1. Introduction

Metasurface, composed of subwavelength planar elements, enables a high degree of freedom in controlling amplitude, phase, and polarization of light [1–7]. The ability to control the optical properties point-by-point provides a powerful approach to realizing high-performance optical components, such as meta-lenses [8–10], wavefront shaping devices [11–14], image displays [15–18], and so on. Therein, nanoprinting using optimized nanostructures to encode spatially varied intensity or color information on the structure surface has attracted extensive interest due to their outstanding advantages of the subwavelength resolution, full-color, arbitrary grayscale printing and durable properties. Early, researchers in nanoprinting field focus on adjusting the shapes, sizes, and materials of the structure to achieve more vivid colors [19–21]. To achieve more information encoding and extend the functionality, polarization multiplexing [22–24], wavelength multiplexing [25,26], spatial frequency multiplexing [27], and angle multiplexing schemes [28,29] have been proposed. The above-mentioned multifunctional metasurfaces do not consider propagation direction which is an important optical property.

Propagation-direction-dependent metasurfaces exhibit asymmetric optical response in forward and backward transmissions, i.e., different optical phenomena can be observed by changing the propagating direction [30–36]. For example, Frese et al. and Yao et al. used dual-layered metasurface to achieve asymmetric holographic displaying [30] and lens focusing [31], respectively. However, the holographic image or the focal spot is designed to generate only in the forward transmission, while disappearing for backward incidence. That is, these metasurfaces are asymmetric but not bidirectional optical devices. A bidirectional device is defined as two functionalities possession for lightwave propagating along forward and backward directions. Recently, bidirectional metasurfaces have been extensively studied for information multiplexing. Liang et al. designed an asymmetric Fresnel-type meta-hologram to project two different holographic images in the forward and backward directions with single-sized nanostructed metasurface [32]. Naveed et al. combined the propagation phase and geometric phase to realize asymmetric Fourier-type holographic images reconstruction [33]. Chen et al. utilized a cascaded multi-layer metasurface to break out-of-plane symmetry and produce asymmetric electromagnetic wave transmission, resulting in directional meta-hologram in the microwave frequency [34]. In addition to bidirectional phase manipulation, Kim et al. [35] and Wu et al. [36] achieved bidirectional spectrum manipulation, resulting in different color contrasts in forward and backward transmission. In summary, these current schemes cannot fully decouple the bidirectional light intensity due to the limitation of design degree of freedom, which would hinder the development of asymmetric photonic devices.

In this paper, we hold the goal of achieving bidirectional nanoprinting to design and simulate a bilayer metasurface working in the visible region, which can fully decouple the bidirectional light intensity and simultaneously display two continuous grayscale images under the illumination of forward and backward incident light respectively, as shown in Fig. 1(a). In our approach, the asymmetric but still bidirectional optical response can be formed by stacking two layers of metasurfaces with different functionality in space. The nanostructures in the first- and second-layers act as a half-wave plate and a polarizer, respectively. We made simulated verification in the visible region to validate the design principle and its feasibility. Interestingly, our proposed nanoprinting metasurfaces are proved that can work not only in transmission mode but also in reflection mode, which can bring great convenience for practical applications. In addition, the proposed nanoprinting device has an asymmetric optical property for forward transmitted light and backward reflected light, which allows the generation of two different grayscale images on the same side of the proposed metasurface. Due to the similar phenomena of the forward reflected light and the backward transmitted light, two different grayscale images can be generated in the other side of the proposed metasurface. In a word, our work extremely expands the design freedom for metasurface device, and is expected to play a significant role in the field of optical display, information multiplexing, etc.

 

Fig. 1. Working principle and schematic of the unit cell. (a) The working principle of the proposed bidirectional nanoprinting metasurface. (b) Top view, (c) Side view and (d) Bottom view of the designed unit cell. The top nanobrick marked as nanobrick I is designed with height H₁ of 380 nm, width W₁ of 60 nm, length L₁ of 150 nm, periodicity C 300 nm and orientation angle θ₁. The bottom nanobrick II is designed with length L₂ of 143 nm, width W₂ of 80 nm, and height H₂ of 220 nm, which rotates in-plane with an orientation angle θ₂. The spacing of the nanobricks I and II D₁ is set to 300 nm.

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2. Working principle and unit cell design

To realize the asymmetric but still bidirectional transmission, nanostructures in the first- and second-layer are designed as optical elements with different functionality. We start by considering the forward incident light. As incident linearly polarized (LP) light passes through a half-wave plate with an in-plane orientation θ₁ and a polarizer with an in-plane orientation θ₂, the Jones vector of the output beam is,

When incident LP light illuminate the bilayer metasurface from the opposite direction, the Jones vector of the output beam can be expressed as

From Eqs. (2) and (4), we can find that the intensity manipulation of forward and backward light is independent. Specifically, when the polarization direction of incident light is fixed, I₁ and I₂ can be designed at will by arranging the orientation angles of the nanostructures in the first and second layers. The introduction of the bilayer metasurface breaks the conventional reciprocal optical behavior of single-layer metasurfaces, which provides us an extra degree of freedom and imparts the capability for achieving bidirectional optical devices.

It is well known that a half-wave plate can reverse the chirality of circularly polarized (CP) light and convert a CP beam into the oppositely circular polarized one. Therefore, the optimization goal of the nanobrick in the first layer is to maximize the conversion efficiency of cross-polarized light while suppressing the co-polarized part to near zero. Since a polarizer can convert the incident light into LP light, the optimization objective of the second nanostructure is to reflect a beam with a polarization direction aligned with the long axis of the nanobrick while transmitting that along the short axis, or vice versa. In the numerical simulation, we conducted unit-cell design by utilizing CST Microwave Studio software. The top view, side view, and bottom view of the unit cell structure are shown in Fig. 1(b)–1(d). The proposed unit-cell made of dielectric materials consists of three parts: the first layer of silicon nanobrick, the second layers of silicon nanobrick embedded in a layer of glass, and a fused silica substrate with a refractive index of 1.457. The refractive index of silicon can be found in Appendix A. The nanobricks in the first and second layer are labeled as nanobrick I and II, respectively. Based on waveguide theory [37], nanostructures with different geometric dimensions have different effective refractive indices. Therefore, we need to elaborately design the geometric parameters of the nanostructure to achieve desired optical responses. There are ten structure parameters in bilayer nanobrick: heights (H₁, H₂), lengths (L₁, L₂), widths (W₁, W₂), orientation angles (θ₁, θ₂), cell size (C), and the space of first and second layer nanobrick (D₁).

We firstly made an optimization design for two single-layer nanostructures respectively. Figure 2(a) shows the simulated efficiencies when a normally incident CP beam illuminates the nanobrick I. As a result, when nanobrick I is designed with cell size C of 300 nm, length L₁ of 150 nm, width W₂ of 60 nm, and height H₁ of 380 nm, the transmitted cross-polarized conversion efficiency T_cro can reach as high as 97%, while all the unwanted co-polarized parts T_co can be suppressed to below 1% at the working wavelength of 633 nm. Therefore, nanobrick I can work as a transmission-type half-wave plate. Figure 2(b) shows the simulated results of nanobrick II with cell size C of 300 nm, length L₂ of 143 nm, width W₂ of 80 nm and height H₂ of 220 nm. We can see that the reflectivity R_x and transmissivity T_y reach 98% and 97% at an operation wavelength of 633 nm, and the unwanted R_y and T_x can be suppressed to below 3% and 1%. That is, the incident light with polarization direction aligned with the long axis of the nanobrick is almost totally reflected, while that along the short axis is nearly totally transmitted. It shows that nanobrick II can work as a nano-polarizer not only in transmission mode but in reflection mode. It is worth noting that the polarization directions of reflected and transmitted light obtained from the nano-polarizer are orthogonal to each other.

 

Fig. 2. Simulated results of the single-layer and bilayer nanobricks. (a) Simulated cross-polarized T_cro, R_cro and co-polarized parts T_co, R_co under a normal CP light incidence of nanobrick I. (b) Simulated reflectivity R_x, R_y and transmissivity T_x, T_y of the nanobrick II under the illumination of LP light. (c) Simulated transmitted light intensity I₁ of the bilayer nanobrick versus orientation angles θ₁ and θ₂ under a forward LP light incidence with the polarization of 0°. (d) Simulated transmitted and theoretical intensity I₁ of the bilayer nanobrick plot for orientation angle θ₁, in which the orientation angle of bottom nanobrick θ₂ was designed to be 0° and 90° respectively. (e) Simulated transmitted light intensity I₂ of the bilayer nanobrick versus orientation angles θ₁ and θ₂ under a backward LP light incidence with the polarization of 0°. (f) Simulated transmitted and theoretical transmitted intensity I₂ plot for orientation angle θ₂ when the orientation angle of nanobrick I θ₁ was set to be 0° and 90° respectively. Since the bottom nano-polarizer acts as a polarized beam splitter and it only allows the transmission of light polarized along the short axis and reflection of light polarized along the long axis, the intensity functions of (d) (θ₂= 0) and (f) exhibit a sine.

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After completing the design of two single-layer nanobricks, we evaluate the performance of bilayer nanbrick. To simulate the transmitted intensity of forward and backward incident light passing through bilayer nanobricks, we swept the orientations of nanobricks I and II from 0° to 180° in steps of 5°. In this simulation, the polarization direction of incident light was set as 0°, the working wavelength was 633 nm, and the spacing between the upper and lower nanobricks D₁ was set to 300 nm. Figure 2(c), 2(e) shows the color-coded values of simulated intensity ${I_1}$ as a function of nanobrick orientations θ₁ and θ₂ under the illumination of forward and backward incident light separately. We can easily find that the light waves emitted in the forward and backward directions have different optical effects with a variation of nanobrick’s orientation. To better understand the phenomena, we have drawn two curves of the output light intensity I₁ versus orientation angle of nanobrick θ₁, in which the orientation of nanobrick II θ₂ was 0° and 90° respectively, as shown in Fig. 1(d). Obviously, the simulated results agree quite well with theoretical results, which can be described by mathematical functions ${\sin ^2}2{\theta _1}$ and ${\cos ^2}2{\theta _1}$ corresponding to the θ₂ is 0° and 90°. It can be deduced from Eq. (2) due to the polarization direction of transmitted light of the nanobrick II along with the short axis. Similarly, when the backward incident light passes through the bilayer nanobrick, the simulated results of transmitted light intensity I₂ are found to be in good agreement with the presented theories ${\sin ^2}{\theta _2}$, as shown in Fig. 2(f). The simulation results prove that precise, continuous, bidirectional, and independent intensity modulation for forward and backward incident light can be realized by arranging the orientation of nanobricks.

3. Demonstration of bidirectional nanoprinting

Based on the optimized bilayer nanobrick and two intensity functions, we utilized Lumerical FDTD solution (Version: 2020 R2) to build a simulation model of a bilayer nanobrick array. The nanobrick array aligns 150 × 150 nanobricks with different orientations to produce the required intensity distribution. Each bilayer nanobrick cell corresponds to one image pixel. According to the function ${I_2} = {I_0}{\sin ^2}({\theta _2})$ and the target image (Fig. 2(b)), we calculated the orientations distribution of nano-polarizer array by the inverse operation. Similarly, we obtained the orientations distribution of nanobrick half-wave plate array by utilizing ${I_1} = {I_0}{\sin ^2}(2{\theta _1} - {\theta _2})$ and the target image (Fig. 2(a)). The transmitted light and reflected light are collected by field monitors with 100 nm from the upper and lower surfaces of metasurface. The incident light is an LP light with a polarization angle of 0° and an operating wavelength of 633 nm. A bidirectional nanoprinting metasurface is simulated. The first and second columns of Fig. 3 show the target and simulated images respectively. Obviously, two different meta-images of a “dog” and a “cat” (Fig. 3(e), 3(f)) are generated when forward and backward incident LP light shine into the metasurface respectively, which is notably consistent with the corresponding target images (Fig. 3(a), 3(b)) and shows high fidelity. Since the bidirectional nanoprinting device can work in both transmission and reflection modes, we obtained the reflected intensity distributions by utilizing reflected field monitors, which are illustrated in Fig. 3(g) and 3(h). Interestingly, the reflected results are complementary grayscale images of transmitted results, that is, the brightest and darkest areas are reversed. It can be explained that the polarization directions of transmitted and reflected light of nanobricks II are orthogonal to each other. The same simulated results can be obtained in reflection mode as in transmission mode by changing the polarization direction of incident light to 90°. Therefore, our proposed nanoprinting metasurface can bring great convenience for practical applications since the working modes can be chosen at will. It is worth noting that there is a slight discrepancy between the target and the simulated image (Appendix B), which is mainly caused by the coupling between neighboring nanostructures and can be weakened by constructing super-cells or increasing the cell size.

 

Fig. 3. Target and simulated images under the illumination of forward and backward incident light. (a)-(d) designed target images for forward and backward incident light. (e)-(h) corresponding simulated images obtained by FDTD simulation software. The scale bars are 10 µm and the working wavelength is 633 nm.

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The above-mentioned printing images are formed on the transmission space or reflection space, that is, two independent meta-images can be observed on either side of the metasurface. In practical application, these bidirectional optical devices may be integrated with other optical components, and thus there exist some situations in which observation equipment cannot or is not easily moved. Therefore, it is necessary to develop a bidirectional optical element which can generate multi-images in one side space of device. Interestingly, our proposed nanoprinting metasurface has been found with asymmetric optical property for the forward transmitted light and backward reflected light. In theory, when forward incident LP light passes through the bilayer nanobricks, the intensity of forward transmitted light can be described as ${\cos ^2}(2{\theta _1} - {\theta _2} - {\alpha _1})$. When incident LP light passes through bilayer nanobricks from the opposite direction, the intensity of backward reflected light can be described as ${\sin ^2}({\theta _2} - {\alpha _1})$. That is, the intensity modulation for the forward transmitted light and backward reflected light are independent. Two different grayscale images can be generated on the same side of the proposed metasurface by elaborately arranging the orientation of bilayer nanobricks. In addition, similar phenomena also exist for the forward reflected light and backward transmitted light, which makes two different grayscale images can be simultaneously generated on the other side.

To prove it, we utilize the intensity modulation functions and bilayer nanobrick to design a new bidirectional nanoprinting metasurface. Figure 4 shows the target image and simulated near-field intensity distribution of bilayer metasurfaces consisting of 150×150 nanostructures. Obviously, simulated results are in good agreement with the target images. Specifically, when incident LP light with the polarization direction of 0° passes through a bilayer, the forward transmitted light and backward reflected light can generate two different printing images (a “cat” and a “dog”), as shown in Fig. 4 (e) and 4(f). At the same time, we collected the forward reflected light and backward transmitted light by field monitor with 100 nm from the upper surfaces of the metasurface. The obtained results are shown in Fig. 4(g) and 4(h) and complementary to Fig. 4 (e) and 4(f), which confirms two independent grayscale images can also be generated under another incidence and observation condition. Our work extremely expands the working modes of metasurface devices, which can bring great convenience for practical applications and provides a new pathway for information encoding and encryption.

 

Fig. 4. Target and simulated results under other incidence and observation conditions. (a, b) and (e, f) target and simulated results of forward transmitted light and backward reflected light. (c, d) and (g, h) target and simulated results of forward reflected light and backward transmitted light. All results are obtained at the working wavelength of 633 nm. The scale bar is 10 µm.

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In addition to qualitative evaluation, we introduced two commonly used image quality evaluation indicators, the peak signal-to-noise ratio (PSNR) and correlation coefficient (CC) to quantitatively evaluate the fidelity of simulated results. The PSNR evaluates the image based on the error between the corresponding pixels. The greater the value of PSNR, the better the image quality. The CC is used to compare the similarity between the target images and simulated images. The PSNR and CC between the simulated images and the corresponding target images have been calculated, and all results are shown in Appendix C. There are some inconsistencies between the results of the PSNR and the qualitative observations of the human eye. This is because the PSNR is based on error-sensitive image quality evaluation and does not consider the visual characteristics of the human eye. The CC for all channels are higher than 0.68, indicating that the simulated results are in good agreement with the design and have good fidelity.

In addition, it is possible to merge bidirectional nanoprinting with the Malus metasurfaces [1,7,15,16,18] to achieve full-space light manipulation. Malus metasurface is a new concept that have been proposed, which indicates a class of metasurface inspired by Malus law to manipulate the optical property of light. The most important feature of such a metasurface is that it does not require complex structural design and is capable of independently controlling of the intensity and phase properties simply by arranging the orientation of single-sized nanostructures. Therefore, combining our proposed bidirectional nanoprinting with Malus metasurfaces, light manipulation will be not limited to be in the near-field, and it can be further extended to full-space and achieve simultaneous manipulation of near-field and far-field light under the illumination of forward or backward incident light. More importantly, the above-scheme does not increase the complexity of fabrication or decrease the image quality. We expect that it is promising to pave a new way for developing full-space, high-density, and multifunctional optical devices.

4. Conclusion

In summary, we present and demonstrate bidirectional nanoprinting based on bilayer metasurfaces, which can fully decouple the bidirectional light intensity and provide a new route for bidirectional light manipulation. The proposed bilayer metasurfaces introduce asymmetric but still bidirectional optical response by stacking two-layer nanostructures with different functionality in space, resulting in two different continuous grayscale images displaying in the forward and backward incidence respectively. The proposed bilayer metasurfaces consist of nanobricks I acting as half-wave plates and the nanobricks II functioning as nano-polarizers. Due to nanobrick II working as both transmission-type and reflection-type polarizers, our proposed bidirectional nanoprinting metasurface can work not only in transmission mode but also in reflection mode. Interestingly, two different grayscale images also can be generated on same side of the proposed metasurface by changing the incidence and observation conditions. Therefore, a significant feature of our scheme is flexible working modes, and it can bring great convenience for practical applications. In addition, it is promising to combine bidirectional nanoprinting with the Malus metasurfaces to achieve full-space light manipulation. Overall, we introduce a new design degree of freedom and propose a feasible and extendable scheme in bidirectional light manipulation. We expect it may have promising applications in anti-counterfeiting, information encryption, optical storage, image display, and many other related applications.

Appendix A: dispersion curves of silica and amorphous silicon

Figure 5 shows the dispersion curves of silicon used in the numerical simulations.

 

Fig. 5. Refractive index of silicon. (a) The real part n. (b) imaginary part k

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Appendix B: analysis of the discrepancy between target and simulation

Based on the transmitted/reflected intensity of the bilayer nanobricks and the orientation distribution of the bilayer nanobrick array, we calculated the ideal result that can be obtained with our optimized bilayer nanobricks (utilizing MATLAB software), as shown in Fig. 6. It is obvious that the theoretical calculated images and the target images are good agreement, and the difference between the corresponding pixels is less than 1%. This proves that a slight discrepancy between target and simulation obtained by the electromagnetic simulation software is mainly caused by the coupling between neighboring nanostructures, rather than our optimized imperfect polarizer. Therefore, we can weaken this coupling and improve image quality by constructing super-cells or increasing the cell size.

 

Fig. 6. Target images, theoretically calculated images, and its difference images.

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Appendix C: quantitatively evaluate the fidelity of simulated results

The PSNR evaluates the image based on the error between the corresponding pixels. Assuming the sizes of ${\textrm{I}_{tar}}$ and ${\textrm{I}_{sim}}$ are both M×N, then the PSNR can be calculated by following Eqs. (5) and (6)

(5)$$\textrm{PSNR = }10\cdot {\log _{10}}(\frac{{Ma{x_\textrm{I}}^2}}{{MSE}}).$$

(6)$$MSE = \frac{1}{{M \times N}}\sum\limits_{i = 1}^M {\sum\limits_{j = 1}^N {({\textrm{I}_{tar}}(i,j) - {\textrm{I}_{sim}}(i,j))} } ,$$

where $Ma{x_\textrm{I}}$ is the maximum grayscale value of the image I. Such as, for an 8-bit grayscale image, the $Ma{x_\textrm{I}} = {2^8} - 1 = 255$. MSE represents the mean square error of ${\textrm{I}_{sim}}$ and reference image ${\textrm{I}_{tar}}$. The unit of PSNR is dB. The larger the value of PSNR, the smaller the distortion of image.

The correlation coefficient (CC) can be used to compare the similarity between the target images and simulated images. The correlation coefficient can be calculated by Eqs. (7)–(9):

(7)$$\textrm{CC = (}{\textrm{I}_{tar}}\textrm{, }{\textrm{I}_{sim}}\textrm{) = }\frac{{Cov({I_{tar}},{I_{sim}})}}{{Std({I_{tar}})\cdot Std({I_{sim}})}}.$$

(8)$$Cov({\textrm{I}_{tar}},{\textrm{I}_{sim}}) = \frac{1}{{M\cdot N - 1}}\sum\nolimits_{i,j} {[{\textrm{I}_{tar}}(i,j) - \frac{{\sum {{\textrm{I}_{tar}}(i,j)} }}{{M\cdot N}}]} \cdot [{\textrm{I}_{sim}}(i,j) - \frac{{\sum {{\textrm{I}_{sim}}(i,j)} }}{{M\cdot N}}],$$

(9)$$std({\textrm{I}_{tar}}) = \sqrt {Cov({\textrm{I}_{tar}},{\textrm{I}_{tar}})} ,std({\textrm{I}_{sim}}) = \sqrt {Cov({\textrm{I}_{sim}},{\textrm{I}_{sim}})} .$$

where ${\textrm{I}_{tar}}(i,j)$ and ${\textrm{I}_{sim}}(i,j)$ denotes target image and simulated image respectivily. “ Cov (,)” is the covariance operation, and “Std (,)” stands for the calculated standard deviation. The larger the value of CC, the smaller the image distortion.

Based on Eqs. (5)–(9), the PSNR and CC between the simulated images (Fig. 3(e), 3(f), 3(g), 3(h), 4(e), 4(f), 4(g) and 3(h) and the corresponding target images can be evaluated, and the results are shown in Table 1.

Table 1. PSNR and CC between the target and simulated images

View Table

Funding

National Natural Science Foundation of China (12104402); Special Science and Technology Innovation Program of China (19-163-21-TS-001-068-01); Commonweal project of Zhejiang Province (LGC22F050004); Natural Science Foundation of Zhejiang Province (LY22A040003).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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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