## 2 Structure and Method  
The schematic of the structure is shown in Figure 1. The proposed structure is composed of a single layer of patterned graphene, a layer of silicon dioxide as a loss layer and a mirror layer of perfect electrical conductor (PEC). Among them, the thickness of SiO\({}_{2}\) is \(t=28\)\(\upmu\)m, which is considered the permittivity \(\varepsilon=3.9\), and the thickness of PEC is \(h=3.5\)\(\upmu\)m. In order to control the Fermi level of the top graphene, we set the Au electrodes as the top gate and a patterned ion-gel above the graphene, and a conductor below the graphene. We patterned the ion-gel into a three-layered split-ring structure in Figure 1. Each layer of the split-ring was connected to an Au gate. Thus, three Au gates were used to separately adjust each layer of graphene. The size of the ion-gel was similar to the graphene's three-ring pattern. We hope to use this method which the Fermi level is dynamically adjustable to achieve many kinds of absorption patterns in one absorber. The ion-gel pattern which was omitted to simplify the calculation is designed to discretely adjust the three graphene nanorings [22; 23]. We also provide some evidence in Figure S1 to prove this point. And some researchers believe that the phonons between the ion-gel and oxide silica will affect the absorption of the absorber [12; 24]. In addition, as shown in Figure 1, we give the results of the graphene patterning process. We have designed a pattern of three concentric rings of graphene. On the one hand, this pattern is a good perfect symmetrical structure, which can solve the problem of polarization sensitivity. On the other hand, through the regulation of the three rings and the mutual coupling between the three rings, we can achieve a variety of functions, such as continuous perfect absorption and mode conversion of the absorption frequency. In the process of FDTD simulation, we set the convergence time \(\tau=1\) ps, \(\mu=2\)\(\times 10^{4}\) cm\({}^{2}\cdot\)V\({}^{-1}\cdot\)s\({}^{-1}\) (there is a corresponding relationship between \(\tau\) and \(\mu\)). The design of graphene's electron-phonon relaxation time can be achieved by using the mechanical exhalation method in high-quality graphene in other work [25; 26]. In our work, we give \(E_{f}=0.7\) eV of any initial value, and obtain the simulated data by scanning the values of different Fermi levels without changing the structural parameters. We set override x mesh and y mesh is 5 nm and override z mesh is 1 nm. The size of mesh is much smaller than the minimum size of the pattern to ensure the accuracy of the absorption and the using of 1 nm in the setting of the z-axis mesh is to ensure that the single-layer graphene structure is well scanned. In addition, according to the data results from FDTD--the reflectivity \(R\) (\(\omega\)) in the upper space and the transmittance \(T\) (\(\omega\)) in the bottom space, we can get the result of the absorption rate of the absorber \(A\) (\(\omega\)) = \(1-R\) (\(\omega\)) - \(T\) (\(\omega\)), this method is widely used by researchers [13; 17; 18; 19]. Regarding the conductivity tunability of graphene, it can be known from the Kubo formula [27] that the conductivity is determined by the internal and external conductivity [28; 29; 30],  
\[\sigma(\omega)=\sigma_{intra}(\omega)+\sigma_{inter}(\omega) \tag{1}\]  
\[\sigma_{intra}(\omega)=\frac{2e^{2}k_{B}T}{\pi\hbar^{2}}\frac{i}{\omega+i/\tau} \ln\left[2\cosh\left(\frac{E_{f}}{2k_{B}T}\right)\right] \tag{2}\]  
\[\sigma_{int\sigma}(\omega)=\frac{e^{2}}{4\hbar^{2}}\left[\frac{1}{2}+\frac{1}{ \pi}\arctan\left(\frac{\hbar\omega-2E_{f}}{2k_{B}T}\right)-\frac{i}{2\pi}\ln \frac{\left(\hbar\omega+2E_{f}\right)^{2}}{\left(\hbar\omega-2E_{f}\right)^{2} +4(k_{B}T)^{2}}\right] \tag{3}\]  
where \(\omega\) is the frequency of the electromagnetic wave, \(E_{f}\) is the chemical potential (Fermi level), \(\tau\) is the electron-phonon relaxation time, and \(T\) is the ambient temperature.