## 1 Introduction
As shown in Figure 1a, the incident light is set to come from the top region of air in the \(xz\) plane. Figure 1b shows numerically computed reflectance (\(R\)) and transmittance (\(T\)) spectra at a normal incidence. The spectra were calculated for a metasurface of \(P\) = 400 nm, \(D\) = 300 nm, and \(H\) = 220 nm, and shown with red and blue curves, respectively. In the wavelength range beyond 1200 nm, \(T\) is dominant, and \(R\) is suppressed, meaning that the metasurface is anti-reflective. As the wavelength becomes shorter, a fairly broad high-\(R\) band appears at 860-950 nm, and \(T\) is suppressed. In the shorter wavelength region than the high-\(R\) band, high-\(T\), and high-\(R\) peaks alternatively appear in 600-840 nm. Next, we examine electromagnetic (EM) modes at the high-\(R\) and high-\(T\) wavelengths indicated by the arrows labeled c and g, respectively. Figure 1c-j shows the EM-field distributions on resonances indicated by the arrows in Figure 1b. Figure 1c,d represents absolute value of the electric field \(\mid\)E\(\mid\) at 939.7 nm, which is a resonant wavelength of the high-\(R\) peak indicated by the arrow labeled c in Figure 1b. The \(xy\)- and \(xz\)-section \(\mid\)E\(\mid\) distributions are shown in Figure 1c,d, respectively. The \(z\) position of the \(xy\) section in Figure 1c is indicated by a black arrow from Figure 1d. The scale bar of the \(\mid\)E\(\mid\) is shown at the right-hand side of Figure 1d, and is in common to Figure 1c. Incident \(\mid\)E\(\mid\) was set to unity. Thus, it is found that resonantly, several-fold enhanced \(\mid\)E\(\mid\) is strongly localized at the sidewall of the Si rod. Figure 1e,f shows the absolute value of the magnetic field \(\mid\)H\(\mid\), corresponding to Figure 1c,d. The \(xz\)- and \(xy\)-section \(\mid\)H\(\mid\) are shown in Figure 1e,f, respectively. It is clear that the magnetic field is strongly localized and enhanced in the Si rod. The maximum value of \(\mid\)H\(\mid\) is 7.8 for the incident \(\mid\)H\(\mid\) = 1, meaning that the intensity \(\mid\)H\(\mid\)\({}^{2}\) exceeds 60. Thus, the \(\mid\)E\(\mid\) and \(\mid\)H\(\mid\) distributions in Figure 1c-f indicate that the resonant mode is a magnetic dipole mode, which is understood as a Mie resonance. Figure 1g-j exhibits resonant EM-field distributions at 831.3 nm, which is indicated by the arrow g in Figure 1b. The presentations are similar to those in Figure 1c-j. The resonant EM-field distributions exhibit electric dipole mode in the Si rod. In particular, one of the features of the electric dipole mode is that the maximum value of \(\mid\)H\(\mid\) is 16.7, and therefore, the intensity \(\mid\)H\(\mid\)\({}^{2}\) exceeds 270, meaning the extreme magnetic-field enhancement. Thus, the \(R\) dip and \(T\) peak at the longest wavelength of 831.3 nm represent a Mie resonance of the electric-dipole type. From these EM-field analyses for the Si-rod-array metasurface in Figure 1a, we found that high-\(R\) modes originate from magnetic multipole modes, and that high-\(T\) modes originate from electric multipole modes or guided modes inside the Si rods. The origins of optical resonances in Si-rod-array metasurfaces are classified in similar manners. Further information on these two resonant EM modes and other higher resonances which appear in the shorter wavelength range are shown in the Supplementary Materials (Figures S1-S4). Qualitatively, in this wavelength range of 600-1000 nm, we can classify the high-\(R\) modes into magnetic resonances and high-\(T\) (or low-\(R\)) modes into electric-dipole or guided modes in the Si rods. The qualitative understanding of the Si-rod-array metasurface is helpful to grasp optical spectra, such as \(R\) spectra, in experiments. Figure 1: (**a**) Schematic of Si-rod-array metasurface on a SiO\({}_{2}\) substrate. The \(xyz\) coordinates and optical configuration are shown. (**b**) A typical reflectance (\(R\)) and transmittance (\(T\)) spectra, shown with red and blue curves, respectively.