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

Abstract

The effective constitutive parameters of a hightemperature 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 YBa 2 Cu 3 O 7 split-ring resonator (SRR) arrays are placed inside a WR-90 waveguide with two different orientations and are excited with the dominant TE 10 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.Index Terms-High-temperature superconducting (HTS), magnesium oxide (MgO), split-ring resonators (SRRs), yttrium barium copper oxide (YBCO).

A compact CRLH metamaterial with wide band negative index characteristics

“…MS46322A) at the two ports of the waveguides with the MUT placed in between the cross-sections of the waveguide as shown in figure 19. The MUT needs to be prepared for proper fitting within the waveguide, the prototype array of 7 × 3 unit cells of the proposed balanced CRLH unit cell is fabricated considering the homogeneous properties [21,45] and is shown in figure 20. However, in simulation, the MUT is considered as a two port network as illustrated in figure 2.…”

Coupling analysis between resonating metamaterial slabs using scattering parameters

“…2(b) is realized by repeating 7 times the unit cell in the 𝑥 direction and 4 times in the 𝑦 direction (after reversing). The periodicities of the first MM slab in 𝑥 and 𝑦 directions are 𝑢 𝑥 = 3.27 mm and 𝑢 𝑦 = 2.54 mm, both of which are much less than the free-space wavelength (30 mm) corresponding to 𝑓 = 10 GHz [42]. This shows that 𝑎 = 7𝑢 𝑥 and 𝑏 = 4𝑢 𝑦 , meaning that the first MM slab fills the whole cross section of the X-band waveguide.…”

“…To reduce the effect of the air gap between substrates over the cross section of the guide, we inserted two unpatterned FR4 substrates with thicknesses of 0.77 mm over the 𝑦𝑧 plane (and lengths of 2.54 mm) right at the guide walls where the electric field intensity is minimum [20]. The periodicities in the 𝑥 and 𝑦 directions are approximately 𝑢 𝑥 = 3.266 mm and 𝑢 𝑦 = 2.54 mm, which are almost one-tenth of the free-space wavelength at the mid-frequency [42].…”