Fracton contribution to the optical linewidth in glasses

Abstract

We use the previous formalism of Lyo [Phys. Rev. Lett. 48, 688 (1982)] for optical linewidths of paramagnetic impurities in glasses to include the effects of fractal excitations (fractons). We find the optical-linewidth temperature dependence for interactions between the two-level systems and the optically active center of dipole-quadrupole and quadrupole-quadrupole character to be $T^{1+\left(\frac{\overline{\stackrel{―}{d}}}{4}\right)}$ and $T^{1+\left(\frac{2\overline{\stackrel{―}{d}}}{5}\right)}$, respectively, where $\overline{\stackrel{―}{d}}$ is the spectral dimensionality of Alexander and Orbach. Use of the percolating network value for $\overline{\stackrel{―}{d}}$, $\frac{4}{3}$, predicts a temperature dependence $T^{1.33}$ for the former coupling in reasonable agreement with very recent experimental results of Völker and collaborators in organic glasses.