# Terahertz Broadband Adjustable Absorber Based on VO2 Multiple Ring Structure
## 4 Discussion  
To explain the adjustable principle, the electric field distribution at the center frequency of 5.17 THz is studied at a variety of conductivities from 2 \(\times\) 10\({}^{2}\) S/m to 2 \(\times\) 10\({}^{5}\) S/m in Figure 5. The results show that the electric field distribution is very weak and nearly negligible at a conductivity of 2 \(\times\) 10\({}^{2}\) S/m in Figure 5a. When the conductivity is increased  
Figure 4: Change of dielectric constant of VO\({}_{2}\) under different conductivities in (**a**) the real part and (**b**) the imaginary part. Figure 3: (**a**) Absorption spectrum and (**b**) reflection spectrum of absorber under different conductivities of VO\({}_{2}\). Figure 2: (**a**) Optimal absorption and reflection spectrum and (**b**) absorption spectrum at different polarization angles when \(\sigma\) = 2 \(\times\) 10\({}^{5}\) S/m. to \(2\times 10^{5}\) S/m, the electric field intensity is greatly strengthened because the resonance absorption effect of the gaps is improved, thereby enhancing the overall absorption effect in Figure 5d. Therefore, the dynamic function of the absorber can be achieved by regulating the conductivity of VO\({}_{2}\). In the meantime, when VO\({}_{2}\) stands in the metal phase, the corresponding impedance of the absorber matches that of the vacuum. Here, the relative impedance \(Z_{\tau}\) is given when the conductivity of VO\({}_{2}\) is \(2\times 10^{5}\) S/m, as in Figure 6. The value of the impedance of free space \(Z_{0}\) is equal to 1, and that of the absorber is \(Z\), which is expressed by Formula (4) [44]:  
\[Z=\frac{\mu(\omega)}{\varepsilon(\omega)}=\sqrt{\frac{\left(1+S_{11}\right)^{ 2}-S_{21}^{2}}{\left(1-S_{11}\right)^{2}-S_{21}^{2}}},Z_{\tau}=\frac{Z}{Z_{0}} \tag{4}\]  
The \(S_{11}\) and \(S_{21}\) are the reflection and transmission coefficient of the S-parameter, respectively. When \(Z\) is equal to \(Z_{0}\), the surface reflection of the absorber reaches zero, indicating the attainment of the impedance matching. The figure reveals that the real part and imaginary part of the relative impedance are approximate to 1 and zero from 3.01 THz to 7.27 THz, explaining that the impedance between the absorber and free space is almost consistent, which conforms to the perfect absorption mechanism. Thus, the perfect absorption mechanism can be well illuminated through the impedance-matching theory. It is also important to analyze the effect of the geometric structure of the designed absorber on the absorption spectrum from optimizing the key parameters. Here, the VO\({}_{2}\) and SiO\({}_{2}\) with different thicknesses are applied to sweep the parameters of the top and  
Figure 5: Electric field distribution at the center frequency of 5.17 THz when the conductivity of VO\({}_{2}\) is (**a**) \(2\times 10^{2}\) S/m, (**b**) \(2\times 10^{3}\) S/m, (**c**) \(2\times 10^{4}\) S/m, and (**d**) \(2\times 10^{5}\) S/m. Figure 6: Relative impedance \(Z_{\tau}\) diagram of the absorber at a conductivity of \(2\times 10^{5}\) S/m. middle layers in Figure 7. In Figure 7a, the absorption intensity first arises along with the addition of the top layer thickness, and then decreases with the further increase beyond the optimal value. Obviously, the absorption of the absorber is easily affected by the thickness of VO2. The coupling effect of VO2 with the bottom metal is very weak when its thickness is very thin. However, when its thickness turns thick enough, it exhibits a strong reflection effect, which is not conducive to matching the impedance of the vacuum. The optimal thickness of VO2 is 0.2 \(\upmu\)m, and the broadband absorption range over than 90% absorptivity varies from 3.01 THz to 7.27 THz. In addition, the absorption spectrum affected by the dielectric thickness is also discussed in Figure 7b.