Signal transmission analysis of backward-pumped fiber Raman amplifiers

We present a fast numerical method for the design and transmission analysis of backward-pumped fiber Raman amplifiers (FRAs). Our method groups pump-and-signal channels to exclude unimportant spectral bands between the groups during the simulation. Neglecting the weak pump channel modulation by the counterpropagating signal channels, we find the signal and pump evolutions from the FRA input toward the FRA output. The initial conditions at the FRA input may be obtained from the conventional power analysis. Our method may provide amplifier-induced transmission penalties that become increasingly important in high bit rate long-haul wavelength-division multiplexing transmissions.