## 2 Materials and Methods
### Optical Measurement  
\(R\) spectra were measured in a wide range from 500 to 1600 nm by using a spectrometer with incident-angle-resolving unit (V7200, JASCO Corporation, Tokyo, Japan). The incident polarization was set to p or s polarizations. When the plane of incidence is set to the \(xz\) plane as shown in Figure 1a, p polarization is the incident electric-field vector \(\mathbf{E}_{\text{in}}\) parallel tothe \(xz\) plane, whereas s polarization is \(\mathbf{E}_{\text{in}}\) parallel to the \(y\) axis.  
Figure 3: A series of measured enhanced fluorescence (FL) (colored curves) and \(R\) spectra (black dashed curves). The FL comes from the R590 molecules dispersed on the SOI–rod metasurfaces. (**a**) A set of FL (green curve) and \(R\) (black dashed curve) spectra on a metasurface of a SOI of 200 nm thickness and \(P\) = 330 nm. (**b**) FL-intensity enhancement factor in (**a**) is shown with a green curve. (**c**) A set of FL (orange curve) and \(R\) (black dashed curve) spectra on a metasurface of a SOI of 200 nm thickness and \(P\) = 400 nm. (**d**) FL-intensity enhancement factor in (**c**) is represented by an orange curve. (**e**) A set of FL (blue curve) and \(R\) (black dashed curve) spectra on a metasurface of a SOI of 340 nm thickness and \(P\) = 400 nm. (**f**) FL-intensity enhancement factor in (**e**) is shown with a blue curve. Note that the reference FL spectrum is shown with a black curve in (**a**,**c**,**e**), and that the \(R\) spectra in (**a**,**c**,**e**) are plotted for the right axes. The definition of the enhancement factor is described in the text.  
FL measurements were conducted in an illumination-and-collection setup. Incident laser light of wavelength 532 nm was emitted by a single-mode continuous-wave laser and was focused onto the metasurfaces. This laser light was focused using a 10\(\times\) objective lens of numerical aperture 0.26. The typical incident laser power on the sample surface was 1.0 mW. FL emitted by rhodamine 590 (R590) molecules (Exciton Inc., Lockbourne, OH, USA) was collected using the objective lens, and was measured by a charge-coupled device camera attached to a monochromator. The exposure time in measuring the FL signals was 5 s.  
The R590 molecules were dispersed on the metasurfaces as methanol solution. Typically, a 2 \(\upmu\)L drop of the R590 solution of concentration 50 nM was dispersed on the metasurfaces, then run promptly over the metasurfaces, and dried within a few seconds. From the dispersed area, we estimated the average molecular density on the metasurfaces. In order to quantitatively evaluate the FL-intensity enhancement factor, we prepared a reference configuration using a flat Si wafer, on which the FL intensity of dispersed R590 molecules was far smaller than that on the metasurfaces, so that we dispersed 5 \(\upmu\)M methanol solution of R590 molecules on the Si wafer and used the FL spectrum as a reference for normalizing experimental conditions, that is, the dispersed molecular density and the optical measurement condition. We note that the reference FL spectrum went through a smoothing process on graphical software to definitely evaluate the FL-intensity enhancement; as a result, the reference spectrum looks smoother, at a glance, than the FL spectra on the metasurfaces, which does not imply a better signal-to-noise ratio in the reference spectrum.