## 3 Material Characteristic and Numerical Analysis
Additionally, as the dielectric resonator has a symmetry shape, the absorptivity is independent of the polarization angle of the incident waves. For simplification, only the \(x\)-polarized incident wave is considered here. The simulated absorption spectra of the proposed dielectric-resonator-based absorber (black line), under the condition that the incident angle equals to 0\({}^{\circ}\), is shown in Figure 3a. From this figure, one can see that the high absorptivity (higher than 90%) can be obtained from 3.9 to 12 GHz. When the frequency is higher than 12 GHz, apparent ripples can be found in the absorptivity spectra. This is mainly caused by the array diffraction effects of the dielectric resonator, as the lattice constant \(p\) is comparable to the wavelength. Due to high instability, the absorption higher than 12 GHz is not considered here. In the band from 3.9 to 12 GHz, four peak values can be observed, namely, 4.41, 6.24,8.61 and 10.76 GHz, which have been marked as \(f_{1}\) to \(f_{4}\) in the figure, respectively. The four peak values correspond to four resonating modes. The lower two peak values \(f_{1}\) and \(f_{2}\) correspond to the fundamental magnetic dipole mode, or \(\text{HEM}_{11\delta}\) mode, of the dielectric resonator, where \(0<\delta<1\)[65]. The third peak corresponds to the higher order magnetic dipole mode, or \(\text{HEM}_{11,1+\delta}\) mode, of the dielectric resonator, while the forth peak corresponds to the grating mode of the dielectric resonator. This will be discussed in detail later. As mentioned above, the dielectric loss of the materials is quite high over the whole band of interest. To give a comprehensive understanding of the merit of the designed absorber, we also simulate two other cases utilizing the same material for comparison. Case I is a dielectric plate with a metal plate backed. In this case, the dielectric plate has a thickness that is the same with the height of the dielectric resonator. Case II consists of the dielectric resonators that are not metal-backed, and the dimensions of the resonator are the same as that of the designed absorber. The simulated results for the two comparison cases are plotted in Figure 3a. From the results, in Case I, the average level of absorptivity is only about 50% over the band of interest, as the permittivity of the dielectric is quite different to that of the air, leading to impedance mismatching at the interface of the dielectric and air. Most of the incident wave is reflected by the dielectric and cannot be absorbed. In addition, two local peak values can be observed at about 7.17 GHz and 12.2 GHz, at which the thickness of the dielectric layer is about 1/2 and 3/4 wavelength, corresponding to the operating frequency. Under these conditions, the dielectric layer can be treated as the impedance matching layer for the incident waves, and good impedance matching can be obtained. However, the bandwidth for the high absorptivity in this case is quite narrow, and the level of absorptivity is low, which is not enough for microwave absorption applications. In Case II, an increasing trend can be observed. Two local peak values can be found in the absorption spectra. These two peak values correspond to the DR mode and grating mode of the dielectric resonator. However, the average level of absorptivity is only as high as 60% and, again, is not enough for microwave absorption applications. To provide further understanding of the designed absorber, the normalized input impedance of the designed absorber is simulated and plotted in Figure 3b. From the figure, we can see that the real part of the input impedance is near-unity, and the imaginary part is near-zero at the four frequencies, \(f_{1}\) to \(f_{4}\), indicating that good impedance matching at the interface of the dielectric resonator and air can be obtained at these frequencies, ensuring that the incident wave can propagate into the absorber and then be absorbed entirely as high dielectric loss of the dielectric material.