Ergodicity of Phase Fluctuations for Free-Space Optical Link in Atmospheric Turbulence

The knowledge of atmospheric turbulence is quite imperative for free space optical (FSO) communications. This letter reveals the relationship between spatial and temporal phase fluctuations in an FSO link. We demonstrate that the phase fluctuation is an ergodic process in stationary and homogeneous turbulence. On the basis of wave structure which sets up a bridge between spatial and temporal phase characteristics, we theoretically derive the power spectrum and the autocorrelation function which predict the conditions of ergodicity. A series of experiments were carried out to test theoretical predictions where coordinate optical phase was measured for a wide range of turbulent strengths. As a result, we show that both the temporal and spatial phase spectra have low-pass characteristics and both their average and autocorrelation show ergodic behavior, following the same law with the variation of turbulent strength. This letter indicates that the spatial and temporal statistics of phase fluctuations could be interconverted for free-space optical communication and other applications related to the propagation of optical signals in the atmosphere.