## 3 Method and Physical Explanation  
Using the following equation, the absorbance efficiency can be calculated-  
\[A(\omega)=1-|S_{11}|^{2}-|S_{21}|^{2}=1-[R(\omega)+T(\omega)] \tag{1}\]  
where \(A(\omega)\), \(R(\omega)\) and \(T(\omega)\) denote the efficiency of absorption, reflection and transmission respectively [38; 39; 40]. If \(R(\omega)\) and \(T(\omega)\) are at a minimum then absorption \(A(\omega)\) will be at the maximum. As the copper back is enough thick to inhibit all incident EM wave i.e., \(T(\omega)=0\) then the absorption efficiency, \(A(\omega)=A(\omega)_{\text{max}}\). In this case, reflection efficiency is the only consideration to obtain the maximum absorption which follows the equation  
\[A(\omega)=1-|S_{11}|^{2}=1-R(\omega) \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Dimension (mm)** & **Parameter** & **Dimension (mm)** \\ \hline a & 8 & c & 4 \\ b & 8 & d & 1.3 \\ h & 1.8 & e & 1.6 \\ g & 0.4 & f & 1 \\ r\({}_{1}\) & 4 & r\({}_{2}\) & 3.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parametric description of the unit cell.  
Figure 1: PMA unit cell **(a)** Front view **(b)** Perspective view **(c)** Back Copper **(d)** Boundary condition.  
To achieve the expected dual band resonance from a metamaterial, the physical unit cell parameters should be cautiously optimized. The simulated result of reflection coefficient (S11), transmission coefficient (S21), and absorption scenario is presented in Figure 2. For a better understanding of the physical sensitivity and performance of the absorbers, the electric and magnetic field and the surface current distribution are investigated in addition to the surface current for all resonance frequencies.  
A wide-ranging physical analysis is accomplished in this segment to comprehend the authentic activities of this metamaterial absorbers. First, we concentrated on the query as to how every sub-module keeps its own behavior in such as a quarantined device. As a basic physical elucidation, the connection with the electrical permittivity (\(\epsilon_{r}\)) and the electric polarization (\(P\)) can be defined by the following fundamental equation  
\[\begin{split} D=&\in_{0}E+P_{\epsilon}=(1+\chi_{ \text{e}})\in_{0}E\\ \text{or, }&\frac{D}{E}=&\in_{0}(1+\chi_{ \text{e}})\dots\end{split} \tag{3}\]  
With the condition \(\chi_{\text{e}}<-1\), then \(\epsilon_{r}\) turns into the adverse, fulfilling the identical sub wavelength situation. The similar tactic may be applied to scrutinize the association with the effective magnetic susceptibility (\(\chi_{\text{m}}\)) and the magnetic field (\(B\)) with the second corresponding formula  
\[\begin{split} B=\mu_{0}H+\mu_{0}P_{\text{m}}=(1+\chi_{\text{m}}) \mu_{0}H\\ \text{or, }&\frac{B}{H}=\ \mu_{0}(1+\chi_{\text{m}}) \end{split} \tag{4}\]  
Finally, the metamaterial perfect absorber (PMA) efficiency is studied here to deliberate accurate losses in the metals, which are called surface power loss and volume losses in the dielectric substrates called volume loss power [41]. In this regard, the simulation and the power loss estimation have been investigated with a FIT-based CST microwave studio. The dissolute power on the imperfect dielectric layer roughly depends on the parameters of the loss tangent value taken as \(tan\delta\) = 0.005.  
Figure 2: Simulated results for reflection coefficient, transmission coefficient and absorption condition.