1. Introduction

Metasurfaces, which possess the ability of precisely manipulating optical properties such as phase, polarization, amplitude and frequency, have fascinated scientists for several years [1–9]. Based on these, many novel metasurface-based applications have been put forward, including wearable augmented reality (AR) display [10], optical differentiation [11–13], optical random number generation [14], ultrasensitive hyperspectral biosensing [15], nanophotonic light-field camera [16] and so on. Since metasurfaces can modulate optical intensity or spectrum cell-by-cell at the subwavelength scale, one can design metasurfaces to record nanoprinting images with ultra-high resolution and capacity [17–21]. By designing nanostructures with variable geometric sizes, nano-resonators can be created to modulate the spectrum, which finally accounts for plenty structural-colors with high color saturation and spatial resolutions [22–25]. For instance, plasmonic color palettes are proposed by controlling the plasmon resonant characteristic of metal nanostructures, which promotes the development of color-nanoprinting with both high resolution (31,750 dots per inch, DPI) and abundant colors (more than 300), enabling the printing of photorealistic images [22]. Similarly, Mie resonance existing in dielectric nanostructures can also be used to produce plenty of structural-colors and display vivid nanoprinting images [23–25]. On the other hand, single-sized nanostructures can be used to accomplish continuous-grayscale nanoprinting, governed by the classic Malus’s law. Specifically, orientation states of anisotropic nanostructures acting as half-wave plates or polarizers can be employed to control the polarization state of output light. Thus, a 256-level grayscale image with ultra-high resolution (63,500 DPI) and good information security can be recorded into a single-size nanostructured metasurface [26,27]. In addition, color-nanoprinting images with vivid visual impacts can be displayed by combining the orientation state with resonant characteristic of the nanostructure, where unit-cells consisting of several nanostructures with different dimensions and orientations are designed to generate structural-colors with ultra-smooth brightness variations [28,29].

Recently, nanoprinting has been developed from single-channel to multi-channel [30–35] or multi-functional integration [36–42], by fully exploiting the DOFs of nanostructured metasurfaces. Polarization multiplexing, usually conducted by changing the dimensions of anisotropic nanostructures to generate distinct spectral responses under different polarization states, has become an efficient approach to create multi-mode metasurfaces for multi-channel nanoprinting display with improved information capacity. For example, by utilizing the anisotropy of nanostructures with variable dimensions, different spectral responses can be realized under two orthogonal polarization directions, which accounts for dual-mode color-nanoprinting with high resolution [43,44]. Besides, two states of orientations can be used to create hidden watermarks covering on a structural-color nanoprinting image, which costs nanostructures with variable sizes [45]. Polarization multiplexing can also be implemented in non-orthogonal polarization directions [46–51]. Among them, single-size design strategy has attracted broad interests since it can increase the information channel number without at the cost of reduced information density, complex metasurface design and nanofabrication. For instance, by introducing the orientation degeneracy into metasurface design, a single-size nanostructured metasurface can be employed to generate independent watermark patterns covering on a continuous grayscale image [46]. Moreover, tri-channel grayscale nanoprinting containing a continuous grayscale image and two binary images have been realized by furtherly utilizing the orientation degeneracy of single-sized nanostructures [47]. However, a single-size nanostructured metasurface usually cannot display structural-colors since it has only one DOF, i.e., the orientation angles of nanostructures. Therefore, how to fully exploit the DOF of orientation angles, thus displaying dual-channel color-nanoprinting image with a single-size nanostructured metasurface is still a challenge.

In this paper, with the capacity of resonance and non-orthogonal polarization control of light, we propose and experimentally demonstrate the dual-channel anticounterfeiting color-nanoprinting with a single-size nanostructured metasurface. By exploring the characteristic of Mie resonance and the orientation degeneracy of anisotropic dielectric nanostructures, a strategy for generating different structural-colors based on single-size nanostructured metasurface is established and can be assembled for applications of color-image-assisted anticounterfeiting or information multiplexing. The basic concept of the dual-channel anticounterfeiting color-nanoprinting is shown in Fig. 1. The designed metasurface is composed of anisotropic dielectric nanostructures with identical period size (P), length (L), width (W) and height (H), but different orientations (β). Under the illumination of natural light, a color-nanoprinting image of cartoon tiger as well as another anticounterfeiting pattern of lotus can be observed with an analyzer of different polarization angles (0° and 135° for channel 1 and 2, respectively).

 

Fig. 1. Schematic illustration of the dual-channel anticounterfeiting color-nanoprinting based on a single-size nanostructured metasurface. The metasurface consists of single-sized nanostructures with identical dimensions but different orientations. Each nanostructure acts as a nano-resonator to generate different structural-colors along its long- and short-axis directions, respectively. When natural light illuminates the metasurface, a color-nanoprinting image of cartoon tiger (channel 1) as well as an anticounterfeiting pattern of lotus (channel 2) can be displayed under two polarization-controlled light paths, which is established by introducing an analyzer. The polarization angle of the analyzer is set to be 0° (channel 1) and 135° (channel 2) for dual-channel color-nanoprinting.

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2. Unit-cell design and simulation

In previously reported works, it is proved that Mie resonance can be used to redistribute the incident light energy at different frequencies [24,25], which brings us inspiration for changeable structural-color modulation through a simple nanostructure design strategy. By optimizing the geometric sizes of an anisotropic nanostructure, resonant responses along the long- and short-axis directions can be controlled for different spectral modulations. In this work, single-sized nanostructures were employed to realize dual-axis Mie resonances along the long- and short-axis directions, respectively. Silicon-on-sapphire (SOS) material was selected to design the single-size nanostructured metasurface, corresponding dispersion characteristics are provided in Appendix A. CST STUDIO SUITE software was employed to simulate the SOS nanostructure with a periodic boundary condition. Simulated performance of the optimized SOS nanostructure (P = 400 nm, L = 130 nm, W = 80 nm and H = 230 nm) is shown in Fig. 2. As indicated in Figs. 2(a) and 2(b), the amplitude (A_s and A_l) and phase parts (Phase_s and Phase_l) of transmission coefficients along the long- and short-axis directions (t_l and t_s) are obvious different, especially at the green and red bands (510 ∼ 670 nm). The essential reason is that electromagnetic enhancements happened inside the SOS nanostructure are different along the two orthogonal directions, which forces the effective refractive indexes along two directions to change. Figures 2(c)–2(f) show the normalized electromagnetic field distributions inside the SOS nanostructure. Apparently, Mie resonances with different frequency responses happen, and there are two main resonant peaks along both long- and short-axis directions in the visible band. By comparing the simulated results shown in Fig. 2(a) with the electromagnetic field distributions shown in Figs. 2(c) and 2(e), we can directly find that two main valley locations of A_l (at 581 nm and 638 nm) are consistent with the maximum electromagnetic enhancement locations. Similarly, two main valley locations of A_s (at 525 nm and 548 nm) accords closely with the electromagnetic enhancement ones when comparing Fig. 2(a) with Figs. 2(d) and 2(f). Obviously, a nano-resonator with dual-axis resonance has been successfully proposed by controlling the resonant responses of the nanostructure along its two orthogonal axes.

 

Fig. 2. Simulated results of the designed SOS nanostructure. (a) Amplitude and (b) phase parts of the transmission coefficient along the long- (l) and short-axis (s) directions. Transmission coefficients along the two orthogonal directions can be expressed by t_l= A_l·exp(i·Phase_l) and t_s= A_s·exp(i·Phase_s), respectively. (c),(d) Normalized electric and (e),(f) magnetic field distributions along the x- (E_x and H_x) and y-axis directions (E_y and H_y), respectively. The simulation probe is located in the x-o-y plane center of the nanostructure, and its z position varies from 0 nm to 230 nm along the height direction. The simulated SOS nanostructure is with orientation of β = 0°. The polarization of the excitation source is along x-axis (y-axis) direction when simulating t_l, E_x and H_y (t_s, E_y and H_x).

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3. Design of single-size nanostructured metasurface for dual-channel anticounterfeiting color-nanoprinting

The designed SOS nanostructure possesses strong anisotropy so that we can establish a non-orthogonal polarization-controlled structural-color generation mechanism by changing its orientation state. Since the sapphire substrate is slightly anisotropic, we decided to control the polarization direction of the output light instead of the input one. Then, under the effects of normally natural light incidence and an analyzer with polarization angle of α, the spectrum of the transmitted light versus different orientations can be theoretically calculated by:

In our work, a quartz halogen lamp was employed as the light source, and I_in(λ) is determined by the measured data, as provided in Appendix B. The resonant characteristic of the SOS nanostructure decides transmission coefficients [t_l(λ) and t_s(λ)], and further influences the distribution of I(α, β, λ). More importantly, I(α, β, λ) can be flexibly modulated by adjusting α and β. According to the structural-color generation method (SCGM) provided in Appendix C [17–25], a mapping relation between structural-colors and nanostructures can be established [ Fig. 3(a)]. The single-sized nanostructure can be used to generate different structural-colors which lie within the black dashed line segment. It is also worth noting that the identical structural-color can be generated by a nanostructure with two different orientation options (β and 180°-β), as illustrated in Fig. 3(b). With the inspiration of this one-color-to-two-orientations strategy (OCTOS), we propose an approach to realize dual-channel anticounterfeiting color-nanoprinting with a single-size nanostructured metasurface, and Fig. 3(c) shows the design process. By employing SCGM, the target color-nanoprinting image can be recorded into the single-size nanostructured metasurface. Here, β of each SOS nanostructure is calculated by Eq. (4) and satisfies 0° < β < 90°. The enlarged partial view of the original orientation profile is shown in Fig. 3(c), and the color of the nanostructure represents the orientation state, which is consistent with that shown in Fig. 3(b). Then, by utilizing OCTOS, the orientation profile can be encoded to write an additional anticounterfeiting pattern. That means, once a SOS nanostructure records the green part of the anticounterfeiting pattern, its orientation has been changed to another value [i.e., also be calculated by Eq. (4) but satisfies 90° < β < 180°], and kept unchanged without recording the green part information. After the two-step operation, we obtained the final orientation profile [enlarged partial view is shown in Fig. 3(c)] to generate a color-nanoprinting image covered with a reconfigurable anticounterfeiting pattern based on a single-size nanostructured metasurface. Yellow nanostructures in the enlarged partial view of the final orientation profile represent the green part of the anticounterfeiting pattern. With the final orientation profile, we calculated the theoretical results under an analyzer with different polarization angles (Fig. 4). Obviously, the color distribution of the calculated image changes with the polarization control.

 

Fig. 3. Design principle of the dual-channel anticounterfeiting color-nanoprinting with a single-size nanostructured metasurface. (a) Simulated structural-colors under the polarization-controlled light path. An analyzer of α = 0° is used to adjust the polarization direction of the output light. (b) Examples for OCTOS. Identical structural-colors can be generated with two different orientations. Orientation states at the five example groups are (10°, 170°), (30°, 150°), (45°, 135°), (60°, 120°) and (80°, 100°), respectively. (c) Schematic illustration of the non-orthogonal polarization-controlled dual-channel color-nanoprinting with the designed single-size nanostructured metasurface. The target color-nanoprinting image of cartoon tiger is recorded into the original orientation profile through SCGM, and the anticounterfeiting pattern of lotus is encoded into the final orientation profile by utilizing OCTOS. Two color images are with the same dimensions of 500 × 500 pixels.

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Fig. 4. Calculated color-nanoprinting images under an analyzer with different polarization angles: α = 0°, 30°, 45°, 60°, 90°, 120°, 135°, and 150°.

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4. Experiments

After design, a SOS metasurface sample with dimensions of 200 × 200 µm² was fabricated by using the standard electron-beam lithography (EBL). Fabrication details are provided in Appendix D. To verify our design principle, we utilized a commercial optical microscope (Motic BA310MET-T) for observation. Figure 5(a) shows the sketch of the microscope, and the fabricated metasurface sample is put on an objective table. When natural light sequentially passes through the metasurface sample and the 20 × objective, nanoprinting images can be captured by a CMOS camera. If an analyzer is inserted into the microscope system, nanoprinting images under different polarization states can be observed as well. Figures 5(b)–5(d) show the experimentally captured nanoprinting images under different polarization controls (with the analyzer of α = 0°, 135° and without the analyzer). Obviously, a color-nanoprinting image of a cartoon tiger can be directly observed with the analyzer of α = 0° (channel 1), a clear anticounterfeiting pattern of lotus appears with the analyzer of α = 135° (channel 2) while both disappear without the analyzer. The experimental results with high image fidelity [Figs. 5(b) and 5(c)] are consistent with theoretical ones calculated by Eq. (4) (shown in Fig. 4). As the scanning electron microscopy (SEM) photo shown in Fig. 5(e), all fabricated nanostructures are with identical dimensions, so structural-colors generated under unpolarized illumination should be uniform, which is in good accordance with the result shown in Fig. 5(d).

 

Fig. 5. Experimental setup and results of the metasurface-based dual-channel anticounterfeiting color-nanoprinting. (a) Sketch of the optical microscope. (b)-(d) Experimentally captured nanoprinting images under different polarization controls. b: with the analyzer of α = 0° (channel 1), c: with the analyzer of α = 135° (channel 2) and d: without analyzer. (e) A SEM photo of the fabricated metasurface sample. All scale bars are shown.

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To further study the polarization sensitivity of the single-size nanostructured metasurface, we observed nanoprinting images with the analyzer of different polarization angles (Fig. 6). Obviously, the cartoon tiger with clear visual effect can be clearly seen when α is 0° and 90°. Except for this, color-nanoprinting images at α ≥ 90° have reverse color with the ones at α-90°, and this phenomenon can be explained by introducing α and α - 90° (α ≥ 90°) into Eq. (4). We also find that when increasing α from 0° to 60° (or from 90° to 150°), the color-nanoprinting image of the cartoon tiger turns blurred while the anticounterfeiting pattern turns clear with bright pink color (or cyan color) at α = 45° (or 135°). Thus, we can draw an important conclusion that the clear color-nanoprinting image or the clear anticounterfeiting pattern can only be observed at specific polarization controls (α = 0°, 45°, 90° or 135°). In addition, the pattern details in all experimental results are in good accordance with the theoretical results shown in Fig. 4, which proves the correctness of our metasurface design. However, distinct color hue difference exists, and this is due to nonnegligible sampling error of the CIE system, fabrication errors of metasurface sample and some experimental errors.

 

Fig. 6. Experimentally captured nanoprinting images with the analyzer of different polarization angles: α = 30°, 45°, 60°, 90°, 120°, and 150°. All scale bars are shown.

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Figure 7 shows the experimental results at different wavelengths. The nanoprinting images under 480 nm, 540 nm and 633 nm reveal the RGB components of the experimental results under natural light incidence. Clearly, the tiger and lotus pattern can be readily distinguished with reverse brightness profile under 540 nm and 633 nm respectively. This result is in accordance with the simulated transmission coefficient shown in Figs. 2(a) and 2(b), and indicates that our metasurface sample possesses good robustness under different illumination conditions. Additionally, the experimental nanoprinting images at blue light (480 nm) are with low image contrasts, because there is no resonance happened and the difference between transmission coefficients along long- and short-axis directions is slight.

 

Fig. 7. Experimentally captured nanoprinting images at different wavelengths: λ = 480 nm, 540 nm, and 633 nm. The analyzer is with α = 0°, 45°, 90°, and 135°, respectively. Different optical filters are put into the microscope system to control the operating wavelength. All scale bars are shown.

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In above experiments, we chose to adjust the polarization direction of output light instead of that of incident one because the sapphire substrate has slight anisotropy. To prove this, we also observed nanoprinting images by using a polarizer with different polarization angles (θ = 0°, 45°, 90°, and 135°, respectively), and experimental results are shown in Fig. 8. The anisotropy has non-negligible effect in orientation-controlled structural-color generation, so details of the cartoon tiger is hard to be observed and only a general outline can be distinguished. However, since the anticounterfeiting pattern has strong robustness against orientations, we can still clearly observe it.

 

Fig. 8. Experimentally captured nanoprinting images under different linearly polarized light incidences: θ = 0°, 45°, 90°, and 135°. The analyzer and the filter are both removed from the microscope system. All scale bars are shown.

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At last, we observed the nanoprinting images under different polarization states of both incident and output light in order to deeply analyze the polarization sensibility (shown in Fig. 9). When polarization states of incident and output light change simultaneously, the nanoprinting image varies with both color hues and brightness. Obviously, the experimental results at θ = 45°, α = 45° and θ = 135°, α = 135° are with higher brightness, while those one at θ = 45°, α = 135° and θ = 135°, α = 45° are with another color profile (orange and dark green colors instead of pink and cyan colors). Equation (4) is not suitable for this case, instead, the transmitted spectrum is with a new modulation (corresponding theoretical derivation is provided in Appendix E). We think this peculiar spectral response provides an interesting method for color-image-assisted anticounterfeiting, which means not only simple anticounterfeiting pattern is recorded, but also a non-duplicated structural-color generation mechanism is established. Specifically speaking, once we adjust polarization states of the incident and output light to particular combinations, we can get a security proof from the special structural-color distribution. Both OCTOS and the anisotropic characteristic of the sapphire substrate help to accomplish this unique polarization response.

 

Fig. 9. Experimentally captured nanoprinting images under different polarization-controlled paths. Both incident and output light polarization states are adjusted. θ is set to be 0°, 45°, 90°, and 135° respectively, while α is set to be 0°, 45°, 90°, and 135° respectively. All scale bars are shown.

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5. Conclusions

In summary, we propose and experimentally demonstrate a dual-channel anticounterfeiting color-nanoprinting metasurface by implementing the dual-axis resonance and non-orthogonal polarization control. Single-sized SOS nanostructures with dual-axis resonance along the long- and short-axis directions are employed to modulate the transmitted spectrum, and the concept of orientation degeneracy is introduced to improve the color information capacity of a metasurface. Through careful design, we establish a “1-to-2” mapping strategy for dual-channel structural-color generation, and successfully record two color-nanoprinting images into a single metasurface with the single-sized nanostructure design strategy. In the experiment, a color-nanoprinting image as well as an anticounterfeiting pattern can be readily observed under natural light illumination with specific polarization controls, which shows nice performance and good advantages of ultra-compactness, high information capacity and vivid colors. Based on these characteristics, our approach has succeeded in dual-channel color-nanoprinting and processes broad application prospective in fields including high-end anticounterfeiting, optical encryption, information storage, information security, multiplexing optical display, etc.

Appendix A: Dispersion characteristics of crystalline silicon and sapphire

Figure 10 shows the refractive indexes versus wavelength (400 ∼ 750 nm) of crystalline silicon and sapphire used in SOS material. Magenta and cyan curves in Fig. 10(a) represent the real and imaginary parts of the refractive index, respectively.

 

Fig. 10. Dispersion characteristics of (a) crystalline silicon and (b) sapphire versus wavelength (400 ∼ 750 nm).

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Appendix B: Spectrum of the quartz halogen lamp

We used a spectrograph (Thorlabs CCS100) to detect the spectrum of the quartz halogen lamp, and the normalized spectrum is shown in Fig. 11.

 

Fig. 11. Normalized spectrum of the quartz halogen lamp.

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Appendix C: Principle of the SCGM

Chromaticity coordinates of generated structural-colors are calculated by using CIE system. According to Eq. (4), transmitted spectrum of a SOS nanostructure with variable orientations (β) can be acquired. Then, corresponding tristimulus values of the generated structural-color can be calculated by:

(5)$$X = K \cdot \sum\limits_{\lambda = 400}^{750} {I({\alpha ,\beta ,\lambda } )} \mathop x\limits^ - (\lambda )\Delta \lambda ,$$

(6)$$Y = K \cdot \sum\limits_{\lambda = 400}^{750} {I({\alpha ,\beta ,\lambda } )} \mathop y\limits^ - (\lambda )\Delta \lambda ,$$

(7)$$Z = K \cdot \sum\limits_{\lambda = 400}^{750} {I({\alpha ,\beta ,\lambda } )} \mathop z\limits^ - (\lambda )\Delta \lambda ,$$

where $\bar{x}$(λ), $\bar{y}$(λ) and $\bar{z}$(λ) denote the tristimulus values of visual perception, while K denotes the normalization coefficient which is used to adjust Y value of the illumination to 100. Finally, chromaticity coordinate of the generated structural-color can be expressed by:

(8)$$({x,y} )= \left( {\frac{X}{{X + Y + Z}},\frac{Y}{{X + Y + Z}}} \right).$$

Appendix D: Sample fabrication

Our metasurface sample was fabricated with SOS material by using a standard EBL process. Firstly, we cleaned the SOS material by sequentially putting it into the acetone, ethyl alcohol, and deionized water. Secondly, we dried the SOS material by using a hot plate, and coated a conductive polymer mask on the SOS material. Next, we patterned nanostructures on the conductive polymer mask by using EBL (Raith 150, 30 kV). After resist development, we deposited a 30 nm chromium film acting as an etch mask on the sample via the thermal evaporator. Subsequently, we used ultrasonic waves to remove the redundant chromium and resist. Then, silicon-free part was removed by using reactive ion etching (RIE), and chromium-free part was removed by chromium etchant. Finally, the silicon nanostructure arrays were fabricated on the sapphire substrate.

Appendix E: Theoretical derivation of the transmitted spectrum with both polarizer and analyzer

When a polarizer and an analyzer are simultaneously used to control the polarization of both incident and output light, the transmitted spectrum can be represented by:

(9)$${I_1}({\alpha ,\beta ,\theta ,\lambda } )= {|{{J_{Analyzer}}(\alpha )\cdot J({\beta ,\lambda } )\cdot {J_{Sapphire}}(\lambda )\cdot {J_{Polarizer}}({\theta ,\lambda } )\cdot {E_{in}}(\lambda )} |^2},$$

where J_Sapphire(λ) and J_Polarizer(θ, λ) denote the Jones Matrixes of the anisotropic sapphire substrate and the polarizer:

(10)$${J_{Sapphire}}(\lambda )= \left[ {\begin{array}{{cc}} 1&0\\ 0&{{e^{i\delta (\lambda )}}} \end{array}} \right],$$

and

(11)$${J_{Polarizer}}(\theta )= \left[ {\begin{array}{{cc}} {{{\cos }^2}\theta }&{\sin \theta \cdot \cos \theta }\\ {\sin \theta \cdot \cos \theta }&{{{\sin }^2}\theta } \end{array}} \right].$$

Here, δ(λ) represents the transmitted phase difference along optical fast- and low-axis directions of the slightly anisotropic sapphire substrate. According to the abovementioned equations, the transmitted spectrum can be simplified as:

(12)$$\begin{aligned} {I_1}({\alpha ,\beta ,\theta ,\lambda } )= &{I_{in}}(\lambda )/2 \cdot \left|{{t_l}(\lambda )\cdot \cos ({\beta - \alpha } )\cdot \left[{\cos \beta \cos \theta + \sin\beta \sin\theta \cdot {e^{i\delta (\lambda )}}} \right]+ } \right.\\ & {\left.{{t_\textrm{s}}(\lambda )\cdot \sin({\beta - \alpha } )\cdot \left[{\sin \beta \cos \theta - \cos \beta \sin \theta \cdot {e^{i\delta (\lambda )}}} \right]} \right|^2}. \end{aligned}$$

Funding

National Key Research and Development Program of China (2021YFE0205800); National Natural Science Foundation of China (12174292, 11904267, 91950110); China Postdoctoral Science Foundation (2022TQ0243); Fundamental Research Funds for the Central Universities (2042022kf1013, 2042022kf0024, 2042021kf0018).

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.

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