Retrieval of effective electromagnetic pa- rameters of isotropic metamaterials using reference-plane invariant expressions

Abstract

Three di®erent techniques are applied for accurate constitutive parameters determination of isotropic split-ring resonator (SRR) and SRR with a cut wire (Composite) metamaterial (MM) slabs. The first two techniques use explicit analytical calibration- dependent and calibration-invariant expressions while the third technique is based on Lorentz and Drude dispersion models. We have tested these techniques from simulated scattering (S-) parameters of two classic SRR and Composite MM slabs with various level of losses and di®erent calibration plane factors. From the comparison, we conclude that whereas the extracted complex permittivity of both slabs by the analytical techniques produces unphysical results at resonance regions, that by the dispersion model eliminates this shortcoming and retrieves physically accurate constitutive parameters over the whole analyzed frequency region. We argue that incorrect retrieval of complex permittivity by analytical methods comes from spatial dispersion effects due to the discreteness of conducting elements within MM slabs which largely vary simulated S-parameters in the resonance regions where the slabs are highly spatially dispersive.