## 3 Results  
Reflection spectra of the sample before ODT adsorption are shown in Figure 2a for different incident angles. At 30\({}^{\circ}\) angle, the reflection spectrum shows four reflection dips, corresponding to four resonant modes. These modes can be understood via their angle-dependent behaviors. The modes at 8.557 and 4.356 \(\upmu\)m (labeled as L1 and L2) exhibit negligible angle-dependence, which, according to Equation (1), using an effective refractive index of \(n_{\mathrm{eff}}=3.29\), are attributed to the LSPRs with mode number \(L=1\) and \(2\), respectively. In addition, the other two modes at 6.714 and 3.385 \(\upmu\)m (labeled as P1 and P2) show significant redshifts as the angle increases, which are identified as the PSPs with \(m=-1\) and \(-2\), respectively, according to Equation (2). Figure 2b shows a reflectance contour plot of the sample at different angles. The calculated angular dispersions using Equations (1) and (2) are shown in dashed and dotted lines, respectively, which nicely support our analysis of the LSPRs and PSPs.  
Figure 3a shows a comparison of reflection spectra of the sample before (black) and after (red) adding the ODT molecules at an incident angle of 30\({}^{\circ}\). From close-up views of the spectra shown in Figure 3b-e, redshifts of the resonances are observed. In particular, the LSPRs, i.e., L1 and L2,  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(P\) (\(\upmu\)m) & \(W\) (\(\upmu\)m) & \(h\) (nm) & \(d\) (nm) & \(t_{1}\) (nm) & \(t_{2}\) (\(\upmu\)m) \\ \hline
4.502 & 1.28 & 105 & 113 & 310 & 520 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Geometric parameters of fabricated metagrating sample.  
Figure 1: (a) Schematic of designed metagrating for octadecanethiol (ODT) detection. The relevant dimension parameters are \(P=4.5\)\(\upmu\)m, \(W=1.3\)\(\upmu\)m, \(h=100\) nm, \(d=110\) nm, \(t_{1}=300\) nm, and \(t_{2}=500\)\(\upmu\)m. The incident light is TM-polarized in \(y\)–\(z\) plane. Top-view SEM images of the fabricated metagrating before (**b**) and after (**c**) ODT adsorption.  
are shifted by 10 and 9 nm, respectively. Meanwhile, the PSPs, i.e., P1 and P2, are shifted by 2 and 5 nm, respectively. As the angle increases, the wavelength shifts of these four modes are plotted in Figure 4a, and their specific values are listed in Table 2. We can observe an overall trend of redshifts of both LSPRs and PSPs caused by refractive index change of a monolayer ODT. In particular, the P1 and P2 modes exhibit redshifts of 2-5 nm, while the L1 and L2 modes are shifted by 5-16 nm. Therefore, the LSPRs exhibit larger wavelength shifts than the PSPs. In addition, the LSPRs, i.e., L1 and L2, work only in narrow band with wavelength variations of less than 0.193 \(\upmu\)m, while the PSP modes, i.e., P1 and P2, operate in a broad band with a tuned wavelength range of more than 0.782 \(\upmu\)m, as resulted from their different angular dispersions.  
Figure 3: (**a**) Measured reflection spectra of the metagrating sample with and without octadecanethiol (ODT) at 30\({}^{\circ}\) angle. Close-up view of the spectrum for propagating surface plasmon resonances (PSPs), i.e., (**b**) P2 with mode number \(m=-2\) and (**d**) P1 with mode number \(m=-1\), and local surface plasmon resonances (LSPRs), i.e., (**c**) L2 with mode number \(L=2\) and (**e**) L1 with mode number \(L=1\).  
Figure 2: (**a**) Reflection spectra and (**b**) reflectance contour plot of the metagrating sample at different incident angles.