Scalar potential for representing the topology of electromagnetic beams

It was established by Green and Wolf in 1953 that an electromagnetic wave can be characterized by a complex scalar potential, including its energy and momentum densities. In this paper, we show that, for electromagnetic beams, this scalar potential can be used to fully describe the beam’s topology. We further demonstrate that this scalar potential can be used to characterize a partially coherent vector beam, and introduce a set of scalar Stokes-like parameters for this purpose.