Are scaling laws of sub-optical wavelength electric field confinement in arrays of metal nanoparticles related to plasmonics or to geometry?

In this work, we describe finite element simulations of the plasmonic resonance (PLR) properties of a self-similar chain of plasmonic nanostructures. Using a broad range of conditions, we find strong numerical evidence that the electric field confinement behaves as (Xi/lambda)(PLR) alpha EFE-gamma, where EFE is the electric field enhancement, Xi is the linear size of the focusing length, and lambda is the wavelength of the resonant excitation. We find that the exponent gamma is close to 1, i.e. significantly lower than the 1.5 found for two-dimensional nanodisks. This scaling law provides support for the hypothesis of a universal regime in which the sub-optical wavelength electric field confinement is controlled by the Euclidean dimensionality and is independent of nanoparticle size, metal nature, or embedding medium permittivity. (C) 2012 Optical Society of America