A moment method for analysis the gain spectrum in fiber Raman amplifier with broadband pumps

The governing equations of optical fiber Raman amplifier with broadband pumps in the steady state are systems of uncountable nonlinear ordinary differential equations (NODE). In this paper, the Moment method is used to reduce the uncountable system of NODE to a system of finite number of NODE. This system of equations is solved numerically. The results are compared with that of the full numerical method. It was shown that the Moment method is a precise and efficient technique for analysis of optical fiber Raman amplifier with broadband pumps.