Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements

Artificially structured metamaterials with unit-cell dimensions on the order of 1/10th of a wavelength (lambda/10) have been shown to be well approximated by an effective medium description which mimics a continuous material. In this paper we present data for transmission and reflection from a planar array of split-ring resonators (SRRs) at varying angles of incidence. We attempt to model the form of the angle-dependent response of the SRRs using the Fresnel equations formulated from effective medium theory-treating the array as a thin continuous anisotropic crystal. This model is then fit to experimental data taken on a planar array of split rings to gauge the model accuracy, and to produce values for the frequency-dependent permeability and permittivity of the experimental SRR array. Simultaneous fitting of the transmission and reflection at multiple angles helps to avoid multiple solutions for the permittivity and permeability. This forward fitting approach using multiple angles is advantageous, as it enables a characterization of the optical constants without the need for phase information, and it avoids many of the branch problems inherent in the numerical inversion methods used so far on metamaterials. The work presented here shows the feasibility of this method. A refined procedure will be particularly advantageous for experimental characterization of higher frequency structures (i.e., THz and above), where phase information is difficult or impossible to obtain.