Density Effects on the Negative Refractive Index of a Split Ring Resonator Metamaterial

Abstract: Perfect lensing and cloaking based on complementary media are possible applications of negative refractive index materials. Metamaterials represent the natural candidates to realize such property by tailoring the effective dielectric permittiviy and magnetic permeability. The fine tuning of $n<0$ of metamaterials is limited by coarse grained inclusions which give discreteness to the electromagnetic parameters as a function of their density. We study the negative refractive index of a metamaterial as a function of the linear density of the lattice period at microwave frequency. The negative refractive index is obtained by a waveguide filled with a split ring resonator array in a frequency band below the cut off frequency of the waveguide. The special value of $n=-1$ typical of perfect lensing is maintained by tuning the density on a bandwidth of 1 GHz. A cut-off density above which the metamaterial operates is observed. A second critical density above which the transmission saturates is found close to the Pendry limit. Such results on the density of negative refractive index metamaterials open new paths towards the fine tuning of constitutive parameters at wanted values by means of transformation optics.