Optical Properties of Aggregated Metal Systems. I. Theory

Abstract

In this part, the simplest optical theory of aggregated metal systems, due to Maxwell-Garnett, is analyzed. The complex dielectric constant of the system, and that of the constituent metal aggregates, are represented as transformations. The functions show single and double poles in certain regions of physical interest, indicating resonance behavior. These features are explored for free-electron metals, and an optical "conduction resonance" for the aggregated system is discovered. The resonance frequency and the magnitude of the optical conductivity are calculated, along with the plasma frequency and the magnitude of the bulk electron loss function. A relation between conduction and plasma resonances is established and it is found to be independent of the free-electron parameters of the metal. This, and other results, indicate that the conduction resonance is a macroscopic effect, being due to a collective polarization interaction between the constituent metal aggregates, and it may be looked upon as a kind of transverse plasma resonance. In the second part, the present results will be applied to real metals.