Closed form formulas and tunability of resonances in pairs of gold-dielectric nanoshells

Analyses of the resonances of both symmetric and antisymmetric polarization states in pairs of tightly coupled nanoshells, made of either a gold-core/dielectric-shell or a dielectric-core/gold-shell, are carried out at optical frequencies. The nanoparticles are modeled as single electric dipoles, at first considering only the static (non retarded) field terms and resorting to closed-form expressions to investigate the transverse and longitudinal (with respect to the pair axis) plasmonic resonance frequencies of the nanoshell pair. These approximate resonance values are then compared to the ones obtained including all dynamical retarded field terms, and with full wave simulations. We also show how the additional degree of freedom provided by using nanoshells, in contrast to using solid metallic nanoparticles, can be exploited for tuning the symmetric and antisymmetric resonance frequencies in pairs of tightly coupled nanoshells. Indeed, optical resonances of nanoshells can be varied over hundreds of nanometers in wavelength, across the visible and into the infrared region of the spectrum, by varying the relative dimensions of the core and shell. This makes the pair suitable as a constituent for metamaterials since it supports an antisymmetric mode that can be interpreted as an effective magnetic dipole; therefore, it is useful for providing artificial magnetism in metamaterials that may support backward propagation or have equivalent high/low characteristic wave impedance. Furthermore, we show the field enhancement between the two nanoparticles which may find applications in surface enhanced Raman scattering. We also show how an incident field excites the transversal and longitudinal modes supported by the pair.