Asymptotic evolution of transient pulses undergoing stimulated Raman scattering

Propagation of short, transient pulses undergoing stimulated Raman scattering over long length scales is considered. It is shown that under common experimental circumstances the evolution has two different regimes: an I regime, at short lengths, where the pump changes little and the Stokes rapidly grows, and a J regime, at long lengths, where the Stokes intensity is close to saturation and the pump intensity decreases slowly as the square root of distance. The distance at which the J regime is reached is determined numerically.