Transient Raman Amplification

Abstract

Raman scattering is a 3-wave interaction process which is nonlinear by essence, due to the wave coupling. It works as if the medium (a two-level system) would transfer the energy of the pump to the Stokes wave, hence depleting the pump. A classical treatment of Raman amplification consists in assuming an instantaneous response of the medium. In that case the problem is explicitely solvable but wipes out a lot of interesting aspects as for instance phase properties. We study here transient Raman scatering for which we first establish the basic equations including effects of group velocity dispersion. Although this results in a fully nonlinear process, we will derive explicit formula for the output intensities for arbitrary input pump and Stokes waves in a medium initially in the ground state. This formula will be then illustrated with three applications: the generation of Raman solitons from the boundaries, the spectral properties of the output pump, and the interpretation of the experiments of long pulse propagation in H ₂ gas.