Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: XIII. Conditions of applicability of the ergodic hypothesis for fiber ring interferometers

Abstract

Some additional conditions of applicability of the ergodic hypothesis to fiber ring interferometers (FRIs) with a loop consisting of a single-mode optical fiber (SMOF) with random inhomogeneities are considered. It is shown by mathematical modeling that the change in the phase difference of counterpropagating waves at the FRI output with the SMOF temperature is not a stationary random process. However, in a fairly narrow temperature range, this dependence can be assumed to be locally stationary. The conditions determining this temperature range are formulated. It is shown for a fairly large ensemble of independent realizations of random inhomogeneities in an SMOF that, even when all conditions of ergodicity are satisfied with a large margin, there will always be at least one realization violating strict ergodicity. Thus, only conditional (approximate) ergodicity occurs in this case. Nevertheless, in calculation of the FRI zero drift in this situation, averaging over an ensemble of independent realizations of random inhomogeneities in the SMOF of an FRI loop can be performed with sufficient accuracy. As a result, calculations are simplified significantly. In the general case, when at least one of the conditions of ergodicity is not satisfied, averaging over temperature for each realization with subsequent averaging over the entire ensemble should be performed. It is shown also that, within this problem, we can speak only about quasi-ergodicity or emulation of ergodicity, since a change in the temperature of the SMOF of an FRI loop and successive enumeration of independent realizations of random inhomogeneities in the SMOF loop are radically different random processes. The parameters characterizing quasiperiodic temperature changes in the phase difference of counterpropagating waves at the FRI output are refined.