Retrieval of Effective Permittivity and Permeability of Periodic Structures on Dielectric and Magnetic Substrates

This paper presents the retrieval of effective permittivity and permeability of periodic structure on dielectric and magnetic substrates. The retrieval approach is based on investigating the equivalent circuits of periodic structures. For demonstration, a single square loop-based periodic structure is served as an example to elaborate the retrieval process. First, the equivalent circuit of the freestanding single square loop-based structure is modelled with inductor and capacitor, where the values of these components are determined by the simulated Z-matrix of the free-standing structure; the effects of supporting substrates (dielectric or magnetic substrates) are then considered, where the compensating principles are deduced from inductive grids and capacitive patches periodic structures to compensate the corresponding values in the former equivalent circuit on purpose. The compensating values are also determined from the simulated S-parameter of the structure with supporting substrates. The formulas of effective permittivity and permeability are readily deduced and obtained from the original and compensating values of components in the equivalent circuits. The proposed retrieval process provides a new understanding of effective permittivity and permeability of periodic structures.