Localization of collective dipole excitations on fractals

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Abstract
Dipole optical excitations on fractals are numerically simulated. It is shown that dipole eigenmodes of fractals are localized. The corresponding localization length dependence on the generalized frequency parameter (dispersion law) has been calculated. The value of optical spectral dimension found from the dispersion relations is in agreement with the result obtained earlier from calculations of the density of eigenstates.