Coordinate invariance in stochastic singular optics

Abstract

The study of optical vortices in stochastic optical fields involves various quantities, including the vortex density and topological charge density, that are defined in terms of local expectation values of the distributions of optical vortices. The complexity of these quantities often poses a formidable challenge. Here we address this challenge with the aid of the invariance that these quantities have with respect to rotations of the coordinate axes. This property allows one to express the quantities in terms of singlets of the SO(2) group that represents the coordinate rotations, resulting in expressions that are significantly simpler. We also show that the singlets can help to identify relationships among the different quantities.