Self-similar properties of the far-infrared and optical absorption of fractal metallic clusters

Abstract

We show that the electrical deterministic fractal lattice (DFL) model can provide a good physical and theoretical understanding of the far-infrared anomalous absorption properties of fractal metallic clusters as well as the cluster ``surface''-plasmon resonances discussed previously by means of numerical methods. Using the analytical properties of the DFL model, it is possible to calculate exactly the power-law exponents of the enhancement factors B, of the crossover localization length ${\mathit{L}}_{\mathrm{\ensuremath{\omega}}}$ as well as the Cantor structure of the self-similar cluster-plasmon resonance spectrum in terms of the fractal characteristics of the aggregate.