## 3 The Influence of Structure Parameters
### The Thickness of Substrate  
To investigate the influence of the thickness of substrate on reflected light, we kept all other parameters fixed and change only the thickness of the substrate \(H_{\text{s}}\) from 100 nm to 300 nm and ran the simulation again. Results show that the changes of the reflection spectra are complex. A monotonous increase or reduction with the increase of the thickness of substrate does not exist.  
With the thickness of the substrate \(H_{\text{s}}\) increasing, it is clear that the peak position tends to shift towards shorter wavelength, and the maximal peak always lies in the red band, but the bandwidth of the maximal peak varies periodically, as shown in Figure 7. This is because the position of the maximal reflectivity is decided by the structural size of the nanodisk, and the thin-film interference gives the reflectivity more detail. The incident light reaching the dielectric layer, experiences multilayer interference at the air-dielectric interface because of the existence of the dielectric layer and the substrate. According to the thin-film interference theory, when the wavelength of light under normal incidence meets the formula  
\[2H_{\text{d}}n_{1}+2H_{\text{s}}n_{2}=(m-\frac{1}{2})\lambda, \tag{2}\]  
Figure 6: The reflection spectra of different \(H_{\text{d}}\). (**a**) The reflection spectra with \(H_{\text{d}}\) = 30 nm. (**b**) The reflection spectra with \(H_{\text{d}}\) = 60 nm. (**c**) The reflection spectra with \(H_{\text{d}}\) = 90 nm. (**d**) The reflection spectra with \(H_{\text{d}}\) = 120 nm.  
Where \(n_{1}\) and \(n_{2}\) are the refractive index of dielectric layer and substrate respectively, constructive interference will occur. As a result, the reflectivity of the corresponding positions will increase, which will lead to the increase of the saturation of the reflected light expected to be red. For example, when \(H_{\text{s}}\) = 100 nm, 170 nm and 270 nm, the saturation of the reflected light gets lower, as shown in Figure 7a,c,e. On the other hand, due to the existence of the multilayer interference, the spectra change periodically. For instance, the spectra at \(H_{\text{s}}\) = 140 nm and \(H_{\text{s}}\) = 230 nm are similar. When \(H_{\text{s}}\) = 140 nm, the maximum reflectivity is about 87.8% and the FWHM is about 95 nm. When \(H_{\text{s}}\)= 230 nm, the maximum reflectivity is about 88% and the FWHM is about 90 nm, as shown in Figure 7b,d.  
From the above simulations, we find that the diameter of nanodisk has a great influence on the distribution of the structural color, that is, the diameter of the nanodisk decides the hue of structural  
Figure 7: The reflection spectra of different \(H_{\text{s}}\). (**a**) The reflection spectra with \(H_{\text{s}}\) = 100 nm. (**b**) The reflection spectra with \(H_{\text{s}}\) = 140 nm. (**c**) The reflection spectra with \(H_{\text{s}}\) = 170 nm. (**d**) The reflection spectra with \(H_{\text{s}}\) = 230 nm. (**e**) The reflection spectra with \(H_{\text{s}}\) = 270 nm. (**f**) The reflection spectra with \(H_{\text{s}}\) = 300 nm.  
color, while the height of the nanodisk, the thicknesses of the dielectric layer and substrate mainly have effects on the saturation of structural color. The tilt angle has no impact on the hue and the saturation of the structural color but influence its brightness. According to this conclusion, we can obtain the colormap based on FDTD simulations by adjusting the diameter of the nanodisk from 30 nm to 210 nm and gap size \(g\) from 20 nm to 200 nm, as shown in Figure 8.