⇦Chinese Physics Letters, 2020, Vol. 37, No. 7, Article code 077801 Multiplexed Metasurfaces for High-Capacity Printing Imaging Zhenyu Fang (方振宇), Haofei Xu (徐昊飞), Yaqin Zheng (郑雅芹), Yuelin Chen (陈悦琳), and Zhang-Kai Zhou (周张凯)* Affiliations State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-sen University, Guangzhou 510275, China Received 27 March 2020; accepted 6 May 2020; published online 21 June 2020 Supported by the National Natural Science Foundation of China (Grant Nos. 11974437 and 61675237), the Guangdong Natural Science Funds for Distinguished Young Scholars (Grant No. 2017B030306007), the Guangdong Special Support Program (Grant No. 2017TQ04C487), and the Pearl River S&T Nova Program of Guangzhou (Grant No. 201806010033).
*Corresponding author. Email: zhouzhk@mail.sysu.edu.cn Citation Text: Fang Z Y, Xu H F, Zheng Y Q, Chen Y L and Zhou Z K et al. 2020 Chin. Phys. Lett. 37 077801    Abstract We successfully overcome the problem of cross-talk in multiplexed metasurface design and realize the multiplexed metasurface with five printing images in both theoretical and experimental aspects, by employing the coherent pixel design considering coherent superposition of all the sub-elements. Compared with most previous studies where the integrated printing images were usually no more than three, our study shows obvious improvement. More importantly, in our approach all the sub-elements, which were crystalline silicon nanobricks with the size of $320\times 80\times 230$ nm$^{3}$, were arranged in a square space of $1.45 \times 1.45$ μm$^{2}$ following the closest packing way, enabling our multiplexed metasurface to have a potential of effective physical information capacity of printing image reaching the optical diffraction limit. Our study not only enlarges the information capacity of metasurfaces by expanding the integrated number of printing image in one metasurface, but also can promote metasurface applications in various fields such as information storage and encoding. DOI:10.1088/0256-307X/37/7/077801 PACS:78.67.Pt, 78.67.-n, 78.68.+m, 42.82.-m © 2020 Chinese Physics Society Article Text The miniaturization and integration of devices have been regarded as one of the core goals of nanoscience and nanotechnology, since such investigations have led to numerous remarkable achievements, which greatly promoted the developments of various fields, such as electronics,[1] biochemistry,[2] and quantum science.[3] However, the miniaturization of optical devices is a tough problem because of the requirement of a long propagation distance for phase accumulation. Fortunately, such a problem can be ideally addressed by metasurfaces.[4] Constructed by a monolayer of antenna arrays (called 'meta-atoms') with subwavelength thickness, metasurfaces enable the precise control of the amplitude, phase and polarization of incident light at nanoscale. Based on metasurfaces, a large variety of nanoscale optical devices have been proposed, including metalens,[5–8] orbit-angular-momentum generators[9–12] and other novel functionalities[13–18] that are not available with conventional components. These devices not only possess extreme compatibility for miniaturization and integration, but also exhibit outstanding optical properties because of the unparalleled capacity of metasurfaces in on-demand control of light. During its rapid developments, metasurface imaging, which contains two types of printing and hologram images, has gradually been cultivated as an important field, due to the advantages of ultrathin thickness, high-resolution, long duration, and profound applications.[19–24] For example, information encryption has gained growing attention, and various metasurfaces with the capacities of both printing and hologram image generations have been employed for information encryption, demonstrating unparalleled functionalities for physical information encoding in nanoscale, such as high security ensured by ghost imaging, multiple keys, and countersurveillance property.[25–30] To further promote the study of metasurface imaging, as well its applications such as information encryption or storage, expanding the information capacity by integrating multiple images in one metasurface is of great importance.[31] This aim is relatively easy to realize for hologram imaging because different hologram images can be generated at different image planes, avoiding the cross-talk between various images.[32,33] However, for the printing images whose imaging planes are always the metasurface structural plane, serious cross-talk that greatly decreases the image quality is inevitable. To the best of our knowledge, the integration of more than three printing images in one metasurface is still challenging. Herein, based on our concept of coherent pixel design,[34,35] we realize the design and fabrication of the multiplexed metasurface with five printing images, greatly expanding the information capacity of metasurface printing imaging. We firstly introduce the definition of the pixels for the multiplexed printing technique. As shown by the left column of Fig. 1(a), if one wants to present one image using metasurfaces, only two pixels are required. These two pixels can be defined as 1 and 0, respectively, which means they exhibit high and low transmittances for the incident light. When the case goes to two-picture generation under two incident lights, a more complicated design is needed because at least four pixels are necessary. To be specific, as illustrated in the right column of Fig. 1(a), these four pixels can be named as 11 (high transmittance under both $I_{1}^{\rm in}$ and $I_{2}^{\rm in}$), 01 (low transmittance for $I_{1}^{\rm in}$, but high transmittance for $I_{2}^{\rm in}$), 10 (high transmittance for $I_{1}^{\rm in}$, but low transmittance for $I_{2}^{\rm in}$), and 00 (low transmittance under both $I_{1}^{\rm in}$ and $I_{2}^{\rm in}$).
cpl-37-7-077801-fig1.png
Fig. 1. Definition of the metasurface pixel for multiplexed imaging. (a) The schematic diagrams of pixel design origins for a one-image metasurface (left) and a two-image metasurface (right), respectively. Generally, the numbers 1 and 0 respectively represents high and low transmittances for the pixel under a certain incident light. Since two independent pixels with high and low transmittances are required for generating one image under one incident light, $2^{n}$ kinds of pixels are needed for the $n$-image metasurface. (b) The diagrammatic sketch of the multiplexed metasurface with five printing images under five incident lights, whose fundamental pixels are 00100, 11010, 11111, etc. ($2^{5}=32$ in total).
As a result, one can conclude that since two independent pixels with high and low transmittances under a certain incident light are required for presenting one image, $2^{n}$ kinds of pixels will be needed if one wants to integrate $n$ images in one metasurface. The idea for multiplexed imaging can be easily understood. However, the practical design strategy and fabrication can be extremely tough. The reason can be attributed to the fact that the increasing of image integration number always brings about the increasing of sub-element number, because one sub-element usually can only respond to one incident light. Therefore, in order to realize multiplexed printing images, each metasurface pixel always has several sub-elements (such as the nanobrick applied in our study), which largely increases the difficulty of design and fabrication. As a consequence, the multiplexed metasurface with five printing pictures is still under investigation,[31,34,36–38] due to the lack of its required $2^{5} = 32$ pixels (i.e., 00100, 11010, 11111, etc., as shown in Fig. 1(b)). Generally, multiplexed metasurfaces are enabled by the pixel units with multiple sub-elements. However, the coupling between those sub-elements unavoidably leads to cross-talk among them, which can greatly decrease the quality of metasurface images. Fortunately, an emerging idea of coherent pixel design proposed by our group can overcome the problem of cross-talk,[30] because the intensity of the coherent pixel is dependent on the coupling between sub-elements, which means that the pixel intensity is considered to be the coherent superposition of all the sub-elements within it. Also, according to the coherent design approach, the geometry of the sub-elements can be exactly the same, greatly reducing the fabrication difficulties. Therefore, we employ the coherent pixel design to construct our five-image metasurface, in which a basic coherent pixel contains five sub-elements of crystalline silicon nanobricks with the size of $320\times 80\times 230$ nm$^{3}$ (Fig. 2(a)). With the aim of facilitating device miniaturization and integration, the size of each single nanobrick should be as small as possible. However, small size also increases the fabrication difficulty. In the present study, we choose the geometric parameters of a single nanobricks with considerations of both high fabrication reproducibility and relatively large optical response at every incident light wavelengths we required (such a light wavelength is theoretically arbitrary, but it may be limited by experimental conditions such as the output wavelength of the employed laser). As shown in Fig. 2(a), in a given coordinate system, for each sub-element of nanobrick, there are two key parameters, which are the rotation angle of the nanobrick ($\phi$) and the $x$-axis value of its center ($X$). Therefore, for the $k$th sub-element of nanobrick with ($X_{k}, \phi_{k}$), the Jones matrix is given by $$\begin{align} &J=R(-\phi_{k})\begin{pmatrix} t_{x} & 0 \\ 0 & t_{y} \end{pmatrix} R(\phi_{k}),\\ &R(\phi_{k})=\begin{pmatrix} \cos\phi_{k} & \sin\phi_{k} \\ -\sin\phi_{k} & \cos\phi_{k} \end{pmatrix} ,~~ \tag {1} \end{align} $$ where $t_{x}$ and $t_{y}$ are the complex transmission coefficients of incident light along the fast and slow axes. If the incident light is with arbitrary polarization of $1 \choose \sigma $, the scattered coefficient of light polarized orthogonally to the incident one can be written as $A_{k} =(-\sigma ,1) J{ 1 \choose \sigma }$. Note that herein the light polarization is expressed by $\sigma$. For instance, right and left circular polarizations (RCP, LCP) can be expressed by $\sigma =+1i$ and $\sigma = -1i$, respectively, and $x$-linear polarization is $\sigma = 0$, etc.
cpl-37-7-077801-fig2.png
Fig. 2. Design of the required pixel by the idea of coherent pixel. (a) Scheme for a basic coherent pixel using the mutiplexed metasurface with five printing images. The basic coherent pixel contains 5 nanobrick sub-elements with the size of $320\times 80\times 230$ nm$^{3}$. In order to minimize the physical size of the coherent pixel, the five nanobricks are arranged following the closest packing way in a square space of $1.45\times 1.45$ µm$^{2}$. (b) The calculations and FDTD simulations of the pixel intensity (left 00001, right-top 11100 and right-bottom 11101). In our calculations, the pixel intensities of high and low transmittances (can also be called bright and dark intensities) should have a ratio larger than 16.
Therefore, considering the coherent superposition of all the five sub-elements, the transmitted scattered intensity of a coherent pixel (i.e., pixel intensity) along $+z$ direction under a certain incident light with a polarization of $\sigma_{i}$, a wavelength of $\lambda_{i}$, and an incident angle of $\theta_{i} (I_{i}^{\rm in} (\lambda_{i},\theta_{i},\sigma_{i}))$ can be inferred as[34] $$\begin{align} I_{i}^{\rm out} (\lambda_{i},\theta_{i},\sigma_{i})=\Big| \sum\limits_{k=1}^5 A(\sigma_{i},\phi_{k})&\exp (i2\pi \sin \theta_{i} X_{k} /\lambda_{i}) \Big|^{2},\\ &i=1,2,3,4,5.~~ \tag {2} \end{align} $$ Therefore, by solving inequality groups, the geometric parameters of sub-elements can be obtained. For example, in order to obtain the sub-element structural parameters (i.e., the $X_{k}$ and $\phi_{k}$, $k = 1$, 2, 3, 4, 5) of pixels 00001, 11100, and 11101, one only needs to solve the following inequality groups (3)–(5) (the numbers of 4 and 0.25 are in an arbitrary unit), respectively. It should be mentioned that, in order to obtain a high image contrast, the pixel intensities of bright and dark pixels should have a ratio as large as possible. However, the difficulty for solving the inequality groups is dramatically increasing with greater bright/dark ratio. Based on our investigations, if such a bright/dark ratio is larger than 16, there will be an optimized value for the five-image metasurface (Fig. 2(b)). Also, during solving these inequality groups via the genetic algorithm, it is found that a coherent pixel containing five nanobricks supports the least number of required degrees of freedom for valid solutions. For the sake of minimizing the size of coherent pixels, we choose to use five sub-elements of nanobrick to construct an individual coherent pixel. $$ \left\{ { \begin{array}{l} I_{1}^{\rm out} (\lambda_{1},\theta_{1},\sigma_{1}) < 0.25, \\ I_{2}^{\rm out} (\lambda_{2},\theta_{2},\sigma_{2}) < 0.25, \\ I_{3}^{\rm out} (\lambda_{3},\theta_{3},\sigma_{3}) < 0.25, \\ I_{4}^{\rm out} (\lambda_{4},\theta_{4},\sigma_{4}) < 0.25, \\ I_{5}^{\rm out} (\lambda_{5},\theta_{5},\sigma_{5})>4, \\ \end{array}} \right.~~ \tag {3} $$ $$ \left\{ { \begin{array}{l} I_{1}^{\rm out} (\lambda_{1},\theta_{1},\sigma_{1})>4, \\ I_{2}^{\rm out} (\lambda_{2},\theta_{2},\sigma_{2})>4, \\ I_{3}^{\rm out} (\lambda_{3},\theta_{3},\sigma_{3})>4 \\ I_{4}^{\rm out} (\lambda_{4},\theta_{4},\sigma_{4}) < 0.25, \\ I_{5}^{\rm out} (\lambda_{5},\theta_{5},\sigma_{5}) < 0.25, \\ \end{array}} \right.~~ \tag {4} $$ $$ \left\{ { \begin{array}{l} I_{1}^{\rm out} (\lambda_{1},\theta_{1},\sigma_{1})>4, \\ I_{2}^{\rm out} (\lambda_{2},\theta_{2},\sigma_{2})>4, \\ I_{3}^{\rm out} (\lambda_{3},\theta_{3},\sigma_{3})>4, \\ I_{4}^{\rm out} (\lambda_{4},\theta_{4},\sigma_{4}) < 0.25, \\ I_{5}^{\rm out} (\lambda_{5},\theta_{5},\sigma_{5})>4. \\ \end{array}} \right.~~ \tag {5} $$ On the basis of the above discussions, we turn on to calculate structural parameters of the 32 pixels. Herein, the incident lights are given, and theoretically they can be five arbitrary combinations of incident angle, polarization and light wavelength. As a demonstration without the loss of generality, we choose the five incident lights as ($\lambda_{1} = 532$ nm, $\theta_{1} = 45^{\circ}$, $\sigma_{1}=i$), ($\lambda_{2} = 532$ nm, $\theta_{2} = 38^{\circ}$, $\sigma_{2} = -i$), ($\lambda_{3} = 633$ nm, $\theta_{3} = 31^{\circ}$, $\sigma_{3}=i$), ($\lambda_{4} = 532$ nm, $\theta_{4} = 24^{\circ}$, $\sigma_{4} = -i$), and ($\lambda_{5} = 671$ nm, $\theta_{5} = 17^{\circ}$, $\sigma_{5} = 0$), respectively. Furthermore, after obtaining all the structural parameters of the 32 pixels, we employ a commercial finite-difference time-domain (FDTD) software (FDTD solutions, Lumerical Inc.) to verify the calculated results. In our simulations, the empirical bulk dielectric function is used for Si[39] and reflective index of 1.45 for the glass substrate. The polarized component of transmitted scattered light which is orthogonal to the incident light is extracted as ${E}'(k_{x},k_{y})$. In order to ensure that all the five sub-elements can be taken as a whole coherent pixel, relatively small NA should be applied for the image collecting system, which means that the transmitted scattered lights should be collected along the normal direction ($+z$ axis) with a small scattering-angle range. Therefore, herein the images at the sample plane are reconstructed by $$\begin{align} &E(x,y)=\sum\limits_{k_{x},k_{y} } {{E}'(k_{x},k_{y})e^{i(k_{x} x+k_{y} y)}},\\ &\sqrt {k_{x}^{2} +k_{y}^{2} } /k_{0} \leqslant {\rm NA=0.1}. \end{align} $$ As shown in Fig. 2(b), which gives the results of three typical pixels, the FDTD simulations agree well with the calculated ones, which further confirms the correctness of our designs. The metasurface samples were fabricated following theoretical designs. First, we deposited 230-nm-thick Si using inductively coupled plasma chemical vapor deposition (ICP-CVD, PlasmaPro System 100ICP180-CVD) on a glass wafer. Then, a 200-nm-thick HSQ electron beam resist layer was spin-coated at 4000 rpm in 1 min onto the sample and then baked on a hot plate for 5 min at 90℃. Then, a 50-nm-thick aluminum layer (thermal evaporation, Q150) was deposited to serve as the charge dissipation layer. Next, the pattern is exposed using electron beam lithography (EBL, Raith Vistec EBPG-5000plusES) at 100 keV. After exposure, the aluminum layer was removed by 5% phosphoric acid, and the resist was developed with tetramethylammonium hydroxide (TMAH). Finally, the inductively coupled plasma (ICP, PlasmaPro System 100ICP180) was used to etch the substrate with resist mask and obtain the final metasurface structure. As shown in Fig. 3, which gives the scanning electron microscope (SEM) images of four typical pixels (00000, 11111, 01110, and 10001), one can find that our fabricated samples all have the patterns in high accordance with their theoretical designs, which promises the experimental realization of the multiplexed metasurface with five printing images. Also, it should be mentioned that the design solution for these 32 pixels is not unique. However, in order to maximally increase the image resolution, we minimized the physical size of our coherent pixels. As demonstrated in Figs. 2(a) and Fig. 3, one can find that the five sub-elements of a basic coherent pixel were arranged following the closest packing way in a square space of $1.45\times 1.45\,µ$m$^{2}$, permitting a minimal size. Since each of the coherent pixel can be used for generating five images, the effective size can be regarded as 1/5 of its physical size (i.e., $290 \times 290$ nm$^{2}$), which will allow our five-image metasurface to have a potential of high physical information capacity reaching the diffraction limit of visible light.
cpl-37-7-077801-fig3.png
Fig. 3. SEM photography of four typical pixels. (a)–(d) The pixels 00000, 11111, 01110 and 10001. For each pixel, (i) and (ii) are top-view images based on low and high magnifications, and (iii) is the image of 45$^{\circ}\!$-titled view with high magnification. The inset in (i) is the corresponding design model of each pixel. The scale bar in (i) is 2 µm and the scale bars in (ii) and (iii) are 300 nm.
Figure 4(a) illustrates the experimental setup for the optical measurements of our metasurfaces. In short, a coherent light with arbitrary polarization is generated by a quarter waveplate (named as QWP$_{1}$) together with a polarizer ($P_{1}$). Then, this light is incident on the metasurface sample from the substrate side with an angle of $\theta$. The transmitted scattered light of the metasurface is collected by a $4\times$/0.10 objective and filtered by a pair of QWP and polarizer (QWP$_{2}$ and P$_{2}$), which only pass the light polarized along the orthogonal direction of the incident light. In order to obtain the metasurface printing images, two lenses are applied to focus the transmitted scattered light of metasurface into a charge-coupled device (CCD) camera. In our experiments, the transmitted scattered light collected by the CCD is with polarization perpendicular to the incident light, and it is also almost perpendicular to the metasurface due to the employed objective with NA of 0.1. With the aim of fully exhibiting the optical response of all the 32 pixels, we intended to arrange an image of $4 \times 8$ array, which consists of all the as-prepared pixels, and the configuration of this array is given in the left column of Fig. 4(b). Comparing the theoretical images and experimental results of this array under the five chosen incident lights (right column of Fig. 4(b)), one can clearly see that they are highly fitted with each other, demonstrating our success in realizing the multiplexed metasurface with five printing images. Although the images presented here are relatively meaningless, one can apply the design of these 32 basic pixels to form arbitrary images on-demand. Moreover, using the design idea proposed here, it is also facile to obtain other 32 basic pixels which work under five other arbitrary incident lights.
cpl-37-7-077801-fig4.png
Fig. 4. Experimental demonstration of the five-image metasurface. (a) The experimental setup for the optical measurements. QWP: quarter waveplate, P: polarizer. (b) The configuration and the measurement results of all the 32 pixels under five given incident conditions. An image of $4 \times 8$ array is chosen to fully exhibit optical response of all the fabricated coherent pixels. The good agreement of theoretical and experimental results demonstrate the successful realization of 32 pixels, as well as the multiplexed metasurface with five printing images.
In summary, based on the concept of coherent pixel, we have designed and fabricated all the 32 pixels required by the multiplexed metasurface with five printing images. A basic coherent pixel contains five sub-elements, which are nanobricks with the size of $320\times 80\times 230$ nm$^{3}$. All the sub-elements are arranged following the closest packing way in a square space of $1.45\times 1.45\,µ$m$^{2}$, making our multiplexed metasurface possess a potential of high physical information capacity reaching the diffraction limit of visible light. Optical measurements and theoretical designs are in good accordance with each other, which strongly confirms the success in realizing the multiplexed metasurface with five printing images. Our study not only demonstrates the feasibility of coherent pixel design for expanding the integrated number of printing image in one metasurface, but also enlarges the information capacity of metasurfaces, promoting their applications in various fields such as information storage and encoding, as well as novel display techniques. References Plasmonics: Merging Photonics and Electronics at Nanoscale DimensionsA modular microfluidic architecture for integrated biochemical analysisQuantum plasmonics get appliedTailor the Functionalities of Metasurfaces Based on a Complete Phase DiagramUltrahigh Numerical Aperture Metalens at Visible WavelengthsA broadband achromatic metalens for focusing and imaging in the visibleA broadband achromatic metalens in the visibleMetalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imagingMultichannel Polarization-Controllable Superpositions of Orbital Angular Momentum StatesGenerating and Separating Twisted Light by gradient–rotation Split-Ring Antenna MetasurfacesA Minimalist Single‐Layer Metasurface for Arbitrary and Full Control of Vector Vortex BeamsPhotonic Spin Hall Effect at MetasurfacesNarrow and Dual-Band Tunable Absorption of a Composite Structure with a Graphene MetasurfaceDielectric gradient metasurface optical elementsInfrared hyperbolic metasurface based on nanostructured van der Waals materialsImaging-based molecular barcoding with pixelated dielectric metasurfacesWideband linear-to-circular polarization conversion realized by a transmissive anisotropic metasurfaceHigh Refractive Index Ti 3 O 5 Films for Dielectric MetasurfacesArbitrary Manipulation of Light Intensity by Bilayer Aluminum MetasurfacesOptical Information Multiplexing with Nonlinear Coding MetasurfacesPlasmonic colour generationStructural colour using organized microfibrillation in glassy polymer filmsMetasurface holograms reaching 80% efficiencyFlexible Nanowire Cluster as a Wearable Colorimetric Humidity SensorSingle-pixel computational ghost imaging with helicity-dependent metasurface hologramLaser-Splashed Three-Dimensional Plasmonic Nanovolcanoes for Steganography in Angular AnisotropyIntegrated Metasurfaces with Microprints and Helicity‐Multiplexed Holograms for Real‐Time Optical EncryptionResonance-enhanced three-photon luminesce via lead halide perovskite metasurfaces for optical encodingPerturbative countersurveillance metaoptics with compound nanosievesTunable Resonator‐Upconverted Emission (TRUE) Color Printing and Applications in Optical SecurityNoninterleaved Metasurface for (2 6 -1) Spin- and Wavelength-Encoded HologramsFour‐Wave Mixing Holographic Multiplexing Based on Nonlinear MetasurfacesCoherent Pixel Design of Metasurfaces for Multidimensional Optical Control of Multiple Printing-Image Switching and EncodingFull-colour nanoprint-hologram synchronous metasurface with arbitrary hue-saturation-brightness controlDual Color Plasmonic Pixels Create a Polarization Controlled Nano Color PaletteProgresses in the practical metasurface for holography and lensMetasurface‐Empowered Optical Multiplexing and Multifunction
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