Theory of Localized Plasmons for Metal Nanostructures in Dielectrics

A theory of localized bulk and surface plasmons for metal nanostructures in dielectrics is derived in the random phase approximation at the high frequency condition. The induced charge density in dielectrics is added to the induced charge density by the plasmons appeared in the previously reported integral equation for the scalar potential. The integral equation is composed of the local electron density in metal nanostructures, the local electric susceptibility of dielectrics and the retarded Green's function. In the quasi-static approximation, the integral equation is transformed into the one that is composed of the local dielectric functions for metals and dielectrics and the Coulomb potential. Using a model where the local dielectric functions have step function shapes at the interfaces between the metals and dielectrics, it can be analytically solved in the quasi-static approximation. The localized surface plasmon frequencies and the light emission intensities are then derived for metal nanostructures such as ultrathin layer, nanowire, and nanosphere.