  Bragg scattering of polaritons by a coherent acoustic wave is mediated and
strongly enhanced by the relevant exciton states resonant with the acoustic and
optic fields simultaneously. In this case, in sharp contrast with conventional
acousto-optics, the resonantly enhanced Bragg spectra reveal the multiple
orders of diffracted light, i.e., a Brillouin band structure of parametrically
driven polaritons can be directly visualized. We analyze the above scheme for
polaritons in (GaAs) semiconductor microcavities driven by a surface acoustic
wave (SAW) and show that for realistic values of the SAW, $\nu_{\rm SAW} = 1$
GHz and $I_{\rm ac} \lesssim 100$ W/cm$^2$, the main acoustically-induced band
gap in the polariton spectrum can be as large as $\Delta^{\rm MC}_{\rm ac}
\simeq 0.6$ meV, and the Bragg replicas up to $n=3$ can be observed.
