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Abstract
Dynamic color tuning has significant application prospects in the fields of color display, steganography, and information encryption. However, most methods for color switching require external stimuli, which increases the structural complexity and hinders the applicability of front-end dynamic display technology. In this study, we propose polarization-controlled hybrid metal-dielectric metasurfaces to realize full-color display and dynamic color tuning by altering the polarization angle of incident light without changing the structure and properties of the material. A bidirectional neural network is trained to predict the colors of mixed metasurfaces and inversely design the geometric parameters for the desired colors, which is less dependent on design experience and reduces the computational cost. According to the color recognition ability of human eyes, the accuracy of color prediction realized in our study is 93.18% and that of inverse parameter design is 92.37%. This study presents a simple method for dynamic structural color tuning and accelerating the design of full-color metasurfaces, which can offer further insight into the design of color filters and promote photonics research.
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1. Introduction
Structural colors generated by the interaction between the incident visible light and periodic nanostructures have attracted extensive interest in the fields of color display [1–4], information encryption [5,6], and high-efficiency color filters [7]. As structural colors with high saturation and brightness largely depend on the nanostructure size and arrangement, they can be designed by altering the geometric size of the nanostructure [8–13]. However, most structure-dependent colors lack post-fabrication tunability, limiting their practical application in several fields. Furthermore, the automatic tuning of structural colors across the entire visible spectra remains a challenge.
Several studies have attempted to realize the structural color tunability of metasurfaces using phase change materials [14,15], electrochromic polymers [16], and stretchable elastic substrates [17]. Duan et al. [15] developed a multistate optical system based on VO2, a phase change material, and realized a dynamic optical display by altering temperature and modulating with different dopants. Along with changing the chemical properties of the material, Tseng et al. [17] proposed color change through the reconstruction of the nanostructure arrangement by mechanically stretching a PDMS elastomeric substrate. However, this requires external stimuli, increasing the difficulty of practical operation. It was demonstrated that structural colors could be changed by changing the polarization angle of the incident light without any external stimuli [18–25]. Kim et al. [20] introduced an active metasurface that used different incident polarization angles to selectively excite different plasma nanorods for dynamic color switching. Based on the principle of primary color mixing, Feng et al. [25] designed three different primary color modules using polarization-related plasma nanoantenna with different sizes and directions. Each primary color module dominated at a specific polarization angle, and the colors presented by the other polarization angles were a mixture of the three primary colors.
Currently, the design scheme for structural colors mainly depends on electromagnetic simulation. Spectral calculation is performed using parameter sweep and manual trial and error, which is time consuming and requires high computing power, resulting in large errors in the target color [26]. A wide range of colors is required in fields such as color printing and image display. Multiple structural parameters need to be adjusted to display millions of different colors to ensure that practical application requirements are satisfied. However, for structures with mixed design parameters such as the period, shape, and size, it is difficult to establish a large database within a short period using traditional electromagnetic simulation technology [27,28]. Therefore, deep learning, which has been extensively used in face recognition and image processing, has become a powerful tool for solving large amounts of computing problems. In all aspects of nanophotonics, deep neural networks have made remarkable progress in fields such as spectral prediction, structural design, and structural color prediction [29–36]. Gao et al. [29] trained a bidirectional deep neural network to realize a panchromatic display by altering the geometric parameters of silicon nanostructures. The results indicated that the accuracy of inverse prediction exceeded 95%. Long et al. [31] established an inverse neural network to learn the relationship between photonic crystal geometric parameters and the Zak phase, and obtained the required photonic crystal structure. Sajedian et al. [32] adopted deep Q-learning technology to optimize the structural parameters of silicon nanoblocks in each step. Geometric properties that could generate purer red, green, and blue colors were found.
However, the aforementioned technology for realizing full-range dynamic color tuning requires the material properties to be changed, which increases the cost and structural complexity. Utilizing the polarization sensitivity of rectangular nanostructures, this study proposes hybrid metal-dielectric metasurfaces for color tuning through polarization regulation to achieve a wider color gamut compared to the sRGB color space. Only employing polarization control without external stimulation to realize color tuning on fixed structures is very beneficial for applications such as information encryption and active camouflage. At the same time, the expansion of color space can accelerate the application of advanced display in different scenes. Furthermore, to accurately predict the structural colors of numerous nanoblocks, relatively few electromagnetic simulation data sets are used for training a bidirectional deep neural network to predict the color generation, and the geometric parameters required are inversely designed based on the target colors. Compared with the complex electromagnetic simulation process and the single color of the fixed structure, this study combines the deep learning model with the color tuning realized by varying incident polarization angle, which provides a convenient method for the inverse design of the structural colors and a simple way to realize the color tuning. This provides a reference for the design of structural colors and can be beneficial for practical applications such as color-tunable printing, image dynamic display, and information anticounterfeiting.
2. Structure and design
Owing to the polarization sensitivity of rectangular nanoarrays, the resonance wavelength shifts with the variation in the polarization angle, resulting in several different colors, thereby, dynamic tuning of structural colors can be realized. In this study, we propose a method for the dynamic display of color utilizing the polarization sensitivity of hybrid metal-dielectric metasurfaces, which was first proposed by Yang et al. [37], as shown in Fig. 1(a). The metasurfaces comprise Al, Si3N4, and SiO2 layers from top to bottom, where Si3N4 and Al nanoblocks are successively deposited on a glass substrate. Electromagnetic simulation of the nanostructure models is performed using FDTD simulation software. To ensure the accuracy of the calculation results, we conduct model verifications, as shown in Supplement 1, Fig. S1. Based on the verification cases above, the method used in this work can reliably calculate the spectral properties of metasurfaces. A periodic array structure is vertically irradiated by a plane wave source with a wavelength range of 360-830 nm. For periodic array simulations, periodic boundary conditions are used along X-direction and Y-direction. Perfectly matched layers (PMLs) are used for the top and bottom boundaries, which are perpendicular to the propagation direction. The material data for Al, Si3N4, and SiO2 are obtained from Palik [38]. The thicknesses of the Al and Si3N4 layers are 60 nm and 150 nm, respectively, according to previous research [37]. To investigate the influence of the polarization angle (φ) of the incident light on color tuning, the gaps (Gx, Gy) represent the difference between the period (P) and the width (W) of the nanoblocks, i.e., Gx = P – Wx and Gy = P – Wy. After several trial calculations in the early stage, the range of P, Gx, Gy, and φ are set as 260-420 nm, 80-200 nm, 80-200 nm, and 0-90°, respectively. The specific details of the dataset are shown in Supplement 1, Table S1. We use the finite-different time-domain method to simulate 6160 samples with different parameter combinations.
Fig. 1. (a) Schematic of nanostructures with period (P) and gap (Gx, Gy). (b) 6160 colors produced by the hybrid metal-dielectric metasurfaces in the CIE 1931-XYZ chromaticity diagram.
To comprehensively demonstrate the color properties of the simulation results, we first calculate the tristimulus values according to the following equation [39]:
The CIE 1976-Lab color space is consistent with CIE 1931-XYZ, but it is more suitable for accurately identifying color difference color space, where L represents the brightness, a represents the redness (+) and greenness (−), and b represents the yellowness (+) and blueness (−) [33]. The conversion relation between (X, Y, Z) and (L, a, b) is stated as [40]:
with Xn, Yn and Zn being the tristimulus values of a reference white object:For the standard illuminant D65 and a 2° standard colorimetric observer they amount to Xn = 95.049, Yn = 100 and Zn = 108.891. The CIE 1976-Lab color space is more suitable for identifying the color difference function ΔE [40]:
All the colors obtained are plotted in the CIE 1931-XYZ chromaticity diagram, as shown in Fig. 1(b). The color gamut formed is expected to exceed the standard color space (sRGB). We observe the complex relationship between the structural color and polarization angle, and the metasurfaces comprising rectangular nanoarrays expand the color gamut coverage in the CIE chromaticity diagram, compared to those in previous reports.
3. Results and discussion
3.1 Structural colors of hybrid metal-dielectric metasurfaces
Strong coupling between the metasurfaces and incident light produces resonance in the transmission spectra, and the resonance wavelength is closely related to the structural colors. Alteration of the nanoarray size and arrangement period leads to a shift in the resonant wavelength. In this study, we focus on the influence of the nanoblock size and arrangement period on the structural colors of the hybrid metal-dielectric metasurfaces.
To analyze the effect of the nanoarray size on the structural colors, we calculate the spectral transmittance of different nanostructure gaps in three different periods and plot the corresponding structural colors. Here, the polarization angle of incident light φ is fixed at 0°. The results show that certain special rules govern the relationship between the colors and the gap of unit cells. As shown in Figs. 2(a)-(c), the color changes significantly as Gx increases from 80 to 200 nm when Gy is fixed. Conversely, when Gx is fixed, the color shows a constant trend. Figures 2(d)-(i) present the spectral transmittance contours of nanoarrays with a fixed period and varying gaps. It can be observed that Gx and Gy have different degrees of influence on the transmission spectra. The position of the resonance peak in the transmission spectra is considerably sensitive to the change in Gx, whereas it hardly shifts with the variation in Gy, which is consistent with the color change mentioned earlier. This can be attributed to the fact that when the incident polarization angle is 0°, the vibration direction of polarized light is the X-direction. Therefore, the interaction between the incident light and nanoblocks is more intense owing to the change in the spacing of the structural units along the X-direction. Simultaneously, when Gx increases, the width of the resonance peak expands, degrading the purity of the transmission color. For nanoblock gaps below 120 nm, the resonance peak is narrow, and its intensity is large, resulting in higher purity and brighter colors. However, when Gx is beyond 180 nm, the transmitted light appears white in Fig. 2(a). As shown in Supplement 1, Fig. S3, when Gx = 180 nm, the transmittance exceeds 0.7 for light with a wavelength greater than 500nm. Especially, when Gx is fixed at 200nm, the transmittance of almost all visible light exceeds 0.7, which will cause the visible light of various colors to be fully mixed and finally appear white.
Fig. 2. Generated colors of the hybrid metal–dielectric metasurfaces for different periods with (a) P = 270 nm, (b) P = 330 nm, and (c) P = 390 nm. Spectral transmittance contours of the colors with (d) P = 270 nm, Gx = 80 nm, and different Y-direction intervals, (e) P = 330 nm, Gx = 80 nm, and different Y-direction intervals, and (f) P = 390 nm, Gx = 80 nm, and different Y-direction intervals. Spectral transmittance contours of the colors with (g) P = 270 nm, Gy = 80 nm, and different X-direction intervals, (h) P = 330 nm, Gy = 80 nm, and different X-direction intervals, and (i) P = 390 nm, Gy = 80 nm, and different X-direction intervals.
To directly compare the influence of the period on the structural colors, we plot the chromaticity coordinates of different periods in the CIE 1931-XYZ chromaticity diagram, as shown in Figs. 3(a)-(c). Figures 3(d)-(f) illustrate the simulated transmittance spectra of the hybrid metal-dielectric metasurfaces, whereas Figs. 3(g)-(i) show the corresponding color property parameters L, a, and b of the generated colors. As shown in Figs. 3(a)-(c), the hue of the colors gradually varies from purple to red with the increase in the period from 260 to 400 nm in 20 nm increments. Simultaneously, as the gap between the nanoblocks increases, the color coverage caused by the period gradually decreases. When the gaps in the X and Y directions are 80 nm and 200 nm, respectively, the color coverage is consistent with the standard color space (sRGB). Increasing the period while maintaining the other variables unchanged causes the resonance wavelength to shift toward a longer wavelength, as shown in Figs. 3(d)-(f). When Gy increases from 100 nm to 200 nm for a small period, the width of the resonance peak increases drastically, deteriorating the color purity. When the gap size is set to 80 and 100 nm, respectively, the transmission spectra exhibit a high-monochromatic resonance peak, which produces high saturation structural colors. Figures 3(g)-(i) present the trend of the color properties with the period. The change trend of the brightness L is relatively stable and shows an increasing trend before decreasing. However, the periodicity of the nanoblocks has significant impact on the chromaticity. The maximum change values of chromaticities a and b are above 100. The chromaticity value of the structural color is consistent with the change trend of the period.
Fig. 3. Structural colors with the increase in the period from 260 to 400 nm in increments of 20 nm. Chromaticity coordinates for different periods with (a) Gx = 80 nm, Gy = 100 nm and φ = 0°, (b) Gx = 80 nm, Gy = 160 nm and φ = 0°, and (c) Gx = 80 nm, Gy = 200 nm and φ = 0°. Corresponding changes in the (d–e) transmittance and (g–i) color properties.
3.2 Dynamic color tuning by varying the polarization
The preceding sections describe the change trend of the structural colors with the structural geometric characteristics. It is worth noting that the color display of a metasurface is fixed when processed and produced. From the perspective of cost savings, it is crucial to continuously and accurately control the color. With the vigorous development in manufacturing and the development of new materials, research on the dynamic tuning of structural colors has made remarkable progress. Various chemical and physical methods can enable panchromatic tuning by altering the properties of the structural units. In addition, dynamic color tuning can be realized by altering the incident polarization angle while maintaining the surrounding environment and metasurface property unchanged.
Figure 4 shows the transmission spectra, color coordinates, and color properties (L, a, b) of metasurfaces having three different geometric parameters, with the variation in the incident polarization angle. It can be observed that incident polarization angle variation leads to a shift in the resonant wavelength position. As shown in Fig. 4(a), when the incident polarization angle φ varies from 0° to 45°, the resonant wavelength shifts towards a longer wavelength, and the structural colors gradually change from blue to purple. However, when φ continues to increase from 45° to 90°, the spectral transmittance with a wavelength of more 600 nm gradually increases, and the structural colors change gradually from purple to red. The corresponding color properties, ΔL = 30.36, Δa =−20.94, and Δb = 92.91, are depicted in Fig. 4(e). As shown in Figs. 4(b) and (c), the structural colors gradually vary from green to blue and yellow to green, respectively. Similarly, the spectral transmittance corresponding to a long wavelength increases as the polarization angle increases, degrading the color purity. The corresponding color property changes are ΔL = −11.34, Δa = −76.63, and Δb = −58.99 and ΔL = −6.56, Δa = −79.88, and Δb = −37.57, respectively, as shown in Fig. 4(e). Figures 4(a)-(c) show that the spectral transmittance in the red wavelength region rises significantly with the increase of polarization angle. As shown in Supplement 1, Fig. S3, when the wavelength is fixed at 830nm, the resonance between light and the nanoarray gradually weakens with the increase of polarization angle, which contributes to the decreasing absorption of the nanoarray. Therefore, the energy passing through the nanoarray increases due to the decrease of nanoarray absorption and spectral reflectance. Figure 4(d) presents the chromaticity coordinates corresponding to the structural color change caused by the polarization angle. The specific chromaticity coordinate values (x, y) of each color are shown in Supplement 1, Fig. S4. Furthermore, by matching different geometric parameters, the structural colors can be dynamically tuned in the entire range of visible light by varying the incident polarization angle.
Fig. 4. Multiple color generation based on the color switching mechanism of incident light polarization. The geometric parameters of the generated structural colors are (a) P = 270 nm, Gx = 80 nm, Gy = 140 nm, (b) P = 310 nm, Gx = 80 nm, Gy = 140 nm, and (c) P = 380 nm, Gx = 80 nm, Gy = 200 nm. φ in (a), (b), and (c) varies from 0° to 90°in 15° intervals. (d) Change in the chromaticity coordinates corresponding to the structural colors. (e) Color properties corresponding to the structural colors.
Additionally, the results indicate that the polarization angle of the incident light mainly affects the chromaticity value of the hybrid metal-dielectric metasurfaces, and the brightness L remains almost unchanged. At a small polarization angle, the resonance peak width of the transmission spectra is narrow and the transmission color has high-color purity. When the polarization angle becomes larger, multiple resonances appear in the transmission spectra, and the structural color purity decreases.
To further analyze the effect of the incident polarization angle on the structural colors, the color saturation ${C_{\textrm{ab}}} = \sqrt {({a^2} + {b^2})}$ [41] is introduced and discussed. Figure 5(a) shows the saturation of the generated colors as a function of the polarization angle for different periods. Note that the gaps are Gx = 80 nm and Gy = 200 nm. The color saturation Cab initially decreases and then increases with the increase in the polarization angle and is more intense for small periods. Moreover, when the polarization angle is fixed at 0 °, the color saturation is the highest. Figure 5(b) shows the Cab of different geometric parameters when P = 320 nm, and Gx = 80 nm. When Gy increases from 100 nm to 140 nm, the color saturation gradually decreases with the polarization angle; however, the overall saturation remains high. When Gy changes from 160 nm to 200 nm, the color saturation initially decreases and then increases; however, the overall saturation is low. This indicates that the polarization angle significantly impacts the color properties. When the gap between the structural units is large, variation in the polarization angle generates a wide range of color changes. However, the color saturation is relatively low.
Fig. 5. Variation of the saturation with the polarization angle φ: (a) Saturation for a fixed structural unit size and (b) saturation for a fixed structural unit period.
Overall, by changing the four selected design parameters, the color gamut space is expanded, and dynamic color tuning is realized. However, the structural colors simulated through electromagnetic simulation are only a part of the color gamut space. If a database is to be generated for practical application, the amount of data required would increase exponentially. Therefore, it is impractical to simulate such large amounts of data through traditional calculation methods.
3.3 Direct color prediction
The recent deep learning technology can improve the calculation speed by several orders of magnitude by establishing a neural network and determining the complex relationship between the training data and the prediction parameters. In this study, a forward neural network that comprises an input layer, multiple hidden layers, and an output layer is established to accurately predict the structural colors generated by the metasurfaces, as shown in Fig. 6(a). It is necessary to simulate a certain amount of data in the early stage to predict the structural colors using a neural network. Initially, in a dataset with 6160 groups, 4928 groups are used as the training set to train the forward neural network, 616 groups are used as the verification set to check the training effect, and the remaining 616 groups are used as the test set to verify the accuracy of the neural network. The mean square error (MSE) between the predicted value (Lpredicted, apredicted, bpredicted) and the true value (Ltrue, atrue, btrue) is defined as the loss function:
Fig. 6. Forward neural network for color prediction. (a) Input layer, multiple hidden layers, and output layer of the forward neural network, (b) loss functions of the training and validation sets, (c-e) test data comprising 616 groups presented in the scatter plot of the true colors (L, a, b) and predicted colors (L’, a’, b’), (f) ΔE between the predicted colors and true colors, and (g) proportion of different color difference distributions in the test set.
The average test loss of the forward neural network and the probability of ΔE ≤ 1 in different layers are plotted in Supplement 1, Fig. S5. Evidently, when the number of layers of the neural network reaches eight, the error reaches a minimum of 0.57. Therefore, after fixing the number of hidden layers at eight, we analyze the influence of the number of neurons in each layer on the performance of the neural network. When the number of neurons in each hidden layer is 1100, the average test loss decreases to 0.16, and the probability reaches 93%. Furthermore, we consider the impact of the batch size on the performance of the neural network in Supplement 1, Fig. S5. The results show that the performance of the neural network is the best when the batch size is 28. After a series of hyperparameter tuning, the forward neural network is finally optimized with 8 hidden layers, with each hidden layer comprising 1100 neurons, and the size of the batch is 28.
As shown in Fig. 6(a), we consider the structural parameters (P, Gx, Gy) of the metasurfaces and the incident polarization angle (φ) as the input layer and the color properties (L, a, b) as the output layer. The neural network uses training data to continuously alter the connection weight during the training process. With continuous training, the error gradually decreases until it reaches convergence. As shown in Fig. 6(b), the loss function of the training and verification sets gradually decrease with the increase in the number of epochs. After 4000 epochs, the training and verification loss values decrease to 1.483 × 10−5 and 0.109, respectively. We use 616 groups of untrained data as the test set, and compare the simulated color properties (L, a, b) with the color properties (L’, a’, b’) predicted by the forward neural network, as depicted in Figs. 6(c)-(e). The results demonstrate that only a few predictions deviate from the true value within a small range, and most of the initial true values are highly consistent with the values predicted by the forward neural network. To further explore the accuracy of the forward neural network, we plot the color difference function ΔE between the predicted and true colors in Figs. 6(f) and 6(g). The data with ΔE ≤ 0.5 accounts for 70.78% of all data, and the probability of 0.5 < ΔE ≤ 1 is 22.4%. As mentioned above, when ΔE ≤ 1, there is no color difference. Therefore, the prediction accuracy of the forward neural network is 93.18%, the probability of 1 < ΔE ≤ 5 is 6.49%, and ΔE > 5 for only a few predicted values. We plot three groups of colors with ΔE > 1 (Fig. 6(g)). The results indicate that although the color difference function of these three groups is large, it is not distinguishable by the human eye. In conclusion, the neural network can predict the structural colors with high-accuracy, significantly reducing the computational cost of electromagnetic simulation and facilitating practical application.
3.4 Inverse design prediction from the colors
Owing to the increasing requirements of structural color design, the inverse design of metasurfaces has attracted wide interest. However, the nonuniqueness of inverse design renders it more complex than the design of the forward neural network. A bidirectional neural network with tandem autoencoder architecture is effective for solving the nonuniqueness problem [43,44]. Figure 7(a) shows the bidirectional neural network structure. The target colors (L, a, b) are the input, and the design parameters (P, Gx, Gy, φ) are the output, denoted as the intermediate layer. These four parameters are input into the trained forward neural network to output the predicted color value (L’, a’, b’). The MSE between the target color properties and the design color properties is considered as the loss function. After continuously minimizing the loss function, the optimal inverse network architecture is determined as 8 hidden layers, with 200 neurons in each hidden layer, as shown in Fig. 7(a). Figure 7(b) depicts the values of the training and validation losses in the training process. The losses decrease gradually when the number of epochs is small. As the number of epochs increases, the decrease in these losses is steep at first and then slows down. After a sudden drop at the 200th epoch, the downward trend of the loss function gradually slows. A precipitous decline at 200th epoch is due to the removal of the inverse error term (the mean square error between the original structural parameters and predicted structural parameters) in the loss function. Finally, at the 2000th epoch, the training and validation losses are 1.62 × 10−5 and 0.10, respectively. As the test set to verify the accuracy of the inverse design process, 616 groups of unused data were used. As shown in Figs. 7(c)-(e), the target colors are consistent with the design colors. The color difference value and its probability distribution are plotted in Figs. 7(f) and 7(g), respectively. The total of 569 color difference values is less than 1, indicating that the proposed bidirectional neural network for color prediction has an accuracy of more than 92.37%. Meanwhile, we plot three groups of colors with ΔE > 1 (Fig. 7(g)). The results show that it is almost difficult to distinguish the color difference with human eyes, which also proves the reliability of our model. Overall, compared with the electromagnetic simulation calculation that takes about several weeks, after the training of the bidirectional neural network model, the color prediction and inverse design only take a few seconds, which can greatly reduce the cost and time of color design. The detailed training process of neural network and FDTD simulation parameters are described in Supplement 1.
Fig. 7. Bidirectional neural network for color prediction. (a) Bidirectional neural network with an input layer, multiple hidden layers, and the pretrained forward neural network, (b) loss functions of the training and validation sets, (c-e) test set comprising 616 groups presented as a scatter plot of the target colors (L, a, b) and designed colors (L’, a’, b’). (f) ΔE between the target and designed colors, and (g) proportion of different color difference distributions in the test set.
To demonstrate the panchromatic display of the model and verify the accuracy of the bidirectional neural network, we select seven target colors (red, orange, yellow, green, blue, and purple) and determine the design colors, as shown in Fig. 8(a). It is difficult to observe the difference between the designed and target colors with the naked eye. The specific design parameters corresponding to the colors are shown in Supplement 1, Fig. S6. Figure 8(b) shows a photograph of the Qingdao Campus library in Shandong University; we extract the color values of all the 1080 × 605 (653400) color pixels in the original photo and input them to the bidirectional neural network. Thereby, the design geometric parameters of all the pixels are obtained, and the generated color drawing is shown in Fig. 8(c). The color difference function ΔE distribution of each pixel in the picture and the inverse designed photo after the polarization angle is rotated 90° are shown in Supplement 1, Fig. S7. We can see that the inverse designed colors by our bidirectional neural network are extremely accurate for most pixels. If the color brightness value is large, it is difficult for the hybrid metal-dielectric metasurface to present the color and the real value. However, identification of the difference between the two images is difficult with the naked eye, proving the accuracy of our bidirectional neural network in designing a wide gamut of colors. Simultaneously, when the incident polarization angle is rotated 90° as shown in Supplement 1, Fig. S7, the overall color of the photo changes greatly. However, the features in the photo can still be distinguished, which also reflects the superiority of our neural network in color design.
Fig. 8. Practical application of structural color inverse design. (a) Color display of the target and designed colors, (b) designed color photo, and (c) inverse-designed structural colors of the photo.
4. Conclusion
Inspired by the polarization sensitivity of rectangular nanostructures, this study proposed polarization-controlled hybrid metal-dielectric metasurfaces. The range of the color space is expanded by altering the structural parameters of nanoarrays and incident polarization angle. The color gamut coverage can exceed the RGB color space and dynamic tuning of structural colors can be achieved in the visible range, which will accelerate the application of color display in different fields. To minimize the cost of electromagnetic simulation, deep learning technology is used instead of the traditional trial-and-error strategy, and a bidirectional neural network is established using 6160 groups of simulation data. According to the color recognition ability of human eyes, the proposed neural network can achieve an accuracy of the 93.18% and 92.37% for the prediction of structural colors and the inverse design of geometric parameters, respectively. Our findings are beneficial in eliminating simulation steps, accelerating the structural color design process, exploring a larger color space, and can contribute to practical display applications.
Funding
National Natural Science Foundation of China (51906127, 52076123); China Postdoctoral Science Foundation (2019M662353, 2020T130365, 2021T140401); Young Scholars Program of Shandong University.
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 may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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