## 4 Application for Color Display  
In this section, we used silicon nanodisks to realize the display of the letter T in different colors. From the results in Section 3, we know that the diameter of the nanodisk has a great influence on the hue of the structural color, while the height of the nanodisk, the thicknesses of dielectric layer and substrate mainly affect the saturation of the structural color. Therefore, the letter T with different colors can be obtained by only changing the diameter of nanodisk \(D\) and keeping the height of nanodisk and the thicknesses of the dielectric layer and the substrate at their optimal values (130 nm, 70 nm and 140 nm, respectively). Here, the letter T consisted of 6300 nanostructure unit cells and every nanostructure unit cell is the same as the one shown in Figure 1. The horizontal part of the letter T was made up of 50 rows \(\times\) 75 columns of nanodisks, and the vertical part of the letter T consisted of 50 rows \(\times\) 51 columns of nanodisks. We set the diameter of every nanodisk at 190 nm, the gap size between nanodisks to be 100 nm, and obtained a red letter T. A part of the corresponding red reflection spectra is shown in Figure 9a. By adjusting the diameter of the nanodisk to 115 nm and the gap size between nanodisks to 175 nm, we obtained a green letter T. A part of the green reflection spectra is shown in Figure 9b. By adjusting the diameter of the nanodisk to 100 nm and the gap size between nanodisks to 90 nm, the blue letter T was obtained. A part of the blue reflection spectra is shown in Figure 9c. In the above simulations, the boundary conditions in x and y directions are periodic, and in the z directions are PML.  
As the amount of the simulation calculation is too large to be performed by our workstation, the incident wavelength was divided into several segments. Taking the red letter T as an example, the wavelength of the incident light is between 600-680 nm in Figure 9a, and the reflectivity is greater than the other wavelength according to the simulation. Due to using the same parameters, the letter T has the same reflection spectra as the individual nanostructure, and the color of the letter T would be the same as that of the individual nanostructure. From the reflection spectra simulated in Section 2, we can obtain the color of individual nanostructure by calculating the chromaticity coordinate. After, we can get the dyeing diagram of different color letter T by recoloring the electric field distribution diagram obtained from the monitor in FDTD Solutions, as shown in Figure 10.  
Figure 8: The colormap based on FDTD simulations. \(D\) varies from 30 nm to 210 nm, \(g\) varies from 20 nm to 200 nm.  
Figure 10: _Cont._  
Figure 9: The corresponding reflection spectra of the letter T with different nanostructures. **(a)** The reflection spectra of letter T with \(D\) = 190 nm and \(p\) = 290 nm for every nanostructure, \(\lambda\) varies from 600 nm to 680 nm. **(b)** The reflection spectra of letter T with \(D\) = 115 nm and \(p\) = 290 nm for every nanostructure, \(\lambda\) varies from 500 nm to 560 nm. **(c)** The reflection spectra of letter T with \(D\) = 100 nm and \(p\) = 190 nm for every nanostructure, \(\lambda\) varies from 450 nm to 510 nm.  
Based on the above results, we know that these letter Ts composed with different nanostructures have a good reflection on the corresponding wave band. In other words, the simulated color of the letter T with different structural parameters is consistent with what we expected.