## 2 Results and Discussion
### 1D Periodic PLAs Made of W-SiN-W Membranes  
Figure 4 shows absorptance spectra of on-top 1D periodic W-SiN-W membranes. The schematic is shown in Figure 1d. We set the periodicity \(P\) to be 1000 nm and the incidence was set to be normal; we found signatures of diffraction at 1000 nm such as small steps in Figure 4a and kinks in Figure 4b. Various absorptance spectra represent light absorption in the 1D periodic W-SiN-W membranes with different widths of air slit \(S\), which was varied from 150 to 850 nm. Accordingly, the width of metal, \(W_{d}\), was varied from 850 to 150 nm because \(P=S+W_{d}\). The linear optical responses (\(R_{mn}\) and \(T_{mn}\)) were numerically computed and the absorptance was evaluated using Equation (1). As \(S\) increases under p polarization in Figure 4a, the absorptance spectra for \(S=450\) (purple curve) to 750 nm (red curve) have perfect-absorption peaks around 1300 nm. For \(S=750\) nm, another nearly perfect-absorption peak appears at 2200 nm, whose signature is seen for \(S=650\) nm (green curve) at the longest wavelength edge. As \(S\) increases under s polarization in Figure 4b, the absorptance gradually increases and reaches almost 1 for \(S=500\) nm (blue curve), and keeps the perfect absorption at approximately 1050 nm for larger \(S\). Color cones in Figure 4 indicate some of the perfect-absorption peaks for which we next examine the EM fields. Symbols such as 5a and 6a associated with the color cones denote the corresponding EM distributions shown in Figures 5a and 6a, respectively. Figure 5 presents EM-field distributions at perfect-light-absorption conditions of 1D W-SiN-W membranes with air slit \(S=550\) nm and width of the metal \(W_{d}=450\) nm. The incidence conditions of  
Figure 4: (**a,b**) Absortance spectra of 1D periodic W-SiN-W membranes under p and s polarizations, respectively. The schematic is given in Figure 1d. The incidence was set to be normal. Width of air slit, \(S\), was varied from 150 to 850 nm, which is symbolized as \(S150\) to 8850, respectively, while the periodicity was fixed at 1000 nm. The color usage is in common with (**a,b**). polarization and wavelength are indicated in Figure 4 with the sky-blue cones. The absolute values \(|\mathbf{E}|\) and \(|\mathbf{H}|\) are shown in linear scale in the minimum-to-maximum-value manners. Figure 5a,b shows an \(xz\)-section view of \(|\mathbf{E}|\) and \(|\mathbf{H}|\) distributions under the incidence condition indicated by the sky-blue cone in Figure 4a (p polarization and 1350.2 nm). The incidence was normal, being normalized such that the incident \(|\mathbf{E}|=|E_{x}|=1.0\) and \(|\mathbf{H}|=|H_{y}|=1.0\). The boundaries of the involved materials are shown with green lines, except for the air/W boundary in Figure 5a because of the high contrast and to avoid concealing small hot spots by the lines. The electric field is locally amplified at the W corners, exhibiting the small hot spots, whereas the magnetic field is localized at the flat SiN/W interface. The \(|\mathbf{H}|\) profile is quite similar to the two-layer system in Figure 3. We point out that the so-called gap mode in the W-SiN-W structure is not responsible for the perfect absorption. Figure 5c,d shows the \(|\mathbf{E}|\) and \(|\mathbf{H}|\) distributions in the \(xz\) section under another perfect-absorption condition, indicated by the sky-blue cone in Figure 4b (s polarization and 1032.1 nm). Then, the incident polarization vector is parallel to the \(y\)-axis and satisfies \(|\mathbf{E}|=|E_{y}|=1.0\); accordingly, the incident \(|\mathbf{H}|=|H_{x}|=1.0\). Figure 5c shows that there is no hot spot and the electric field reaches the bottom W layer unless the top W bar interrupts the propagation. Figure 5d shows that the magnetic field is mainly enhanced at the flat SiN/W interface, similarly to Figure 5b. Thus, in this 1D periodic system of \(S=550\) nm, the perfect absorption takes place with a mechanism similar to that in the two-layer membrane structure.