## 2 Structure and Research Methods  
Figure 1 illustrates the structure of a terahertz tunable broadband absorber using VO\({}_{2}\) in its unit cell. The depicted structure reveals its three-dimensional arrangement, progressing from the uppermost layer downwards. The structure consists of two VO\({}_{2}\) pattern layers and a continuous gold reflection layer separated by two dielectric layers. The period of the unit cell is \(p=35\)\(\upmu\)m, the thickness of the gold reflection layer is t\({}_{1}=0.2\)\(\upmu\)m, and the conductivity of gold is \(\sigma_{\text{Au}}=4.56\times 10^{7}\) S/m. The thickness of the VO\({}_{2}\) pattern layer is t\({}_{3}=0.1\)\(\upmu\)m and the thickness of the PTFE dielectric layer is t\({}_{2}=\)t\({}_{4}=7.5\)\(\upmu\)m. The dielectric constant is 2.1 and the loss angle tangent tan\(\delta=0.0002\). The parameters of the optimized structure are: d = 2 \(\upmu\)m, p\({}_{1}=30\)\(\upmu\)m, r\({}_{1}=6\)\(\upmu\)m, and r\({}_{2}=3\)\(\upmu\)m.  
Figure 1: Schematic diagram of the geometry of the absorber. (**a**) Stereogram of periodic units; (**b**) top view of the two-storey VO2 structure designed in the periodic unit; (**c**) side view of the periodic unit. The key feature of this structural unit is that it has symmetry in both the \(x\) and \(y\) directions, which is also the intrinsic reason for its polarization insensitivity. The metasurface was developed to address some of the limitations of traditional metasurfaces, such as limited bandwidth, beam shift, high loss, etc., and one of its significant differences compared to other metasurfaces that are also used for the same purpose is its higher design flexibility and modulation capability. The geometry of the metasurface has an important influence on its absorption range, and the metasurface is usually composed of microscopic scale structures. In this paper, when the designed structure is asymmetrical or the structural parameters change, the absorption range will be affected and the performance will decline, and the structure and parameters presented in this paper can achieve the best absorption performance. Therefore, in the design of a metasurface, it is necessary to consider the shape, size, periodicity, and other factors of its micro-nano structure to achieve effective control and regulation of light waves and meet the requirements of having a specific absorption range. In the THz frequency [30] range, the dielectric constant \(\varepsilon(\omega)\) of VO\({}_{2}\) can be represented by the Drude [21] model:  
\[\varepsilon(\omega)=\varepsilon_{\infty}-\frac{\omega_{p}^{2}(\sigma)}{ \omega^{2}+i\gamma\omega} \tag{1}\]  
where \(\varepsilon_{\infty}\) = 12 is the high-frequency relative permittivity, \(\omega_{p}\) is plasma frequency, \(\sigma\) is conductivity of VO\({}_{2}\), \(\omega\) is the angular frequency of THz waves, \(\gamma\) = 5.75 \(\times 10^{13}\) rad/s is collision frequency, and \(\omega_{p}\) can be approximated as \(\omega_{p}^{2}(\sigma)=\frac{\sigma}{\sigma_{0}}\omega_{p}^{2}(\sigma_{0})\), where \(\sigma_{0}\) = 3 \(\times 10^{5}\) S/m, and \(\omega_{p}(\sigma_{0})\) = 1.4 \(\times\) 10\({}^{15}\) rad/s. The temperature has a direct impact on the conductivity of VO\({}_{2}\), thus, the simulation calculation in this work is mainly carried out for room temperature and high temperature (350 K). The conductivity of VO\({}_{2}\) is set to \(\sigma\) = 200 S/m when T = 300 K. When the temperature increases to 350 K, VO\({}_{2}\) exhibits a metallic state and its conductivity is \(\sigma\) = 2 \(\times\) 10\({}^{5}\) S/m. In the THz frequency range, the conductivity of VO\({}_{2}\) may also be influenced by frequency. For example, in the THz frequency range, the electron transport in VO\({}_{2}\) films may be influenced by the frequency. When the THz wavelength matches the characteristic scale of electron migration time and charge carrier density, it can trigger oscillation and cyclotron motion of charge carriers, leading to changes in conductivity.