Theoretical description of transient stimulated Raman scattering in optical fibers

The authors derive a single-wave equation which describes transient stimulated Raman scattering in optical fibers. The equation is valid for forward traveling waves whose bandwidths are less than ≈1/3 the carrier frequency. It correctly conserves a classical photon number and not the total optical energy as is appropriate for Raman scattering problems. From this equation, the authors derive a formula for the small-signal gain spectrum which includes the effects of Raman scattering, four-wave mixing, and modulational instabilities. Examples of numerical integrations are given which show the generation of short soliton pulses from the nonlinear evolution of a noise band around a continuous wave pump