Statistics of signal-to-noise ratio and path-accumulated power due to concatenation of polarization-dependent loss

The authors present analytical expressions for the signal and noise statistics due to the concatenation of a large number of low-polarization-dependent loss elements. By solving the governing stochastic differential equations, using perturbation methods for the cases with and without power stabilization, they obtain important bounds on signal-to-noise ratio fluctuations and other quantities for the design of agile long-haul fiber communication systems.