SURFACE BRILLOUIN-SCATTERING SPECTROSCOPY OF MEDIA WITH NONUNIFORM ACOUSTOOPTIC PROPERTIES

We present a theoretical tool to compute the Brillouin-scattering cros s section for shear horizontal (SH) surface phonons in an inhomogeneou s medium with any type of depth profiles of elastic, dielectric, and e lasto-optic properties. The acoustic eigenmodes are found by means of numerical solution of a self-adjoint Liouville equation with the bound ary conditions of a finite slab. Both discrete and continuous phonon s pectra are studied. The layer projected phonon density of states for t he SH polarization is used to analyze the surface character of the mod es. Also, the transmitted (zeroth-order) electromagnetic field and the reflection coefficient are obtained numerically solving Maxwell's equ ations. The scattered field is computed (in a way similar to that of t he zeroth-order field) by first-order perturbation theory as a result of the smallness of the phonon excitations. The backscattering p-s Bri llouin spectrum is obtained by summing the scattering intensity from i ndividual acoustic modes over the density of phonon states at a generi c incidence angle. As an example, we present the case of a Si/SiO2, bi layer on a Si(001) substrate with sharp or smooth interfaces between s ilicon and silica. We think the method is promising in view of the app lication of surface Brillouin-scattering spectroscopy to real imperfec t materials.