  We predict and experimentally observe a nonlinear variant of stimulated
Brillouin scattering in a single-mode fiber that arises from consideration of
higher-order processes for phonon generation. The effect manifests itself at
high laser excitation as the appearance of Stokes gain for a detuning equal to
half of the conventional Brillouin frequency in the fiber, with no accompanying
anti-Stokes absorption at the opposite detuning, and requires
counter-propagating pump beams for phase-matching. We believe that this could
be a new nonlinear optical effect that has not been observed before.
