Theory of fiber optic co- and counter-pumped Raman polarizers

The goal of our work is to construct a theory which is capable of predicting the main characteristics of Raman polarizers: their overall gain, the average SOP of the outcoming signal beam, and the output signal degree of polarization (DOP) that results whenever the polarizer is fed by unpolarized light. The final result of our theory is the formulation of a set of partial differential equations governing the evolution of the Stokes parameters of the signal and the pump beams with space-dependent coefficients, which in its turn can be found by solving a simple set of ordinary differential equations. When numerically implemented, this procedure takes a computational time of the order of one minute on a laptop computer. This represents a substantial advance over standard Monte-Carlo numerical procedures for the numerical modelling of light propagation in randomly birefringent fibers, which typically require solving the propagation equations for each of-10000 realizations of fibers, followed by a proper statistical averaging over the ensemble of all these realizations. Given that a single propagation run takes about one second, we may estimate overall computational time of three hours. This is the time which is needed to process only a single input SOP: for processing scrambled beams consisting of 150 SOPs randomly distributed over the Poincare sphere, the calculation time would then rise up to 17 days.