Spatial eigenmodes of light in atmospheric turbulence

Abstract

We carry out a numerical analysis of the spatial structure of the eigenmodes of light in atmospheric turbulence and assess the distribution of the singular values under variable turbulence conditions characterized by the Fried parameter and Rytov variance. Under weak scintillation, the highly transmitting eigenmodes found here possess a modal structure that is reminiscent of Laguerre-Gaussian (LG) modes and their simple superpositions. When scintillation becomes significant, we establish that the optimal eigenmodes for communication differ substantially from LG modes and tend to have highly localized transverse intensity distributions.

Robust structured light in atmospheric turbulence

“…they are fixed under the action of the channel. This differs from a singular value decomposition procedure [87] which does not return eigenmodes, but instead requires two different basis sets, one for the input FIG. 8.…”

Robust structured light in atmospheric turbulence

“…Because of the unitarity of the problem, the eigenvector equation is numerically stable and can be solved by a variety of standard numerical tools, so the task is to decompose the channel operator as matrix elements. There are a variety of approaches to do this, with successful theoretical demonstrations including using SVD in turbulence with OAM and pixel modes at the transmitter and receiver, 82 , 83 and experimental demonstrations using point sources for eigenmodes of scattering media 84 , 85 . In the language of quantum mechanics, the nature of the problem lends itself to a process tomography of the channel, 86 which by the isomorphism of channel and state means that a quantum state tomography 87 will completely retrieve the channel matrix, as shown in quantum channels of complex optical fiber 88 as well as in channels through turbulence 89 , 90 .…”