Abstract
Monochromatic light can be characterized by its three fundamental properties: amplitude, phase, and polarization. In this work, we propose a versatile, transmissionmode alldielectric metasurface platform that can independently manipulate the phase and amplitude for two orthogonal states of polarization in the visible frequency range. For proofofconcept experimental demonstration, various singlelayer metasurfaces composed of subwavelengthspaced titaniumdioxide nanopillars are designed, fabricated, and characterized to exhibit the ability of polarizationswitchable multidimensional lightfield manipulation, including polarizationswitchable grayscale nanoprinting, nonuniform cylindrical lensing, and complexamplitude holography. We envision the metasurface platform demonstrated here to open new possibilities toward creating compact multifunctional optical devices for applications in polarization optics, information encoding, optical data storage, and security.
Introduction
A coherent beam of monochromatic light can be characterized by three fundamental properties: phase, amplitude, and polarization^{1}. For hundreds of years, humans have developed innovative approaches to manipulate these fundamental properties, resulting in bulk optical components omnipresent in current day technology, such as cellphones and cameras, as well as in complex freespace optical experiments, such as in the Laser Interferometer GravitationalWave Observatory (LIGO)^{2} or the recently demonstrated photonic quantum computer^{3}. Typical examples of bulk optical components include optical lenses and spatial light modulators for phase control, neutral density filters for amplitude control, and waveplates for polarization control. In recent years, optical metasurfaces, which consist of an array of twodimensional (2D) subwavelength nanostructures, has been shown to provide a compact and efficient platform for modifying the amplitude, phase, and polarization of light^{4,5,6,7,8,9,10,11,12,13,14}. Various planar metasurface devices have been demonstrated to exhibit equivalent optical functionalities as their bulk counterparts, but instead in a significantly smaller and complementary metal oxide semiconductormanufacturable footprint^{15,16,17,18,19,20,21,22,23}. For example, metalenses—one typical subcategory of metasurface optics exhibiting only phase control—can offer desired phase engineering to achieve excellent diffractionlimited achromatic focusing for highresolution imaging applications^{24,25,26,27,28,29,30,31}.
Most common metasurface embodiments, such as a metalens, rely on nanostructure design targeted to manipulate only one property of light. While, in fact, each subwavelength nanostructure that constitutes an optical metasurface can be designed to instead simultaneously manipulate multiple properties of light. Therefore, it is possible to design singlelayer metaoptic devices offering fascinating multifunctional responses and able to synchronously manipulate two or more properties of incident light, something that is either not possible with conventional optics, or require complex optical setups made up of two or more optical components. As an example, by simultaneously controlling the amplitude and phase of light at a desired wavelength, complexamplitude holograms or synchronous nanoprinting holograms has been achieved using a singlelayer metasurfacebased optic^{32,33,34,35,36,37}. Furthermore, various recently reported research results have demonstrated polarizationcontrolled phasetuning metasurface optics to achieve polarizationswitchable imaging^{38,39,40}, holography^{41,42,43,44,45}, and beam shaping^{46,47}. However, how to interlink phase and amplitude with polarization to achieve encoding independent amplitude and phase functions into a pair of orthogonal polarization states of light is still a challenge. Such a capability can lead to the development of complex functionality, multichannel, and multifunctional metaoptical devices for engineering of light in a compact footprint. A plasmonic metasurface embodiment to realize independent amplitude and phase control of light for linearly polarization was recently demonstrated^{48,49}. Nonetheless, this approach suffers from large losses due to ohmic absorption in the metal at optical frequencies, and only operated in refection mode, which significantly limits its applicability in common experimental scenarios.
In this work, we demonstrate a transmissionmode alldielectric metasurface platform that can simultaneously and independently manipulate the amplitude and phase for a pair of orthogonal states of polarization at visible frequencies. In contrast to a previous demonstration that only relies on geometricphase modulation to tune the amplitude and phase for a fixed polarization state^{29}, here, by combining geometric phase with propagation phase, the proposed metasurface optics is able to completely decouple any combination of two arbitrary amplitude and phase profiles, and encode their information into two orthogonal polarization states. Various singlelayer metasurfaces composed of subwavelengthspaced titaniumdioxide (TiO_{2}) nanopillars on a fusedsilica substrate are designed and fabricated to exhibit the ability of polarizationswitchable multidimensional lightfield manipulation. Examples of proofofconcept experimental demonstrations shown here include polarizationswitchable nanoprinting, nonuniform cylindrical lensing, and complexamplitude holography. To the best of our knowledge, this is the first experimental realization of a singlelayer metasurface that integrates four independent channels of different optical information for a pair of orthogonal polarization states. This capability is elegantly demonstrated here by incorporating two nearfield nanoprinting images and two farfield hologram images, within the same metasurface. We envision this type of metasurface platform to open new possibilities of creating compact multifunctional optical devices for applications in polarization optics, information encoding, optical data storage, and security.
Results
Design principle
By leveraging the effective optical response of a metasurface to the three properties of incident light, a transmissionmode metasurface is envisioned to simultaneously and independently tailor the amplitude and phase for a pair of arbitrary orthogonal polarization states (this transformation is schematically shown in Fig. 1). When a monochromatic light beam with a specific state of input polarization λ_{1}^{+}〉 is incident on the metasurface, the output wavefront can be described by an amplitude and phase distribution profiles of E_{1} and φ_{1}, respectively. Similarly, when the input light beam is in the orthogonal state of polarization λ_{2}^{+}〉 with respect to λ_{1}^{+}〉 and is incident on the same metasurface, the output wavefront is described by two independent amplitude E_{2} and phase φ_{2} profiles. For a metasurface composed of linearly birefringent elements, there is also a restriction that the handedness of the output polarization is opposite to that of the input polarization. Therefore, for any two arbitrary orthogonal states of polarization, including circular, elliptical, or linear, the output wavefront has oppositehandedness polarization (λ_{1}^{−}〉, λ_{2}^{−}〉), with respect to the input polarization (λ_{1}^{+}〉, λ_{2}^{+}〉).
First, we consider two arbitrary orthogonal states of polarization in the linear polarization basis, λ_{1}^{+}〉 = [cos χe^{iδ}sin χ]^{T} and λ_{2}^{+}〉 = [−sin χe^{iδ}cos χ]^{T} incident on the metasurface, where parameter χ and δ determine the respective polarization states. As mentioned earlier, the output wavefronts are in the orthogonal polarization states, denoted by (λ_{1}^{−}〉, λ_{2}^{−}〉), and are complex conjugates of (λ_{1}^{+}〉, λ_{2}^{+}〉) with amplitude and phase profiles given by (E_{1}, E_{2}) and (φ_{1}, φ_{2}), respectively. The metasurface can be described by a Jones matrix J(x,y), which simultaneously satisfies the transformations, \(J(x,y)\left {\lambda _1^ + } \right\rangle = E_1(x,y)e^{i\varphi _1(x,y)}\left {\lambda _1^  } \right\rangle\) and \(J(x,y)\left {\lambda _2^ + } \right\rangle = E_2(x,y)e^{i\varphi _2(x,y)}\left {\lambda _2^  } \right\rangle\), at each spatial pixel location (x,y). The required Jones matrix is calculated as (see Supplementary Note 1 for details):
This is a nonunitary matrix and thus cannot be directly diagonalized. Mathematically, the complex amplitude \(E_{1,2}\left( {x,y} \right)e^{i\varphi _{1,2}\left( {x,y} \right)}\) can be decomposed as:
where \(E_{1,2}\left( {x,y} \right) = \cos \left( {\frac{{\varphi _A^{ + ,  }  \varphi _B^{ + ,  }}}{2}} \right)\) and \(\varphi _{1,2}\left( {x,y} \right) = \left( {\varphi _A^{ + ,  } + \varphi _B^{ + ,  }} \right)/2\). By substituting Eq. (2) into Eq. (1), J(x,y) can be rewritten as:
where
and
In terms of the unitary conditions, J_{A}(x,y) and J_{B}(x,y) can be diagonalized by solving their characteristic equations and rewritten in a standard form J_{A}(x,y) = R_{A}Λ_{A}R_{A}^{−1} and J_{B}(x,y) = R_{B}Λ_{B}R_{B}^{−1}, respectively, where R_{A,B} is a real unitary matrix and Λ_{A,B} is a diagonal matrix. This new formula for J (x,y) indicates that a metasurface composed of two different types of linearly birefringent optical elements can achieve the aforementioned transformations. The eigenvectors and eigenvalues of J_{A}(x,y) and J_{B}(x,y) determine the required fast axis orientation angles and phase shifts of the two linearly birefringent optical elements, respectively.
Next, we describe the metasurface design procedure to achieve arbitrary and independent amplitude (E_{1}, E_{2}) and phase (φ_{1}, φ_{2}) control for any two orthogonal states of input polarization. First, for two orthogonal circular polarizations (χ = π/4 and δ = π/2), the analytical solutions for the required phase shifts and orientation angles of nanopillar A and nanopillar B are calculated as (see Supplementary Note. 2 for details)
Nanopillar A:
Nanopillar B:
Note that for input orthogonal circular polarization states, a combination of geometric phase and propagation phase is required to achieve independent amplitude and phase control. These equations determine the size and orientation of the nanopillars at any spatial coordinates (x,y) of the metasurface.
Second, for two orthogonal linear polarizations (χ = 0 and δ = 0), we can also obtain analytical solution of Jones matrix in the linear polarization basis. The required phase shifts of nanopillars are expressed as (see Supplementary Note. 2 for details):
Nanopillar A:
Nanopillar B:
For orthogonal linear polarization states, only propagation phase is required to achieve the desired amplitude and phase control. Equations (6)(9) determine the analytical solutions for control of orthogonal circular and linear polarization states. For a more general case of elliptical polarization, although the eigenvalues and eigenvectors of J_{A} (x,y) and J_{B} (x,y) do not yeild analytical solutions for the required phase shifts and orientation angles of nanopillar A and nanopillar B, numerical solutions can instead be employed to achieve the requisite nanopillar design for a desired metasurface response.
The design flow of multifunctional metasurface is illustrated in Fig. 2a–c. First, according to the desired functionality of the required metasurface optics, the target complexamplitude profiles (\(E_1e^{i\varphi _1}\) and \(E_2e^{i\varphi _2}\)) encoded on the metasurface are determined (Fig. 2a). Second, given a pair of orthogonal circular or linear polarization states, the required phase shifts (δ_{Ax}, δ_{Ay}, δ_{Bx}, and δ_{By}) and orientation angles (θ_{A} and θ_{B}) provided by nanopillar A and nanopillar B can be calculated based on Eqs. (6)–(9), respectively. Then the dimensions and rotation angles of the mapped nanopillars A and B are determined by the calculated phase shifts and orientation angles (Fig. 2b). Finally, by combining nanopillar A with nanopillar B, the entire metasurface is successfully created (middle panel of Fig. 2c). Nanopillar A and nanopillar B, made of TiO_{2} are alternately arranged in a 2D square grid (with nominal lattice constant U = 450 nm) on a fusedsilica substrate. Four TiO_{2} nanopillars arranged on a 2 × 2 square grid are used to define one metasurface superpixel. Each rectangular TiO_{2} nanopillar is chosen to be of a fixed nominal height H = 600 nm and their inplane dimensions D_{Ax}, D_{Ay}, D_{Bx}, and D_{By}, respectively, determine the propagation phase shifts δ_{Ax}, δ_{Ay}, δ_{Bx}, and δ_{By} along the nanopillars’ symmetry axes. The geometric phases are, respectively, controlled by the orientation angle θ_{A} and θ_{B} of the nanopillar relative to its fast axis. According to the desired phase shifts derived from the solution of the metasurface Jones matrix, a set of nanopillar satisfying the phase requirement while exhibiting a relatively high transmission efficiency is selected from the simulation library for the metasurface design.
Based on above design guidelines, Fig. 2d shows an example where the desired arbitrary and independent amplitude and phase distributions, (E_{1}, E_{2}) and (φ_{1}, φ_{2}), respectively, for any two orthogonal states of polarization are plotted. The corresponding phase shifts along the two symmetry axes and orientation angles of nanopillars are calculated and shown in the top panel of Fig. 2d for orthogonal circular polarization states, and bottom panel of Fig. 2d for orthogonal linear polarization states.
Independent amplitude control of orthogonal states of input polarization
For simplicity, we first experimentally demonstrate the ability of the proposed metasurface platform to achieve independent amplitude control for circular and linear orthogonal states of input polarization. To illustrate this capability, we design a metasurface (labeled MF1) to imprint nanoprinting images of Kelvin’s portrait and Madame Curie’s portrait, respectively, to the two orthogonal circular polarization states of incident light. A second metasurface (labeled MF2) is designed to imprint nanoprinting images of “orchids” and “lotuses” to the two orthogonal linear polarization states. Based on the requisite intensities of the desired grayscale images, the lateral size and orientation of each nanopillar as a function of the spatial coordinates (x,y) in the metasurface plane are calculated (Figs. S1 and S2). The metasurface devices are fabricated using electronbeam (ebeam) lithography followed by atomic layer deposition (ALD) and dry etching process (see “Methods” section for details). Figure 3a shows the optical microscopy and scanning electron microscopy (SEM) images of the fabricated metasurface device (MF1). The fabricated sample is illuminated by a collimated beam, at the design wavelength of ~530 nm, generated from a semiconductor laser. The intensity distribution of the transmitted light after exiting the metasurface is captured using a 20× objective lens, and subsequently imaged with a chargecoupled device camera. Schematic of the experimental setup is shown in Fig. S3. By using a combination of linear polarizer and a quarter waveplate (QWP), light incident on MF1 is converted to the desired circular polarized state. By rotating the fast axis of QWP from 45° to −45°, we capture two independent grayscale nanoprinting images, Kelvin’s portrait for rightcircular polarization (RCP) and Madame Curie’s portrait for the leftcircular polarization (LCP), as shown in Fig. 3b. Because of the ability of the metasurface device to spatially control amplitude at will, it can be clearly seen that the metasurfacegenerated nanoprinting images for the two orthogonal input polarization states exhibit the desired response with high optical contrast and low crosstalk. Equivalently, Fig. 3c shows the optical microscopy and SEM images of the metasurface device MF2. By replacing QWP with a half waveplate (HWP) and rotating the fast axis of HWP from 0° to 45°, we capture, in transmission, two nanoprinting images, “orchids” for linearly polarized input light along the xaxis, and “lotuses” for linear polarization along the yaxis (Fig. 3d). Similar to MF1, the distinct spatial features on each of the acquired nanoprinting images can be easily distinguished with high contrast. The results presented in Fig. 3c, d clearly illustrate the ability of proposed platform to achieve independent amplitude control for two orthogonal states of polarization with high fidelity.
Simultaneous and independent phase and amplitude control of orthogonal states of input polarization
In addition to only controlling amplitude or phase independently for the two orthogonal polarization states, the proposed metasurface platform can simultaneously and independently control both amplitude and phase for the two polarizations. As an experimental demonstration, we first design a metasurface device (labeled MF3) to realize polarizationdependent cylindrical lens focusing with nonuniform intensity distributions for two orthogonal circular polarization states (RCP and LCP). The corresponding cylindrical lens phase and amplitude profiles encoded on the metasurface for the two orthogonal circular polarization states are given in Fig. S4. The phase shifts (δ_{Ax}, δ_{Ay}, δ_{Bx}, and δ_{By}) and rotation angles (θ_{A} and θ_{B}) of the nanopillars A and B as a function of spatial coordinates (x,y) in the plane of metasurface (MF3) are shown in Fig. S5. Upon illumination of the metasurface MF3 with RCP light, a line focus along the xdirection in the transverse x–y plane is captured approximately at the design focal length of z = 0.5 mm (Fig. 4a). By switching the input polarization to LCP, a focal line along the ydirection in the x–y plane is captured approximately at a different design focal length of z = 1.0 mm (Fig. 4b). The intensity crosssections of the twoline focus along the x and the ydirections are shown in Fig. 4c, d, respectively. The cylindrical lens function only utilized the ability of the metasurface to control independent phase profiles for the two polarizations; however, to illustrate simultaneous control of amplitude, the metasurface line focus was designed to linearly vary in intensity along its length. The superimposed simultaneous amplitude control results in the measured line focus intensity for RCP illumination to decrease gradually from left to right (along the xdirection), and for LCP illumination to decrease gradually from top to down (along the ydirection). As shown in the insets of Fig. 4c, d, the measured fullwidth at halfmaximum of the line focus for RCP and LCP light are, respectively, 723 nm (±15 nm) and 1252 nm (±21 nm), which are close to the theoretical values of 612 and 1125 nm, as calculated by the Rayleigh criterion (0.514λ/NA, where NA is the numerical aperture of the cylindrical lens).
In addition to the chiralitydependent nonuniform cylindrical lensing function, we design another metasurface (labeled MF4) to achieve disparate complexamplitude holograms for two orthogonal states of linear polarization. The complexamplitude holograms generated by a set of independently controlled amplitude and phase functions are computed by the Fresnel diffraction formula. The nearfield amplitude and phase profiles that can produce two independent farfield images of a “Penrose triangle” for xpolarized light, and a “Mobius strip” for ypolarized light, are shown in Fig. S6. The spatial distribution of the required phase shifts imparted by the nanopillars A and B along the metasurface plane are shown in Fig. S7. Experimentally, by changing the orientation of linear polarization incident on the metasurface MF4 from xpolarization to ypolarization, two holograms, a “Penrose triangle” (Fig. 4e) and a “Mobius strip” (Fig. 4f) are successfully captured at a distance of z ≈ 5 mm away from the metasurfaceexit plane. The vivid threedimensional visual effects with regions of bright and dark contrast in the captured hologram images are made possible by the ability to control amplitude and phase simultaneously in the proposed platform. The difference between the experimental and simulated results mainly arises from limited sampling of target amplitude and phase encoded on the metasurface and the morphological deviations (such as disparity of diameters, heights, or roughness) between the designed and the fabricated nanopillars. These experimental results, both for orthogonal circular and linear polarizations, clearly verify that metasurface platform can simultaneously and independently control both the phase and amplitude profiles for two orthogonal states of input polarization.
Synchronous fourchannel nanoprintinghologram generation using a metasurface
Benefitting from the freedom in design and the multifunctional response of the proposed metasurface platform, we experimentally demonstrate, for the first time to our knowledge, imprinting of four arbitrary independent images, consisting of two nearfield nanoprinting images and two farfield hologram images, all encoded onto a singlelayer metasurface. Figure 5a illustrates the metasurface design flow chart for synchronous fourchannel nanoprintinghologram image generation based on a modified Gerchberg–Saxton algorithm^{50}. First, we extract the amplitude of target hologram image in the farfield A_{1,2}′(x,y) and add a random phase φ_{1,2}′(x,y) to it. An inverse fast Fourier transform (FFT) step is implemented to the constructed complex amplitude. Second, the amplitude I_{1,2}′(x,y) of generated complex amplitude is substituted with the nearfield amplitude A_{1,2}(x,y) of the nanoprinting image. Utilizing a FFT step to \(A_{1,2}(x,y)e^{i\varphi _{1,2}(x,y)}\), the new complex amplitude at the target hologram plane can be obtained and its amplitude of I_{1,2}(x,y) is replaced by the amplitude A_{1,2}′(x,y) of the target hologram image. After few iterations, when the computed intensity I_{1,2}(x,y) at the farfield hologram plane is close to the target amplitude A_{1,2}′(x,y), we can obtain the phase distribution φ_{1,2}(x,y) at the nearfield nanoprinting plane. The same sequence of steps is then repeated for the other orthogonal state of polarization. Finally, by combining geometric phase and propagation phase modulation, the dimensions and orientations of nanopillars at each spatial point (x,y) on the metasurface plane can then be determined by the amplitude A_{1,2}(x,y) and phase φ_{1,2}(x,y) for the two orthogonal states of light.
For the proofofconcept demonstration of this concept, we chose two orthogonal circular polarization input states to design the metasurface device for synchronous generation of fourchannel nanoprintinghologram images. The computed phases and amplitudes are shown in Fig. S8. Accordingly, the phase shifts and rotation angle of the nanopillars A and B as a function of spatial coordinates in the metasurface (labeled MF5) plane are shown in Fig. S9. The optical microscopy and SEM images of the fabricated metasurface MF5 are shown in Fig. 5b. For RCP incident light, a nanoprinting image of “person” is captured near the metasurfaceexit surface, and a hologram image of “Chinese knot” is simultaneously captured at a propagation distance of z ≈ 5 mm away from the metasurface (Fig. 5c). For LCP incident light, a nanoprinting image of “bird” is captured near the metasurface and a hologram image of “Eight Trigram” is captured at z ≈ 5 mm (Fig. 5d). The measured nanoprinting images near the metasurface are composed of several blocks with varying brightness, and are consistent with the original images. The experimental results also agree well with the simulation predictions for the reconstructed farfield hologram images (Fig. S10).
Discussion
In summary, we demonstrated a transmissionmode metasurface platform for simultaneous and independent control of phase and amplitude for two orthogonal states of input polarization. A singlelayer dielectric metasurface device, composed of polarizationdependent birefringent nanopixels and leveraging both geometric and propagation phase modulations, is shown to directly achieve complex multidimensional wavefront transformations. As a proofofconcept demonstration, we designed, fabricated, and characterized a series of metasurface devices, based on TiO_{2} as the constituent material, with polarizationswitchable lightfield manipulation capabilities, including nearfield nanoprinting, farfield complexamplitude holography, and nonuniform cylindrical focusing. Finally, benefiting from the design freedom of the proposed metasurface platform, a fourchannel metasurface is experimentally demonstrated to realize the integration of four independent images for switchable synchronous nanoprinting and holography.
Due to its broadband response (Fig. S11), in principle, our proposed transmission dielectric metasurface platform can be designed to generate fullcolor holograph by leveraging sensitivity of higher order diffraction in metasurface to wavelength and angle^{49}. Another alternative approach would be to design a metasurface with spatial multiplexed superpixels, where each superpixel consists of nanopillars that offer multilevel phases for each of the R, G, and B component, enabling realization of polarizationdependent fullcolor nanoprinting and holograph display. We envision this work to inspire creation of ultracompact flatprofile nanophotonic platforms, and provide new avenues for applications in polarization optics, information security, optical data storage, and multifunctional photonics.
Materials and methods
Numerical simulation of metasurface
Fullwave numerical simulations are performed using the finitedifference timedomain technique. Rectangular TiO_{2} nanopillars with a fixed height of 600 nm are arranged on a fusedsilica substrate with a lattice constant of 450 nm. The complex refractive index of TiO_{2} as a function of wavelength is shown in Fig. S12. The incident plane wave is polarized along x or yaxes, and illuminates the nanopillars from the substrate side. Along x and yaxes, periodic boundary conditions are applied and perfectly matched layer boundary condition is used in the zdirection. The phase shifts (P_{x} and P_{y}) and power transmission (T_{x} and T_{y}) are obtained by parameter sweeping of the inplane dimensions (D_{x} and D_{y}) of the nanopillars by varying them between 50 and 350 nm at an interval of 5 nm (Fig. S13). As shown in Fig. S14, the optical fields are all confined within each nanopillar guaranteeing that a superpixel composed of four nanopillars can approximate a local pixel in the Jones matrix.
Nanofabrication of metasurface devices
At first, a nominally doubleside polished fusedsilica substrate was vaporcoated with a monolayer of hexamethyldisilazane, and then a layer of ~600 nm thick positivetone ebeam resist was spincoated onto it. In order to suppress the charging effect during the ebeam lithography step, the sample was coated with a thin layer of aluminum via thermal evaporation. Afterward, ebeam lithography (at a nominal accelerating voltage of 100 kV and beam current of 2 nA) and resist development (in hexylacetate for ~120 s) was performed. Next, the patterned sample was coated with TiO_{2} using ALD at a low temperature of ~90 °C, and the overcoated TiO_{2} layer was etched using an inductively coupled plasma reactiveion etching, with a gas mixture of Cl_{2} and BCl_{3}. The etching was stopped when the overcoated TiO_{2} has been fully removed and the ebeam resist was exposed. Finally, after exposed to ultraviolet irradiation, the resist is removed by soaking in nmethyl2pyrrolidone and the array of TiO_{2} nanopillars is obtained.
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Acknowledgements
The work is supported by the Key Research and Development Program from Ministry of Science and Technology of China (2017YFA0303700 and 2016YFA0202100), National Natural Science Foundation of China (11774163) and Fundamental Research Funds for the Central Universities (021314380194) . M. L. and T. Xu acknowledge technical support from microfabrication and integration technology center from Nanjing University. W. Z., L. C. and A. A. acknowledge support under the Cooperative Research Agreement between the University of Maryland and the National Institute of Standards and Technology, Award#70NANB14H209, through the University of Maryland. M. L., W. Z. and P. H. contributed equally to this work.
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Liu, M., Zhu, W., Huo, P. et al. Multifunctional metasurfaces enabled by simultaneous and independent control of phase and amplitude for orthogonal polarization states. Light Sci Appl 10, 107 (2021). https://doi.org/10.1038/s41377021005523
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DOI: https://doi.org/10.1038/s41377021005523
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