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Single-mode or mode multiplexed free-space atmospheric optical channels drawincreasingly more attention in the last decade. The scope of their possibleapplications spans from the compatibility with the telecom WDM technology,fiber amplifiers, and modal multiplexing for increasing the channel throughputto various quantum communication related primitives such as entanglementdistribution, high-dimensional spatially encoded quantum key distribution, andrelativistic quantum cryptography. Many research papers discuss application ofspecific mode sets, such as optical angular momentum modes, for communicationin the presence of atmospheric turbulence. At the same time some basicproperties and key relations for such channels exposed to the atmosphericturbulence have not been derived yet. In the current paper we present simpleanalytic expressions and a general framework for assessing probability densityfunctions of channel transmittance as well as modal cross-talk coefficients.Under some basic assumptions the presented results can be directly used forestimation of the Fried parameter of the turbulent channel based on themeasured statistics of the fundamental mode transmittance coefficient.

Turbulence-induced optical loss and cross-talk in spatial mode multiplexed or single-mode free-space communication channels