## 3 Results and Discussion  
### Symmetric Spiral Disks  
In the beginning of our study, we searched for the optimal design of spiral disks having narrow-band resonances in the region of 0.2-0.5 THz to allow the testing of the fabricated structures with the BWO spectrometer. Under the normal illumination of distantly spaced (\(p=768\)\(\upmu\)m) spiral disks, the azimuthal symmetry of the disk enables the excitation of the only dipole LSPR modes [18]. To produce high order localized \"dark\" modes (electric or magnetic [21]), we proposed to break the symmetry by placing a C-shape resonator near the disk (see Figure 1c). The C-resonator exhibited a \"bright\" mode resonance, which excited the nearby dark spectral modes of the disk. We fixed the resonator radius at \(R_{\mathrm{C}}=204\)\(\upmu\)m, while the resonator arch angle \(\alpha\) was a variable parameter. Figure 2a shows the calculated transmittance spectra of the spiral disks with different \(\alpha\) for normal illumination (\(\theta=0^{\circ}\)) by an \(X\)-polarized EM wave. Starting from \(\alpha=90^{\circ}\), the new dark mode narrow resonances were well excited (see red circles in Figure 2b). With increasing \(\alpha\), the resonances move towards the lower frequencies due to the decrease in the bright mode frequency of the C-resonator. For the following simulations we selected \(\alpha=90^{\circ}\), at which there were several narrowband resonances in the region of 0.2-0.5 THz (see the highlighted region in Figure 2a). Another way to excite multipole resonances with a high \(Q\)-factor is through the oblique illumination of the structure, which also breaks the excitation symmetry [20; 34]. The TM-transmittance spectra of distantly spaced spiral disks with a \(90^{\circ}\) C-resonator at oblique incidence with \(\theta=0\), \(20^{\circ}\) and \(40^{\circ}\) simulated for two orthogonal orientations (\(\varphi=0\) and \(\varphi=90^{\circ}\)) are plotted in Figure 3a. The analysis shows that the bright mode of the C-resonator in the vicinity of frequency \(\approx\)0.5 THz (see Figure 2, \(\alpha=90^{\circ}\)) was excited most efficiently when in the XY plane projection of the incident \(\mathbf{E}\)-field was parallel to the resonator (\(\varphi=0\): \(E_{X}\
eq 0\), \(E_{Y}=0\)); in the opposite case (\(\varphi=90^{\circ}\): \(E_{X}=0\), \(E_{Y}\
eq 0\)), the bright mode was not revealed. For both orientations, upon increasing \(\theta\), the main resonances shifted a little and became weaker due to the decreasing \(\mathbf{E}\)-projection on the PMS plane. We may also track new resonances arising above 0.38 THz, whose positions depend on the incidence angle and probably originate from the hybridized nature of these modes. The experimentally measured TM-transmittance spectra of the distantly spaced spiral disks with a \(90^{\circ}\) C-resonator patterned on the 15 \(\upmu\)m PP substrate are shown in Figure 3b. Reasonable mutual agreement was demonstrated between the experimental and simulated data. There are some discrepancies in the spectral region near 0.38 THz. In the simulations, there were two narrowband resonances which were degraded in the experiment. We attributed these differences to several factors: (a) the higher THz absorption in the real metal-dielectric structures; (b) the non-ideal collimation of the probing THz beam in the spectrometer that yields its non-zero angular divergence; (c) some technological spread in the dimensions of the PMS micro-pattern upon its lithographic fabrication, which we observed with the optical microscope. To characterize the sensing performance of the fabricated metasurfaces, we covered the metallized face of the samples with thin layers of photoresist used as the analyte. The analyte thicknesses after deposition were \(d=0.3\), \(1\), \(5\) and \(10\)\(\upmu\)m (from \(2\times 10^{-4}\)\(\lambda\) to \(7\times 10^{-3}\)\(\lambda\)). Depositing thicker layers was not feasible due to the insufficient viscosity of the employed photoresist.