Orbital angular momentum and topological charge of a Gaussian beam with multiple optical vortices

Here we study theoretically and numerically a Gaussian beam with multiple optical vortices with unitary topological charge (TC) of the same sign, located uniformly on a circle. Simple expressions are obtained for the Gaussian beam power, its orbital angular momentum (OAM), and TC. We show that the OAM normalized to the beam power cannot exceed the number of vortices in the beam. This OAM decreases with increasing distance from the optical axis to the centers of the vortices. The topological charge, on the contrary, is independent of this distance and equals the number of vortices. The numerical simulation corroborates that after passing through a random phase screen (diffuser) and propagating in free space, the beams of interest can be identified by the number of local intensity minima (shadow spots) and by the OAM.