# Terahertz Broadband Adjustable Absorber Based on VO2 Multiple Ring Structure
## 2 Structure Design and Simulation  
The broadband adjustable absorber adopts a sandwich structure based on a VO2 multiple ring structure, which is shown in Figure 1. The bottom metal structure applies gold as the reflect layer, and SiO2 (a dielectric constant of 3.8) as the dielectric layer. The top layer employs the phase-change material VO2, which consists of two square ring structures \(L_{1}\) and \(L_{2}\) with different sizes and a patch structure \(L_{3}\). It is worth noting that a gap with a certain thickness of 0.08 \(\upmu\)m is left in the middle to enhance the resonance absorption effect. The optimized structural parameters are as follows: the cell period \(p\) = 24 \(\upmu\)m, the bottom layer thickness \(h_{1}\) = 0.2 \(\upmu\)m, the medium layer height \(d\) = 7 \(\upmu\)m, and the top layer thickness of the VO2 \(h_{2}\) = 0.2 \(\upmu\)m. The dimensions of the ring structure and patch structure are followed by \(l_{1}\) = 20 \(\upmu\)m, \(l_{2}\) = 12 \(\upmu\)m, and \(l_{3}\) = 4 \(\upmu\)m, with a width of \(w\) = 2 \(\upmu\)m. In the THz range, the optical characteristics of VO2 can be described through the Drude model [40; 41], as shown in Formula (1):  
\[\epsilon(\omega)=\epsilon_{\infty}-\frac{\omega_{p}^{2}}{(\omega^{2}+i\gamma \omega)} \tag{1}\]  
where the high-frequency dielectric constant \(\epsilon_{\infty}\) and the collision frequency \(\gamma\) are 12 and 5.75 \(\times\) 10\({}^{13}\) rad/s, respectively. What is more, the plasma frequency \(\omega_{p}\) can be expressed by Formula (2):  
\[\omega_{p}^{2}=\frac{\sigma}{\sigma_{0}}\omega_{p}^{2}(\sigma_{0}) \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Reference**} & \multirow{2}{*}{**Material**} & \multicolumn{2}{c}{**Bandwidth**} & \multirow{2}{*}{**Relative Bandwidth (\%)**} & \multirow{2}{*}{**Tunable Range (\%)**} \\  & & **(Absportance over & & & \\  & & **90\%) (THz)** & & & \\ \hline
[32] & VO2 & \(0.99-0.47=0.52\) & 71.2 & 5–100 \\
[33] & VO2 & \(5.57-4.32=1.25\) & 25.3 & 15–96 \\
[34] & VO2 and graphene & \(3.21-1.69=1.52\) & 62.0 & 22.6–99.2 \\
[35] & VO2 and graphene & \(3.08-1.29=1.79\) & 81.9 & 20–99 \\
[36] & VO2 & \(4.19-1.87=2.32\) & 76.6 & \\  & \(10.73-8.70=2.03\) & 20.9 & 2–94 \\
[37] & VO2 & \(4.30-1.85=2.45\) & 79.7 & 4–100 \\
[38] & VO2 & \(6.79-3.01=3.78\) & 77.1 & 2.7–98.9 \\ This paper & VO2 & \(7.27-3.01=4.26\) & 82.9 & 4–100 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of absorption performance of other absorbers with that of the absorber proposed in this paper.  
The conductivity \(\sigma_{0}\) in Formula (2) is 3 \(\times\) 10\({}^{5}\) S/m and \(\omega_{p}(\sigma_{0})\) is 1.4 \(\times\) 10\({}^{15}\) rad/s. We mainly study the influence of conductivity caused by the temperature change of VO\({}_{2}\) from the insulation phase to the metal phase on the absorption performance [42]. Here, the conductivity of VO\({}_{2}\) is 200 S/m when the external temperature is 300 K, and changes dramatically to 2 \(\times\) 10\({}^{5}\) S/m when the external temperature is 350 K. Then, the finite element method with periodic boundary conditions (PBC) is set in the \(X\) and \(Y\) directions to simulate Figure 1b. The electromagnetic wave is perpendicular to the surface of the structure along the negative \(Z\) direction. The conductivity of Au is 4.56 \(\times\) 10\({}^{7}\) S/m and the thickness is more than the skin depth of THz. Thus, the transmission of THz can be ignored so that the transmittance of the electromagnetic wave after the incident is equivalent to zero. Then, the absorption performance of the electromagnetic wave can be expressed as Formula (3):  
\[A(\omega)=1-R(\omega)=1-|S_{11}(\omega)|^{2} \tag{3}\]  
where \(R(\omega)\) and \(S_{11}(\omega)\) are the reflectivity and the reflection coefficient from the frequency-dependent \(S\) parameter.