Direct measurement of the orbital angular momentum mean and variance in an arbitrary paraxial optical field

Abstract: We introduce and experimentally demonstrate a method for measuring at the same time the mean and the variance of the photonic orbital angular momentum (OAM) distribution in any paraxial optical field, without passing through the acquisition of its entire angular momentum spectrum. This method hence enables one to reduce the infinitely many output ports required in principle to perform a full OAM spectrum analysis to just two. The mean OAM, in turn, provides direct access to the average mechanical torque that the optical field in any light beam is expected to exert on matter, for example in the case of absorption. Our scheme could also be exploited to weaken the strict alignment requirements usually imposed for OAM-based free-space communication.