Spatial correlation vortices in partially coherent light: theory

Coherent optical beams may contain optical vortices that are characterized by a dark core and a well-defined azimuthally harmonic phase.1,2 In contrast, different points in a spatially incoherent beam are uncorrelated, and the phase structure of an optical vortex is ill defined. In the transitional regime of partially coherent light, one should take the statistical properties of light into account to quantify global phase properties.3,4 Recent investigations suggest that vortices in partially coherent light are destroyed.5,6 By relating the vortex phase to the spatial variations in the mutual coherence function4 (MCF), we found robust vortex attributes that do not vanish in partially coherent light. The coherence properties of optical vortices have become an active branch of inquiry in singular optics over the past several years. Coherence filtering properties of an optical vortex were recently investigated numerically7 and experimentally.8 We employed the MCF, which describes the correlation between two points in a beam, to study the propagation of partially coherent beams.9 Recently the MCF was used to study phase singularities in partially coherent light emerging from two pinholes10,11 and to analyze sources with separable phase.12 Here we describe our numerical investigation of the MCF of a partially coherent vortex beam. We found spatial correlation vortices (SCVs) in the MCF, which are analogous to the composite vortices in coherent beams.2,13 Furthermore we demonstrate how both the coherence length and the displacement of the conventional vortex in a beam affect the SCVs. An on-axis vortex in a partially coherent beam may result in a circular dislocation line in the MCF.14 We found that this dislocation breaks into two spatial correlation vortices as the conventional vortex is moved off axis.