Collective surface modes in a fractal cluster of spheres

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Abstract
We present a theory for finding the collective surface modes in the quasistatic approximation for a fractal cluster of spheres constructed in a recursive manner. The surface-mode positions and strengths are given in terms of the spectral representation for the polarizability of the cluster. Calculations using the dipole approximation for a cluster constructed recursively from an octahedral arrangement of six spheres show that the surface-mode spectrum is approximately self-similar. We calculate the distribution of scaling indices, f(α), for this spectrum as a function of the fractal dimension of the cluster in Euclidean space.