BRILLOUIN-SCATTERING FROM LONGITUDINAL ACOUSTIC PHONONS IN SUPERLATTICES WITH DIFFUSE INTERFACES

The computation of the Brillouin cross section for scattering of light off longitudinal acoustic (LA) bulk phonons in a superlattice with di ffuse interfaces between the layers is presented for the case of norma l incidence. Unlike in previous work concerning the problem of diffuse interfaces, both the modulation of the acoustic and elasto-optic para meters, and the modulation of the refractive index are taken into acco unt. The acoustic phonon spectrum is computed by means of numerical so lution of a self-adjoint Liouville equation, and the dispersion relati on is obtained using a wavevector selection rule. The transmitted (zer oth-order) electromagnetic wave, and the consequent fluctuating polari zation 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 Br illouin differential cross section is computed by summing over the den sity of phonon states satisfying the wavevector selection rule. As an application, we present some results for the GaAs-AlAs superlattice, p roviding evidence for the differences from the case with diffuse and s harp interfaces.