## 3 Material Characteristic and Numerical Analysis
There are various methods for analyzing the working principle of the absorbers in the literature, such as the effective medium theory [66], transmission line method [67], multi-layer method [68] and scattering theory [69]. These methods are developed for different types of absorbers. The effective medium theory and transmission line method require that the period of the element be much smaller than the wavelength. In the scattering method, the element is treated as the scatterer, and different modes in the element are analyzed. As the period of the element in the absorber proposed here is comparable to the wavelength, the scattering method is used here. The detailed calculation is not the main contribution of this paper, so we only give a qualitative analysis. To deeply investigate the working principle of the designed absorber, the field distribution in the resonator, including the electric field and the magnetic field, at \(f_{1}\) to \(f_{4}\) are simulated and plotted in Figure 4. As only the dielectric resonator mode and grating mode are excited, the surface wave [70] is not discussed here. The coordinate system is the same as that shown in Figure 1a. First, the field distribution at frequency \(f_{1}\) is discussed. In addition, the power loss density in the resonator at different frequencies is also plotted in Figure 4. As shown in Figure 1a,b, a half loop can be observed in the \(E\)-field, while the \(H\)-field clearly exhibits a dipole-type-like feature. Considering the resonator is backed with a metal plate, one can include that the fundamental magnetic dipole mode or \(\text{HEM}_{11\delta}\) mode of the dielectric resonator is excited. Observing the field distributions at \(f_{2}\) shown in Figure 4d,e, we can see that they are quite similar to those at \(f_{1}\), indicating that the same mode is excited at this frequency. This phenomenon can be explained using the dielectric resonator theory. Giving a dielectric resonator with fixed dimensions, the resonating frequency of the structure can be approximately calculated as \(f_{r}=a/\sqrt{\varepsilon_{r}}\), where \(a\) is the function of dimensions and \(\varepsilon_{r}\) is the relative permittivity of the materials used. With reference to the expression, we can see that if the permittivity of the dielectric is constant, the resonator will resonate at a single frequency. However, if the permittivity of the dielectric decreases with the frequency, the structure may resonate over a broad bandwidth, but not at a single frequency. Based on this, it is possible for the magnetic dipole mode to occur at different frequencies, namely \(f_{1}\) and \(f_{2}\). As the dielectric resonator mode is excited at these two frequencies, the field is highly confined in the dielectric and absorbed by the material. In addition, observing the power loss density in Figure 4c,f, we also can find that the main loss of the incident power occurs in the cylindrical resonator, which can further prove the excited mode in the dielectric resonator. Figure 3: **(a)** Simulated absorption spectra of the designed dielectric-resonator-based absorber. The simulated results for the two comparison cases, namely, the dielectric plate with the metal back and the dielectric resonator without the metal back, are also plotted. The four absorption peaks of the designed absorber are marked as \(f_{1}\),\(f_{2}\),\(f_{3}\), and \(f_{4}\) in the figure; **(b)** Simulated input impedance of the designed dielectric-resonator-based absorber, with the four absorption peaks marked. Figure 2: **(a)** Image of the printed cube sample; **(b)** The experimental setup of the permittivity measurement system; **(c)** Measured and fitted data of the permittivity of the material. Next, the working principle at \(f_{3}\) is investigated. With reference to Figure 4g-i, a complete and a half loop can be observed in the \(E\)-field distribution.