## 3 Results and Discussion
### Simulation Data of the Metamaterial Perfect Absorber (MPA)  
The MPA was simulated using the finite-difference time-domain method (FDTD) with a transverse electric (TE) plane wave. To design a device with \(A=1\), the dimensions and structural parameters were optimized by simulation. In the FDTD simulation, a source was selected within the visible range with a downward propagation along the \(z\) axis, whereas the electric field \(E\) was polarized in the \(x\) direction. Preliminary simulations were performed to optimize the thickness of the Al\({}_{2}\)O\({}_{3}\) interface layer and the GST thin film, and to optimize the dimensions of Ag nano-squares. Based on the achieved results, we fixed the thicknesses of GST and Al\({}_{2}\)O\({}_{3}\) at 25 and 7 nm, respectively. The absorbance over the visible range of the spectrum was simulated for the amorphous GST-based metadevice with different thicknesses (\(t_{\mathrm{Ag}}\)) of the top Ag electrode (60, 80, 100, 140, 180, and 220 nm) (Figure 4a). A thickness of \(t_{\mathrm{Ag}}=60\) nm yielded an \(A\) of about 0.98, and a thickness of 80 nm \(\leq t_{\mathrm{Ag}}\leq 220\) nm yielded an \(A=1.0\) at \(560\leq\lambda\leq 690\) (Figure 4a). Therefore, we selected the minimum \(t_{\mathrm{Ag}}\) that achieved an \(A=1.0\) (i.e., \(t_{\mathrm{Ag}}=80\) nm for \(\lambda=560\) nm, and \(t_{\mathrm{Ag}}=100\) nm for \(\lambda\sim 600\) nm). By using GST film in a crystalline state, a broadband perfect absorber was achieved for \(600\leq\lambda\leq 900\) nm (Figure 4b). The Ag squares governed the electric dipole resonances, and the Pt layer controlled the magnetic dipolar resonances. The simulation results confirmed that the dimensions and thickness of the nanopatterns, and thickness of the BS, are important factors that affect absorbance [37]. Figure 4: Metamaterial perfect absorbance (MPA) effect by finite-difference time-domain (FDTD) simulation. Reconfigurable perfect absorbance for (**a**) amorphous GST by changing the thickness of Ag nanoarrays from 60 to 220 nm. (**b**) Broadband MPA effect using crystalline GST at Ag thicknesses from 60 to 160 nm. Figure 3: Dielectric constant (**a**) \(n\) and (**b**) \(k\) in the \(200\leq\lambda\leq 1000\) nm wavelength range for the amorphous and crystalline phases of Ge\({}_{2}\)Sb\({}_{2}\)Te\({}_{5}\), obtained from ellipsometry data. The narrow absorption peaks of the MPA with amorphous GST were changed to broadband absorbance when the GST was crystalline. Perfect absorbance was likely to be caused by plasmonic resonance. Due to the matching impedance of MPA with the vacuum, low reflectance and high absorbance over the entire visible domain were achieved by using a crystalline GST layer. Adjustments of resonances in \(\varepsilon\) and \(\mu\) matched the impedance of the MPA to that of free space, producing an effective absorber [44]. To investigate the effect of BS on the ability to achieve perfect absorbance, and to gain insight into the importance of the localized surface plasmon resonance (LSPR), the electromagnetic distribution was calculated at a normal incidence (i.e., in the \(x\)-\(z\) plane) (Figure 5a-d). The simulation considered Ag metallic squares with sides of 110 nm and a pitch of 220 nm under periodic conditions. Absorbance was calculated from the electric field as  
\[A=\frac{1}{2}Re(-i\omega.\varepsilon.\varepsilon_{0}.E^{*}.E), \tag{1}\]  
where \(\varepsilon\) and \(\varepsilon_{0}\) are the permittivity of the material and free space, respectively. The electric field, magnetic field, and absorption were calculated for \(\lambda\approx 610\) nm (Figure 5b-d). Two resonances were represented: one was an electric dipole between upper parts of Ag squares, the other was a magnetic dipole between their lower parts. The simulations suggest that electric fields responsible for the energy absorption through the BS layer propagated towards the base of the square patterns in a forward direction (Figure 5b, white arrows).