The inelastic polarized and depolarized scattering of light from the vibrations in aerogels recently studied experimentally by Courtens, Vacher, and collaborators are analyzed with use of fracton-model scaling and crossover considerations. We discuss the implications of the short-range fractal structure and the way the strongly localized vibrations on the short-range fractal structure of the gel (fractons) show up in the scattering. For this purpose we extend existing discussions of the implications of assuming a connected self-similar fractal structure for the vibrations, and also discuss the relationship of fractons to elastic-scattering theory and to Anderson localization. The disordered fractal structure of the underlying mass density and the three-dimensional character of the vibrations are included by treating the inelastic light scattering as Mie scattering from the vibrating fractal blobs. We find a maximum in the scattering cross section when the wavelength of the scattered light is comparable to the size of the fracton and smaller than the coherence length of the structure, and discuss the different frequency dependence of the polarized and depolarized scattering. The results contradict extrapolations of the Brillouin-scattering expressions from the low-frequency Rayleigh regime. We also discuss the structure of the vibrational eigenmodes and show that the indices measured are new phenomenological indices which are not related to standard fractal dimensions or to superlocalization.

• Received 2 June 1989

DOI:https://doi.org/10.1103/PhysRevB.40.7953