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The fluid equations governing medium response to stimulated Brillouin scattering (SBS) are solved in the quasi steady-state approximation to obtain the gain of the scattered signal as a function of changes in the large-scale velocity and temperature of the medium. These equations are coupled with the field amplitude equations in one dimension to obtain the scattered signal intensity at each time step in the incident pulse. After calculating the incident and scattered pulse intensities at each z step for a given time step, the change in the large-scale fluid variables for the next time step is determined by finite difference. During the early history of the pulse, the frequency shift between the incident and scattered waves is such that the scattered wave has maximal gain. As the pulse evolves, second order terms in the fluid equations cause large-scale motion of the medium as well as the oscillatory motion associated with the acoustical wave. This large-scale motion causes a Doppler shift in the resonance condition of the medium such that the scattered signal no longer has maximal gain. Second order terms in the fluid equations also result in large-scale heating of the medium which affects the resonance condition by increasing the acoustic velocity, thereby causing further reduction in scattered signal gain. A few calculations were run using parameters corresponding to an experiment performed by Dolgopolov et al. involving a single pulsed iodine laser (wavelength 1.315 microns) incident upon a 70 atmosphere nitrogen cell. Although the gain near the front of the interaction region was greatly reduced during typical pulse times (5 - 10 microsecond(s) ec), there was no substantial impact on the final scattered wave intensity since the reduction in gain did not occur until after this signal had grown to high intensities. This gain reduction merely had the effect of shortening the effective interaction region by a few gain lengths, and could not explain the drastic reduction in scattered wave intensity observed at incident pulse intensities exceeding 1000 MW/cm2 in the Dolgopolov experiment. Contrary to our initial hypothesis, it appears that nonlinear terms in the fluid equations governing medium response to SBS have little effect on scattered signal intensity or phase conjugation fidelity in the case of single pulse experiments. However, the predicted large-scale fluid motion and heating can propagate as an acoustical pulse long after the decay of the incident laser pulse, which may affect the scattered signal fluence of future pulses in a pulse train. A three-dimensional large-scale fluid model would be required, however, to properly analyze this effect.
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