Theory of acousto-optic scattering in opaque media in the regime of nonlocal optics

A theory of acousto-optic scattering from solid-state plasmas, which, on the basis of the Boltzmann equation, takes into account nonlocal electronic transport effects is established. To emphasize the influence of nonlocal effects on the principles of acousto-optic scattering the treatment is limited to the case where the scattering takes place from a purely transverse bulk sound wave which does not ripple the surface. The coherent inelastic scattering from both the incident and reflected acoustic field is considered. The integro-differential equation for the anti-Stokes field is solved with the assumption that the conduction electrons are scattered specularly from the surface. It is demonstrated that the scattering from a $p$-polarized incident electromagnetic field besides a well-known contribution from the plasmaritonlike part of the incident field is composed of free and forced wave terms arising from the plasmonlike part of the incident field and from branch-cut contributions which are of non-plane-wave character. The scattering from a fully degenerate plasma is considered in the fully nonlocal and almost local regimes. Resonant anti-Stokes scattering is treated and a general condition for resonance in the opaque nonlocal frequency regime is given. A few numerical calculations on Al and $n-\mathrm{I}\mathrm{n}\mathrm{S}\mathrm{b}$ are presented and it is shown that first-order Brillouin scattering via the nonlocal part of the incident light field should enable one to scatter from acoustic phonons far out in the Brillouin zone. The theoretical methods used in the present work are similar to those used in studies of the anomalous skin effect and the photoemission process. These methods almost seem to have been overlooked in light scattering studies. It is shown that the present theory is in agreement with the well-known results of local theories of acousto-optic scattering in opaque media in the appropriate limit.