1. Introduction

Structural colors exist widely in nature such as in the wings of butterflies and birds, fish scales, and flower petals. They are the manifestations of light-matter interactions as the various tiny structures allow light to be transmitted, reflected, or scattered at certain specific wavelengths so that the transmission or reflection spectrum is modulated, giving rise to different colors [1]. With the advancement of nanofabrication technology, artificial structural colors can be made possible using metasurfaces consisting of specially designed subwavelength units (meta-atoms) in a two-dimensional plane. Metasurface shows the salient ability to manipulate electromagnetic waves at the subwavelength level, paving a new way for spectral modulation [2,3]. By designing the geometric sizes of meta-atoms, high-resolution colored nanoprinting images have been achieved with good tunability, near-permanent fade resistance, high resolution, and many other benefits [4–11]. However, these works are mostly static and only display a single color image since the meta-atoms are all in an isotropic shape.

To satisfy the demand for applications including multi-image display, information encryption, and anti-counterfeiting, the strategy of tunable structural color is proposed. Polarization as one of the fundamental properties of light waves can be adopted to customize the spectrum without changing the configuration and material properties of metasurfaces and therefore is a simple solution to achieve color tuning [12–24]. For instance, a meta-image displaying different colors has been largely investigated [12–14]. To achieve information encryption, researchers have accomplished colorful nanoprinting images that display different colored images when switching the incidence of light polarization [15–21]. In addition, by carefully designing the meta-atoms, the color nanoprinting image can be revealed under one polarization state while hidden in another [22–24]. In the abovementioned schemes, polarization serves as the only key for encryption/decryption and more specifically focused on the full visible spectrum. Optical intensity is another fundamental property of light waves, and it is largely reported that metasurface can be designed to realize the light intensity control at the subwavelength scale for a given wavelength [25–30], so that the security key can be further extended to discrete wavelengths. It is anticipated that more images will be possibly integrated into one metasurface if the broadband spectrum and optical intensity at a single wavelength can be simultaneously manipulated. However, among the work that has been reported, there are few image display devices that combine spectral modulation with intensity modulation, that is, metasurfaces with multiple information encryption combining colorful nanoprinting images and grayscale images. In the field of information encryption, to ensure the security of the information and enhance the security level further, more keys at different decryption levels with various decryption complexities are seemingly more advantageous since the information hidden at a low encryption level that is easily decrypted can be intentionally used to confuse the public and make the extraction of the correct information more complex and challenging.

In this work, we propose a three-fold information encryption strategy based on hydrogenated amorphous silicon (a-Si:H) metasurface through elaborate design of its spectral and intensity modulation. The encryption scheme is capable of encoding three different images on the same metasurface platform. The three images are embedded at different encryption levels and thus their decryptions need different keys. The transmission spectra of the designed meta-atoms or nanobricks under white light are numerically investigated and all metasurfaces show nearly identical spectra upon white light illumination with x-polarization, while displaying different spectra for y-polarization. Moreover, 2-bit or four combinations of transmission intensity values are obtained at two selected wavelengths with predesigned polarizations. By elaborately arranging the nanobricks with proper geometric size, a colorful image and two grayscale images are successfully shown. The proposed three-fold information encryption scheme is expected to pave a new way for information encryption and anti-counterfeiting with high-security requirements.

2. Results and discussion

Figure 1 illustrates the proposed concept of three-fold information encryption, where the a-Si:H metasurface will display a vivid colorful nanoprinting image when illuminated by white light under the specific y-polarization state and no image pattern can be seen under x-polarization. Note that this colored image only serves as a display channel and delivers no valid information. Instead, another two channels are designed to conceal the real information, including two binary grayscale images that can only be decrypted by switching to two monochromatic lights with predesigned y-polarization. Messy grayscale images carrying spurious information will be witnessed once illuminated by light of non-designed wavelength or polarization. As schematically shown in Fig. 1, the proposed metasurface is an array of a-Si:H nanobricks placed atop a glass substrate. Here, a-Si:H is used to construct the nanobricks to validate the proposed three-fold information encryption strategy as an example, as it features a relatively high refractive index and near-zero extinction coefficient in the visible regime. The refractive index of a-Si:H is plotted in Supplement 1, Fig. S1. Other low-loss materials including silicon nitride, gallium nitride, or titanium dioxide are also suitable as the constituent material of the nanobricks. The unit cell of the metasurface can be described by several pivotal geometric parameters: the nanobrick lengths (L_x, L_y) along x- and y-axes, the nanobrick height H, and the unit cell periodicities (P_x, P_y) along x- and y-axes.

 

Fig. 1. Schematic of the unit cell of the proposed a-Si:H metasurface for three-fold information encryption, wherein the hiding and revealing of colored and binary grayscale images can be controlled by different keys.

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Through the elaborate design of these geometric parameters, the spectral characteristics of the nanobrick can be engineered, which in turn engenders the structural color under white light illumination, while their intensity under specific light wavelength can also be customized to dictate a binary grayscale image used for encryption. In our metasurface design, anisotropic nanobricks with different geometrical dimensions concurrently manipulate spectra and intensities upon x- and y-polarizations, thereby promising polarization-modulated encryption for both colorful nanoprinting and grayscale images. To commence, the nanobricks are expected to exhibit similar transmission spectra under the incidence of x-polarization, providing a chance for steganography of both colored and grayscale nanoprinting images in this channel. Conversely, the nanobricks must yield distinctive transmission spectra when subjected to y-polarized light so that color nanoprinting images can be manifested. In the binary grayscale image, a nanobrick with high transmittance is designated as a bright pixel, denoted as “1”, while a low transmittance assumes the identity of a dark pixel, denoted as “0”. To embed two grayscale images independently into the metasurface, the nanobricks are required to present 2-bit or four combinations of grayscale values of “00”, “01”, “10” and “11” at two specific wavelengths. The other party cannot easily crack the key of wavelength we designed for hidden images with encryption information, significantly improving the security of the hidden information.

The dimension of the anisotropic nanobrick is an essential factor in producing different colors. Utilizing the finite difference time domain (FDTD) method (Lumerical FDTD), we conduct simulations to ascertain the transmittance of periodically arranged a-Si:H nanobricks with varying dimensions. The periodicities of P_x and P_y are both fixed at 300 nm, while H is fixed at 260 nm. Here, a source type of plane wave with a wavelength range from 380 nm to 780 nm is applied to mimic the white light. The corresponding light intensity characteristics of the applied plane wave source depending on the wavelength are plotted in Supplement 1, Fig. S2. By fixing the L_y to various values from 50 nm to 150 nm in a step of 20 nm, while scanning its L_x from 50 nm to 250 nm in a step of 5 nm, the transmission spectra of the nanobricks are numerically examined for x- and y-polarization incidences, and the results can be found in Figs. S3 and S4. It is seen that among various L_y values, the spectrum variations are quite obvious in the y-polarization incidence than in the x-polarization incidence. Such a feature offers a chance that through proper selection of the nanobrick, similar colors can be achieved upon x-polarization incidence, while dissimilar colors can be realized under y-polarization incidence. Note that this effect is quite interesting but might be a bit challenging since nanostructures with different dimensions generally produce different colors regardless of polarization.

Toward the goal, five nanobricks with ferent dimensions are meticulously selected. Four of these nanobricks are used to implement the above combination of gray values, and their images in x-polarized white light require another structure as a background to hide. The dimensions of selected five nanobricks (denoted as S₁ to S₅) are provided in Fig. 2(a) and their corresponding transmission spectra under x- and y-polarization incidences are also illustrated in Figs. 2(a) and 2(b). For the former case, the transmission spectra of the nanobricks are quite similar in terms of the off-resonance transmission efficiencies, and the on-resonance dip position is around 580 nm. These features make sure that the nanobricks exhibit a similar purple color. However, the nanobricks show quite different transmission spectra features under y-polarization incidence. In this case, the different resonance wavelength positions and the variant off-resonance efficiency lead to distinct colors of yellow, magenta, purple, green, and earthy yellow corresponding to the nanobrick from S₁ to S₅. Considering the 300 nm period, high-order diffraction may occur for the shorter wavelengths. Consequently, the transmission spectra without considering the diffraction were investigated. As an example, the simulation results of the nanobrick with L_x = 85 nm and L_y = 110 nm are shown in Supplement 1, Figs. S5(a) and S5(b). A slight discrepancy in transmission spectra can be seen from 380 nm to 440 nm for the cases considering and without considering diffraction. Similar phenomena can be obtained for other nanobricks, yet, such difference does not significantly affect the color of the nanobricks, as shown in Fig. S5(c). It can be anticipated that with proper arrangement of the nanobricks, a colorful image and a uniform purple color image will be seen under y- and x-polarizations.

 

Fig. 2. Transmission spectra of nanobricks and grayscale values under monochromatic wavelengths. Simulated transmission spectra of selected nanobricks for (a) x- and (b) y-polarized white light. Color and Grayscale brightness values of selected nanobricks at five different wavelengths for (c) x- and (d) y-polarized incidences.

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In addition to the white light incidence, we aim to encode more information to a single metasurface device at discrete wavelengths. The different transmission spectra of the five nanobricks under y-polarization open an avenue to conceal additional information at monochromatic wavelengths. It is previously shown that a transmittance difference greater than 0.4 is sufficient for displaying a binary grayscale image [31,32]. Following this guideline, the transmittance of nanobricks from S1 to S5 at five wavelengths of λ1 = 565 nm, λ2 = 600 nm, λ3 = 620 nm, λ4 = 650 nm, and λ5 = 690 nm are investigated, as depicted in Fig. 2(b). Details of the transmission efficiencies are listed in Table 1. At the wavelength of λ1 = 565 nm, the transmission value for nanobrick S₃ is near 0.16, which could be defined as a dark pixel. For other nanobricks, a minimum transmission value of 0.6 is obtained at the same wavelength and thus all can be defined as the bright pixel since the transmission difference between these nanobricks and S₃ is good enough. Similarly, at the other four wavelengths, nanobricks from S₁ to S₅ can be mapped to bright or dark pixels. Figure 2(c) depicts the colors and grayscale values of these structures under white light incidences and at five selected wavelengths for x-polarization. Figure 2(d) shows the corresponding results for y-polarization incidence. It can be found that λ2 = 600 nm and λ4 = 650 nm hold the capacity to conceal two binary grayscale images since the grayscale combinations of “00”, “01”, “10”, and “11” can be fulfilled.

Table 1. Y-polarized transmission of nanobricks at different wavelengths

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Additional simulations are performed to further elucidate the working principle of nanobricks as nano pixels. Figure 3 presents the electromagnetic field profiles in xy-, xz-, and yz-planes of a selected nanobrick S₄ at the two resonance wavelengths of 585 nm and 620 nm for x- and y-polarization incidences. In detail, Figs. 3(a) and 3(c) are the electric field distributions for x-polarized light at the wavelength of 585 nm (position of the transmission resonance valley). This configuration exhibits a marked enhancement of the electric field at the nanobrick’s x-direction boundary, while the magnetic field, shown in Figs. 3(b) and 3(d), is confined in the nanobrick. In the scenario of incident light being y-polarized at a wavelength of 620 nm (resonance wavelength), analogous electric field enhancement becomes evident along the y-direction, as presented in Figs. 3(e) and 3(g). Correspondingly, the magnetic field in Figs. 3(f) and 3(h), is confined to the central region of the nanobrick. In near field simulation, the linearly polarized beam tends to localize at the edges of the nanobrick. An individual nanobrick without the periodic boundary condition is also investigated, where similar field distribution can be seen, as shown in Supplement 1, Fig. S6. The resonance wavelength depends mainly on the geometry of the nanostructures, therefore it is possible to adjust the position of the resonance valley by varying the L_x and L_y of the nanobrick [33–35].

 

Fig. 3. Simulated electric and magnetic field distributions in the nanobrick. (a) Electric and (b) magnetic field distribution in xy-plane (z = H/2) of the x-polarized incident light at λ = 585 nm. (c) Electric and (d) magnetic field distribution in xz-plane (y = L_y/2) of the x-polarized incident light at λ = 585 nm. (e) Electric and (f) magnetic field distribution in xy-plane (z = H/2) of the y-polarized incident light at λ = 620 nm. (g) Electric and (h) magnetic field distribution in yz-plane (x = L_x/2)of the y-polarized incident light at λ = 620 nm.

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To validate the proposed three-fold information encryption strategy, three distinct metasurfaces are numerically investigated. Two metasurfaces (MS1 and MS2) consisting of the five nanobricks with various spatial locations are constructed and shown here, and the simulated model is portrayed in Fig. 4(a). First, Fig. 4(b) depicts the theoretical appearance of the entire metasurface under x-polarized white light. A uniform purple color without any effective information can be expected for both MS1 and MS2. Contrarily, when the metasurfaces are illuminated by white light with y-polarization, two distinct colored pattern numbers of “8” with identical yellow background color come into view. Therefore, the polarization of the white light can be adjusted to show or hide the colorful nanoprinting images. By filtering the white light to monochromatic light at wavelengths of aforementioned λ₂ and λ₄, grayscale images carrying two different pieces of information are obtained. For instance, MS1 displays the numbers of “7” and “4” respectively at the two wavelengths (Figs. 4(e) and 4(f)). Figures 4(h) and 4(i) show that MS2 conveys the characters of “F “ and the number “2”. To evaluate fidelity level of the simulated grayscale images, we calculate the correlation coefficient (CC for short) relating to the simulated grayscale images (Figs. 4(e), (f), (h) and (i)) and the corresponding theoretical images, as summarized in Table S1. The detailed definition of CC is presented in the Supplement 1. It is verified that all the values are greater than 0.6, implying a high fidelity of the simulated images. Conversely, neither numbers nor characters are displayed under the two wavelengths with x-polarization, as given in Figs. 4(c) and S7. Specifically, λ₂ = 600 nm is near the transmission resonance valley of the spectrum, and the highest transmission of all nanobricks is 0.25 and thus can be considered as dark pixels. Resultantly, the field profiles at this wavelength are quite dark as presented in Supplement 1, Figs. S7(a) and S7(c) and no valid information can be extracted. Therefore, the information hidden in the metasurface can only be decoded with the correct keys of light polarization and wavelength. No information or only fake information can be seen in other cases.

 

Fig. 4. Simulated colored and grayscale nanoprinting images. (a) Constructed metasurface model in simulation. (b) Metasurface appearance under x-polarized white light. (c) Simulated electric field profile revealing the metasurface appearance under x-polarized light at the wavelength of 650 nm. (d) Appearance of MS1 under y-polarized white light. Simulated electric field profiles of MS1 under the y-polarized incidence of light at wavelengths of (e) 600 nm and (f) 650 nm. (g) Appearance of MS2 under y-polarized white light. Simulated electric field profiles of MS2 under the y-polarized incidence of light at wavelengths of (h) 600 nm and (i) 650 nm. (j) Appearance of MS3 under y-polarized white light. Simulated electric field profiles of MS2 under the y-polarized incidence of light at wavelengths of (k) 650 nm and (l) 690 nm.

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The encryption capability of the proposed metasurface can be further extended by considering an expanded range of wavelength dimensions. For instance, in addition to the wavelengths λ₂ and λ₄, other wavelengths may also be considered. This augmentation not only heightens the complexity of deciphering the metasurface information but also bolsters its security. Note that results in Fig. 2 clearly demonstrate that the selected nanobricks only support the independent 2-bit light intensity manipulation at the wavelengths of λ₂ and λ₄, meaning that the two images are hidden but at other wavelengths, for instance, λ₄ and λ₅, will suffer some limited freedom. This scenario is exemplified in Fig. 4(j), where only four out of the five nanobricks are selected to configure the metasurface (MS3). In the case of two mutually orthogonal white light illuminations, the metasurface still shows the overall purple and colored pattern number of “8”, respectively. However, the grayscale images of the metasurface illuminated by the wavelengths λ₄ and λ₅ light sources appear to be the number “3” and the number “1” as in Figs. 4(k) and 4(l). The CC values relating to the simulated grayscale images (Figs. 4(k) and (l)) and the corresponding theoretical images can be found in Supplement 1, Table S1. Fig. S8 illustrates a grayscale image of the same metasurface displayed at the wavelength λ₂ that we used in the previous section, conveying information like the character “E” which does not leak the real information (“3” or “1”). The design freedom of the images at λ₄ and λ₅ may be further enhanced through further optimizing and designing more nanobricks. Moreover, if more nanobricks can realize the desired polarization-dependent transmission spectra and provide intensity combinations from “000” to “111” at three wavelengths, it is possible to realize three distinct encryption grayscale images. In this case, the encrypted information can be extended to four-fold.

3. Conclusion

In summary, three-fold optical information encryption has been fulfilled by an a-Si:H metasurface. The metasurface serves to either conceal or unveil a colorful nanoprinting image while clandestinely embedding two binary grayscale images, and extraction of these information mandates different complexity keys. Specifically, the polarization of the broadband visible light serves as the first category of key, while the two monochromatic wavelengths are referred to as the second or third key. Toward the goal, we adopted a variety of anisotropic nanobricks, which produce similar/different spectral responses under x- and y-polarizations in relation to colored nanoprinting. Based on the selected nanobricks, two monochromatic wavelengths were also found, allowing independent 2-bit intensity control that enables two binary grayscale nanoprinting images. In order to prove the claimed encryption concept, we designed three metasurfaces and simulated the function of nanoprinting image hiding/displaying by adjusting polarization and spectrum of light. Our proposed metasurface is advantageous in terms of high information security and flexible switching mechanisms, which is anticipated to have a promising future in a variety of fields including multi-image display, high-density optical storage, optical anti-counterfeiting, and encryption, among others.