A perturbation method for analysis of TDM-pumped fiber Raman amplifier

We propose a perturbation method for time division multiplexed (TDM) pumping fiber Raman amplifier (FRA). The method is based on the solution of Raman partial differential equations (PDEs) by a closed integral form. Taking the signals and pumps power as the interim solution and updating their values in an iterative process, Raman gain and pump/signal evolution can be calculated in any order of accuracy. In the first order of perturbation, some analytical formulas for the FRA dynamic control are obtained. Analytical formulas are employed for gain ripple minimization and also the gain clamping problem under channel reconfiguration.