# Design of a Polarization-Insensitive and Wide-Angle Triple-Band Metamaterial Absorber
## 3 Analysis and Discussion  
The simulation of MMA using the parameters of Table 1 in the software is shown in Figure 4 for the absorption curve of 2-16 GHz electromagnetic waves. There are three absorption peaks in the figure, located at 4.23 GHz, 7.403 GHz, and 14.813 GHz, respectively, and the corresponding absorption rates reach 99.05%, 99.3%, and 97.9%. In principle, the refractive index and impedance can be calculated by substituting the S parameters into the above formula, but since \(S_{21}\) appears in the denominator in the inversion formula, \(S_{21}\) is required to be a non-zero value. On the back of the structure, a layer of copper is set to prevent the electromagnetic wave from penetrating, which will make \(S_{21}\) zero, and means that the formula cannot be inverted. After consulting the literature [70], we found that [PERSON] of Zhejiang University mentioned in the article published in PRL that four very small holes can be set on the metal backplane, so that the absorption rate of the structure can be simulated without changing the transmission coefficient \(S_{21}\) to zero. In the simulation process of this article, four round holes with a diameter of 0.02 mm are set on the copper layer under the dielectric layer, so that the subsequent S parameter inversion method can be calculated. The center point of the unit structure is defined as (\(0,0\)), and the coordinate points of the four round holes are (\(4,4\)), (\(4,-4\)), (\(-4,-4\)), and (\(-4,4\)). Figure 5a shows the real and imaginary parts of the absorber impedance. It should be noted that the impedance here refers to the impedance relative to vacuum, which is 377 \(\Omega\). It can be found that at three absorption frequencies, 4.23 GHz, 7.403 GHz, and 14.813 GHz, the real part of the relative impedance is 1 and the imaginary part is 0. This indicates that near these three frequencies, the absorber achieves impedance matching and fulfills the condition of efficient absorption. Figures 5b and 5c show the comparison of the real and imaginary parts of the equivalent permittivity and equivalent permeability of the absorber, respectively. It can be found that the permittivity and permeability change greatly around 10 GHz. The former changes from a normal negative value to a normal positive value, while the latter changes from a positive value to a negative value. The mutation near 10 GHz will be emphasized in the subsequent analysis of the refractive index and dispersion. It is worth noting that near 4.23 GHz and 7.403 GHz, the permittivity briefly becomes greater than 0, and the permeability decreases to near 0. Finally, the real and imaginary parts of the permittivity and permeability are consistent near these two frequencies. Consistent with the situation of the first two frequencies, near the third absorption frequency of 14.813 GHz, the permittivity greater than 0 decreases and intersects with the permeability. In addition, near the three absorption frequencies, the real parts of the permittivity and permeability are all negative, which is beneficial for enhancing the absorption performance. The equality of the permittivity and permeability indicates that the electric resonance and magnetic resonance intensities are balanced, which is beneficial for achieving stable electromagnetic resonance and perfect absorption. Figure 4: Absorption spectrum diagram of the MMA. As shown in Figure 6a, the refractive index curve shows significant peaks and valleys with increasing frequency, which are associated with the absorption frequencies, respectively. Before 10 GHz, the refractive index changes abruptly at the absorption frequency, and the real part has a higher numerical value, indicating that the first two absorption frequencies correspond to strong local resonance modes. There is no corresponding absorption band near 10 GHz, but the refractive index still changes abruptly, and this change is not accompanied by an obvious decrease, indicating that the absorption mechanism may have changed after 10 GHz.