Theory of Localized Plasmons for Multiple Metal Nanostructures in the Random Phase Approximation

Abstract

A theory is derived for localized plasmons in multiple metal nanostructures by developing the theory of localized bulk and surface plasmons for metal nanostructures in the random phase approximation (RPA) at the high frequency condition. The local electron density in multiple metal nanostructures is expressed as the sum of the electron density of each metal nanostructure. Self-consistent integral equations derived in the RPA give determinants to calculate the localized surface plasmon frequencies for multiple metal nanospheres with step-function-like electron density at their surfaces. The frequencies are analytically calculated in the dipole approximation for a dimer and chain of metal nanospheres. The frequencies are red- or blue-shifted depending on the spacing between the metal nanospheres. A light emission formula is also derived for multiple metal nanostructures in the dipole approximation. The light emission intensities from the dimer and chain are analytically calculated using the step-function-like electron density model. The retardation effect on the localized plasmons for multiple metal nanostructures is then investigated by applying the structural Green's function method, which is used to calculate the electronic structures of condensed matter. [DOI: 10.1380/ejssnt.2015.391]