Young's double-slit experiment with a partially coherent vortex beam.

We perform a Young's double-slit experiment with a partially coherent vortex beam (PCVB) and explore its cross-spectral density (CSD) at the focal plane after passing through a double-slit. Our results reveal that the phase of the CSD distribution with respect to an on-axis reference point can simultaneously quantitatively characterize the sign and magnitude of the topological charge (TC) carried by such a beam. In particular, the magnitude of the TC is half of the number of coherence singularities and the sign of the TC is determined by the phase winding of the coherence singularities (i.e., counterclockwise- and clockwise increases correspond to positive and negative, respectively). Based on this property, we present and demonstrate experimentally a simple technique to measure the sign and magnitude of the TC of a PCVB through its CSD distribution after a double-slit. Our method allows for easy measurement of the TC by being conceptually simpler than other methods.