Microwave calibration-independent measurement methods for determination of electromagnetic properties of isotropic metamaterials

It is well understood that near their resonance frequencies higher-order Bloch modes and near eld e ects become non-negligible at the boundaries of MMs. Also, their a ective thickness lengths and the reference-plane distances along the wave propagation direction play a key role throughout the electromagnetic parameters extraction process of MMs. Due to these reasons, we propose a retrieval method for reference-plane invariant and thickness independent determination of electromagnetic parameters of MM slabs involving boundary e ects. Our method rst succeeds determination of e ective length of MMs and referenceplane factors using scattering parameter measurements, away from the resonance region, of two identical MMs with di erent lengths. Our method then incorporates near eld e ects in accurate retrieval of electromagnetic properties of MMs. The method is veri es by scattering parameters simulated for a homogeneous conventional material and a weakly or negligibly coupled inhomogeneous MM slab made by two metallic concentric split-ring resonators. Also, we propose a calibration-independent line-line method for broadband and simultaneous constitutive parameters determination of homogeneous MM slabs. It is shown that the su cient condition for parameters retrieval by the proposed method is to measure uncalibrated (raw) complex scattering parameters of measurement cells which are completely and partially loaded by the two identical MM slabs. We have validated the proposed method by using simulated scattering parameters of a MM slab with split-ring resonators and then by comparing the extracted electromagnetic parameters with those of a general method used in the literature in the cases with and without a small o set in reference-plane positions.