## 3 Results Analysis  
### Absorption Characteristics  
The absorption characteristics depend on the impedance matching of the structure. The relative impedance (Z) of the proposed three-layer sandwich model was calculated using Equation (2) [32], and Figure 4a presents the relative impedance of both TE and TM modes. The near-unity value of the real part and near null value of the imaginary part shows that the proper effective impedance of the structure matches with the free space impedance, which offers a high absorption level. \[Z=\sqrt{\left(1+S_{11}\right)^{2}-S_{21}^{2}/\left(1-S_{11}\right)^{2}-S_{21}^{ 2}}=\sqrt{\mu/\epsilon}/Z_{0}=\sqrt{\mu_{r}/\epsilon_{r}} \tag{2}\]  
where \(\mu=\mu_{r}\mu_{0}\) and \(\epsilon=\epsilon_{r}\epsilon\) are the permeability and permittivity of the MMA, respectively. \(\mu_{r}\) and \(\epsilon_{r}\) are the relative permeability and permittivity of the medium, respectively. \(\mu_{0}\) and  
Figure 3: Absorption of different values: (**a**) ground plane thickness, (**b**) dielectric thickness value, (**c**) patch thickness, (**d**) outer ring length, (**e**) inner ring length, and (**f**) inner ring slot length. \(\epsilon_{0}\) are the permeability and permittivity of free space, respectively. Thus, the free space impedance is \(Z_{0}=\sqrt{\mu_{0}/\epsilon_{0}}\). The reflectance (\(R\)) of the TE and TM mode can be calculated by Equations (3) and (4), respectively [17]:  
\[R_{TE}=\left|r_{TE}\right|^{2}=\left|\mu_{r}\cos\theta-\sqrt{n^{2}-\sin\theta}/ \mu_{r}\cos\theta+\sqrt{n^{2}-\sin\theta}\right|^{2} \tag{3}\]  
\[R_{TM}=\left|r_{TM}\right|^{2}=\left|\epsilon_{r}\cos\theta-\sqrt{n^{2}-\sin \theta}/\epsilon_{r}\cos\theta+\sqrt{n^{2}-\sin\theta}\right|^{2} \tag{4}\]  
where \(n\) is the refractive index, and \(\theta\) is the incident angle of the wave for typical incidence. Thus, Equations (3) and (4) become:  
\[R_{TE,TM}=\left|Z-Z_{0}/Z+Z_{0}\right|^{2}=\left|\sqrt{\mu_{r}}-\sqrt{\epsilon _{r}}/\sqrt{\mu_{r}}+\sqrt{\epsilon_{r}}\right|^{2} \tag{5}\]  
Equation (5) represents the reflectance of the MMA, which is significantly controlled by impedance matching as well as the metamaterial. As the transmission is zero due to the back layer, absorption (\(A\)) can be calculated by \(A=1-R\). The reflectance, transmittance, and absorption characteristics of TE and TM modes are illustrated in Figure 4b. The symmetrical design of the proposed MMA provides a unique absorption curve for both TE and TM modes. A peak absorption of 99.99% is realized at a wavelength of 523 nm, and an absorption above 99% appears from 474.36 to 578.75 nm. In addition, an absorption more than 92.2% is obtained for the entire visible optical wavelength region with an average absorption of 97.1%. This near-unity absorption feature of the proposed MMA can be used for solar energy harvesting at visible optical wavelengths, stealth technology, sensors, and micro-imaging technology [21]. Absorption characteristics can also be calculated by applying the Interference Theory (IT) model, which also explains the underlying physics of the metamaterial absorber [33; 34]. The patch (layer 1) with a particular metallic pattern acts as a partial reflection surface. This layer modifies complex transmission and reflection coefficients, and the ground plane (layer 3) works as a perfect reflector. Figure 5a shows the patch between air and a dielectric substrate. The incident EM wave partially transmits and reflects the atmosphere with transmission coefficient \(\widetilde{t}_{12}(\omega)=t_{12}(\omega)e^{i\theta_{12}(\omega)}\) and reflection coefficient \(\widetilde{\tau}_{12}(\omega)=r_{12}(\omega)e^{i\varphi_{12}(\omega)}\). The transmitted wave constantly propagates until reflected from the ground plane.