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Optical properties of fractals : theory and numerical simulation

A scale-invariant theory is derived for the linear optical properties of nontrivial fractals (fractal clusters) in the collective region, i.e., near the center of the absorption band. A model of dilute fractals is introduced and is used to find the shape of the wings of the absorption line in the binary approximation. Strong fluctuations of the local fields in nontrivial fractals are described. These fluctuations cause a giant intensification of the Raman and nonlinear parametric scattering of light by fractals. A theory is proposed for the spectrally selective and polarization-selective threshold photomodification of fractals. The linear spectra and photomodification of fractals have been simulated numerically by the Monte Carlo method. The results of this simulation are compared with the analytic theory. The values of the optical spectral dimension are found for fractals ofthe types studied.