Reference-plane-invariant and thickness- and branch-index-independent retrieval of effective parameters of bi-anisotropic metamaterials

We propose a retrieval method for reference-plane-invariant electromagnetic parameter measurements of bi-anisotropic metamaterial slabs without resorting to accurate information of the slab thickness and the branch index. To extract reference-plane distances, the slab thickness, and the branch index, we first approximate wave impedances and refractive index away from the slab resonance frequency and then use scattering parameters to calculate the refractive index and the branch index. Once these quantities are determined, they are used as inputs for the retrieval of electromagnetic properties of slabs over the whole band. Different approximations for refractive index and wave impedances are applied to demonstrate the applicability and accuracy of our proposed method. We tested our method for electromagnetic parameter extraction of bi-anisotropic split-ring-resonator and Omega-shaped MM slabs with different number of unit cells. From our analysis, we note that inaccurate information of reference-plane distances, the slab length, and the branch index not only changes the amplitude but also shifts the response of the electromagnetic properties. We show that the presented method can be applied for accurate electromagnetic parameter extraction of bi-anisotropic MM slabs.