Optimization of Raman gain spectrum using Lagrangian multiplier method

Based on Lagrangian multiplier method (LMM), the gain spectrum of distributed multi-pump Raman amplifier (DMRA) is optimized. Beside of governing rate equations in Raman amplifiers, we consider two applicable constrains on cost function for optimizing the gain spectrum. Because of more accurate and controllable designing of DMRAs, a maximum power for each input pump wave is considered as well as average gain value as two constrains. LMM reduces the optimization problem with constrains to solve a two-point boundary value problem for each solution. This method is applied to minimizing gain ripple of full bandwidth (60 nm) a 100 Km Raman amplifier for different number of pumps.