1. Introduction

Wavelength, amplitude, phase, and polarization are four fundamental optical properties, which can be manipulated individually or in combination by innovation approaches, thus resulting in various optical components. Typical examples of optical elements include optical filters for amplitude control, optical lenses for phase control, and bulky-polarizer for polarization control. In recent years, metasurface, an artificial material composed of subwavelength planar nanostructure, has attracted widespread attention due to its superior performance in manipulating light waves point-by-point [1–9]. Because of its advantages of light weight and miniaturization, early metasurfaces were mainly used to replace traditional optical components to achieve the miniaturization of optical systems, such as gratings [10], lenses [11], and holograms [12]. However, one fabricated metasurface is only endowed with one specific function. Then, the researchers fully explored the degrees of freedom contained in the metasurface, and realized multifunctional integration. By tailoring the materials, dimension, orientation or/and distribution of nanostructures, the phase, amplitude and polarization of orthogonal linearly polarized (LP) or circularly polarized (CP) light can be partially or totally controlled. As a result, dual-channel nanoprinting devices [13,14], step-zoom lenses [15], asymmetrical device [16–18], vectorial holograms [19,20], and various multifunctional devices can be realized [21–25].

Thereinto, nanoprint-hologram metasurfaces for simultaneous phase and amplitude/spectrum/polarization modulations have attracted more attention in image displaying and information encoding field. These multitasked metasurfaces are mainly achieved by four approaches, in which super-celled nanostructures [26–33], single-celled nanostructures [34], size-adjustable nanostructures [35–38], and single-sized nanostructures [39,40] are utilized as the unit/response cell, respectively. The first approach is to achieve independent manipulation of amplitude and phase by interleaving multiple metasurfaces in plane [26–29] or stacking metasurfaces in space [30–33]. That is, each response unit-cell contains multiple cells. The second approach perform manipulations of light by assigning two types of nanostructures with different geometry [34]. The third approach is based on tailored nanostructures with polarization-selective responses. The phase or amplitude of orthogonal LP light can be independently controlled by changing the dimensions of nanostructure [35–37]. Furthermore, the phase and intensity of orthogonal CP Light in two polarization modes can be independently modulated by elaborately designing the dimensions and orientations of nanostructures [38]. These schemes mentioned above either require complex nanostructure design or sacrifice some control of the optical transmission matrix, which therefore burdens the fabrication process or decreases the information density of each image channel. In comparison, the fourth method is simpler, which can achieve independent manipulation for both the amplitude and phase only by orientation degeneracy [39,40]. However, these exists an extremum-mapping problem in this scheme. That is, if the intensities of the near-field images are all extreme values (0 and 1), then for the one-to-two mapping strategy, the holographic image cannot be reconstructed in the far field, and for the one-to-four mapping strategy, the inevitable twin-image will be generated. It may limit its further applications and result in the capability of holographic images being halved.

In this paper, we propose a new multifunctional metasurface platform inspired by redundancy, which can solve the extremum-mapping problem existing in single-sized schemes while does not increase the complexity of the nanostructures. As shown in Fig. 1, when a binary image is encoded in the near field, a multi-steps holographic image without twin-image can be reconstructed in the far field. Our proposed scheme can be realized by finding the balance between the redundancy of image recognition and the redundancy of hologram design. The introduction of the redundancy of intensity modulation builds a one-to-four mapping between the intensity and Pancharatnam-Berry (PB) phase, which will provide more degrees of freedom to joint optimization of the near- and far-field meta-images. Then, the orientation distribution of the single-sized nanostructures can be obtained by utilizing the optimization algorithm. To prove its feasibility, we fabricated a piece of multifunctional metasurface consisting of single-sized silver nanobrick arrays. The proposed multifunctional metasurfaces, featuring flexible working mode, broadband response, and high robustness against the fabrication error, have potential applications in information multiplexing, high-end optical anti-counterfeiting, information hiding and encoding, image display for AR/VR, optical storage, and many other related fields.

 

Fig. 1. The schematic diagram of single-sized multifunctional metasurfaces for simultaneously encoding a binary image and a multi-steps holographic image without twin-image.

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2. Result and discussion

In order to simultaneously encode nanoprinting and holographic images into a piece of metasurface, it is need to manipulate the amplitude and phase independently. In previous works [39,40], a simple scheme is proposed to achieve independent amplitude and phase modulation based on single-sized nanostructures. Specifically, when an incident LP beam passes through a nano-polarizer with orientation angle $\theta $, the normalized intensity of outgoing beam can be expressed as ${\cos ^2}\theta $. When an incident LP light successively passes through a nanostructure and a bulk analyzer, the normalized intensity of output light can be simplified as ${\cos ^2}2\theta $. Therefore, any desired outgoing light intensity can be obtained by elaborately configuring the nanobrick orientation, which guarantees the feasibility of forming a continuous grayscale image in near field. Additionally, when a CP beam illuminates the birefringent metasurfaces, the outgoing beam includes one part with opposite handedness as the incident CP light possessing a phase delay of ${\pm} 2\theta $, which only depends on the orientation and can be used to design phase elements. Note that the functions ${\cos ^2}\theta\,and\;{\cos ^2}2\theta $ are non-monotonic in the in interval [0, π], which builds the one-to-many correspondence between the output light intensity and orientation angles. Thus, it provides the degrees of freedom to manipulate amplitude and phase in two information channels independently.

However, this single-sized scheme has an extremum-mapping problem, as shown in Figs. 2(a)-(c). That is, for one-to-two mapping scheme, when the output light intensities are extreme value of 0 or 1, the orientation angle of nanostructure has only one choice and the corresponding PB phase is a fixed value, under which the integration of a nanoprinting image and a holographic image cannot be achieved. For one-to-four mapping scheme, when the output light intensities are extreme value of 0 or 1, the orientation angle of nanostructure has two choices and there are two corresponding values of PB phase. Thus, when a binary image is encoded in the near field, the holographic image with the inevitable twin-image will be reconstrued in the far field, which will limit its further application and result in the capability of the holographic image being halved. In order not to increase the complexity of the nanostructures for developing high-density and multifunctional metasurfaces, we introduced the concept of tri-redundancy. In this paper, tri-redundancy includes three parts: image recognition, hologram design and intensity modulation, as shown in Fig. 2(d). Specifically, redundancy of image recognition refers to the non-uniqueness of image recognition. Even if the image has some noise or changes, it can still be recognized. For hologram design, redundancy refers to its robustness to additional phase or amplitude errors. To be specific, for the reconstruction of a specific target holographic image, there are a variety of hologram phases to choose. The redundancy of intensity modulation refers to the one-to-four mapping between the intensity and orientation angles. For one specific outgoing light intensity, there are four choices of orientation angles in the interval [0, π]. These redundancies provide an extra freedom for simultaneously achieving the near-field and far-field meta-images display.

 

Fig. 2. The design flowchart of the multifunctional metasurfaces. (a)-(c) Extremum-mapping problem existing in current single-sized schemes. (d) The tri-redundancy of image recognition, hologram design and intensity modulation provide a design freedom for simultaneously recording a binary meta-image and a multi-steps holographic image without twin-image on a piece of single-sized metasurface.

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When incident LP light with intensity ${I_0}$ successively passes through an anisotropic nanostructure and a bulk-optic analyzer, the intensity of the transmitted light can be expressed as

If the nanostructure is a general anisotropic scatterer (A≠B) and α₂=α₁+π/2, we can simplify Eq. (1) as

Equation (2) indicates that our proposed scheme is not limited to be applied in a linear polarizer or half-wave plate, and the desired intensity of transmitted beam can be achieved in any birefringent nanostructure (A≠B) by rotating the polarization direction of an anisotropic nanostructure. It is worth noting that the fabrication error will lead to the fluctuation of the transmission or reflection coefficient, thus affecting the efficiency of the outgoing light, but the contrast of the image will not be affected.

The key step in designing such kind of multifunctional metasurfaces is to obtain suitable orientation distribution of the single-sized nanostructures. To prove the feasibility of our proposed scheme, we designed to encode a quick response (QR) code image in the near field and a 16-steps holographic image in the far field. Firstly, the white pixels of the QR code image are introduced into four kinds of noises, whose intensity values are 0.85, 0.50, 0.146, 0.00 respectively. Then, a QR code image consisting of m white pixels has ${4^m}$ different candidate QR code images, which can link to the same preset information but correspond to different geometric phase distributions for incident CP light. Due to the redundancy of intensity modulation, the four noises introduced in each white pixel correspond to 16 geometric phase delays, which meets the requirement of achieving a 16-steps holographic image reconstruction. To find a balance between the redundancy of image recognition and redundancy of hologram design, a simulated annealing (SA) algorithm [39] is applied. The SA algorithm is an iterative optimization algorithm. When some stopping criterions are satisfied (e.g., a pre-specified maximum number of iterations has been executed or a satisfying solution has been found), we can get an optimal phase distribution, which determines the orientation distribution of the designed multifunctional metasurface. More details about the SA algorithm are given in appendix A. As a result, the designed multifunctional metasurfaces enable the generation of a QR code image in the near field and the projection of an independent 16-steps holographic image in the far field.

To create a physical realization of a multifunctional metasurface, we also need to confirm the geometric dimension of nanostructure. In this paper, we built a nanostructure unit cell composed of silver nanobricks and a dielectric SiO₂ substrate. Figure 3(a) shows the schematic diagram of one unit-cell. CST Microwave Studio software is employed to perform the numerical simulations. The reflectivity and transmissivity were obtained by the reflection and transmission ports and electromagnetic field distributions were collected by field monitors. We swept L and W from 50 nm to 240 nm in steps of 5 nm while the cell size C was fixed at 400 nm and height H was fixed at 70 nm. The reflectivity and transmissivity of the well-designed silver nanobrick are illustrated in Fig. 3(b), whose sizes are L = 130 nm (length), W = 85 nm (width), H = 70 nm (height), and C = 400 nm (cell size). From Fig. 3(b) we can see that that most of the incident beam with polarization direction along the long axis of the nanobrick is reflected (83.7%), while the incident beam with polarization direction along the short axis is transmitted (96.8%) at the wavelength of 633 nm. Figure 3(c) shows the simulated electric field distributions at the cross-section of the nanostructure, which also indicates that the incident light polarized along the long axis of nanobrick can be nearly reflected and that polarized along the short axis of the nanobrick can be totally transmitted. Therefore, the well-designed silver nanobrick can serve as a transmission or reflection nano-polarizer at the wavelength of 633 nm.

 

Fig. 3. Illustration of a unit-cell and simulation results. (a) Schematic diagram of a nanobrick unit-cell. (b) Simulated reflectivity and transmissivity verse wavelengths (550 nm -700 nm) with incident light polarized along the long and short axes of the Ag nanobrick. (c) Electric fields at the cross-section of nanobrick for x-polarized and y-polarized incident light respectively. (d) Scanning electron microscope (SEM) image of fabricated sample. The scale bar is 1 µm.

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To prove that such multifunctional metasurface can simultaneously encode a binary nanoprinting image and a holographical image without twin-image, we fabricated a sample by electron beam lithography (EBL), whose SEM image is shown in Fig. 3(d). More details about sample fabrication are shown in appendix B. A 2 × 2 periodic array of the designed metasurface was used to avoid the appearance of laser speckles [12], in which the area of each array is 200 × 200 µm² for encoding 500 × 500 pixels images. The near-field meta-image is recoded on the surface of metasurface, which can be observed with an optical microscope of magnification 50×. The far-field image is reconstructed in the Fraunhofer diffraction region, which can be observed by an optical screen. Appendix C shows the experimental setups used in this work. The experimental results in reflection mode are shown in Fig. 4. When the transmission axes of the polarizer and analyzer are orthogonal (e.g., α₁=-45° and α₂= 45°, α₁= 0° and α₂= 90°), we can observe the clear QR code images and their complementary pattern linking to a designed word of “metasurface”. When the polarization direction of incident light deviates from the designed value, QR codes are blurry and can’t be recognized, as shown in Figs. 4(c) and (d). When the sample is illuminated by RCP light and LCP light, high-fidelity holographic images without twin-image can be obtained. When LP light illuminates the sample, a holographic image with twin-image occurs due to the PB phase [39]. The experimental results agree well with the theoretical design, demonstrating the feasibility of our proposed scheme.

 

Fig. 4. The near-field and far-field experimental results for the multifunctional metasurface in reflection mode. (a)-(d) The reflected nanoprinting images are captured by an optical microscope. (e)-(g) The reflected holographic images are reconstructed in far field. The scale bar is 40 µm. The red and black arrows represent the transmission axis directions of the polarizer and analyzer, respectively.

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In addition, we obtain the experimental results in transmission mode. Figures 5(a)-(d) shows the near-field results captured at different transmission axes of the polarizer and the analyzer. It is obvious that the near-field images in transmission mode are complementary to that in reflection mode, which can be explained by the fact that the transmission axis of the optimized nano-polarizer in the reflection mode is perpendicular to that in transmission mode. The near-field meta-images obtained in the transmission mode agree with those in the reflection mode. That is, only when the polarizer and the analyzer are perpendicular to each other, clear QR code images can be identified with a conventional smartphone QR reader and it could be verified that they are successfully connected to the designated word “Metasurface”. When incident light is CP light, the transmitted holographical images without twin-image are with high fidelity. It proves that our proposed multifunctional metasurface has flexible work modes, which will greatly facilitate its practical application. For the near-field, the efficiency is difficult to measure since it is recorded right at the sample surface. In addition, as the near-filed pattern is generated by intensity modulation, the efficiency depends on the grayscale distribution of the target image. The measured hologram efficiency, defined as the ratio of the power of the target holographic image to the power of the incident beam, is 3% at the operating wavelength of 633 nm. Such a relatively low value could be improved by more precise fabrication procedures, reducing the extending angles of the holographic image, using low-loss dielectric materials and employing half-wave plate nanostructures.

 

Fig. 5. The near-field and far-field experimental results for the multifunctional metasurface in transmission mode. (a)-(d) The transmitted nanoprinting images are captured by an optical microscope. (e)-(g) The transmitted holographic images are reconstructed in far field. The scale bar is 40 µm. The red and black arrows represent the transmission axis directions of the polarizer and analyzer, respectively.

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In practical application, broadband response characteristic will greatly reduce the observation requirements, facilitating the applications of optical device in different scenerios. To explore the broadband response of multifunctional metasurface in the near field, we acquired QR code images under the illumination of a quartz halogen lamp. The first column shows the result of the sample being illuminated directly with a quartz halogen lamp, and the second and third columns are the result with the green and red filters additionally inserted. As shown in Fig. 6, all near-field QR images are clear, which can be explained by the light intensity modulation function shown in Eq. (2). This function indicates the incident light source only affects the optical efficiency rather than the meta-image contrast. In addition, we found that the fluctuations of the reflection/transmission coefficients caused by fabrication errors do not affect the image quality. Then, we utilized a supercontinuum laser to illuminate the sample and explore the broadband response in the far field. As shown in the third and fourth rows of Fig. 6, all far-field holographic images have high fidelity in both transmission and reflection modes when the wavelength varies within the range of 540–660 nm. Therefore, it proves that our proposed multifunctional metasurface has broadband response and high tolerance against fabrication errors, which would significantly expand the practical application scenarios. Another notable feature of our proposed scheme is scalability. Since our proposed multifunctional metasurface can be realized only by arranging the orientations of single-sized nanobricks, it is feasible to combine with previous approaches to provide more degrees of freedom. For example, inspired by Refs. [41,42], the wavelength information can be merged with our work to achieve multichannel information encoding. The introduction of deep learning into structure design [43], multifunctional metasurfaces with better optical information would be realized.

 

Fig. 6. Broadband response of the multifunctional metasurface. (a)-(c) reflected nanoprinting images are obtained by an optical microscope configuring a halogen lamp or narrow-band filters (550 nm and 650 nm). (d)-(f) the corresponding transmitted nanoprinting images. (g)-(j) reflected holographic images generated by illuminating the samples with a super-continuum laser source in the range from 540 to 660 nm in steps of 40 nm. (k)-(n) the corresponding transmitted holographic images.

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3. Conclusion

By introducing the tri-redundancy, we propose a new multifunctional metasurface platform based on arbitrary anisotropic single-sized nanostructures. The tri-redundancy of image recognition, hologram designing and intensity modulation provides an extra degree of freedom and allows the encoding of a binary image in the near-field, and reconstructing a multi-steps holographic image without twin-image in the far-field, which solves the extremum-mapping problem existing in current single-sized multifunction metasurfaces. We have designed a metasurface consisting of nano-polarizer that generates a QR code image at the sample surface while projecting 16-steps phase-only holographic images in the far field. The experimental results demonstrate multi-steps phase modulation functionality can be merged with two-steps intensity modulation functionality with simple nanostructures. In addition, our proposed scheme has many unparalleled advantages, such as flexible working mode (transmission or reflection), broadband response, nanostructural insensitivity and high robustness against fabrication errors, which will provide great potential in practical applications and spur a new wave of multifunctional optical devices.

Appendix A: Flowchart of optimization algorithm

Figure 7 shows the flowchart of the simulated annealing algorithm. It starts from an initial phase $\varphi $, which is calculated according to the grayscale distribution of the target binary image and is exactly twice of the orientation angle. Then, a new phase ${\varphi _{new}}$ is generated randomly at some predefined ranges. Based on the Metropolis acceptance criterion [44], the candidate phase ${\varphi _{new}}$ is accepted as the current solution based on the customized search mechanism, that is, $Cost({{{|{FFT({{e^{i{\varphi_{new}}}}} )} |}^2}{\rm{,\;}}{I_0}} )< Cost({{{|{FFT({{e^{i\varphi }}} )} |}^2}{\rm{,\;}}{I_0}} )$ or ${e^{({{\rm{\varDelta }}I{\rm{ - \varDelta }}{I_{new}}} )/{t_k}}} > rand({0,1} )$, where ${t_k}$ is the temperature of the $k$-th iteration, FFT represents the Fourier transform and rand (0,1) indicates a random number in the interval [0,1]. When some stopping criterions are satisfied, the final phase distribution can be confirmed.

 

Fig. 7. Flowchart of the simulated annealing algorithm.

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Appendix B: Sample fabrication

To process the metasurface sample, a PMMA film was first spin-coated on a fused quartz substrate. Then, the substrate was covered by PEDOT: PSS film and followed by exposed with the electron beam lithography to pattern the designed nanostructural arrays. Afterward, the exposed resist was developed at room temperature for 80 s, immersed in IPA for 30 s, and dried by nitrogen. Finally, a 70 nm silver film was deposited by the thermal evaporator and then lift-off in 85 °C hot acetone.

Appendix C: Experimental setups

Since the near-field image is recorded in the structure surface and its size is the same as the fabricated sample, the experimental results in reflection and transmission modes can be observed by an optical microscope (Motic BA310MET-T), as shown in Fig. 8(a). Figures 8(b) and (c) show the experimental setups of obtaining far-field holographic images. The polarization state of an incident beam from a He-Ne laser was converted into circular polarization after passing through a LP and a quarter-wave plate (QWP). Then, the metasurface sample was illuminated by the CP light after passing through an iris.

 

Fig. 8. Experimental setups of obtaining the near-field and far-field images. (a) An optical microscope is used to capture the near-field nanoprinting images; (b) experimental setup is used to obtain the reflected holographic image; (c) experimental setup is used to obtain the transmitted holographic image.

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Funding

National Natural Science Foundation of China (12104402); Fundamental Research Funds for the Central Universities (2042022kf1011); 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 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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