# Liquid Crystal Tunable Dielectric Metamaterial Absorber in the Terahertz Range
## 2 Tunable Dielectric Metamaterial Absorber  
The configuration of the absorber is illustrated in Figure 1a. Both substrates were 500-\(\upmu\)m-thick fused silica and covered with graphene electrodes. One of them could be spincoated with a 5-\(\upmu\)m-thick polydimethylsiloxane (PDMS) film. The silicon pillar array could be fabricated on a 60-\(\upmu\)m-thick heavily-doped silicon on insulator (SOI) using a Bosch process. Then it was bonded to the substrate with oxygen-plasma-treated PDMS [19]. Subsequently, the top SOI handle was stripped off with a lateral force. The unit geometry of the silicon pillar array is shown in Figure 1b. The PDMS layer separated the pillar array from the graphene electrode and worked as a refractive index matching layer simultaneously. Both substrates could be spincoated with a sulfonic azo dye (SD1) alignment layer, and then separated by a 110-\(\upmu\)m-thick Mylar film to form the cell [20], as shown in Figure 1a. Finally, a home-made high-birefringence LC NJU-LDA-4 with \(n_{\text{o}}=1.59+0.006i\) and \(n_{\text{e}}=1.90+0.001i\) around 0.80 THz could be infiltrated [21] to obtain the tunable THz dielectric MMA. We use hybrid dielectric waveguide resonances to explain the principle of this absorber. When the THz wave is incident along the \(z\)-axis (Figure 1a), the dielectric pillar works like a common waveguide. The resonator supports two different groups of hybrid modes, HE and EH. For HE mode, \(\text{H}_{\text{z}}/\text{E}_{\text{z}}<<1\); while for EH mode, \(\text{E}_{\text{z}}/\text{H}_{\text{z}}<<1\). Three dimensions of the field variation in the silicon pillar are denoted by different indices, i.e., \(\text{HE}_{\text{nml}}\) and \(\text{EH}_{\text{nml}}\). Here, only the lowest magnetic dipole mode (\(\text{HE}_{111}\)) and electric dipole mode (\(\text{EH}_{111}\)) are taken into account [22]. Each pillar is represented by an ideal Huygens'  
Figure 1: (a) The decomposition diagram of the LC integrated dielectric MMA. The yellow arrows indicate the alignment direction. (b) The unit dimension of the pillar resonator: lattice periodicity, \(p\): 210 \(\upmu\)m; radius, \(r\): 64 \(\upmu\)m; height, \(h\): 60 \(\upmu\)m.  
source, i.e., a pair of electric and magnetic dipoles oriented in the \(x\)- (EH\({}_{111}\)) and \(y\)- (HE\({}_{111}\)) direction respectively [23]. When both resonances occur at the same frequency, impedance matching is satisfied, which means the THz wave is totally absorbed. HE\({}_{111}\) always exists for a given resonator, while EH\({}_{111}\) has a cutoff condition. At a resonance wavelength of \(\lambda_{0}\), the cut off condition for a pillar dielectric resonator is given by [24]:  
\[r=0.61\frac{\lambda_{0}}{\left(n_{Si}^{2}\ -\ n_{LC}^{2}\right)^{1/2}} \tag{1}\]  
Wherein, \(r\) is the radius of the pillar, and \(n_{Si}\) and \(n_{LC}\) are the refractive indices of silicon and surrounded LC respectively. For the lowest modes, the desired minimum height \(h\) of the resonator can be approximated as a half-wave dipole with  
\[h=\ \frac{\lambda_{0}}{2n_{Si}} \tag{2}\]  
Therefore, the pillar parameters are set as shown in Figure 1 to ensure both HE\({}_{111}\) and EH\({}_{111}\) are supported at the same frequency when the surrounding refractive index was 1.59 (bias saturation state). After turning off the bias, the surrounding refractive index increased to 1.90, inducing the cutoff of EH\({}_{111}\). The HE\({}_{111}\) and EH\({}_{111}\) no longer existed at the same frequency. Therefore, the absorption peak degenerated into two different parts, leading to the resonance vanishing at the same frequency. The simulations were carried out using the commercial Lumerical FDTD Solutions. The refractive index of the silicon was \(3.41+0.12\)i. Since a thin layer high transparent PDMS was utilized, we only consider the real part of its refractive index, i.e., 1.60. The LC orientation FDTD module was applied to simulate the optical properties of the absorber along with the variation of LC directors.