## 3 Results
### Analysis for Scenario with a Dielectric Layer  
Finally, an analysis of tunable metasurface sensor interaction with an additional thin dielectric layer was performed. The goal was to find the changes of tunability characteristics (as shown in Figure 8a) caused by changes of thin layer dielectric properties (because of inhomogeneities or thickness variations). The layer has been designed and placed 15 \(\upmu\)m above the metasurface. Such a situation is possible if the measuring head of the THz spectroscopy is fixed with an MS sensor (which is in the focal point of the terahertz Gaussian beam) and the examined dielectric foil is in vicinity of the sensor. The behavior of the model has been studied for different values of dielectric permittivity of the thin layer. Simulations were performed for permittivity values from 1 to 5. Shifts in resonance frequencies are shown in Figure 9. By manipulating the value of the permittivity coefficient, both the amplitude and frequency of the selected resonances is changed significantly. As can be seen in Figure 9 in the TE and TM modes, increasing the value of the permittivity caused a decrease in the resonant frequency fR. The resonant frequency in the TM mode responded with less sensitivity to I-shaped metal bar shifts. Figure 10 shows reflection coefficient S11 frequency response changes caused by various permittivities of an additional layer in case of a fixed arrangement of the eSRR geometry, i.e., Q = 0 \(\upmu\)m and U = 8 \(\upmu\)m. As can be seen in Figure 10a, there are several resonances, although they respond with the same shift to the dielectric layer. The influence of additional layer permittivity change on resonant frequencies is more efficient than metasurface tenability range. The plots of Figure 10 show exactly how large the jumps between the resonance frequencies are for various layer properties. A dielectric layer 15 \(\upmu\)m thick with a permittivity coefficient equal to two resulted, as seen in Figure 11b, leading to a shift in the reduction of the resonant frequency by 30 GHz in the TE mode. Increasing the coefficient to three results in a decrease by another 40 GHz. Finally, from the initial value at a factor of five, the resonant frequency decreases by 110 GHz. In the TM mode, as seen in Figure 11a, applying a layer with a permittivity coefficient of two to the unit cell resulted in a shift, reducing the resonant frequency by 40 GHz. Increasing the coefficient to three results in a decrease of another 40 GHz. Finally, from the initial value with a coefficient equal to five, the resonant frequency decreases by 190 GHz. The electric field norm for TE and TM modes are shown in Figure 12. Such a figure shows the differences in the distribution of the electric field in different modes. Figure 9: Resonance change as a function of permittivity value of an additional layer: (**a**) change in resonant frequency in TE mode; (**b**) change in resonant frequency in TM mode. Figure 10: S\({}_{11}\) frequency response change caused by various permittivities of an additional layer for geometry Q = 0 \(\upmu\)m and U = 8 \(\upmu\)m with larger sample step equal to 0.01 THz: (a) TE mode, (b) TM mode. Figure 11: Resonant frequency change as a function of permittivity of an additional layer—2D plot in case of: (**a**) TM mode, (**b**) TE mode. The distributions of resonant frequency as a function of displacement \(U\) and dielectric layer relative permittivity \(\varepsilon r-fR(U,\varepsilon r)\) were approximated using simple polynomial expressions, as follows:  
\[f_{\text{R\,TE}}(U,\varepsilon_{\text{r}})=1939+9.049\cdot U-0.464\cdot U^{2}-29 \cdot\varepsilon_{\text{r}} \tag{1}\]  
\[f_{\text{R\,TM}}(U,\varepsilon_{\text{r}})=1948+-0.3734\cdot U-0.0027\cdot U^{2 }-49\cdot\varepsilon_{\text{r}} \tag{2}\]  
where: \(f_{\text{RTE}}\) and \(f_{\text{RTM}}\) are resonant frequencies (in GHz) in the case of the TE and TM modes, respectively.