Singularities and Scaling of Optical Responses in Cluster Composites

We have recently shown that despite earlier predictions and observations, the optical responses in clusters and cluster-based composites do not possess spectral scaling.(M.I.Stockman, L.N.Pandey, L.S.Muratov, and T.F.George, Phys. Rev. B 51), 185 (1995) The reason for that has proven to be the absence of strong localization of dipolar eigenmodes (surface plasmons).(M.I.Stockman, L.N.Pandey, and T.F.George, Phys Rev. B 53), 2183 (1995). At any frequency, there exist surface plasmons with any localization lengths, from the interparticle distance to the total size of the system. We called this phenomenon inhomogeneous localization. Our goal in this paper is to further investigate this phenomenon and its ramifications. In particular, we calculate the dynamic form factor of the system containing information on its elementary excitations. Using it, we show there are essential singularities of local fields in disordered clusters on a minimum spatial scale. We discuss applications of the theory to various nonlinear optical phenomena.