Effective Constitutive Parameters of High-Temperature Superconducting Split-Ring Resonator Arrays

The effective constitutive parameters of a high-temperature superconducting (HTS) metamaterial are extracted from measured scattering parameters at liquid nitrogen temperature (≈75.68 K at the National Institute of Standards and Technology, Boulder, CO, USA). The YBa₂Cu₃O₇ split-ring resonator (SRR) arrays are placed inside a WR-90 waveguide with two different orientations and are excited with the dominant TE₁₀ mode in both cases. By treating the SRR array as a homogeneous medium described by the biaxial permittivity and permeability diagonal tensors, the two sets of S parameters allow for the extraction of three out of the six tensor components. The extracted parameters are then compared to full-wave simulations of SRR arrays in free space. The samples are measured from 8.2 to 12 GHz and show a frequency band between 9.25 and 10.45 GHz with a negative effective permeability, as expected. Finally, numerous high-quality factor resonances that accompany the main resonances are observed in both the low-temperature measurement and the low-loss simulation.