All-Dielectric Metasurface with Ultrahigh Color Filtering and Polarization-Independent/Dependent Characteristics

All-dielectric nanostructure-based color lter (CF) has attracted huge interest in many elds due to its excellent optical properties. We present four metasurface-based CFs with different shapes on quartz substrates to generate pure blue, green and red colors. CFs show maximum reection intensities of 99.6%, 99.7%, and 95.1% and the corresponding spectra bandwidths are 13 nm, 16 nm, and 14 nm for blue, green and red colors, respectively. The proposed metasurface-based CFs possess high color saturations and ultra-narrow bandwidths. In addition, metasurface-based CFs with different shapes show the tunability for color switching characteristics. These CFs designs will potentially benet reective display technologies, and their ultrahigh color ltering and polarization-independent/dependent characteristics are particularly useful for high resolution color printing, micro-LED, polarizer-switches, tunable color switches, and so on.

Since the metallic nanoparticles are pioneers employed in the nanostructure-based CFs, the plasmonic gold (Au), silver (Ag), and aluminum (Al) materials are usually used to create various CFs with different nanostructures [21,22]. However, Au and Ag materials are replaced by Al material because of the interband transition of Au in the short visible wavelength below 550 nm and the lower stability of Ag easily being oxidized and sulfureted [22][23][24][25]. Instead, Al not only shows more robust for the fabrication process and cost-effective in promising large-scale economical manufacturing, but also has broad resonance range and strong resonant intensity due to the interband transition located at the infrared (IR) wavelength of about 800 nm and near-UV wavelength range [24,25]. Although Al has such good properties, but the signi cant intrinsic ohmic losses are inevitable occurred for all-metal plasmonic nanostructures due to the material absorption of Al [22,[24][25]. Therefore, the researches on dielectric materials have been studied to overcome the defects of using superimposed metal-dielectric or all-metal nanostructures.
[25-27]. To compare with the superimposed metal-dielectric materials, all-dielectric materials are easier to be manufactured. They are low cost without metal materials and less fabrication steps. Particularly, all-dielectric CFs can generate bright and pure colors due to the low absorption loss.
Among these dielectric materials, silicon (Si) based CFs are widely investigated since it is low-cost, reliable, mature fabrication process, and facile to integrate into the optoelectronics applications [4,24].
However, Si has strong absorption in the visible wavelength range smaller than 450 nm. Therefore, SiO 2 ,   Table I. These results show that CF-1 exhibits ultrahigh color ltering characteristics in the visible spectrum.  Figure 3 shows the electric (E) eld distributions on xy-and xz-planes of RGB colors ltering characteristics in TE and TM modes for CF-1 device. For xy-plane, the E-eld energies are mainly concentrated in the gap of two nanodisks along y-direction in TE mode and x-direction in TM mode. It indicates that this resonant behavior is a dipole resonance. By increasing the resonant wavelength from blue to red spectrum, E-eld distribution appears gradually in the nanodisk. These results are corresponded with the re ection and transmission spectra as shown in Fig. 2. From the cross-sectional views (xz-plane) of E-eld distributions, E-eld energies of green and red spectra are mainly concentrated in the nanodisk for TE mode and the interface of nanodisk and substrate for TM mode. In particular, the resonant intensities of TE and TM modes are very strong for blue spectrum, which are distributed on top and bottom sides of nanodisk for TE mode and gap between nanodisks for TM mode.

Design And Method
The resonant intensity of TiO2 metasurface can be effectively enhanced by adjusting and increasing the aggregation degree of TiO2 scatterers [27]. Therefore, the structural color can be generated by using periodic TiO2 nanodisks. Moreover, the coupling effect of Mie resonances with photonic crystal radiation can help to enhance the re ection intensity and decrease the FWHM value. These effects are useful to design ultrahigh color ltering devices. In view of the theories of Mie resonances and the results in Fig. 2 and Fig. 3, the reason of minor resonances appearing in green and red spectra is owing to the increment of period, the gap between two adjacent TiO2 nanodisks also becomes larger. The numbers of Mie scatters and scattering intensity will be reduced. The enhanced e ciency of resonances is also be attenuated. Therefore, there will produce minor resonances at shorter wavelength.
To investigate the in uence of geometrical parameters of CF-1, Fig. 4(a) and (b) show the re ection spectra of CF-1 with different P and h values for green color ltering characteristic, respectively. In Fig,  4 nm under the conditions of P = 350 nm and 360 nm. They will disappear when P becomes larger. The reason is when other physical parameters determined, the amount of Mie scatters generated between CF-1 is xed. CF-1 will be more compact under the condition of smaller P value, and the Mie resonant intensity will be stronger. Therefore, it generates minor resonances at lower wavelengths. In Fig, 4(b), by increasing h value from 140 nm to 240 nm, the resonances are red-shifted and the resonant intensities are kept as stable. The minor resonances gradually appear at the wavelength of 560 nm when the h value is bigger than 160 nm. It is because of all geometrical parameters are constant except the h parameter of CF-1. The Mie scatter mode is existed and the scatters intensities are enhanced by the increasing h value, which plays an important role in the Mie resonances along with the generation of another scatter mode. These results prove that the Mie resonances of CF-1 are determined by the geometrical parameters of nanodisk. Figure 5(a-c) are the contour maps of re ection spectra of CF-1 with different incident angles for blue, green, and red colors ltering characteristics. The resonant intensities are obviously in uenced by the incident angle, which decrease gradually by increasing the incident angle. The resonant intensities are higher than 0.55 for blue spectrum that the incident angle is larger than 60°. For green and red spectra, the resonant intensity higher than 0.55 is only 30° and will be attenuated at larger incident angles. They possess stronger incident angle-dependent characteristic. The physical mechanism is that h value for blue spectrum is smaller than that for green and red spectra, the in uence of incident angle is less. Figure   5(d-f) are the contour maps of re ection spectra of CF-1 with different polarization angles for blue, green, and red colors ltering characteristics. All resonant intensities are stable by changing polarization angles. It indicates that the CF-1 device is polarization-independence due to the symmetrical structure of CF-1.
This highly polarization-independent characteristic is one of the key performance indicators of modern display technologies. Figure 6 shows the re ection intensities of CF-2 with different r values for RGB colors ltering characteristics. Due to the nanoring structure of CF-2 is symmetric and similar to that of CF-1, CF-2 also possesses polarization-independent characteristic. For RGB spectra, when r value increases to a certain amount, the re ection intensities start to decline gradually. It is because the increment of r value will reduce the resonant area and then attenuate the effect of E-eld coupling accordingly. The inserted E-eld images indicate the re ection intensities of blue and green colors ltering characteristics are stronger than that of red color ltering characteristic due to the smaller physical parameters to constitute more compact TiO 2 nanoring. Therefore, the coupling effect of E-eld is stronger and then resulted in the higher re ection intensities. Figure 7 shows the re ection intensities of CF-3 with different d values for RGB colors ltering characteristics in TE and TM modes. By increasing d values, all re ection intensities decrease rstly and then increase nally. The d value increases until to be tangent to the adjacent split-disk, there will generate new Mie scatters that as same as the original ones and then have the same resonant intensity. It can be found that the same trends for both TE and TM modes, but the resonant intensity recovers to the highest intensity in TM mode is relatively smaller than that in TE mode. The reason is the E-eld coupling effect in TM mode is smaller than that in TE mode. However, the amount of Mie scatters is almost the same for both modes, which will generate the same resonances. Figure 8 illustrates the re ection spectra of CF-4 with different α values for RGB colors ltering characteristics in TE (Fig. 8(a-c)) and TM (Fig. 8(d-f)) modes. By increasing α value, the empty area of CF-4 increases. The E-eld energy con ned within the fan shape decreases gradually and then resulted in a re ection intensity decrease for blue, green, and red colors ltering characteristics, respectively. All re ection intensities in TE mode ( Fig. 8(a-c)) are stronger than those in TM mode (Fig. 8(d-f)) due to the Eeld distributions of TE resonance is larger than those of TM resonance as the inserted E-eld images shown in Fig. 8. Particularly, when α = 30°, there is a signi cant difference in the re ection intensity between TE mode and TM mode. Such results mean that CF-4 has certain polarization-dependent characteristics. In addition, the resonances are almost stable not changed by increasing α value in TE and TM modes.

Conclusion
In     Re ection intensities of CF-3 with different d values for (a) blue, (b) green, and (c) red colors ltering characteristics in TE and TM modes.