## 4 Calculation of Retrieved Effective Physical Parameters
We carried out a numerical simulation analysis of the power loss density (PLD) to better understand the physical workings of the designed metasurface. PLD is measured in W/m\({}^{3}\) and indicates the material's electric power density. PLD distribution evolution at different peak absorption bands (_f1, f2, f3, f4_) when \(\sigma\) = 2 \(\times\) 10\({}^{5}\) m/s (metal phase) is shown in Figure 11a-d. At the absorption bands of 3.2 THz, 4.7 THz, and 5.2 THz, energy is only focused on arc-shaped VO\({}_{2}\) patterns. In comparison, at 3.7 THz, power is concentrated above the VO\({}_{2}\) structure and at the blank middle dielectric layer (Figure 11b). The arc-shaped VO\({}_{2}\) structure and the middle dielectric layer show large PLD distribution due to contact between nearby unit cells. When the VO\({}_{2}\) structure is in the insulator state at \(\sigma\) = 100 m/s, the PLD is low, showing the structure's non-resonant response. The energy dissipation is non-local, in contrast to Figure 11a-d, demonstrating that VO\({}_{2}\) can absorb thin film. First, three broadband absorption peaks (3.2 THz, 4.7 THz, and 5.2 THz) are generated by localized VO\({}_{2}\) absorption, while the fourth (3.7 THz) broadband absorption is mainly caused by unit cell and ground plane interaction. On the other hand, it is found that the thickness of VO\({}_{2}\) and quartz has an effect on the absorber's absorption. In order to keep things short, we only explain the absorption analysis when the incidence is normal. Figure 8: Simulation results (**a**) real part and (**b**) imaginary part of the relative impedance for VO\({}_{2}\) with various conductivities. \[S_{21}=\frac{\left(1-R_{01}^{2}\right)e^{i2 mk_{0}d}}{1-R_{01}^{2}e^{i2 mk_{0}d}} \tag{2}\]0 When \(\sigma\) = \(2\times 10^{5}\) S/m, the effective physical parameters of (**a**) permittivity of the design structure, (**b**) permeability of the design structure, (**c**) refractive index of the design structure, and (**d**) impedance of the design absorber are obtained. Absorption and thickness are shown in Figure 12a when the VO\({}_{2}\) conductivity is held constant at \(\sigma\) = 2 \(\times\) 10\({}^{5}\) S/m, as depicted in the figure. The computed data show that the recommended system's absorption is thickness-dependent under normal incidence. While absorption does not rise substantially if VO\({}_{2}\) thickness is less than 0.5 \(\upmu\)m, when VO\({}_{2}\) thickness crosses this threshold, absorption increases and stabilizes because VO\({}_{2}\) is thick enough to impede the passage of energy. When the thickness (h) of the dielectric layer (quartz) fluctuates from 6 \(\upmu\)m to 12 \(\upmu\)m in increments of 2 \(\upmu\)m across a wide frequency range, the absorption of the proposed absorber increases. Between 2.7 and 5.7 THz, the dielectric layer's absorption must be greater than or equal to 90%, which is why its thickness (11 \(\upmu\)m) was carefully chosen. In real-world applications, the effects of polarization and incidence angle on absorption performance must be considered. Figure 13 displays the absorption spectra for TE polarizations. As can be observed, when the polarization angle is altered from 0\({}^{\circ}\) to 45\({}^{\circ}\), the proposed absorber's absorption spectra remain essentially unchanged. The absorption efficiency from 2.7 to 5.7 THz is still greater than 90% even when the incidence angle is up to 60\({}^{\circ}\). Beyond 45\({}^{\circ}\), the absorption and bandwidth, on the other hand, fall significantly. As the incident magnetic field's \(x\) component shrinks with increasing incident angle, the magnetic polarization cannot be stimulated as efficiently, and the absorber's ability to absorb energy is reduced. Thus, the proposed VO\({}_{2}\)-based metamaterial absorber has excellent absorption capability for TE modes in the 45\({}^{\circ}\) angle range.