Asymptotic evolution of stimulated Brillouin scattering: Implications for optical fibers

We consider the nonlinear three-wave stimulated Brillouin scattering where an initial electromagnetic wave packet grows backward in the expense of a constant input pump wave. For long interaction times we show in particular that the backscattered wave envelope exhibits a set of large peaks of decreasing amplitude, the intensity of the first one growing as $t^2$ while its width shrinks as 1/t. Moreover, the sound-wave amplitude saturates. In the limit case of strong damping of the sound wave the asymptotic behavior is quite different. Implications of these results are considered concerning the observed mechanical fracture of an optical fiber supporting a large laser pulse.