## 1 Introduction
(**a**) simply stacked W-SiN membranes, which are assumed to be formed on SiN membrane grown on a Si substrate. Both-end arrows represent p polarization where the incident electric-field vector is parallel to the plane of incidence; (**b**) a section view of the whole SiN-membrane substrate; (**c**) a photograph of SiN membrane supported by a Si substrate. White dashed line shows a section corresponding to (**b**). The SiN membrane is located at the center and has a dimension of 2 \(\times\) 2 mm\({}^{2}\); (**d**) W-SiN-W membranes with 1D periodic structures on the top. The plane of incidence is set to be parallel to the \(xz\) plane. Both-end arrows show s polarization where the incident electric-field vector is perpendicular to the \(xz\) plane; (**e,f**) W-SiN-W membranes of 2D periodic structures with on-top rectangular and circular W patches, respectively. shows 2D periodic structures of square arrays of W patches; we set the coordinate axes to be similar to Figure 1d. In Figure 1d-f, we define notations \(P\), \(S\), \(W_{d}\), and \(D_{m}\) for the periodic lengths, slit length, width of the W bars or square patches, and diameter of the circular W patches, respectively. In the optical linear response regime, light absorptance \(A\) is evaluated using the following equation:  
\[A=1-\sum_{m,n}(R_{mn}+T_{mn}), \tag{1}\]  
where \(R_{mn}\) and \(T_{mn}\) denote the \(mn\)-th reflective and transmissive diffraction, respectively. \(R_{00}\) and \(T_{00}\) are ordinary reflectance (R) and transmittance (T), respectively. As we describe in detail in Section 3.2, the linear optical responses of \(R_{mn}\) and \(T_{mn}\) are directly computed in a numerically precise way, based on Maxwell equations. Note that Equation (1) is represented in the \((0,1)\) range where 0 and 1 denote 0% and 100%, respectively. Perfect light absorption is related to perfect emittance by reciprocity [10]; therefore, when thermal emitters were produced, researchers tried to attain perfect-absorption structures [2; 3; 4; 5; 6]. Recently, nearly perfect absorption was observed in stacked complementary structures [11], which show significant enhancement of electric-dipole emission loaded on the outmost surfaces [12; 13; 14]. In addition, it was lately reported that high-emittance plasmonic cavities substantially enhance both electric- and magnetic-dipole emissions of Er ions [15]. Thus, it has been quite common to relate efficient light absorption with high emittance. In this study, we aim at designing PLAs made of a set of representative refractory metal and ceramic, based on precise numerical calculations. To propose realistic designs, we conduct the numerical calculations using reliable material parameters. As for the metal W, the complex relative permittivity is taken from the literature [16], and, as for the ceramic SiN, we adopt a representative value, that is, permittivity of 4.3. Further details are provided in Section 3.1. The representative value is sufficient to extract fundamental properties of the W-ceramic systems. We show that the W-SiN membranes are able to serve as PLAs even when they have subwavelength thickness, suggesting that they can function as low-power-consumption thermal emitters near the visible range. We also clarify that the working mechanism of the PLAs is unconventional, robust, and different from that of noble-metal-insulator systems studied so far [2; 3; 4; 5; 6].