Stochastic calculations for fibre Raman amplifiers with randomly varying birefringence

For the first time for the model of real-world forward-pumped fibre Raman amplifier with the randomly varying birefringence, the stochastic calculations have been done numerically based on the Kloeden-Platen-Schurz algorithm. The results obtained for the averaged gain and gain fluctuations as a function of polarization mode dispersion (PMD) parameter agree quantitatively with the results of previously developed analytical model. Simultaneously, the direct numerical simulations demonstrate an increased stochastisation (maximum in averaged gain variation) within the region of the polarization mode dispersion parameter of 0.1÷0.3 ps/km1/2. The results give an insight into margins of applicability of a generic multi-scale technique widely used to derive coupled Manakov equations and allow generalizing analytic model with accounting for pump depletion, group-delay dispersion and Kerr-nonlinearity that is of great interest for development of the high-transmission-rates optical networks.

Stochastic anti-resonance in a fibre Raman amplifier

Stochastic anti-resonance, that is resonant enhancement of randomness caused by polarization mode beatings, is analyzed both numerically and analytically on an example of fibre Raman amplifier with randomly varying birefringence. As a result of such anti-resonance, the polarization mode dispersion growth causes an escape of the signal state of polarization from a metastable state corresponding to the pulling of the signal to the pump state of polarization.This phenomenon reveals itself in abrupt growth of gain fluctuations as well as in dropping of Hurst parameter and Kramers length characterizing long memory in a system and noise induced escape from the polarization pulling state. The results based on analytical multiscale averaging technique agree perfectly with the numerical data obtained by direct numerical simulations of underlying stochastic differential equations. This challenging outcome would allow replacing the cumbersome numerical simulations for real-world extra-long high-speed communication systems.