Enhanced Raman scattering by fractal clusters: Scale-invariant theory

A scale-invariant theory of Raman scattering of light by fractal clusters is developed. The enhancement factor ${\mathit{G}}^{\mathrm{RS}}$ of Raman scattering is shown to scale in terms of a properly chosen spectral variable X. The critical indices of the enhancement factor are found to be determined by the optical spectral dimension of the fractal. Numerical modeling is carried out and shown to support the analytical results obtained. The theory, which does not contain any adjustable parameters, agrees well with experimental data on surface-enhanced Raman scattering over a wide spectral range.