Influence of spontaneous emission and of finite phonon lifetime on Stimulated Raman Scattering

We study the influence of the spontaneous emission and of the damping of the molecular vibrations on Stimulated Raman Scattering in liquids starting from the Heisenberg equations for the laser wave, for the 1. Stokes wave, and for the molecular vibrations. The spontaneous emission is described by fluctuating Langevin forces. In the linearized case the Heisenberg equations are solved analytically. In order to investigate saturation effects the amplitude equations are transformed into generalized rate equations, which are solved numerically. To demonstrate the results they are plotted in several figures, showing the growth and the lineshape of the 1. Stokes wave, the ratio of Stokes photons and phonons and the saturation behaviour of the phonons and the Stokes and laser photons.