## 3 Results and Discussion
Equation (1) was employed to fit experimental transmittance data, as shown for two representative temperatures (6 and 110 K) in Figure 2a,b by open symbols. From the fitting, we extracted the temperature dependence of \(\
u_{res}\), \(\Gamma_{res}\), and \(\beta_{res}\), which are represented in Figures 3 and 4 for the direct and complementary array, respectively. All the parameters exhibit a variation in temperature. More in detail, for the direct SRR array, both the LC and dipolar resonance frequencies display a nonmonotonic behavior with temperature with a dip slightly below \(T_{c}\) (black vertical point-dashed line), corresponding to a redshift of 8% and 2% for the LC and dipolar resonance frequencies, respectively. The smaller redshift of the dipolar resonance frequency is due to its proximity to the YBCO superconducting gap. Indeed, by approaching the superconducting gap, the optical conductivity (real and imaginary part) of a superconductor is progressively less affected by the superconducting transition. The line width for both resonances exhibits a step-like behavior: from 110 K until 6 K, the line width of both LC and dipolar resonances decreases by a factor of \(\simeq\)3, improving resonance selectivity. Finally, the coupling coefficient among different resonators (\(\beta\)) shows a robust increasing behavior while moving from the normal to the superconducting phase. In particular, for both resonances, \(\beta\) is nearly zero above \(T_{c}\), when the material is not superconductive, indicating that each SRR of the system resonates individually, i.e., there is a negligible interaction among split-ring resonators. This interaction strongly increases in the superconducting state, where electrical properties are improved, and the positive sign of both \(\beta\) indicates that both the electric and magnetic fields are involved in the resonator coupling, as explained in [43]. In the complementary SRR device, a similar trend is observed for all the parameters. A modulation of 18% and of 2% for the LC and dipolar resonance frequencies is observed, respectively. Similarly to the case of the direct device, the line width for both resonances decreases by a factor of \(\simeq\)2. Finally, the coupling coefficient \(\beta\) changes by a factor of 18 for the LC resonance, and by a factor of 5 for the dipolar one. Tables A1 and A2 report the  
Figure 4: Fitting results (empty symbols) for the complementary SRR device vs. T, as obtained applying Equation (1) to data in Figure 2b. The dashed color lines are a guide for the eyes. Error bars correspond to the size of diamond symbols. Panels (**a**,**c**,**e**) show the resonance frequency \(v_{LC}\), the line width \(\Gamma_{LC}\), and the coupling coefficient \(\beta_{LC}\) of the LC resonance; (**b**,**d**,**f**) show the same quantities for the dipolar resonance. The black vertical point-dashed lines underline the YBCO critical temperature \(T_{c}=81\) K.  
Figure 3: Fitting results (empty symbols) for the direct SRR device vs. T, as obtained by using Equation (1) applied to data in Figure 2a. The dashed color lines are a guide for the eyes. Error bars correspond to the size of diamond symbols. Panels (**a**,**c**,**e**) show the resonance frequency \(v_{LC}\), the line width \(\Gamma_{LC}\), and the coupling coefficient \(\beta_{LC}\) of the LC resonance; (**b**,**d**,**f**) show the the same quantities for the dipolar resonance. The black vertical point-dashed lines underline the YBCO critical temperature \(T_{c}=83\) K.  
loaded quality factors of both LC and dipolar resonances for direct and complementary devices as a function of temperature. For both devices, the dipolar resonance has a higher quality factor than the LC one, and for both the resonances the quality factors increase by reducing temperature due to the reduction of ohmic losses. We can compare our results with the ones obtained in the work by [PERSON] et al. [44], where they obtained, with a direct gold SRR array (40 \(\upmu\)m periodicity), a Q factor for the LC (dipolar) resonance of \(Q=2.2\) (1.1).