Dielectric resonances at optical frequencies using metal nanoshells

Abstract

A first-principles systematic investigation is reported to identify the dielectric (quasistatic) resonances properties of layered metal–dielectric particles. Specifically, we present remarkable results of finite-element simulations that model the effective permittivity of two-dimensional (or cross sections of infinite three-dimensional parallel, infinitely long, identical, circular cylinders, where the properties and characteristics are invariant along the cylinder axis) three-phase heterostructures made of coated discs embedded in a dielectric host. The derivation assumes that the quasistatic approximation holds valid even at relatively high angular frequencies of the harmonic external field. The coating (shell) material is taken as a conventional Drude noble metal and the core and shell phases are assumed to be dielectric, non-dispersive and lossless. One of the main results of this study is that the real part of the effective permittivity of an isotropic host matrix containing metallic nanoshells is tunable from negative through zero to positive values. The simulations reveal that a Drude–Lorentz-like dielectric function reproduces the overall shape of the effective complex permittivity of these nanostructures over an extended range of frequencies. The data nearly make a complete circle when all the (ε′, ε″) pairs for the various frequencies are included over the bandwidth about each resonance. For a given resonant frequency, the resonant features are determined by the complex permittivity of the metal (shell) phase, but also depend on the dielectric environment. Kramers–Kronig relations provide a consistency test for data of the complex effective permittivity. Numerical simulations are also used to investigate the sensitivity of field enhancement effects against frequency. The position and width of the resonance have the ability to be tailored by the selection of constituent metal phases and their nominal thicknesses.