Standard Deviation of Fiber-Coupling Efficiency for Free-Space Optical Communication Through Atmospheric Turbulence

In fiber-based optical receivers such as coherent receiver, the optical signal reaching the receiver's aperture is coupled to the optical fiber through a set of lenses. Due to atmospheric turbulence, however, the coupling efficiency, which is defined by the ratio of the fiber-coupled optical power to the optical power reaching the aperture, fluctuates over time, and thus should be treated as a random variable. Previous theoretical works predict the average coupling efficiency accurately, but fail to estimate the standard deviation, especially when the turbulence is strong. In this study, we propose new theoretical formulas for the standard deviation of coupling efficiency applicable to a wide range of turbulence conditions. For this purpose, we derive a new approximated formula for the second moment of coupling efficiency using the second-order Taylor expansion. Next, a new formula for the second moment of coupled optical power is developed by introducing the spatial filter to the fourth-order coherence function. The computer simulation is carried out to evaluate the accuracy of the formulas. The results show that our formulas agree with the simulation results over a wide range of turbulence strength. Also, the new formulas provide better accuracy than the previously reported ones.