INHOMOGENEOUS LOCALIZATION OF POLAR EIGENMODES IN FRACTALS

A pattern of localization, called inhomogeneous localization, is found for dipolar eigenmodes (surface plasmons or eigenstates of the corres ponding Schrodinger equation) of fractal clusters. At any given freque ncy, individual eigenmodes are dramatically different from each other, their sizes vary in a wide range, and their internal geometry may be topologically disconnected and singular at the small scale. These prop erties differ principally from the results reported for vibrational ei genmodes of fractals, which is attributed to the long-range interactio n and non-Goldstonian nature of the polar modes.