Impact of anomalous surface boundary conditions on the planar negative-refractive index lens

Abstract

It is shown that anomalous boundary conditions at the surface of a negative-refractive-index metamaterial planar lens severely diminishes the resolution of the lens when its relative permittivity and permeability are both −1. Anomalous boundary conditions arise in practical microwave metamaterials that are typically a periodic array of identical unit cells comprising dielectric and conducting elements. For a unit-cell size much smaller than the wavelength, homogenised permittivity and permeability are the constituent parameters of the average fields. Average fields vary on a scale larger than the unit cell size compared to localised fields associated with the constituent elements. Unlike the tangential components of the localised field, tangential components of the average fields are discontinuous across the surface of such materials. This anomalous boundary condition at the lens surface must be described by generalised sheet transition conditions. This study develops expressions for the negative-refractive-index lens optical transfer functions, as a function of spatial frequency, for transverse-electric waves, that account for anomalous surface boundary conditions. Both the simulations and experimental data are used to verify the expressions at a frequency of 3 GHz.