Raman amplification in multimode fibers with random mode coupling

We present the theory of Raman amplification in long multimode optical fibers, where strong random mode coupling within groups of quasi-degenerate modes is unavoidable. In such fibers, the signal components in modes that belong to the same strongly coupled group experience the same Raman amplification, where the differential gain is linearly dependent on the aggregate powers of the pump in each of the mode groups. The equations that we derive significantly facilitate the numerical and analytical study of Raman amplification in long multimode fibers.