## 2 Results and Discussion
### Nearly PLA of Simply Stacked W-SiN Membrane  
Figure 3 shows typical results on light absorption and electromagnetic (EM) fields in a simply stacked W-SiN membrane. The schematic is shown in Figure 1a. We fix the thickness of the W and SiN layers to be 100 nm because we intend to elucidate representative properties of the two-layer membrane. Figure 3a,b shows 2D color and contour plots of light absorptance under p and s polarizations, respectively. The horizontal and vertical axes represent incident angles and photon energy in eV, respectively. Note that the normal incidence of 0\({}^{\circ}\) is in common with the two polarizations. The absorptance was evaluated using Equation (1). High absorptance of more than 0.8 (or 80%) appears both at p and s polarizations in the 1.0-1.5 eV (that is, 1239.5-826.3 nm in wavelength) range including the normal incidence. Perfect absorption also appears both at p and s polarizations; under p polarization, it is located around 78\({}^{\circ}\) and 2.8 eV, and, under s polarization, it is around 60\({}^{\circ}\) and 1.2 eV. Figure 3a,b explicitly shows perfect absorption by the two-layer W-SiN membrane. Multilayers of noble metals and insulators have been studied since the 1960s [17; 18]. Although several papers reported experimental observations of the optical responses [19; 20; 21; 22; 23], perfect light absorption, to our best knowledge, has not been observed in the noble-metal-insulator multilayer membranes. Thus, the optical response of the two-layer W-SiN membrane turns out to be unconventional. Figure 3c,d shows snapshots of electric-field distributions under conditions of large light absorption; each condition is indicated by open circle (\(\circ\)) and cross (\(\times\)), respectively, in Figure 3b. The corresponding incident angles are 0\({}^{\circ}\) and 60\({}^{\circ}\). Under both conditions, the incident polarization was s polarization; accordingly, the \(E_{y}\) component is plotted with blue-to-red colors in Figure 3c,d. We set the incident \(|E_{y}|\) equal to 1.0. The incident light propagates from the top. The interfaces of air/SiN, SiN/W, and W/air are shown with green lines. Figure 3e,f corresponds to Figure 3c, and shows the absolute value of electric field \(|\mathbf{E}|\) and the profile along the \(z\)-axis, respectively. The green lines indicates the interfaces, similarly to Figure 3c. We set the interface of air/SiN at \(z=0\). Note that Figure 3f is plotted in decreasing order on the horizontal axis. Obviously, the electric field rapidly decays inside the two-layer W-SiN membrane; in other words, it is efficiently absorbed in the membrane. From Equation (1), perfect absorption (\(A=1\)) requires \(\mathrm{R}=0\), which is often called impedance matching. Under the open-circle condition in Figure 3b, although the absorptance is not exactly equal to 1, the electric-field distribution is qualitatively understood to be due to impedance matching and does not arise from a plasmonic resonance. Figure 2: Basic optical properties of constituent materials. (**a**) R and T spectra of W slab (red solid and dotted curves, respectively) and bulk W (blue solid curve). The slab thickness was set to 100 nm and the bulk thickness was 1 mm; (**b**) R and T spectra of SiN membranes. Solid curves denote R spectra and dotted curves T spectra. The thickness \(t\) was set such as \(t=100\) (red), 200 (green), and 300 nm (blue). All the spectra in this figure were computed at the normal incidence. Figure 3g,h corresponds to Figure 3e,f, and shows the absolute value of magnetic field \(|\mathbf{H}|\) and the profile along the \(z\) axis, respectively. The \(|\mathbf{H}|\) profile takes the maximum value at the W/SiN interface.