Dispersion diagram reconstruction of effectively bianisotropic composite periodic media

Abstract

A dispersion diagram reconstruction technique is proposed for arbitrarily bianisotropic composite periodic media, which utilizes a previously introduced parameter retrieval technique based on eigenvalue analysis and field averaging. We initially retrieve the effective electromagnetic parameters of a composite periodic medium consisting of Edge-Coupled Split-Ring Resonators (EC-SRRs) via this homogenization technique using alternative integration approaches for the averaging of the field components. Subsequently, we derive the analytical framework for the wave propagation in a homogeneous medium of arbitrary bianisotropy and extract the appropriate equations which solve for the complex propagation constants. We then involve the retrieved effective parameters in these equations and reconstruct the dispersion diagrams for all three orthogonal directions, thereby spanning the whole irreducible Brillouin zone. An excellent agreement is found between the original dispersion diagrams and the reconstructed ones; a result which further validates the utilized parameter retrieval technique. The reconstruction technique moreover allows one to interpret the slope differences observed in the dispersion diagrams for in-plane and normal incidence modes of the examined composite medium. It may also be used as a tool for the confirmation of the accuracy of other formerly proposed homogenization techniques existing in the literature.