressions for a pair of points on the axis of symmetry and for a pair of points in the focal plane are derived. It is found that the longitudinal and transverse coherence lengths in the focal region change with the variation in the topological charge and coherence parameter of the vortex field, together with the NA values. In addition, the degree of coherence is shown to possess phase singularities.