# Terahertz Broadband Adjustable Absorber Based on VO2 Multiple Ring Structure
## 4 Discussion
Firstly, the central frequency of the spectrum is 5.17 THz, corresponding to the free space wavelength of 58 \(\upmu\)m. Next, the refractive index of SiO2 is \(n=1.95\) (3.8\({}^{0.5}\)), so that the corresponding central wavelength equals 29 \(\upmu\)m in the dielectric layer. Here, the optimal thickness of the middle layer is 7 \(\upmu\)m, which is almost equivalent to one fourth of the central frequency, and meets the interference cancellation effect between the reflected waves and incident waves. Thus, the perfect absorption mechanism can also be explained by the wave-interference cancellation theory. As a result, it is meaningful to study the thickness of VO2 and SiO2 for their improvements to the absorption performance. Figure 8 presents the absorption performance of the different geometric parameters of VO2. The different ring lengths will affect the coupling between the rings, so the optimal ring sizes \(l_{1}\), \(l_{2}\), and \(l_{3}\) can be obtained by scanning different sizes. As a result, the optimal structure parameters include \(l_{1}=20\)\(\upmu\)m, \(l_{2}=12\)\(\upmu\)m, \(l_{3}=4\)\(\upmu\)m, \(w=2\)\(\upmu\)m, and \(t=0.08\)\(\upmu\)m. In Figure 8d, when the ring width increases, the number of absorption peaks in the absorption spectrum will change from one to two and the overall absorption bandwidth will also change greatly. Similarly, the gap width \(t\) on the rings will affect the overall absorption bandwidth and efficiency significantly, as in Figure 8e. The value \(t=0.08\)\(\upmu\)m is the most ideal result of the gap width in the proposed design. It is worth noting that the complete structure shows greater absorption bandwidth and efficiency than a single ring with and without a gap, indicating that the integration of different structures adds to the resonance absorption of different frequencies, as in Figure 8f. Moreover, the increase in the number of rings helps to improve the overall absorption bandwidth and efficiency because the absorption performance of double rings is better than a single ring (Figure 8f). The optimal number of rings can be obtained by simulating the absorption efficiency of the multi-ring structure. Finally, the above discussions mainly focus on the case of vertical incidence; thus, the influence of oblique incidence on the absorption will be further illuminated in this part. To analyze whether the absorber possesses a good absorption performance or not under oblique incidence, the absorption effect at different angles is simulated through the full wave simulation in Figure 9, including transverse electric polarization (TE) and transverse magnetic polarization (TM). Figure 9a shows that for the TE polarized waves, the absorption  
Figure 7: Absorption spectrum of different thicknesses of (**a**) VO2 and (**b**) SiO2 when \(\sigma\) equals \(2\times 10^{5}\) S/m. spectrum will not change at small angles (up to 55\({}^{\circ}\)), and its absorptivity will remain above 75% between 3.01 THz and 7.27 THz. For the TM polarized waves in Figure 9b, the main absorption peak in the spectrum narrows slightly along with increasing the incident angles. The absorption bandwidth narrows and higher-order modes appear as the incident angle reaches 25\({}^{\circ}\). At the same time, the ratio of the wavelength (58 \(\upmu\)m, 5.17 THz) and period (24 \(\upmu\)m) is 2.42, which cannot meet the demand of the sub-wavelength scale for large angle incidence, so it tends to have some grating lobes and high-order diffraction. Thus, the above results show that the absorber works well at small incident angles.