Modified split-step Fourier method for the numerical simulation of soliton amplification in erbium-doped fibers with forward-propagating noise

Using a modified version of the split-step Fourier method, we analyze the effect of noise on soliton propagation inside erbium-doped fiber amplifiers. In fact, noise from forward-propagating amplified spontaneous emission, associated with a Markov immigration process, is included in the analysis of soliton amplification. Moreover, this algorithm accounts for the real spectral gain profile of the fiber amplifier. The frequency jitter, induced during soliton amplification, is compared with the Gordon-Haus effect where optical amplifiers are considered as noisy point-like devices