Detection of multiple coaxial optical vortices with a Shack-Hartman sensor in atmospheric turbulence

The Shack-Hartmann wavefront sensor has proven to be a valuable detector particularly in the context of turbulence and adaptive optics. In this work we take advantage of its capacity of characterizing orbital-angular-momentum (OAM) states under certain conditions, in the context of a free-space optical communication link. First, we propose a method to compute the locations of the light spots created by the lenslet array that is more robust than the simple centroid formula when atmospheric turbulence is present. Second, we propose a "local OAM" estimation that avoids the computation of a circulation integral in the discrete Shack-Hartmann array. Our proposal does not require prior knowledge of beam diameter or OAM state. We show simulations and laboratory experiments for OAM beams in turbulence conditions at which reliable detection is feasible. We analyze the quality of detection as a function of turbulence strength, Shack-Hartmann resolution and number of acquisitions. These ideas can be applied to coherent coaxial superpositions of two or more OAM states if the light rings are non-overlapping. Using the concept of "optical ferris-wheels" introduced by Franke-Arnold et al. (2007), the detection can be implemented for a limited set of pairs of vortices. We propose a generalization of the recipe for generation of ferris-wheels now for pairs of orthogonal vortices with arbitrary OAM states. The proposal is supported by simulations in turbulence conditions. An extension of our work considers the use of error-correcting codes that take advantage of the large set of available combinations of OAM states.