Optical properties of fractal clusters of small metallic particles

In this paper we describe a method to calculate the optical properties of deterministic fractal clusters. Our method takes advantage of the fact that deterministic fractals can be constructed by an iterative rule. We calculate first the optical properties of a small cluster that describes one stage in the iteration. The optical properties of this cluster are then assigned to an “effective particle”. A small number of these produce the next stage in the fractal construction. We performed the calculations for metallic particles with dielectric functions described by the hydrodynamic model. Results in the dipolar and quadrupolar approximations for a cluster at the second fractal stage shows the double extinction peak often seen in experimental studies.