A theory is developed which describes the optical properties of fractal clusters (i.e. of aggregates of non-trivial Hausdorff dimension consisting of interacting monomer particles). It is shown that with respect to these properties fractal clusters differ significantly from both gases and condensed media. The interaction between the monomers is assumed to be dipole-dipole. The theory is based on the self-consistent field equations; it takes into account the fluctuation nature of the fractal cluster (considerable probability for approach of monomers to each other despite an asymptotically zero integral density). An expression is obtained for the linear susceptibility. Combination of the monomers with the formation of a cluster entails the splitting, shift and broadening of the monomer spectra. These changes depend strongly on the fractal (Hausdorff) dimension of the cluster but do not depend on the number of monomers in it (for a cluster of non-trivial dimension). On the other hand, the monomers partially retain their individuality and the susceptibility — its quasi-resonance nature. Broadening, like the imaginary part of the susceptibility, does not depend on dissipation in an individual monomer. It is predicted that giant Raman scattering may occur at an impurity particle fixed near one of the cluster monomers when excitation takes place in the absorption band of the cluster. The enhancement factor for the scattering is also determined by the fractal dimension.
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Shalaev, V.M., Stockman, M.I. Fractals: optical susceptibility and giant raman scattering. Z Phys D - Atoms, Molecules and Clusters 10, 71–79 (1988). https://doi.org/10.1007/BF01425582