Conservation of the orbital angular momentum carried by superposition of optical vortices after passing through a sector diaphragm

Abstract

In optical communications, it is desirable to know some quantities describing a light field, that conserve on propagation or resist to distortions. Typically, vortex beams are characterized by their orbital angular momentum (OAM) and topological charge (TC). Here, we show that the OAM of a single rotationally symmetric optical vortex is not affected by an arbitrary-shape aperture. For superposition of several optical vortices, we study what happens with its OAM behind a sector aperture. We discover that a specific sector angle does not violate the OAM carried by the superposition. The aperture half-angle should be equal to π multiplied by an integer number and divided by the greatest common divisor of all possible differences between the TCs. We show that such a sector aperture also conserves the orthogonality between the complex amplitudes of the constituent vortex beams. This property allows their effective demultiplexing after being distorted by such an aperture.