  Stimulated Brillouin scattering in optical waveguides is a fundamental
interaction between light and acoustic waves mediated by electrostriction and
photoelasticity. In this paper, we revisit the usual theory of this inelastic
scattering process to get a joint system in which the acoustic wave is strongly
coupled to the interference pattern between the optical waves. We show in
particular that, when the optoacoustic coupling rate is comparable to the
phonon damping rate, the system enters in the strong coupling regime, giving
rise to avoided crossing of the dispersion curve and Rabi-like splitting. We
further find that optoacoustic Rabi splitting could in principle be observed
using backward stimulated Brillouin scattering in sub-wavelength diameter
tapered optical fibers with moderate peak pump power.
