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Abstract
In this paper, we proposed a double-layer all-dielectric grating. Under the premise of ensuring the strength of the resonance peak, the upper SiO2 grating layer suppresses the tendency of high-order dipole resonance excitation and improves the transmittance at the non-resonant position (T > 99%). The distribution of chromaticity coordinates on the CIE 1931 chromaticity diagram also proves that suppressing side peaks can effectively increase the saturation of structural colors, which is essential for a high precision imaging system. The cyclic displacement current excites the magnetic dipole resonance, which causes the magnetic field to be confined in the high refractive index material HfO2 grating layer. By adjusting the duty cycle of the grating structure, a reflection spectrum with low full width half maximum (FWHM) (∼2 nm) and high-quality factor Q (∼424.5 nm) can be obtained. And the spectral intensity is more sensitive to the polarization angle. This work is of great significance to the development of sensors, display imaging and other fields. At the same time, the material of the grating filter meets the requirements of high damage threshold of the high-power laser system, and its high-power laser application potential is inestimable.
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1. Introduction
The metasurface structure can flexibly regulate the phase, polarization, and amplitude of electromagnetic waves. This resonant optical mode supported by the structure gives them the ability to manipulate light at the nanometer scale [1–3]. A series of strange electromagnetic responses can be achieved by optimizing the metasurface structure, including negative permeability [4], negative refractive index [5,6], zero refractive index [7], perfect reflector [8]and perfect absorber [9–11]. With these excellent electromagnetic characteristics, the metasurface structure shows considerable application prospects in metalens [12,13], holographic imaging [14,15] and absorber [16,17]. In the research and development process of metasurface structures, only relatively few plasma metasurface structures are used in actual equipment. One of the important factors is that the sub-wavelength metal structure locally heats the structure and the surrounding environment through the Joule heat generated by light absorption, which eventually causes irreversibility damage. Compared with metal materials, dielectric materials have less inherent loss and have good compatibility with COMS. The high refractive index and low loss all-dielectric metasurface structure breaks the diffraction limit and realizes light manipulation, while having the advantages of high radiation efficiency and suitable bandwidth [18]. This makes the all-dielectric metasurface material become one of the current hot topics.
Color is the most important research direction in the field of optics, which is the carrier of natural visual information. The quality of colors is determined by factors such as hue, brightness, and saturation [19,20]. Traditional color dyes are difficult to adapt to harsh environments, and some may even cause environmental pollution or induced cancer. The plasma metasurface or dielectric metasurface can achieve full-tone modulation in the visible range [21–24]. This kind of structural color has the advantages of high resolution and good stability. In the process of regulating the structure parameters of plasma metasurface, absorption is unavoidable, which significantly reduces the saturation of the structural color. Some researchers proposed to use high refractive index materials (such as Si, TiO2 and Si3N4, etc.) to achieve strong dipole resonance, and then replaces the high loss plasma metasurface structure. Structures such as nano-blocks [25,26], cross-shaped [27], nano-prisms [28], and nano-disks [29–31] are used as periodic unit in the array of metasurface structures for color imaging. Although these structures all have excellent performance, the presence of high-order modes in a relatively short wavelength range prevents further improvement of the color saturation. To solve this problem, Jhen-Hong Yang et al. designed the feature size of Si3N4 nano-block structure and used Rayleigh anomalies (RAs) to suppress high-order Mie resonance in the short wavelength range. Although this method effectively suppresses the influence of high-order mode, it still can be improved in the suppression of side peaks [26]. Bo Yang et al. added SiO2 and Si3N4 structures above and below the TiO2 nano-blocks to suppress high-order mode at non-resonant wavelengths, but the additional layers increased the difficulty and cost of the nano-fabrication process [32]. Therefore, proposing a feasible solution to suppress high-order mode is the key to improving color saturation.
The Si3N4 grating structure proposed by Mohammad Jalalal Uddin et al., by adjusting the periodicity of the grating structure to produce unique structural colors in the visible light range, the reflectivity of non-resonant peak position in the reflection spectrum is still high [33]. Therefore, it will seriously affect the quality of structural colors. The single-layer TiO2 grating structure proposed by W. L. Wang et al., obtains high reflection peaks in the visible light range, but the average reflectivity in the long wave range is close to 0.1, and the impact on color quality cannot be ignored [34]. Considering that the sub-wavelength grating structure has the advantages of narrow bandwidth, high diffraction efficiency and excellent sideband suppression. In this article, we adopt a high refractive index HfO2 grating structure to achieve narrow bandwidth and high-quality filtering characteristics. Adding a layer of SiO2 grating structure on the HfO2 grating effectively reduces the influence of high-order modes, as shown in Fig. 1. Based on the physical mechanism of low-order dipoles in high refractive index materials, the distribution range of the reflection spectrum of the double-layer all-dielectric grating structure in the CIE 1931 chromaticity coordinate shows that its color saturation has been significantly improved. By adjusting the structure parameters of the grating, the full width half maximum (FWHM) Δλ is significantly reduced, and the quality factor Q (Q=λc/Δλ) is improved. This work shows the high potential application value of the structure in color and high-quality negative filter.
2. Model building and simulation
In order to accurately analyze the output spectrum of the plane wave perpendicular to the all-dielectric grating, we use the commercial software Lumerical FDTD Solutions to simulate the grating structure. The normal X-polarized incident light propagates along the negative Z-direction. Set the X and Y axes in the simulation area as periodic boundary conditions. In order to eliminate echo interference, the Z axis is set to a perfect matching layer (PML). High grid accuracy is used to ensure the convergence of the simulation structure (mesh accuracy = 6). The structural size is suitable for the current miniaturized and lightweight optical system. The period, size, duty cycle and thickness of each layer of the grating structure are defined as P, D, R (R = D/P), H1 (HfO2), H2 (SiO2), respectively. Through a large amount of data analysis, the fixed duty cycle R = 4/7 and H1 (HfO2) 140nm are more effective and used to analyze the all-dielectric grating.
In order to analyze the influence of the metasurface structure parameters on the final response, each dielectric layer is discussed separately. First, the reflection spectrum of a single HfO2 dielectric grating in the visible range with different sizes D (sweep from 140nm to 240nm) is explored. The reflectance is plotted as a function of grating size D and wavelength λ, as shown in Fig. 2(a). In Fig. 2(a) and Fig. 4(a) we have modified the maximum value of the scale bar to 0.2, thus clearly highlighting the suppression of high-order mode by the SiO2 dielectric grating layer. Comparing the reflectance spectra of different grating sizes in Fig. 2(b), the trend of the influence of high-order mode in the short-wave range becomes more obvious. When the grating size exceeds 210nm, the reflection peak intensity gradually decreases, which will inevitably affect the color quality. In the long-wave red color range, the quality of the color is affected by the peak intensity and the high-order mode. Therefore, while suppressing high-order mode, the increase in peak intensity should also be considered.
Fig. 2. (a) Sweeping reference diagram of a single HfO2 dielectric grating size; (b) reflectance curve when grating size D is 150 nm, 160 nm, 170 nm, 180 nm, 190 nm, 200 nm, 210 nm, 220 nm, 230 nm, 240nm.
Besides, we prepare the same size SiO2 grating on the HfO2 dielectric grating. In order to illustrate the role of SiO2 grating in the total spectral response, Lumerical FDTD Solutions is used to simulate the thickness H2 of SiO2 layer (sweep from 0 nm to 200 nm). The reflectance data was plotted as a function of the thickness of the SiO2 grating and the wavelength λ, as shown in Fig. 3(a). The peak position of the reflection peak only moves in a small range, and the peak reflection intensity still maintains nearly 100%. Figure 3(b) is the comparison curve of the reflection spectrum when H2 = 0 nm and 110 nm. The presence or absence of the SiO2 grating structure in the short-wave range is directly related to the development trend of high-order modes. Figure 3(b) is the comparison curve of the reflection spectrum when H2 = 0 nm and 110 nm. The presence or absence of the SiO2 grating structure in the short-wave range is directly related to the development trend of high-order mode. Choosing an appropriate thickness H2 of SiO2 grating can not only suppress high-order mode, but also improve the anti-reflection characteristics of the non-resonant band, with a transmittance exceeding 99.05%.
Fig. 3. (a) The thickness and size of the HfO2 grating are fixed, and the sweeping reference diagram of the SiO2 layer thickness H2; (b) the reflectance curves confrontation when H2 = 0 nm and 110 nm.
Under the premise of a fixed duty cycle and the thickness of each grating layer, the grating size D of the all-dielectric grating is swept, and the sweeping range is from 140 nm to 280 nm. Grating size is in the sub-wavelength length. Figure 4(a) is a sweeping parameter result diagram of structure reflectance of the all-dielectric grating relative to size D. By adjusting the size D of the grating, the peak position can be manipulated. Comparing the swept parameters of Fig. 2(a) and Fig. 4(a), the influence of the low-order mode in the upper left corner is effectively suppressed. It means that the chromaticity coordinates will cover most of the RGB area, which can provide vivid colors. Figure 4(b) shows the reflectance spectra of gratings with different D, which is in sharp contrast with Fig. 2(b). There is almost no effect on the peak position when introducing the SiO2 grating layer. In this way, it can successfully suppress the excitation of high-order mode in the short-wave region. The peak intensity in Fig. 2(b) decreases rapidly with the increase of size, which becomes a key factor that degenerate the color quality. In Fig. 4(b), it can be confirmed that the SiO2 grating suppresses the high-order mode while increasing the intensity of the low-order mode. The reflection peak of the SiO2-HfO2 grating structure remains above 99%. When the resonance wavelength of the HfO2 grating structure is greater than 525nm, the reflection peak intensity decreases rapidly, as shown in Fig. 4(c). It shows that the SiO2 grating layer effectively suppresses the high-order mode while increasing the strength of the low-order mode. This solution will effectively improve the color saturation in the visible range.
Fig. 4. (a) Diagram of sweeping SiO2-HfO2 dielectric grating size; (b) reflectance curve when grating size D = 150 nm, 160 nm, 170 nm, 180 nm, 190 nm, 200 nm, 210 nm, 220 nm, 230 nm, 240 nm; (c) Comparison curve of reflectivity at the peak position of the two grating structures.
3. Results and discussion
CIE 1931 chromaticity coordinates are a way to describe color quality mathematically. The three primary colors (RGB) can be superimposed into any color according to different quantity values. The quantity values of the three primary colors are defined as the tristimulus value (X, Y, Z). (X, Y, Z) is obtained by the CIE tristimulus value formula [32]:
Fig. 5. The distribution of the chromaticity coordinates of the two grating structures on the CIE 1931 chromaticity diagram.
In high refractive index materials, Mie resonance stimulates the production of electric and magnetic dipoles [35,36]. When the size D of the all-dielectric grating increases, a strong reflection peak appears in the spectrum, and a red shift occurs as the size D increases. The change of physical size causes the resonance position of Mie to change, which in turn affects the final response of the spectrum. In order to explore the physical mechanism of peak generation, we decided to analyze the magnetic field distribution and electric field vector distribution on the XOZ plane at the peak position. When the grating size D = 210 nm, only one reflection peak appears in the visible range, and the peak position is at λ=566 nm, as shown in Fig. 6(a). Using FDTD simulation software, we have drawn the magnetic field distribution and electric field vector distribution at λ=566 nm. In Fig. 6(b), the circular displacement current generated by the incident electromagnetic wave excites the magnetic dipole resonance, and the magnetic field is confined in the HfO2 grating structure [28,29,37]. The saturation of the structural color is destroyed because of the introduction of high-order dipole resonance in the short-wave range. Generation of unique structural colors in the visible range based on Mie resonance modes. By constructing a SiO2 dielectric grating on the HfO2 dielectric grating, the excitation of the high-order dipole mode at a shorter wavelength is suppressed, thereby enhancing the saturation of the color.
Fig. 6. (a) When the grating size D = 210 nm, the reflection spectrum of SiO2/HfO2 all-dielectric grating; (b) when the resonance peak λ=566 nm, the magnetic field distribution and electric field vector distribution of the grating structure.
Then, we extended the duty cycle to 0.95, and reswept the grating size D. Figure 7(a) is the sweeping parameter diagram of the structure size from 140 nm to 420 nm. Although the duty cycle is increased, there is still a tunable reflection peak in the visible range. At the expense of color saturation, we can get a narrow-band reflection peak with a FWHM of about 2 nm. Assuming that dielectric material has a near zero light loss, the sum of the transmittance and reflectance is equal to 1. Figure 7(b) is a comparison diagram of transmittance and reflectance when grating size D = 270 nm. High transmittance is still maintained at non-resonant wavelengths, which means that this structure can achieve high quality factor narrowband filter performance, which is suitable for the application of negative filters in the visible range. Table 1 shows the FWHM and quality factor Q under 20 groups of different grating sizes. The FWHM is maintained between 1-3 nm, and the quality factor can reach up to 424.5. It is difficult to achieve high-Q from low-order Mie resonances. By changing the structure size of the grating, multiple Mie resonances are excited in the HfO2 grating, thereby improving the quality factor Q of the reflection spectrum [38,28].
Fig. 7. (a) Sweeping parameter graph of fixed duty ratio R = 0.95, all-dielectric grating size; (b) comparison curve of transmission and reflection when grating size D = 270 nm.
Table 1. Center wavelength, FWHM and quality factor Q corresponding to different grating sizes D
At last, we also explored the effect of polarization angle on the reflection spectrum. Under the premise that the all-dielectric grating structure size D (210 nm) is fixed, the polarization angle is swept, and the sweeping results are shown in Fig. 8. With the increase of polarization angle, the peak position of the reflection peak shifts in a very small range, and the peak intensity decreases significantly. Comparing the reflectance spectrum of TM and TE polarized light, the reflectivity under TM polarized light is close to 1, and the reflectivity under TE polarized light rapidly drops to around 0.24, forming a significant difference. It has potential application for polarization separation and other fields.
Fig. 8. (a) Sweeping parameter graph of polarization angle; (b) Reflectance spectra of TM and TE incident polarized light.
4. Conclusion
In summary, we propose a kind of all-dielectric SiO2-HfO2 grating, which can realize single reflection peak regulation in the whole wavelength range in the visible range. By comparing with or without SiO2 dielectric grating, it is found that the SiO2 layer not only suppresses the tendency of a single HfO2 grating to be excited in the high-order dipole resonance in the short-wave range, but also improves the peak intensity in the long-wave range. The transmittance at the non-resonant wavelength is as high as 99%, and the saturation of the structural color is significantly improved. The chromaticity coordinates of the double-layer all-dielectric grating on the CIE 1931 chromaticity diagram occupies most of the area. This is of great significance to the development of the imaging display field. The magnetic field distribution at the peak position reveals that its physical mechanism is the magnetic dipole resonance mode. Then, it is found that increasing the duty cycle to 0.95, this structure can realize the narrowband filtering with high quality factor in the visible range, the FWHM is less than 3nm, and the quality factor Q is as high as 424.5. Finally, it is explored that the spectral intensity is more sensitive to the polarization angle, which can be applied to the polarization separation system
Funding
National Natural Science Foundation of China (61875193, 61705226).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
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