Resonant excitations and nonlinear optics of fractals

A scale-invariant theory of nonlinear light scattering by fractal clusters is developed. Due to the presence of very high and strongly fluctuated local fields the scattering is hugely enhanced. The enhancement factor for coherent anti-Stokes Raman scattering (CARS) and optical phase conjugation (OPC) is found. Scaling properties of nonlinear light scattering by collective excitations of fractals are obtained. The corresponding exponent describing a dependence of the scattering enhancement factor on spectral variable is 2d0 + 6, where d0 is the optical spectral dimension. Computer simulations dealing with cluster-cluster aggregates are presented. The numerical results fully confirm the theoretical predictions of the magnitude of the enhanced nonlinear scattering and its scaling behavior as well. The results obtained are in agreement with experimental data on four-wave light scattering by silver fractal clusters.