## 2 Structure Design and Theoretical Analysis
### Multipole Decomposition Analysis  
To explore the electromagnetic properties of this crescent cylinder theoretically and analyze the resonance model inside the unit cell, we employed multipole expansions based on the decomposition of the fields in a single cylinder into Cartesian multipole moments [28; 29; 30]. By this technique, the multiple contributions to the optical responses can be identified. The detailed analysis process can be found in the Appendix A.  
Figure 1: Schematic diagram of device structure and experimental device. (**a**) A schematic representation of the THz metasurface sensing experiment. SEM images of the structure: (**b**) top view and (**c**) side view. (**d**) A schematic representation of the THz-TDS system. PCA: photoconductive antenna. (**e**) The molecular structure of R/S chiral ibuprofen. The results of the multipole decomposition in the unit cell for the two incident polarization directions are shown in Figure 3. The surrounding medium was air and the excitation field was propagating along the \(z\)-axis. According to the multipole decomposition results, in both directions of polarization, for the first resonance the ED and MD were dominant inside the structure, and the higher-order modes were almost negligible. For the second resonance in the higher frequency, besides the ED and MD modes, the EQ and MQ were strongly induced, so much so that they could not be ignored. To further investigate the physical mechanism of the sensor, the electric field and magnetic field at two resonances were monitored and are shown in Figures 4 and 5 for two different polarized directions, respectively. For lower-order resonance, as shown in Figures 4a and 5a, the direction of electric field vectors was consistent with the polarization direction of the incident light; it flowed into the structure from one side and flowed out  
Figure 3: The scattering spectra of multipole decomposition for the unit cell of the metasurface: \(y\)-polarized wave in (**a**) the lower THz frequency range and (**b**) the higher THz frequency range; \(x\)-polarized wave in (**c**) the lower THz frequency range and (**d**) the higher THz frequency range. The positions of the resonances are indicated by the dotted lines in the figures. Figure 2: Simulation transmission spectra of the bare device (black line) and filled with the different refractive index materials by CST simulation. The polarization direction of the incident waves was along the \(y\)-axis (**a**) and \(x\)-axis (**b**). along the geometry of the structure, connected head to tail in the plane without much deflection, which implies that an electric dipole resonant mode was generated at the first resonance. For higher-order resonance, the flow direction of the electric field vectors was not simply along one direction. From Figures 4f and 5f, we found that the direction of the electric field in the middle of the structure was opposite to that around the structure, which resulted in multiple circular electric fields inside the structure, and, thus, electric quadrupole moments were generated. We then analyzed the magnetic field distribution. In Figure 4g for a \(y\)-polarization incident wave, a ring-shaped magnetic field formed inside the structure, and it flowed clockwise in the \(x\)-\(z\) plane, which induced a magnetic dipole resonant mode. For an \(x\)-polarization incident wave, as shown in Figure 5g, two pairs of ring-shaped magnetic fields were generated above and below the structure and flowed in opposite directions, which also induced a magnetic dipole resonant mode. When the frequency increased to around 1.03 THz, for higher-order resonance, the distribution of magnetic fields became more complex; several ring-shaped magnetic fields were formed inside the structure. They flowed in different directions and were distributed throughout the plane. These ring-shaped magnetic fields interact with each other, and their collective contribution results in the magnetic quadrupole moment.