Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity

The existence of a spatial correlation singularity or a ring dislocation in the spatial coherence function when a vortex is present has been demonstrated recently. Here, we investigate how the spatial correlation singularity is affected by both the radial and azimuthal mode indices (p, ℓ) in a partially coherent light field. Theoretically, we find that the spatial correlation singularity may exist even in a non-vortex beam (ℓ = 0) due to the radial index. Numerical simulations show the number of ring dislocations in the far-field cross correlation function is equal to 2p + |ℓ| for the low coherence cases. This is confirmed by our experimental results. This phenomenon may occur in any partially coherent vortex wave.