Multipath Interference in Pulse-Pumped Fiber Raman Amplifiers: Analytical Approach

We present an analytical study of multipath interference (MPI) in pulse-pumped fiber Raman amplifiers (FRAs), caused by the internal reflections from the fiber facets and the effect of Rayleigh backscattering. For the first time, to the best of our knowledge, we derive a generalized expression for the MPI-induced noise on signal in counter-pumped FRAs. The obtained result takes into account four major sources of MPI, suggests their physically transparent classification, and enables us to predict the FRA's noise performance for an arbitrary modulated pump. Using the derived expression, we characterize the MPI-induced noise in a typical 80-km span of single-mode optical fiber. Specifically, we examine the noise enhancement in the pulse-pumped amplifier as compared to the amplifier operating in the continuous-wave regime, and analyze its dependence on the on-off gain and the pump-pulse duty cycle. We also estimate the impact of the MPI-induced noise transfer on the amplifier's performance, and discuss the optimal choice of pump modulation for different values of Q-penalty. The results of our study are important for the design optimization of FRAs with time-division-multiplexed pumping.