Topological Charge and Other Invariants of Gaussian Vortex Light Fields and Their Superpositions

Here, we study both theoretically and numerically a superposition of a Gaussian beam and a Laguerre-Gaussian (LG) beam with zero radial index. Such field has several optical vortices (OV) that carry same-sign unity topological charge (TC) and are uniformly arranged on a circle. The circle with the OV centers can have arbitrary radius. We derive expressions to describe the orbital angular momentum (OAM) and topological charge (TC) of such field. It is known that, generally, the OAM of light a beam is not interconnected with the number of vortices (e.g. astigmatic beam does not contain any vortices but it has nonzero OAM). For the beam studied here though, it is shown that its OAM cannot exceed the number of vortices and decreases with increasing power of the Gaussian beam. On the contrary, the total TC is independent of this power, remaining equal to the number of constituent vortices. In addition to TC, other propagation-invariant quantities are constructed - we call them asymptotic phase invariants. These invariants are shown to be valid for a superposition of arbitrary number of LG beams or of Gaussian optical vortices. When propagated through a random phase screen (diffuser) or in free space, the multi-vortex beams can be identified using both the number of local intensity minima (shadow spots) and OAM with TC, which is verified via numerical simulation.