Amplified spontaneous emission (ASE) and double Rayleigh backscattering (DRBS) degrade the effective noise figure (ENF) and ultimately limit the performance of fiber Raman amplifiers (FRAs). This limitation is especially severe when a time-division-multiplexed (TDM) pumping scheme is employed. In this paper, we theoretically study the joint impact of ASE and DRBS on ENF in pulse-pumped FRAs. We demonstrate that the ASE is the major source of noise for small pump duty cycles, whereas DRBS dominates when a typical FRA operates in the continuous-wave regime. If the pump power is gradually increased, ENF improves until the gain reaches an optimal value. We show the increase of the optimal gain with pump duty cycle and with decreasing fiber scattering efficiency. Our study reveals the importance of taking into account the effects of both ASE and DRBS for an accurate estimation of ENF penalty in pulse-pumped FRAs, especially operating at high gains when pump duty cycle is small.
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