Measuring azimuthal and radial mode indices of a partially coherent vortex field

Abstract

Based on the cross-correlation function, a method for determining the azimuthal mode index (topological charge) of a partially coherent vortex beam, assuming the beam possesses a radial index p = 0, has recently been proposed. Here, we show a new kind of spatial correlation function, i.e., the mutual coherence function of two points (x, y) and (2x, 2y), which we call the double-correlation function. Unlike the cross-correlation singularity, which depends on both radial and azimuthal mode indices, the double-correlation singularity is dependent on the radial mode index only. Based on this property, we propose a method for determining the azimuthal and radial mode indices of a partially coherent beam with a nonzero radial mode index, to our knowledge, for the first time.