## 3 Results  
### Enhanced FL Measurement  
Figure 3 shows a series of enhanced FL of the R590 molecules dispersed on the three types of Si-rod-array metasurfaces. The left-hand-side column in Figure 3 displays the measured FL (colored curves) and \(R\) (black dashed curves) spectra; in addition, the reference FL spectrum of the R590 molecules dispersed on a flat Si wafer is shown, for normalized experimental conditions, with the black solid curve multiplied by a fixed factor for clarity. We note that the \(R\) spectra are plotted for the right axes. The right-hand-side column in Figure 3 presents the FL-intensity enhancement factors (colored curves), which are defined as the ratio of the FL intensity on the metasurface to the reference FL intensity in each panel of the left-hand-side column.  
The enhanced FL spectrum of the R590 molecules (green curve) on the metasurface of a SOI of 200 nm thickness and \(P\) = 330 nm are shown in Figure 3a. The measured \(R\) spectrum is shown with the black dashed line; it was measured at an incident angle of 5\({}^{\circ}\) and p polarization. The reference FL spectrum is shown with a normalization based on the experimental conditions, and with an enlargement of 100-fold for clarity. It is evident that the FL is significantly enhanced at 590 nm, which corresponds to one of the \(R\) peaks. Note that the original FL peak of the R590 molecules is located at about 565 nm, as can be seen in the reference spectrum. Thus, the large FL enhancement takes place together with an evident spectral change. Such spectral changes were found in the experiment exploiting high-emittance metasurfaces, including metallic nanostructures [48; 49], suggesting that FL-emitting electronic transitions in the FL molecules are significantly modified through the coupling with the resonances in the metasurfaces. The FL-intensity enhancement factor (green curve) is shown in Figure 3b, evaluated from the FL spectra in Figure 3a. The most prominent peak of enhancement factor is approximate 950 at 590 nm. Besides, small peaks can be seen near the wavelengths of \(R\) peak and dips (approximately, 630, 650, and 670 nm). The \(R\) spectrum is shown again for comparison, being identical to that in Figure 3a.  
The enhanced FL spectrum of the R590 molecules (orange curve) on the metasurface of an SOI of 200 nm thickness and \(P\) = 400 nm is shown in Figure 3c. The measured p-polarized \(R\) spectrum at 5\({}^{\circ}\), and the reference FL spectrum, are shown in a similar manner to Figure 3a. The reference is enlarged by 50-fold. The FL signals were significantly enhanced, and the spectral shape is modified.  
The FL-intensity enhancement factor (orange curve) is shown in Figure 3d, evaluated from the FL spectra in Figure 3c. The largest peak corresponds to the deep \(R\) dip and is located at 668 nm, showing 1000-fold intensity enhancement. The second largest peak at 556 nm correspond to a small \(R\) peak.  
The enhanced FL spectrum of the R590 molecules (blue curve) on the metasurface of an SOI of 340 nm thickness and \(P\) = 400 nm is shown in Figure 3e. The measured p-polarized \(R\) spectrum at 5\({}^{\circ}\) and the reference FL spectrum are shown in a similar manner to Figure 3c. Four enhanced FL peaks appear, which mostly correspond to \(R\) dips.  
The FL-intensity enhancement factor (blue curve) is shown in Figure 3f, evaluated from the FL spectra in Figure 3e. The largest peaks of this factor exceed 500, and are located at 602 and 630 nm. The corresponding resonant EM modes are analyzed later.