## 2 Results and Discussion
### 2D Periodic PLAs Made of W-SiN-W Membranes  
Figure 7a,b shows absorptance spectra of 2D periodic W-SiN-W membranes of on-top rectangular and circular patches, respectively. The schematics are shown in Figure 1e,f. Each panel in Figure 7 presents two spectra for the 2D periodic membranes with periodicity \(P=1000\) nm and the middle SiN-layer thickness \(t=100\) and \(200\) nm, which are shown with black and green curves, respectively. One side of the W square was set to \(W_{d}=450\) nm and the diameter of the circular W was \(D_{m}=504\) nm, where \(D_{m}\) was chosen to keep the volume of the circular patch equivalent to that of the square one. Figure 6: EM-field distributions of the 1D W-SiN-W membrane of \(S750\) in Figure 4. (**a,b**) \(|\mathbf{E}|\) and \(|\mathbf{H}|\) distributions, respectively; the p-polarized incidence condition is indicated by the red cone with the mark 6a in Figure 4a; (**c,d**) \(|\mathbf{E}|\) and \(|\mathbf{H}|\) distributions, respectively; the p-polarized incidence corresponds to the longer wavelength peak in Figure 4a, indicated by the red cone with the mark 6c. (**e,f**) \(|\mathbf{E}|\) and \(|\mathbf{H}|\) distributions, respectively; the s-polarized incidence condition is indicated in Figure 4b with the red cone with the mark 6e. The green lines commonly represent the boundaries of the 1D W-SiN-W structure. The coordinate axes are shown in common. All the panels are shown in linear scale in the minimum-to-maximum manners. The thickness of the top and bottom layers of W was set to 50 and 100 nm, respectively. Quantitatively, they exhibit similar absorptance spectra, irrespective of the difference of the patch shapes. One common feature in Figure 7a,b is that perfect-absorption bands appear at 1050-1200 nm. We note that, in the 1D periodic membranes in Figure 4, the perfect absorption appears as peaks (not band). This feature is due to the 2D periodic structures and probably originate from the dimensionality. The cone at 1126.8 nm in Figure 7a indicates the wavelength corresponding to EM-field distributions in the next Figure. Figure 8 shows a set of EM-field distributions of the 2D periodic W-SiN-W membrane at a perfect-absorption condition indicated by the cone (1126.8 nm) in Figure 7a. The incidence was set to be normal and to have \(|\mathbf{E}_{\mathrm{in}}|=1.0\) and \(|\mathbf{H}_{\mathrm{in}}|=1.0\). Note that the scales for \(|\mathbf{E}|\) and \(|\mathbf{H}|\) are in common to provide systematic views. Green lines indicate the boundaries in the 2D membrane. Figure 8a,b shows the \(|\mathbf{E}|\) and \(|\mathbf{H}|\) distributions, respectively, in a \(xz\) section that cut through the center of the on-top square W patch. The incident polarization vector \(\mathbf{E}_{\mathrm{in}}\) is parallel to the \(x\)-axis and induces hot spots at the corner of the W patch. The \(|\mathbf{H}|\) distribution takes larger values than the incidence at the interfaces of air/W and SiN/W. Figure 8c,d shows the corresponding \(yz\)-section view through the center of the on-top square W patch. The \(|\mathbf{E}|\) distribution does not include any hot spot whereas the \(|\mathbf{H}|\) distribution is strongly localized at the SiN/W interface, being scattered at the corner of the on-top W patch. Figure 8e displays an \(xy\)-view \(|\mathbf{E}|\) distribution at a representative \(z\) position, which was set to be 1 nm above the air/W interface and indicated by the cones in Figure 8a,c. The position of the square W patch is shown with green lines for better visibility. The \(|\mathbf{E}|\) distribution takes the maximum value at the corners of the W patch and mainly localizes around the W patch. Figure 8f shows an \(xy\)-view \(|\mathbf{H}|\) distribution at a representative \(z\) position, which was set to be 1 nm above the interface of the SiN/W and indicated by the cones in Figure 8b,d. The \(|\mathbf{H}|\) distribution is mostly enhanced at the positions between the on-top W patches and localizes at the SiN/W interface.