Polarization dependent gain in Raman fiber amplifiers with multiple pumps

In this paper, the polarization dependent gain (PDG) in Raman fiber amplifiers (RFAs) with multiple pumps is studied thoroughly. A comprehensive model, which takes the random polarization mode dispersion, the nonlinear coupling between the pumps, and the degree of polarization (DOP) of the pumps into account, is proposed. The complex nonlinear and random coupling inside the optical fiber is described by a set of nonlinear stochastic differential equations (SDEs), which enable co-simulation of the polarized part and the depolarized part of the multiple pumps. It is revealed that the average PDG and the PDG standard deviation are linearly proportional to the DOP of the pumps, which agrees with the single mode case. More importantly, when the pump wavelength is far away from the signal amplification range (pump-signal wavelength difference larger than 100 nm), its DOP still affects the PDG of the signal. Such a phenomenon is caused by the fact that the pumps interact with each other and the pump DOP could transfer among the pumps, which could enhance the PDG of the RFA. The findings in the work will have important implications for the design of the optical transmission systems with the multi-pump RFAs.