## 1 Introduction  
Membrane structures can be used to manipulate light in outstanding ways. One example is photonic crystals made of high-refractive index materials such as semiconductors [1]. However, such membrane structures are generally fragile and difficult to handle since they are free-standing in air and have thickness less than the wavelength of light in vacuum, that is, subwavelength. Today, ceramic membranes can be realized, thanks to reliable thin-film fabrication techniques such as plasma-enhanced chemical vapor deposition. Here, we focus on membrane structures based on free-standing thin films made of ceramics. To make the application clear, we design perfect light absorbers (PLAs) suitable for thermal emitters in the short-wavelength infrared range of 1-2 \(\upmu\)m. Thermal emitters made of nanostructured materials are currently optimized for the mid-infrared range of 2-5 \(\upmu\)m, using metal-insulator-metal structures that typically comprise noble metals [2; 3; 4; 5], aluminum [6], etc., as constituent materials; however, these metals cannot withstand high temperatures. A basic requirement exists for the thermal emitters, that is, high melting points exceeding 2000 K. From this point of view, we chose silicon nitride (SiN) as the ceramic and tungsten (W) as the metal in this study. Both of them are stable at high temperatures. Considering practical application, the thickness of SiN membranes and W are assumed to be 100-200 nm and 50-100 nm, respectively, which are usual values in commercial products [7] and laboratory use. A 3D photonic crystal made of only W was once produced with a similar goal as mentioned above and worked as a thermal emitter at about 2 \(\upmu\)m [8]. However, production of thermal emitters based on such structures still has a high demand and has not been standardized to date; thus, much simpler structures are highly preferred from the viewpoint of practical application. Light absorbers in infrared ranges have a long history. Originally, the idea to obtain PLAs was simple; that is, to use materials as analogous to black bodies as possible. The absorbed infrared light has been converted to electric signals since the 1940s [9]; the devices are well known as conventional bolometers. However, it has been difficult to attain PLAs over the whole wavelength range. Accordingly, PLAs based on the artificially designed structures were conceived for the particular wavelength ranges [2; 3; 4; 5; 6]; in fact, the PLAs do not look like black bodies. Thus, there are distinct differences between black-body-based and artificial-structure-based PLAs. Figure 1 illustrates schematics of W-SiN membrane structures studied in this work. Figure 1a-c shows simply stacked W and SiN layers. The two-layer membrane structure is formed using a SiN membrane on a Si substrate. The section view is shown in Figure 1b. The image of the original SiN membrane is shown in Figure 1c; the central square domain of 2 \(\times\) 2 mm\({}^{2}\) is the SiN membrane. Once deposition of W is performed, the W-SiN membrane structure in Figure 1a,b is obtained. The white dashed line indicates a section corresponding to Figure 1b. Figure 1a also indicates the coordinate axes and optical configuration of p polarization, which is defined such that the incident polarization vector is parallel to the plane of incidence. Without loss of generality, we set the plane of incidence to be parallel to the \(xz\) plane. Figure 1d-f shows schematics of W-SiN-W membrane structures, whose top layers are set to be periodic. Figure 1d also shows the coordinate axes and s polarization. When the plane of incidence is parallel to the \(xz\) plane, s polarization means that the incident polarization is perpendicular to the \(xz\) plane and parallel to the \(y\)-axis. Figure 1d shows a 1D periodic structure along the \(x\) axis. Figure 1e,f  
Figure 1: Schematics of metal-ceramic membrane structures. The metals are W (gray) and the ceramics are SiN (pale blue) in this study.