# Multifunctional Hyperelastic Structured Surface for Tunable and Switchable Transparency
## 3 Results and Discussion  
To reveal the tunability of the proposed design, we numerically computed and experimentally measured the scattering parameter S\({}_{21}\) of the proposed HSS under various mechanical deformations. We computed the scattering parameter S\({}_{21}\) of the HSS for the gradual increase in the mechanical displacement in steps of 5 mm up to 30 mm. The resonance frequency of the HSS in the deformed state (\(f_{0}\)), the RFS, percentage of the RFS with respect to the undeformed resonance frequency (\(\frac{\text{[RFS]}}{f_{0}}\times 100\)) are presented in Table 1. In addition, the change in the scattering parameter of the HSS at the undeformed (\(\Delta S_{21\oplus f_{0}^{\text{(undeformed)}}}\)) and deformed resonance frequency (\(\Delta S_{21\oplus f_{0}}\)) for the applied displacements to the HSS (\(U_{x}\)) in accordance with the generated xx component of the average strain in the unit cell (\(\bar{\epsilon}_{xx}\)) are presented in Table 1.  
Before the experimental measurements, to reduce the [PERSON]'s effect of the PDMS in the experimental results, we applied several loading/unloading cycles to the fabricated HSS. Then, we gradually increased the displacement and measured the resonance frequency of the fabricated HSS. The procedure has been repeated three times and the three datasets are distinguished by Roman numbers as a subscript of the applied displacement in Figure 7, showing excellent repeatability and agreement with numerical predictions. The existing limit in the transmissibility of the moving gripper impeded increasing the deformation above 15 mm. For further elaboration, the scattering parameter S\({}_{21}\) versus frequency is presented in accordance with the applied displacement and the corresponding strains in Figure 8. It is shown that by applying deformations, there is a shift in the resonance frequency of the HSS which shows the tunability of the proposed HSS by applying deformation. Moreover, there is a huge difference in the scattering parameter S\({}_{21}\) of the HSS at the resonance frequency of the undeformed and deformed HSSs. This demonstrated the switchability of the proposed HSS. \begin{table}
\begin{tabular}{c c c c c c c} \hline \(U_{x}\) & \(\bar{\epsilon}_{xx}\) & \(f_{0}\) & **RFS** & \(\frac{\text{[RFS]}}{f_{0}^{\text{(undeformed)}}}\times\text{100}\) & \(\Delta S_{21\oplus f_{0}^{\text{(undeformed)}}}\) & \(\Delta S_{21\oplus f_{0}}\) \\ (mm) & **(\%)** & **(GHz)** & **(GHz)** & **(\%)** & **(\%)** & **(dB)** & **(dB)** \\ \hline
5 & 2.66 & 11.69 & \(-\)0.16 & 1.35 & 46.5 & \(-\)49.3 \\
10 & 5.36 & 11.55 & \(-\)0.30 & 2.53 & 47.8 & \(-\)45.1 \\
15 & 8.10 & 11.39 & \(-\)0.46 & 3.88 & 48.0 & \(-\)45.6 \\
20 & 10.88 & 11.27 & \(-\)0.58 & 4.89 & 48.0 & \(-\)43.6 \\
25 & 13.70 & 11.13 & \(-\)0.72 & 6.08 & 48.0 & \(-\)45.8 \\
30 & 16.79 & 10.95 & \(-\)0.90 & 7.59 & 48.0 & \(-\)49.3 \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of the HSS respond under the applied displacements. Given the results presented in Figure 7, Figure 8 and Table 1, we confirm the expectation that the resonance frequency of the HSS is highly sensitive to the deformation; the HSS shows the RFS of 7.59% for the highest average applied strain of 16.79%. Thus, this HSS is adequate for the purpose of tunability. Moreover, deformation considerably changes the scattering parameter S\({}_{21}\) of the HSS. Upon applying 2.7% strain, the HSS shows a 46.5 dB increase in its scattering parameter S\({}_{21}\) at the undeformed resonance frequency of 11.85 GHz. It is equivalent to changing the surface from opaque to transparent. In reverse, considering the scattering parameter S\({}_{21}\) of the HSS at the undeformed state as the reference, this deformation can move the transmission peak at lower frequencies, turning the initially transparent surface into an opaque one, with a 49.3 dB transmission difference. Furthermore, the experimental results prove the elastic (mechanically reversible) behavior of the HSS.