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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.

We experimentally study the generation of a partially coherent non-diffractive beam by focusing a partially coherent vortex beam with an axicon. The investigation results show that when the partially coherent vortex beam is focused by the axicon, the beam is transferred into a partially coherent higher-order non-diffractive beam. In the non-diffractive zone, the transverse intensity distribution of the partially coherent higher-order non-diffractive beam is invariant during propagation. In addition, the range of the non-diffractive zone is related to the coherence of the partially coherent vortex beam. The poorer the coherence of the partially coherent vortex beam, the shorter the range of the non-diffractive zone.