## 3 Simulation Results and Discussion  
Even though the incident field consists of a single component, the reflected field typically has both \(x\) and \(y\) components. The co-polarized reflection coefficients are defined as \(R_{xx}=\left\lvert\right\rvert Erx\left\lvert\right\rvert\) and the cross-polarized reflection coefficients as \(Ryx=\left\lvert\right\rvert Ery\left\lvert\right\rvert/\left\lvert\right\rvert Exx\left\lvert\right\rvert\) when the incident and reflected fields are \(x\) and \(y\) polarized, respectively. The simulated results of the proposed design for linear reflection coefficient (\(R_{xx}\) and \(R_{yx}\)) under normal incidence are shown in Figure 2. It can be seen from Figure 2 that the cross-polarized reflection coefficient (\(R_{yx}\)) is equal to zero in the interested band when the top layer of VO\({}_{2}\) is in the metal state, while the co-polarization reflection coefficient is almost equal to 0.1 in the frequency range of 2.7-5.7 THz. Therefore, the proposed design achieves perfect absorption in the frequency range of 2.7-5.7 THz as shown in Figure 3. Figure 3a displays the absorber's reflection and absorption spectrum when the top layer of VO\({}_{2}\) is in the metal state. The result shows that the designed absorber achieves more than 90% in the frequency range of 2.7-5.7 THz at a normal incidence angle. For most of the operating band, absorption efficiency exceeds 98%. The absorber features four absorption peaks at resonance frequencies: 3.2 THz, 3.8 THz, 4.7 THz, and 5.2 THz. In practical applications, the impact of wave polarization and incident angle on absorption efficiency must be considered. When electromagnetic radiation is incident vertically, the VO\({}_{2}\) metal phase's absorption spectra are displayed in Figure 3b at various polarization angles. The proposed absorber's absorption spectra are unaffected by polarization angles between 0\({}^{\circ}\) and 45\({}^{\circ}\). As a result, the absorption is indifferent to the polarization angle. This polarization independence is essential in absorbers because the polarization angle is frequently random under actual settings. In order to dynamically control the absorption of the schematic design absorber, the conductivity of arc-shaped VO\({}_{2}\) varies as the intrinsic structure of VO\({}_{2}\) allows it to make the transition from the insulating to the metallic state. Numerical simulations are performed in order to see the effects of variations in the conductivity of  
Figure 2: Magnitude of reflection coefficients of the design structure when conductivity of metal is \(\sigma=2\times 10^{5}\) S/m. VO\({}_{2}\) on the absorption efficiency. As shown in Figure 3, absorption efficiency increases with increase in the conductivity. The design absorber achieves a perfect absorption of more than 90% in the frequency range of 2.7-5.7 THz, resulting in an absorption bandwidth of up to 3 THz. The optical absorption spectra show that by raising the conductivity from 200 to 20 \(\times\) 10\({}^{4}\) S/m, the absorption at resonant frequencies may be continuously tuned from 4% to 100%, with the associated absorptance frequency band reaching 3 THz. Figure 4a shows the absorber's magnitude reflection and absorption spectra when the VO\({}_{2}\) material is in the metal phase. The absorber has four resonance peaks at 3.2 THz, 3.8 THz, 4.7 THz, and 5.2 THz. The results reveal that absorption efficiency is greater than 90% in the range 2.7 THz-5.7 THz on a normal incidence angle. Absorption efficiency surpasses 98% for the majority of the working spectrum. When conductivity changes, the changes in the imaginary parts are far more significant than those in the real parts, as shown in Figure 5. As a result, the spectral intensity shifts substantially, but the peak's placement along the frequency axis remains virtually unchanged. Figure 6 shows that at conductivities of 1.5 \(\times\) 10\({}^{5}\) S/m, 100% absorption spectra in the frequency range of 3.38-5.19 THz is achieved.