Theory of the elasto-optic coupling for surface Brillouin scattering in a supported bilayer

We derive explicit expressions of the electromagnetic scattered field and Brillouin cross section for the elasto-optic coupling in a supported bilayer. We consider p-p light scattering and acoustic sagittal modes. The theory is applied to the system Si/${\mathrm{SiO}}_2$ on Si(001), whose properties are investigated versus the thickness of the Si and ${\mathrm{SiO}}_2$ films. The properties studied are the dispersion relations of surface acoustic modes and pseudomodes, the elasto-optic cross section, and the displacement field profile. A pseudomode of longitudinal character, which is mainly localized in the buried ${\mathrm{SiO}}_2$ film and whose velocity changes monotonically from the longitudinal velocity of Si to that of ${\mathrm{SiO}}_2$, deserves particular interest.