## 4 Discussion  
Impedance matching theory can be used to explain the phenomenon of perfect absorption. The effective impedance of the MPA can be expressed as [30]:  
\[Z_{eff}=\sqrt{\frac{\mu_{eff}}{\varepsilon_{eff}}}=\sqrt{\frac{\left(1+S_{11} \right)^{2}-S_{21}^{2}}{\left(1-S_{11}\right)^{2}-S_{21}^{2}}} \tag{5}\]  
Figure 3: (**a**) Reflection and (**b**) absorption spectra with different conductivity of VO\({}_{2}\). Figure 2: When the conductivity of VO\({}_{2}\) is \(2\times 10^{5}\) S/m. (**a**) The reflection and absorption spectra of the dual broadband absorber. (**b**) Color map of absorption spectra with different polarization angles. where \(\mu_{eff}\) and \(\varepsilon_{eff}\) are the effective permeability and effective permittivity, respectively. It is well known that impedance matching can be achieved as both of them reach the same. The real and imaginary parts of the impedance are derived from the \(S\) parameter. As is shown in Figure 4, when the VO\({}_{2}\) conductivity is \(2\times 10^{5}\) S/m, the real parts of the impedance are close to \(1\), and the imaginary parts of the impedance are close to \(0\) in the frequency range from \(1.87\) to \(4.19\) THz and from \(8.70\) to \(10.73\) THz. This means that the impedance of the absorber gradually matches with free space, which is the typical perfect absorber feature [27]. To further understand the physical mechanism of the absorber, we conducted an electric field analysis. Figure 5 shows the electric field distribution at the four resonance peaks. The first resonance peak is located at \(2.3\) THz, as shown in Figure 5a; the electric field is mainly concentrated in the gap between the long axis of the ellipse of the two structural units. The second resonance peak is located at \(3.6\) THz, as shown in Figure 5b; the electric field is mainly concentrated at the long axis of the ellipse and the edge of the inner ring of the unit structure. The combination of the overlapping regions of the two resonance spectra provides a guarantee for high-efficiency broadband absorption [31]. The third resonance peak is located at \(8.8\) THz, as shown in Figure 5c; the electric field is mainly concentrated in the inner ring and the junction of the two perpendicular ellipses. The fourth resonance peak is located at \(10.4\) THz, as shown in Figure 5d; the electric field is mainly concentrated at the junction of two ellipses and the gap area of the corresponding unit. Both resonance spectra provide the basis for the second broadband absorption. Due to the symmetry of the structure, similar phenomena also apply when the structure is under the Y-polarized incident wave. Figure 4: The relative impedance with the conductivities of VO\({}_{2}\) is \(2\times 10^{5}\) S/m. To illustrate the importance of geometric structure parameters, it is necessary to verify the influence of geometric structure parameters on the absorber. Figure 6 shows the influence of the major axis of the ellipse \(a\), the minor axis of the ellipse \(b\), the radius of the inner circle \(c\) and the thickness of the medium d on the absorptance of the absorber. As shown in Figure 6a, when the major axis of the ellipse becomes longer, the absorption bandwidth becomes wider; however, the absorption efficiency decreases. When the major axis of the ellipse becomes shorter, the absorption bandwidth becomes narrower, but the absorption becomes higher. In Figure 6b, it is obvious that the minor axis of the ellipse has the same changing law. In Figure 6c, conversely, when the radius of the inner circle becomes shorter, the absorption bandwidth becomes wider, and the absorption efficiency decreases. When the radius of the inner circle becomes longer, the absorption bandwidth becomes narrower, and the absorption becomes higher. The position of the resonance peak varies with the change of the major axis and minor axis of the ellipse or the radius of the inner circle. The absorptance and bandwidth will change with the change of the resonance peak position.