Astigmatic tomography of orbital-angular-momentum superpositions

Abstract

We use astigmatic transformations to characterize two-dimensional superpositions of orbital-angular-momentum states in laser beams. We propose two methods for doing this, both relying only on astigmatic transformations, viewed as rotations on the Poincar\'e sphere, followed by imaging. These methods can be used as a tomographic tool for communication protocols based on optical vortices.