Theory of surface acoustic phonon normal modes and light scattering cross section in a periodically corrugated surface

We have developed a theory of surface acoustic phonon normal modes and of Brillouin-scattering ripple cross section for a periodically corrugated surface of an opaque material, in the small corrugation limit. Both the discrete and continuous spectra of acoustic modes on a grating have been studied within the elasticity theory. In the continuum, the Rayleigh wave becomes a resonance and hybridizes with the longitudinal pseudomode of the flat surface, giving rise to a gap. The theory explains quantitatively recent experimental results obtained for a shallow grating on a Si(001) surface.