## 1 Introduction
\[R=\left|r_{12}\right.+\left.\frac{t_{12}t_{21}r_{\text{eff}}\exp(i2k_{0}\tilde {n}_{\text{ITO}}t_{\text{d}})}{1-r_{21}r_{\text{eff}}\exp(i2k_{0}\tilde{n}_{ \text{ITO}}t_{\text{d}})}\right|^{2} \tag{1}\]  
where \(k_{0}\) = \(2\pi/\lambda\) is the free-space wavenumber, \(\lambda\) is the free-space wavelength, \(\tilde{n}_{\text{ITO}}\) is the complex refractive index of ITO, and \(r_{\text{eff}}\), \(r_{12}\), \(r_{21}\), \(t_{12}\), and \(t_{21}\) are the coefficients presented in Figure 3c-h, respectively. Figure 4a shows a spectral absorption map calculated using Equation (1) as a function of the upper ITO layer thickness. The red-colored vertical dashed line indicates a wavelength of 590 nm, at which point the grating is highly absorptive. The corresponding spectral absorption map without the grating (\(w\) = 0) is presented in Figure 4b for comparison. We find from the two results that the spectral absorbance shown in Figure 4a has both the absorption characteristics of the Al grating as well as that of the ITO resonant cavity on the flat Al substrate. In particular, as can be seen from Figure 4a, strong absorption in the Al grating around 590 nm is preserved, albeit there are slight shifts in the resonance frequency due to the effect of the finitely thick ITO layer. Figure 4c,d show the absorption  
Figure 2: (**a**) Calculation geometry for determining reflection and phase shift characteristics in the subwavelength Al grating covered with ITO. (**b**) Spectral reflectance and (**c**) phase shift of the metallic grating for normally illuminated visible light (\(\theta\) = 0) with respect to grating thicknesses ranging from 0 to 70 nm. profiles of the two structures at \(t_{\rm d}\) = 270 nm, as denoted by the dashed lines in Figure 4a,b. There are absorption peaks near 470 nm in both cases, while the absorption peak at 585 nm can only be found when the grating exists. It is clear from these results that the absorption peak at 470 nm primarily stems from the optical losses in the coated ITO layer. On the other hand, most of the light with wavelength near 585 nm is absorbed by the subwavelength grating. Visualizing field distributions in the actual structure provides an intuitive confirmation of the relative contributions of the coated lossy dielectric layer and subwavelength grating. Figure 5 shows the simulated distributions of the magnetic field with respect to normally incident light with two different free-space wavelengths of 470 and 585 nm. In Figure 5a, for incident light with 470 nm wavelength, the magnetic field is primarily confined in the coated ITO layer and at the upper interface of the grating. On the contrary, as shown in Figure 5b, illumination with 585 nm light results in strong localization within the subwavelength grating cavity. It is notable that nearly perfect absorption of TM polarized light can occur at a specific wavelength due to strong confinement of the GSP mode in the grating, and the target wavelength can be tuned at will by tailoring the thickness of the grating cavity (\(t_{\rm g}\)). So far, normally incident light has been assumed when studying the basic absorption characteristics of the structure. However, absorption depending on the illumination angle, and the angular characteristic of a specific absorption band relies on the corresponding dominant absorption mechanism. Hence, we can expect that absorption bands can show different angular dependencies. Figure 6 shows the simulated spectral absorption map when the incident angle \(\theta\) varies from 0 to 80\({}^{\circ}\). The calculation has been conducted by using the TMM. The simulated structure is the same as that  
Figure 3: **(a)** Diagram showing the reflection and transmission coefficients for calculation of the optical response of the metallic grating coated with a lossy dielectric using the numerical effective medium approach. **(b)** Experimentally measured optical constants of ITO and Al. **(c)** Magnitude and **(d)** phase profiles of the reflection coefficient at the interface between ITO and effective medium.