Similarity of dielectric resonance, local field distribution, and optical response in fractal composites

We investigate the dielectric resonance, local field distribution and effective optical response in the fractal structured metallic-dielectric composites using the Green's function formalism. With the evolution of the fractal level, similarity of the density of states (DOS) of dielectric resonances appears due to the self-similar structure, as well as of the inverse participation ratio (IPR) (which is used to represent the localization of field) of local field, and the effective linear optical responses. For a self-similar defect, when the difference admittance ratio $\ensuremath{\eta}\phantom{\rule{0.2em}{0ex}}[=({ϵ}_{2}\ensuremath{-}{ϵ}_{0})∕({ϵ}_{1}\ensuremath{-}{ϵ}_{0})]⪡0$ or $\ensuremath{\eta}⪢1$, DOS and IPR of the defect modes also exhibit the similarity or antisimilarity. However, for $\ensuremath{\eta}∊(\ensuremath{-}1,2)$, the spectra of DOS and IPR become more complicated as the defect modes overlap the original modes. Finally, the existence of the self-similar defect has no obvious influence on the effective optical responses.