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 $\frac{\mathrm{dn}}{d\ensuremath{\lambda}}$ and high Raman frequency ${\ensuremath{\omega}}_{f}$), while a few materials (low $\frac{\mathrm{dn}}{d\ensuremath{\lambda}}$ and ${\ensuremath{\omega}}_{f}$) should show an enhanced gain, ${I}_{S}\ensuremath{\sim}\mathrm{exp}{I}_{L}^{2}$, 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 ${\ensuremath{\omega}}_{Q}+{\ensuremath{\omega}}_{\ensuremath{-}Q}={\ensuremath{\omega}}_{f}$) are suggested.
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