Determining the effective electromagnetic properties of negative-refractive-index metamaterials from internal fields

Effective electromagnetic properties of negative index of refraction metamaterials (NIMs) can be hard to measure. We show through simulations that electromagnetic fields inside a typical, physically realizable wire-SRR (split ring resonator) NIM are more homogeneous than one might expect inside such metamaterials, and sufficiently structured to be useful for interpretation. Specifically, simulations show that the electric field phase is surprisingly smooth inside the NIM, including at the edges of the material, and can thus be used to reliably estimate the effective length of the material, a critical parameter when determining the effective material properties using many methods. The effective length, together with amplitude and phase measurements inside the material, can further be used to measure with good precision and minimum ambiguity the effective material properties of a NIM. To validate this technique, we show that the material properties obtained using it very closely match those derived from S parameters. The inherent redundancy in the field data makes this method less sensitive to measurement errors than one based on transmission/reflection measurements, thus making it suitable for simulations and for experiments. We also show that, for experiments, given the periodicity of the NIM, one measurement per cell is generally enough to retrieve with good precision these material properties.