Raman-Scattering Measurements of Acoustic Superlocalization in Silica Aerogels

Results of depolarized Raman spectroscopy on fractal silica aerogels are presented at frequencies from 0.3 to 50 ${\mathrm{cm}}^{-1\mathrm{}}$. Three distinct vibration regimes are observed. In the fracton range, a power-law dependence of the Raman susceptibility on the frequency is found. It allows a determination of the superlocalization exponent $d_{\phi }$. Alternatively, with use of the "resistance" expression for the exponent $d_{\phi }$, a spectral dimension $\bar{\overline{d}}$ in fair agreement with previous measurements results.