# Liquid Crystal Tunable Dielectric Metamaterial Absorber in the Terahertz Range
## 2 Tunable Dielectric Metamaterial Absorber
For the \(x\)-incident polarization, the refractive index of NJU-LDn-4 could be tuned from \(n_{\text{o}}\) to \(n_{\text{e}}\) using an electric field. Compared to the visible and near-IR range, the feature size of metamaterials in the THz region is much larger and its influence on LC anchoring can be neglected, permitting a better tunability [25]. Schematics of LC orientations in a bias saturated state is illustrated in Figure 2a. In this case, the environmental refractive index was not along \(x\)-axis. As shown in Figure 2b, a strong absorption peak (calculated from corresponding transmittance and reflectance) was observed at 0.79 THz. The side view magnetic and electric field distributions of a single unit at 0.79 THz are illustrated in Figure 2c,d. The images reveal that the magnetic dipoles lay along the \(y\)-axis while the electric dipoles lay along the \(x\)-axis. The intensity distribution indicated that both dipoles were highly localized in the silicon pillar, further facilitating the overlap of HE\({}_{111}\) and EH\({}_{111}\). The impedance match was fulfilled as both the electric and magnetic resonances occurred at the same frequency [26]. After the bias was removed, the LC returned to the original orientation, as shown in Figure 3a. For the same \(x\)-incident polarization, the refractive index changed to \(n_{\text{e}}\). As presented in Figure 3b, the absorption peaks of EH\({}_{111}\) and HE\({}_{111}\) modes separated. Their magnetic and electric field distributions at corresponding resonant frequencies are presented. The resonant frequency of the magnetic dipole was 0.81 THz, and the corresponding side view distribution is shown in Figure 3c. The resonant frequency of the electric dipole was 0.76 THz, and the distribution of the electric field in the \(x\)-\(z\) plane is shown in Figure 3d. The opposite frequency shift caused the degeneration of the absorption peak, further inducing an obvious absorption reduction. It needs to be noticed that the reduction was caused by light confinement but not the loss induced by the imaginary part variation of LC, which contributed less than 5% of total absorption change. To vividly present the evolution of the absorption peak, we depict the dependency of the EH\({}_{111}\) and HE\({}_{111}\) modes on the LC orientation (\(\varphi\)) in Figure 4a. The LC was set as a uniaxial medium in simulation and \(\varphi\) was defined as the angle between the optical axis and \(z\)-axis in the \(x\)-\(z\) plane. When \(\varphi=30^{\circ}\), the effective refractive index (\(n_{\text{eff}}\)) was 1.66 [27], and the absorption peak began to degenerate. As \(\varphi\) increased to \(40^{\circ}\) (\(n_{\text{eff}}=1.70\)), the degenerated absorption peaks already existed. In this  
Figure 3: (**a**) The LC orientation in the bias OFF state. (**b**) Simulated spectra of reflectance, transmittance, and absorbance at bias OFF state. The (**c**) magnetic field of a single unit in the \(y\)-\(z\) plane at 0.81 THz. and the (**d**) electric field in the \(x\)-\(z\) plane at 0.76 THz. Figure 2: (**a**) The LC orientation in the bias saturated state. (**b**) Simulated spectra of reflectance, transmittance, and absorbance at bias saturated state. The (**c**) magnetic field of a single unit in the \(y\)-\(z\) plane, and (**d**) electric field in the \(x\)-\(z\) plane at 0.79 THz. The white rectangles in (**c**,**d**) represent the edge of the pillar unit, same hereinafter. range, the resonance was very sensitive to the refractive index change. We plot the absorbance change along \(\varphi\) at 0.79 THz in Figure 4b. When the refractive index changed from \(n_{\mathrm{o}}\) to \(n_{\mathrm{e}}\), a 47% decrease of absorption was achieved. The absorption was stable in the range of 0-30\({}^{\circ}\). Over 30\({}^{\circ}\), it changed rapidly. This means that this absorber is suitable for measuring the refractive index in this range. After 60\({}^{\circ}\), the absorption changed slowly again.