# Controllable Fano-like Resonance in Terahertz Planar Meta-Rotamers
## 3 Results and Discussion  
Figure 3a demonstrates the simulated amplitude spectra of THz wave transmission for the meta-rotamer displayed in Figure 1a. For the two transition states of the meta-rotamers with different angles of rotation of \(\theta_{y}=0^{\circ}\) and \(60^{\circ}\), the transmission spectra clearly present two resonant dips corresponding to the frequencies of \(f_{1}\) and \(f_{2}\) at \(\theta_{y}=0^{\circ}\) and \(f^{\prime}_{1}\) and \(f^{\prime}_{2}\) at \(\theta_{y}=60^{\circ}\). \(f_{1}\) and \(f^{\prime}_{1}\) represent the second-order LC resonance of the C-shaped SRR, whereas \(f_{2}\) and \(f^{\prime}_{2}\) represent the electric-dipole resonance of the Y-shaped rod. To elucidate the characteristics of the resonances, we simulated the electric near-field distributions at the four resonant frequencies shown in Figure 3a. To clearly observe the spatial shape of each resonance mode, we plotted the out-of-plane electric field (\(E_{z}\)) distributions at the distance of 8 \(\upmu\)m above the surface of the meta-rotamers, as shown in Figure 3b. The figures of \(f_{2}\) and \(f^{\prime}_{2}\) show that the dipole resonance mode corresponding to the two arms of the Y-shaped metal rod lying in the polarization direction of the incident THz waves is well represented for both states of the meta-atoms. In this case, only the position of the electric near-field pattern is changed because of the structural change of the meta-molecules, whereas the shape of the electric near-field pattern and the position of the resonant frequency do not change. On the contrary, in the case of the second-order LC resonance appearing at the frequencies of \(f_{1}\) and \(f^{\prime}_{1}\), a completely different aspect is observed. The resonance mode for the C-shaped meta-atom does not show a clear difference for the two states of meta-rotamers. However, when the angle of rotation is \(0^{\circ}\) for the Y-shaped rod, the electric near-field is activated at the ends of its arms horizontal to the polarization. When the arms of the Y-shaped rod are adjacent to the standing wave antinodes of the second-order LC resonance, the electric near-fields are strongly enhanced at the ends of its arms. This implies that the coherent near-field coupling between the bright modes of two adjacent meta-atoms occurs when the antinodes of the two excited resonances are located close to each other with a gap of 5 \(\upmu\)m.  
To generate a stronger coupling effect, the total length of the C-shaped SRR was tuned; thus, the two resonant modes were close to each other in the spectrum. As the angular gap changed from \(10^{\circ}\) to \(30^{\circ}\), the second-order LC resonance \(f^{\prime}_{1}\) approached the dipole resonance \(f^{\prime}_{2}\) of the Y-shaped rod, as shown by the red curves in Figure 3a,c,e. When the antinode coupling of the two excited resonances at the meta-rotamer state with \(\theta_{y}=0^{\circ}\) appeared, the second-order LC resonance \(f_{1}\) shifted to the longer wavelength regime. Interestingly, the second-order LC resonance changed significantly with an asymmetrical line shape, whereas the dipole resonance was almost unchanged. This implies that, when the standing wave antinodes of the two excited resonances are spatially overlapped, the two resonances strongly interfere with each other, thereby generating Fano-like resonance. It is known that the strong red-shift of \(f^{\prime}_{1}\) in the spectral band is caused by the damping phenomenon of localized surface waves, depending on the coupling strength between the two standing wave antinodes [40; 41]. To quantitatively understand the dependence of coupling strength on the state of meta-rotamer, we plotted the values of resonant frequency extracted from the simulations versus the angular gap \(\theta_{c}\), for the structure with only C-shaped SRR meta-atoms and the meta-rotamers with two different states, which are determined by different angular gaps, as shown by the black squares, red circles, and blue triangles in Figure 4a, respectively.