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This paper presents a modification for the already consolidated analytical model that calculates the gain and ripple in multi-pump Raman amplifiers by considering energy conservation. The original analytical model precisely computes the pump-pump interaction to the C- and L-band for a WDM input signal. However, when this method is used to amplify a large bandwidth, as the entire C and a part of the L band, the increase in the number of pump lasers impacts the obtained results. The error, if compared with results obtained by a numerical method, becomes significant. An analysis in terms of energy is proposed to minimize the discrepancy between analytical and numerical results. An improvement is observed to the gain results.

A correction method for the analytical model in Raman amplifiers systems based on energy conservation assumption