Efficient Extraction of Input Pump Powers From Pump Power Integrals in the Design of Raman Fiber Amplifiers

A novel method of extracting input pump powers from pump power integrals with high efficiency is proposed for the first time. In this method, a set of coupled nonlinear equations of input pump powers for given target pump power integrals are constructed. Finding the input pump powers corresponding to the target pump power integrals becomes finding solution of this set of nonlinear equations. A modified Newton's root-finding method is adopted to solve the nonlinear equations. To verify the proposed method, the input pump powers of a broadband (10 THz) Raman fiber amplifier that contains 100 signal channels and is counter pumped by 4 pumps is searched for given target pump power integrals. It is demonstrated that 3 iterations are enough for the method to achieve a satisfactory convergence. Compared with the previously reported techniques where hundreds of iterations are usually involved, the proposed method reduces the computational effort by two orders of magnitude.