Complex dielectric response of metal-particle clusters

We discuss the complex dielectric response of metal-particle clusters. A self-consistent theory is introduced, which leads to a cubic equation for the cluster dielectric constant. The model is one in which the particles form fractal clusters. Both the electric and magnetic dipole absorptions are found to be enhanced by this fractal clustering. In the low-frequency and long-wavelength limits, analytic expressions for the enhancement factors are obtained. The model is applied to small particle composites, for which a red shift in the Mie resonance is obtained. For superconducting particles, the absorption in the superconducting state ${\alpha }_s$ is found to be greater than that of the normal state at frequencies slightly higher than the gap, provided the fractal dimension is so low that the electric dipole absorption predominates. At very low frequencies, fractal clustering also leads to an enhancement in the diamagnetic susceptibility of superconducting small-particle composites.