Improved detection of vortex superpositions in turbulence using optimal transport theory: simulations and experiments

In the context of OAM-based signal modulation free-space optical communications affected by atmospheric turbulence, we demonstrate a strategy for designing OAM signal constellations using the Wasserstein distance from the Optimal Transport theory. By recording propagated OAM modes with a spatial detector (complex conjugation, mode sorter, and Shack-Hartmann) and delivering OAM spectra from the images, we create a similarity matrix based on the distorted histograms using the Wasserstein distance. From this, we show that optimal sets of superpositions -in the sense of maximizing the mutual distance of the components- can be found, and be used for improving the quality of detection in the presence of turbulence. We present classification results for three optimal OAM constellations and back these results with our first experimental trial, recorded with a 1-km propagation testbed.