Brillouin scattering from longitudinal acoustic phonons in superlattices with diffuse interfaces

Abstract

The computation of the Brillouin cross section for scattering of light off longitudinal acoustic (LA) bulk phonons in a superlattice with diffuse interfaces between the layers is presented for the case of normal incidence. Unlike in previous work concerning the problem of diffuse interfaces, both the modulation of the acoustic and elasto-optic parameters, and the modulation of the refractive index are taken into account. The acoustic phonon spectrum is computed by means of numerical solution of a self-adjoint Liouville equation, and the dispersion relation is obtained using a wavevector selection rule. The transmitted (zeroth-order) electromagnetic wave, and the consequent fluctuating polarization vector field radiating Brillouin light are computed numerically for generic depth profiles of elastic, elasto-optic, and dielectric (optic) properties of the medium. The back-scattered light wave in the superlattice is obtained to first order in perturbation theory. The Brillouin differential cross section is computed by summing over the density of phonon states satisfying the wavevector selection rule. As an application, we present some results for the GaAs - AlAs superlattice, providing evidence for the differences from the case with diffuse and sharp interfaces.