Orbital Angular Momentum of Superpositions of Optical Vortices Perturbed by a Sector Aperture

In optical communications, it is desirable to know some quantities describing a light field, which are conserved on propagation or resistant to some distortions. Typically, optical vortex beams are characterized by their orbital angular momentum (OAM) and/or topological charge (TC). Here, we show analytically that the OAM of a single rotationally symmetric optical vortex is not affected by an arbitrary-shape aperture or by other amplitude perturbations. For a superposition of two or several optical vortices (with different TCs), we studied what happens to its OAM when it is distorted by a hard-edge sector aperture. We discovered several cases when such perturbation does not violate the OAM of the whole superposition. The first case is when the incident beam consists of two vortices of the same power. The second case is when the aperture half-angle equals π multiplied by an integer number and divided by the difference between the topological charges. For more than two incident beams, this angle equals π multiplied by an integer number and divided by the greatest common divisor of all possible differences between the topological charges. We also show that such a sector aperture also conserves the orthogonality between the complex amplitudes of the constituent vortex beams. For two incident vortex beams with real-valued radial envelopes of the complex amplitudes, the OAM is also conserved, when there is a ±π/2 phase delay between the beams. When two beams with the same power pass through a binary radial grating, their total OAM is also conserved. We hope that these findings could be useful for optical communications since they allow for the identification of incoming optical signals by their OAM by registering only part of the light field within a sector aperture, thus reducing the cost of the receiving devices.