Abstract
We develop an analytic theory for multi-longitudinal-mode Raman amplification with an incoherent pump of arbitrary bandwidth and mode spacing in the limit of negligible pump depletion. The closed-form analytical solution assumes the correct form in the limit for which the longitudinal laser mode spacing is wide in relation to the Raman bandwidth. The theory also predicts an enhancement in gain for correlated pump and Stokes beams when the laser mode spacing is much smaller than the Raman linewidth.
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