Stimulated Raman scattering: Enhanced Stokes gain and effects of anti-Stokes and parametric phonon processes

It is shown that the previous parametric-instability explanation of the jump in the Stokes intensity $I_S$ as a function of laser intensity $I_L$ in stimulated Raman scattering experiments is valid for many solids, liquids, and gases (with high optical dispersion $\frac{\mathrm{dn}}{d\lambda }$ and high Raman frequency ${\omega }_f$), while a few materials (low $\frac{\mathrm{dn}}{d\lambda }$ and ${\omega }_f$) should show an enhanced gain, $I_S\sim \exp I_L^2$, which is greater than the usual stimulated-Raman gain but not as great as the jump result. The previously anomalous experimental results of Grun, McQuillan, and Stoicheff and of others, which show the jump in $I_S$, and of Hagenlocker, Minck, and Rado, which show both types of behavior, are explained. The instability is expected to be important in laser damage of Raman-active crystals and possibly in determining the limiting diameter of self-focused beams. The transient solution for the case of high dispersion indicates that the steady state is not reached until a time much greater than the Raman phonon-relaxation time. It is also shown that a phonon parametric instability studied previously in another context can reduce the Stokes intensity. Experiments to detect the phonon instability and measure the magnitude and temperature dependence of "half-frequency" phonons $Q$ (with frequencies ${\omega }_Q+{\omega }_{-Q}={\omega }_f$) are suggested.