Spectral response and far-field pattern of a dipole nano-antenna on metamaterial substrates having near-zero and negative indices of refraction

In this work the resonance, frequency response, and far-field patterns of an optical nano-antenna placed on an interface between air and a metamaterial substrate is obtained through finite element calculations. The metamaterial is characterized by an effective, macroscopic index of refraction which can take negative and near-zero values, or by published values of the effective permittivity and permeability for metamaterials. The results show that the resonant wavelength and response can be fitted to analytical functions that are even functions of the index of refraction, this is consistent with the knowledge that negative indices of refraction allows for wave propagation in the same magnitude but opposite direction observed with positive indices of refraction. The simulations also show that substrates with near-zero index of refraction will enhance the antenna response by 62% compared to substrates with n > 1. Lossy metamaterials are also considered in the simulations. The far-field pattern of the antenna, obtained through a near-field to far-field transformation, behaves the same independently of the sign of the index of refraction, also the far-field pattern for the emission towards near-zero substrates is nearly constant and independent of the angle for the evaluated angular range.