All-Metal Tensor Metamaterials: Characterization and Design

We propose a method to extract the equivalent material parameters and circuit models for all-metallic tensor metamaterials. The metamaterials consist of an arrangement of sub-wavelength metallic pins affixed to the bottom plate of an air-filled parallel plate waveguide (PPW). Isotropic and anisotropic configurations are studied, which are implemented with cylindrical and elliptical pins, respectively. The effective permittivity and permeability tensor of an equivalent lossless, homogeneous PPW are extracted. An equivalent circuit model consisting of series inductances and a shunt capacitance is also extracted. An analytical procedure to perform the extraction is outlined. For isotropic metamaterials, we provide closed-form expressions to obtain the effective material and circuit parameters. Possible simplifications and exhaustive guidelines for the extraction procedure are discussed for anisotropic metamaterials. The procedure is validated using full-wave simulations and circuit theory. Finally, representative designs are presented to show the effectiveness and potential applications of the proposed homogenization technique. The extraction of effective material parameters enables the control of the properties of all-metal metamaterials, enabling the design of perfectly-matched, anisotropic unit cells. Ultimately, the accurate mapping between all-metal metamaterials and their equivalent circuit networks could be exploited to accelerate the inverse design of multi-functional metastructures.