A Fourier Series Approach to Analyze Pump Modulation Induced Noise in Raman Amplifiers With TDM Pumps

In this letter, Raman amplifiers (RAs) with time-division-multiplexed (TDM) pumps are analyzed using a computational cost-effective Fourier series approach. Analytical approximate formulas are derived based on this model. These formulas bring deep insight into the pump modulation induced noise (PMIN) in TDM pumped RAs. Moreover, the approach allows the analytical analysis of the TDM pumped RAs with multiple pumps while previous analytical studies mostly focused on the single pump and single signal channel case. By optimizing the pumping order of the multiple pumps, more than 3-dB reduction of the PMIN can be achieved. For short fibers, by properly choosing the modulation frequency, more than 3-dB reduction of the PMIN can be realized.