The Brillouin line shape is evaluated under the assumption of space- and time-limited coherence of the acoustic field. The coherence limitation, regarded as a means of taking into account the phonon—phonon interaction, is studied by introducing stochastic phase jumps in the acoustic waves. Under this assumption, any acoustic wave contributes to the spectral distribution of the Brillouin line intensity. The main effect is due to the reduced spatial coherence and consists of an asymmetry of the Brillouin line and of a shift of the intensity maximum towards the frequency of the incident light.
R. DE MICHELI and L. GIULOTTO, "Brillouin Scattering by Acoustic Field of Limited Coherence," J. Opt. Soc. Am. 61, 1007-1011 (1971)