Abstract
The theory of Brillouin scattering from the surface of a semi-infinite medium is presented. The electromagnetic field is calculated to first order in the phonon displacements using the Rayleigh method. Both s and p polarisations are considered and the scattering geometry is not limited to the plane of incidence. The cross-section formulae can be interpreted in terms of the ripple and elasto-optic mechanisms. The effects on the displacement field due to the surface are investigated in both the discrete and the continuous part of the frequency spectrum. In particular, a detailed analysis of the so-called 'mixed modes' belonging to the continuum is analytically given for the isotropic medium. The application of the theory to GaAs and the comparison with experimental data (including A1 coated surfaces) will be discussed in paper II.