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An analysis is given of the saturation effect in the stimulated Brillouin scattering of coherent light waves. It is shown that the three coupled nonlinear wave equations describing the complex amplitudes of the forward-traveling primary and acoustic waves and the backward-traveling Stokes wave can be replaced for room-temperature situations by two coupled first-order nonlinear equations for the intensities of the primary and Stokes waves. These resulting equations are solved exactly and the solutions describe completely the process of photoelastic amplification of the coherent Stokes wave via stimulated Brillouin scattering in both the linear and the nonlinear saturated regimes. The results also give a more realistic estimate of the intensity of the hypersonic wave generated in the process than that made on the basis of either the Manley-Rowe relationship, which does not take into account the losses, or the usual linear theories, which do not take into account the saturation effect. It is believed that the Stokes emission observed in the usual experiments on stimulated Brillouin scattering of ruby laser light is due to photoelastic amplification via the stimulated process of Stokes noise generated by the scattering of the laser light via the normal Brillouin process by the thermal phonons present throughout the electrostrictive medium. A detailed analysis of this situation is also given. Explicit formulas for the spectral characteristics and the total integrated intensities of the Stokes and acoustic waves are obtained. The results also describe the noise characteristics of the photoelastic backward-wave amplifier. As an illustration, all these results are applied to the case of stimulated Brillouin scattering of ruby laser light in quartz.
Chun‐Lei Tang (1966) studied this question.