Standard deviation of coupling efficiency to few-mode fiber under atmospheric turbulence

Fiber coupling efficiency significantly affects the received optical power incident to fiber-based optical receivers (e.g., coherent receiver) in free-space optical systems. However, atmospheric turbulence distorts the wavefront of the optical signal propagating through the atmospheric channel, and thus degrades the fiber coupling efficiency. Optical receivers combining few-mode fiber (FMF) coupling with subsequent mode demultiplexing have recently gained considerable attention since they can increase the fiber coupling efficiency by accommodating a few additional spatial modes, compared with single-mode fiber-based ones. In this work, we develop a theoretical model for the standard deviation of FMF coupling efficiency for what we believe to be the first time to the best of our knowledge. We employ a second-order Taylor expansion to approximate the variance of the coupling efficiency. We also apply the spatial filter function based on the two-scale power spectral density from the extended Rytov theory to the fourth-order coherence function to estimate the second-order moments of the coupling efficiency. The coupling efficiencies to FMF estimated by our model agree with the simulation results over a wide range of turbulence conditions, especially when the receiver aperture is large.