Abstract
Achieving simultaneous polarization and wavefront control, especially circular polarization with the auxiliary degree of freedom of light and spin angular momentum, is of fundamental importance in many optical applications. Interferences are typically undesirable in highly integrated photonic circuits and metasurfaces. Here, we propose an interferenceassisted metasurfacemultiplexer (metaplexer) that counterintuitively exploits constructive and destructive interferences between hybrid metaatoms and realizes independent spinselective wavefront manipulation. Such kaleidoscopic metaplexers are experimentally demonstrated via two types of singlelayer spinwavefront multiplexers that are composed of spatially rotated anisotropic metaatoms. One type generates a spinselective Besselbeam wavefront for spindown light and a low scattering crosssection for stealth for spinup light. The other type demonstrates versatile control of the vortex wavefront, which is also characterized by the orbital angular momentum of light, with frequencyswitchable numbers of beams under linearly polarized wave excitation. Our findings offer a distinct interferenceassisted concept for realizing advanced multifunctional photonics with arbitrary and independent spinwavefront features. A variety of applications can be readily anticipated in optical diodes, isolators, and spinHall metadevices without cascading bulky optical elements.
Introduction
Metasurfaces^{1,2}, which are the planar equivalent of metamaterials that are composed of subwavelength metaatoms, have attracted extensive interest due to their easy fabrication and powerful capabilities in wave manipulation. The flexibility of metasurfaces in controlling the amplitudes and phases of electromagnetic (EM) wave scattering, either individually or simultaneously, has attracted enormous attention from both the science and engineering communities due to their potential applications in modern microwave/optical communication systems^{1,2,3,4,5,6,7,8,9,10,11,12,13,14}. Nevertheless, to date, all predefined functions of metasurfaces have been actualized under fixed polarizations, which considerably limit the degree of freedom (DoF) for fullwave controls. This compels us to integrate the features of both phase and polarization to realize precise wavefront multiplexing, which is another crucial DoF of EM waves^{15,16}.
The simultaneous manipulation of polarization/spin and phase^{17}, which is promising for complicated spin and wavefront multiplexing, is extremely challenging in practice. In the traditional methodology, one must combine linear polarizers, waveplates, and specific phase retarders (prisms or lenses) together. Such a strategy of cascading optical devices leads to bulky systems that exhibit low efficiency and degraded performance. Although chiral metamaterials are considered promising candidates for polarization manipulation^{18,19,20,21}, the periodic structures in their homogenous profile restrict their capability in shaping the desired wavefronts. Emerging helicitydependent wavefront control has been realized by PancharatnamBerry (PB) phases that are launched by circularly polarized (CP) waves^{22,23,24,25,26,27}. However, the functionalities under lefthanded (LCP, spinup state with a sign of σ−) and righthanded (RCP, spindown state with a sign of σ + ) CP waves are essentially locked due to the inverse phase profile flipping as the spin state of the incident wave changes. To overcome these limitations, three avenues are available in the open literature: merging the propagation phase and geometric phase across the entire metasurfaces;^{28,29,30} combining the chirality with the geometric phase;^{31,32} and utilizing the nonflat geometry of the metasurface, which can break the symmetry between LCP and RCP waves^{33}. However, these designs either utilized depthseparated two or multilayered metaatoms to form a vertical chirality or obtained singular functionality of different modes, which may complicate the design. The study of the physics and criterion for spinselective functionality is still in its infancy and solutions remain elusive.
Here, we propose a novel strategy for enabling a new paradigm for achieving simultaneous spin and wavefront multiplexing (to serve as a kaleidoscopic metaplexer) by constructive and destructive interferences, as shown in Fig. 1a. The key to this paradigm is to utilize both the propagation and geometric phases to form 180° and 0° phase differences between two counterparts of a metaatom. This is carried out by flipping the spin states of the CP waves, which distinguishes our work from previous PB designs^{22,23,24,25,26,27}. Therein, diodelike asymmetric CPwave reflections, with magnitudes of 0 and 1 in the spinup and spindown states, can be engineered in each metaatom (Fig. 1b). To facilitate the outofphase and inphase interferences, a criterion of 90° propagation phase and ± 90° geometricphase differences is established, which is highly robust for quick and arbitrary designs. For verification, using spatially rotated metaatoms, two proofofconcept kaleidoscopic metaplexers, using spatially rotated metaatoms, are designed using the feature of asymmetric CP reflections. The first metamultiplexer exhibits low RCS in the spinup state and nondiffracting propagation (Bessel wavefront) within the formation zone^{34,35,36,37,38} in the spindown state. The second metamultiplexer manifests multiple versatile vortices^{30,39,40,41,42,43,44} with switched twotofour pencil beams that carry orbital angular momentum (OAM, twisted phase fronts) at different frequencies under the linearly polarized (LP) wave excitation, thereby demonstrating spindetermined generation and steering of OAM beams. Such distinct spinselective functionalities are induced by the total absorption of the spinup wave and the highefficiency reflection of the spindown wave. In contrast to previous designs, our approach to realizing the kaleidoscopic functions in one ultracompact metasurface features a monolayer structure, definite physics, and simple design without introducing chiralityselective bulk metamaterials. We firmly believe that, beyond the functions that are demonstrated in our work, additional functionalities are easily realizable by following the proposed design principle.
Results
Principle and criterion for the diodelike asymmetricspin metaplexer
To realize the newconcept kaleidoscopic CP wavefront control, we first state the interference principle for asymmetric CP reflections and establish a general criterion for design based on a novel metaatom. The basic building block that is proposed here is a metalinsulatormetal reflection structure on a continuous metallic background (Fig. 2a). The top metal structure is comprised of two split ring resonators (SRRs) that exhibit a local mutual twist of ψ = 45°. For convenience, the external and internal SRRs are denoted as SRR_{1} and SRR_{2}, respectively. An F4B dielectric board with dielectric constant ε_{r} = 4.5, thickness h = 3 mm, and loss tangent δ = 0.025 is placed between the composite metallic pattern and backed metal ground. Here, two types of phases are involved: the propagation phase, which is induced by parametric variations, and the geometric phase, which is induced by orientation rotations about its axis. By individually controlling the geometrical parameters of SRR_{1} and SRR_{2}, an arbitrary propagation (reflection) phase difference, which is expressed as Δϕ = ϕ_{1}–ϕ_{2}, can be engineered between two reflections of r_{1++} and r_{2++}, or those of r_{1−−} and r_{2−−} under spindown and spinup wave stimulations. Such a propagation phase difference has no role in controlling the wavefront but induces helicity selectivity. Here, r_{1++} and r_{2++} (r_{1−−} and r_{2−−}) denote the copolarization reflections of SRR_{1} and SRR_{2} in the spindown (spinup) state, respectively.
Initially, we consider a CP wave with normal incidence on the metaatom of SRR_{1} or SRR_{2} with a common global rotation angle Φ. The reflections will gain an additional geometric phase of 2Φ according to PB phase theory. Similar to the Vshaped antenna^{1}, SRR_{1} and SRR_{2} exhibit symmetric and asymmetric modes parallel and perpendicular to the symmetric axis under plane CPwave excitation. This is because any CP wave can be considered composed of two equally contributing orthogonal LP components. At such resonant modes, several reflection zeros are manifested on the r_{−+} and r_{+−} spectra. By cascading these resonant modes of the two SRRs, i.e., merging them into a composite element, broadband highefficiency reflections can be engineered, which can be derived from the Jones matrix of r_{1} and r_{2} (see Fig. S1a and additional details in Supplementary Materials). In the case of negligible weak coupling between SRR_{1} and SRR_{2}, the reflections of the composite metaatom can be simplified as
In a full reflection scheme, it is easy to show that r_{1++} ≈ r_{2++} ≈ 1 and r_{1−−} ≈ r_{2−−} ≈ 1. Then, the residuals ϕ_{1}, ϕ_{2}, Φ, and ψ play a determinant role in obtaining CP asymmetric reflections. To maximize E_{com−} or E_{com+} while minimize the other, the following criteria should be satisfied:
From Eq. (2), we immediately obtain the exclusive solution of Δϕ = −90° and ψ = 45° under the spindown wave; in contrast, Δϕ = −90° and ψ = −45° under the spinup wave, which are general criteria for diodelike spin controls. The abovementioned phase requirement is only related to the local orientations and dimensions of the twoSRR metaatom. Using the above criteria, we can realize full reflection of the spindown/up wave through the inphase constructive interference and total suppression of the spinup/down wave through the outofphase destructive interference in the spindown/up state. According to Eq. (1) and (2), the amplitude of all reflections in the Jones matrix can be tuned by cautiously choosing an appropriate value of ψ. This prediction finds strong support from Supplementary Fig. S1b, where r_{−−} and r_{++} can be continuously and individually modulated by controlling the local ψ within −180^{o}–0° and 0^{o}–180°. Moreover, the phase can be independently and continuously tuned by the global Φ without affecting the amplitude. Although the above criteria, which are derived from interference, exclude the consideration of mode coupling between two SRRs, our coupled mode analysis (Supplementary Fig. S1c) confirms that the coupling is very weak. Therefore, our theory provides an intuitive and nontrivial guideline for asymmetricspin controls. Moreover, such weak coupling can be directly observed in the inset of Fig. 2b, where the current density and distributions (J_{x}) are almost the same on an individual SRR_{1} and a composite SRR.
Design and verification of the diodelike asymmetricspin metaplexer
Based on the established criteria, it is easy to design a spinselective metaplexer that operates at an arbitrary frequency. First, we roughly determine the structures of SRR_{1} and SRR_{2} via individual design of the propagation phase. Then, we finalize the metaatom layout via finely optimizing the parameters of the hybrid SRR_{1} and SRR_{2} with the required orientations. For verification, we characterize the proposed metaatom that is designed from the above criteria via finitedifference timedomain (FDTD) simulations. Figure 2b shows that the handedness of the reflected beam is preserved for both spinup and spindown waves, while the crosspolarization reflections are maintained extremely small across a broadband. Moreover, r_{++} remains above 0.71 over the entire observation band, while r_{−−} undergoes a sudden drop, with its magnitude approaching null at 9.5 GHz, thereby enabling a maximum extinction ratio of r_{++}/r_{−−} = 33.3. Such diodelike asymmetric reflections indicate a giant circular dichroism. The FDTD and theoretically calculated reflection spectra are in reasonable agreement, thereby verifying the physical mechanism of destructive and constructive interferences, as illustrated in Fig. 2b, c, in which the curve that is composed of circle symbols is the theoretical result. The proposed approach is strongly supported by Fig. 2c, d, where the calculated values of r_{1++} and r_{1−−} are almost the same as those of r_{2++} and r_{2−−}, while the phase difference Δϕ = ϕ_{1}ϕ_{2} between them is nearly −90°. These results correspond exactly to the criteria that are specified by Eq. (2). The slight deviation between theory and simulations, especially for the narrowerband absorption in the latter case, is attributed to the slightly altered reflection amplitude of SRR_{2} under the orientations of ψ = 0° and 45^{o} and weak coupling between two closely spaced SRRs. The slight deviation of the reflections between theory and simulations at offinterference (offf_{0}) frequencies and narrowerband absorption in the latter case is attributed to the inevitable coupling between SRR_{1} and SRR_{2} when the frequency exceeds f_{0}. This is because in the theoretical prediction of the composite metaatom, the reflection responses of two individual SRR_{1} and SRR_{2} metaatoms were modeled separately to yield guidelines regarding constructive and destructive interferences. However, in fullwave simulations, an integrated metaatom that involved two SRRs (one SRR in the vicinity of the other) was characterized. Nevertheless, this has little effect on identifying the interference mechanism by which perfect coherence is clearly observed near the center frequency. The almost constant reflection amplitudes of r_{++}, r_{−−}, r_{+−}, and r_{−+} with Φ and the ideal PB phase of r_{++} with 2Φ can be clearly observed in Supplementary Fig. S1dS1f. Such robust amplitude and phase profiles against Φ are crucial for highefficiency wavefront control.
The spinselective asymmetric reflection is not induced by the loss of the dielectric board. This is supported by Fig. 2e, where high absorptions are sustained even if the loss tangent, which is denoted as δ, reaches zero. Nevertheless, the absorption rate of r_{++} increases slightly with δ in the on and offinterference regions and more than 95% reflection efficiency is expected when widely available dielectrics with δ = 0.005 are adopted. The nearperfect absorption in the spinup state originates from the strong localized fields (dissipative loss) that are induced by mutual interference between SRR_{1} and SRR_{2} (inset of Supplementary Fig. S1d).
The proposed metamultiplexer for asymmetricspin control performs robustly at nearly fullangle incidences, as depicted in Fig. 3. Again, a remarkable diodelike asymmetric absorption is clearly observed from a_{L} and a_{R} in the spinup and spindown states on both the xz and yz incident planes. Moreover, the nearunity and null asymmetric absorptions in the spinup and spindown channels are preserved over a wide range of incidences. Even when the incident angle reaches 80°, the absorption of a_{L} exceeds 68% in the xzplane and 76% in the yzplane. The absorptions in the two states maintain a large contrast ( > 50%), even under an incident angle of up to 65°, thereby indicating a robust wideangle absorption behavior. The slight deviation of the absorption behavior a_{L}, namely, red and blue frequency shifts on the xz and yzplanes at large incident angles, is attributable to the simultaneous breaking of mirror and rotational symmetry. Such highcontrast incidenceinsensitive diodelike reflections are highly beneficial for applications in singlemode devices of CP lights.
Multiplexed Bessel beam and RCS reduction
In the following, we demonstrate that our strategy can engineer multiplexed distinctive wavefront controls using such CP asymmetric reflections. The first kaleidoscopic metaplexer is designed to generate nondiffractive Bessel beams^{34,35,36,37,38}. The metamultiplexer targeting at 10 GHz is composed of 31*31 pixels and occupies an area of 217*217 mm^{2}. To form the diffractionfree focusing wavefront in the spindown state, the imparted phase should satisfy^{34}
in which F = 100 mm is the long depth of focus and R = 108.5 mm is half the axicon aperture, as shown in the 2D hyperbolic phase profile and liner phase profile along y = 0 (dashed) in Fig. 4a. Then, the metamultiplexer layout can be easily mapped out by spatially varying the global orientations of metaatoms with constant geometrical parameters, as illustrated in Supplementary Fig. S2a and Fig. 4b. For experimental verifications, a proofofconcept sample is fabricated via the printed circuit board technique. The spinselective nondiffracting reflection and broadangle RCS reduction are measured in a microwave anechoic chamber (see Supplementary Fig. S4 for the experimental details).
Figure 4c, d present the color maps of the Efield intensity distributions on the yzplane at 9.5 and 11 GHz for intuitionistic study. Distinct behaviors are clearly observed under two oppositehelicity channels. For the spindown channel, we observe a nondiffracting propagation (Bessel beams) behavior along the zaxis across a desirable distance over a wide range of frequencies, which serves as the needle beam. In sharp contrast, weak and dispersed energy distributions with diverged fields are observed for the spinup channel. Moreover, the near fields even approach null across the entire plane at 9.5 GHz, where the extinction ratio, which is calculated as the scale of the maximum power of the two channels, is evaluated as more than 50. Such a desirable distinct function is attributable to the diodelike asymmetric reflections of the utilized metaatoms. Figure 4e, f quantitatively compare the FDTDsimulated and experimentally measured Efield intensities across the propagating direction (x = 0) and three yzplanes, respectively. A reasonable agreement of results is observed between simulations and measurements. As expected, the energy is dominantly confined close to the optical axis and extends along the axis for an appreciable distance without diffraction (~75 mm by 3 dB energy attenuation). The halfpower beamwidth in the transverse plane is ~15 mm and remains almost constant as the frequency varies, as shown in Fig. 4f, where satisfactory Bessellike profiles of electric fields with the first zero are clearly observed at 9.5 GHz. Results at other offinterference frequencies are presented in Supplementary Figs. S2cS2d. As expected, in Fig. 4g, the backward RCS has been significantly reduced by more than 7 dB across 8–12 GHz, especially near 9.5 GHz, where the RCS reduction reaches −20.7 dB, as clearly illustrated in the 3D scattering patterns at 9.5 GHz in the inset. Most importantly, the lowRCS behavior is robust against the incidence changes and the RCS reduction behavior is preserved to better than −6 dB, even up to θ = 45°.
Finally, we show the Efield intensity spectra in Fig. 4h at the focal point and use them to quantitatively evaluate the working bandwidth. As expected, the Efield intensity reaches its maximum at ~f_{0} = 10 GHz, thereby demonstrating the highest capability of Besselbeam generation. However, the capability deteriorates when the frequencies exceed f_{0} since the required dispersive hyperbolic phase profile is no longer strictly fulfilled. The working bandwidth, which is characterized by halfpower decay, is ~3.4 GHz (8–11.4 GHz), which is equivalent to a fractional bandwidth of 34%. Slight deviations between the numerical and experimental results are likely induced by the inaccurate alignment of the metamultiplexer and the feed horn and the imperfect nonplanar incoming wavefront. In addition to the generation of a Bessel beam by the impinged wavefront, other functions (e.g., focusing and twisted wavefronts) are readily realized by altering the local rotations of the proposed metaatoms, which can be highly useful in various functional devices.
Multiplexed vortices with versatile beams
Here, we further demonstrate that the CP asymmetric reflections can be utilized to flexibly manipulate multiplexed pencil beams that carry vortex information, or OAM, in two oppositehelicity channels. By encoding several phase profiles into a single metasurface plate^{45}, a composite wavefront and versatile functionalities can be realized, which is promising for capacity enlargement. Here, three phase profiles are mixed, as shown in Fig. 5a: a spiral phase, namely, ϕ_{3}(x, y) = exp(−ilϕ), where l = 1 and 2 denoted the topological charges of vortices, and two linear gradient phases, namely, ϕ_{1}(x, y) = ξ_{x}x and ϕ_{2}(x, y) = ξ_{y}y, along the xand ydirections with ξ_{x} = ξ_{y} = 0.54k_{0} and eight metaatoms in each supercell. The metamultiplexer contains 39*39 metaatoms and occupies a total area of 273*273 mm^{2}, as illustrated in the chiplevel and pixellevel layouts that are shown in Fig. 5b and Supplementary Fig. S3. The main physics of generating multiple vortices with versatile numbers of beams can be understood as follows: First, a pair of symmetric spindown beams with OAM undergo opposite reflections along the + /−xdirections with an elevation angle of θ_{1} = sin^{−1}(ξ_{x}/k_{0}), while a single spindown beam of OAM is shaped along the + ydirection with θ_{2} = sin^{−1}(ξ_{y}/k_{0}) in the spindown state. Then, two symmetric beams interfere with the single beam and eventually form two spindown beams in the direction of \(\theta {\mathrm{ = }}\sin ^{  1}\left( {\sqrt {\sin ^2\theta _1 + \sin ^2\theta _2} } \right)\) and ϕ = 90° ± tan^{−1}(sinθ_{1}/sinθ_{2}), where ϕ is the azimuth angle. In a similar manner, two symmetric spinup beams are directed with the same angle along the + /−xaxis, while a single spinup beam is formed along the –ydirection in the spinup state. Again, these beams form two interfering spinup beams at \(\theta {\mathrm{ = }}\sin ^{  1}\left( {\sqrt {\sin ^2\theta _1 + \sin ^2\theta _2} } \right)\) and ϕ = 270° ± tan^{−1}(sinθ_{1}/sinθ_{2}). Finally, four vortices with different helicities (two spinups and two spindowns) are simultaneously engineered for our metamultiplexer under a plane LP wave with normal incidence (a combination of spinup and spindown waves). The key to manipulating the number of vortex beams is to control the spinup reflections based on our previously established criteria.
Figure 5c illustrates the 3D scattering patterns in the far field at 9.5 and 10.5 GHz. As expected, four symmetric vortices with null amplitude in the centers are precisely directed toward the spatial angles that are predicted theoretically at 10.5 GHz. However, the number of pencil vortices decreases to two at 9.5 GHz, with two spinup beams being totally absorbed. The generation of two asymmetric spindown vortices can be observed within 9.2~9.7 GHz. The performance can be further evaluated quantitatively in Fig. 5d, where the simulated and measured 2D patterns along ϕ = 45° agree well, thereby indicating one and two beams each with central singularities at 9.5 GHz and 10.5 GHz. The extinction ratio of spindown to spinup vortex beams is measured as 18 dB. The slightly raised normal reflections are attributable to the interferences that are induced among several phase profiles. To further evaluate the OAM vortex wavefronts, Fig. 5e shows the Efield (E_{y}) distributions at 10.5 GHz and z = 250 mm above the metamultiplexer with the crosssection perpendicular to one vortex beam. As expected, the doughnutshaped intensity distribution is almost uniformly formed in four regions at 10.5 GHz. However, at 9.5 GHz, only two regions are filled with strong doughnutshaped intensity, while the intensity in the left halfregion is weak. Most importantly, the pure spiral phase fronts with two arms (l = 2) can be clearly observed from the perpendicular crosssection. The wavefront above the metamultiplexer is a combination of anomalous deflections along ϕ = 45° and 135° and a helical wavefront, as presented in the quad fingerprint linespiral wavefronts in Fig. 5f. The one and two forks (optical singularity) in each region correspond to vortex beams that are carrying OAM modes of l = 1 and l = 2. Additional scattering patterns at other offinterference frequencies and a spiral phase wavefront with doughnutshaped intensity are plotted in Supplementary Figs. S3bS3e.
Discussion
In summary, we have proposed a new strategy for CP asymmetric diodelike reflections that is based on constructive and destructive interferences. We established criteria that provide a general guideline for engineering an arbitrary extinction ratio of the CP waves using arbitrary structures. For verification, a type of ultrathin planar metaatom is proposed and demonstrated to selectively reflect the spindown waves with a high efficiency of 95% while completely absorbing the spinup waves. To demonstrate its promising applicability, a kaleidoscopic metaplexer that merges diffractionfree Besselbeam generation and wideangle lowRCS for stealth in one plate and a kaleidoscopic metaplexer for vortexbeam generation with versatile beam numbers are numerically and experimentally characterized. Desirable kaleidoscopic manipulations of spin and wavefronts have been verified. Moreover, the interferenceassisted paradigm can be readily adopted in the highfrequency range (visible or infrared)^{46} if any two individual resonators are weakly coupled and in a transmissive scheme that provides a quasiuniform transmission rate; see Supplementary Fig. S4 and Fig. S5. Our strategy opens an avenue to flexibly controlling both the helicity and wavefront of CP lights with unprecedented ability by integrating artificial intelligence for purposive purposeful and smart selections.
Materials and method
Numerical characterizations
All numerical designs and characterizations are performed via FDTD simulations. In calculations of the reflective amplitudes/phases of the metasurface, we only studied a metaatom with periodic boundary conditions assigned at its four bounds and a Floquet port that is placed 20 mm away from the metaatom plane. In nearfield and farfield calculations, a squareshaped metaplexer that is formed by a set of spatially rotated metaatoms is investigated with open boundary conditions applied at its four bounds. In all scenarios, the metaplexers/metaatoms are illuminated by a normally incident plane wave that is in the LP, spinup or spindown state.
Microwave experiments
To avoid interference from the environment, all farfield (FF) and nearfield (NF) microwave experiments are performed in an anechoic chamber. Supplementary Fig. S6 shows the experimental setup. In NF measurements, the metamultiplexer sample was excited by a CP horn with an axial ratio of less than 3.5 dB and a voltagestandingwave ratio of less than 2.5 at 6–18 GHz. They were fixed with a distance of 1 m. A 15mmlong monopole antenna, which functioned as the receiver, was placed between the sample and the CP horn and was linked to an N5230C Agilent vector network analyzer to record the static EM signals. The monopole was fixed to a 2D electronic step motor that can move automatically in a maximum area of 0.6 m × 0.6 m with a step resolution of 3 mm. By shifting the monopole orientation along the x and ydirections, both the local E_{x} and E_{y} fields can be obtained (with both amplitude and phase). Then, the spinup and spindown components can be calculated as \(E_{{\rm{LCP}}} = \frac{1}{{\sqrt 2 }}\left( {E_x  iE_y} \right)\) and \(E_{{\rm{LCP}}} = \frac{1}{{\sqrt 2 }}\left( {E_x + iE_y} \right)\) by incorporating the measured information. By altering the relative position of the metamultiplexer and 2D monitor, we can obtain the field information in the xz, yz, and xy planes. In all simulated and measured nearfield maps, the incident signal in free space was subtracted from the total fields. In the FF RCS measurements, two CP horns are adopted as the transmitter and receiver and are displaced 1 m from the sample. The receiving CP horn, which was aligned with the metamultiplexer, rotated freely to record the signal that was scattered within −90^{o} < θ_{r} < 90°. In the FF quadbeam pattern measurements, the metamultiplexer was fed by a small LP conical horn at a focal point of F = 100 mm and both of them were secured on a large rigid foam that is capable of rotating freely along the foam’s axial center. The CP receiver was placed 10 m away to record the farfield signals.
References
 1.
Yu, N. F. et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333–337 (2011).
 2.
Sun, S. L. et al. Gradientindex metasurfaces as a bridge linking propagating waves and surface waves. Nat. Mater. 11, 426–431 (2012).
 3.
Liu, L. X. et al. Broadband metasurfaces with simultaneous control of phase and amplitude. Adv. Mater. 26, 5031–5036 (2014).
 4.
Kim, M., Wong, A. M. H. & Eleftheriades, G. V. Optical Huygens’ metasurfaces with independent control of the magnitude and phase of the local reflection coefficients. Phys. Rev. X 4, 041042 (2014).
 5.
Wang, Q. et al. Broadband metasurface holograms: toward complete phase and amplitude engineering. Sci. Rep. 6, 32867 (2016).
 6.
Lee, G. Y. et al. Complete amplitude and phase control of light using broadband holographic metasurfaces. Nanoscale 10, 4237–4245 (2018).
 7.
Ding, J., An, S. S., Zheng, B. & Zhang, H. L. Multiwavelength metasurfaces based on singlelayer dualwavelength metaatoms: toward complete phase and amplitude modulations at two wavelengths. Adv. Opt. Mater. 5, 201700079 (2017).
 8.
Cui, T. J., Qi, M. Q., Wan, X., Zhao, J. & Cheng, Q. Coding metamaterials, digital metamaterials and programmable metamaterials. Light Sci. Appl. 3, e218 (2014).
 9.
Aieta, F., Kats, M. A., Genevet, P. & Capasso, F. Multiwavelength achromatic metasurfaces by dispersive phase compensation. Science 347, 1342–1345 (2015).
 10.
Xu, H. X. et al. Wavenumbersplitting metasurfaces achieve multichannel diffusive invisibility. Adv. Opt. Mater. 6, 1800010 (2018).
 11.
Zhu, B. O. et al. Dynamic control of electromagnetic wave propagation with the equivalent principle inspired tunable metasurface. Sci. Rep. 4, 4971 (2014).
 12.
Chen, K. et al. A reconfigurable active Huygens’ metalens. Adv. Mater. 29, 1606422 (2017).
 13.
Xu, H. X. et al. Dynamical control on helicity of electromagnetic waves by tunable metasurfaces. Sci. Rep. 6, 27503 (2016).
 14.
Qin, F. et al. Hybrid bilayer plasmonic metasurface efficiently manipulates visible light. Sci. Adv. 2, e1501168 (2016).
 15.
Gansel, J. K. et al. Gold helix photonic metamaterial as broadband circular polarizer. Science 325, 1513–1515 (2009).
 16.
Hao, J. M. et al. Manipulating electromagnetic wave polarizations by anisotropic metamaterials. Phys. Rev. Lett. 99, 063908 (2007).
 17.
Li, J. X. et al. Simultaneous control of light polarization and phase distributions using plasmonic metasurfaces. Adv. Funct. Mater. 25, 704–710 (2015).
 18.
Pfeiffer, C., Zhang, C., Ray, V., Guo, L. J. & Grbic, A. High performance bianisotropic metasurfaces: asymmetric transmission of light. Phys. Rev. Lett. 113, 023902 (2014).
 19.
Menzel, C. et al. Asymmetric transmission of linearly polarized light at optical metamaterials. Phys. Rev. Lett. 104, 253902 (2010).
 20.
Mutlu, M., Akosman, A. E., Serebryannikov, A. E. & Ozbay, E. Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling. Phys. Rev. Lett. 108, 213905 (2012).
 21.
Xu, H. X., Wang, G. M., Qi, M. Q., Cai, T. & Cui, T. J. Compact dualband circular polarizer using twisted Hilbertshaped chiral metamaterial. Opt. Express 21, 24912–24921 (2013).
 22.
Zhou, J. X. et al. Broadband photonic spin hall metalens. ACS Nano 12, 82–88 (2018).
 23.
Chen, X. Z. et al. Dualpolarity plasmonic metalens for visible light. Nat. Commun. 3, 1198 (2012).
 24.
Zheng, G. X. et al. Metasurface holograms reaching 80% efficiency. Nat. Nanotechnol. 10, 308–312 (2015).
 25.
Zhang, L., Liu, S., Li, L. L. & Cui, T. J. Spincontrolled multiple pencil beams and vortex beams with different polarizations generated by PancharatnamBerry coding metasurfaces. ACS Appl. Mater. Interfaces 9, 36447–36455 (2017).
 26.
Xu, H. X. et al. Deterministic approach to achieve broadband polarizationindependent diffusive scatterings based on metasurfaces. ACS Photonics 5, 1691–1702 (2018).
 27.
Wen, D. D. et al. Helicity multiplexed broadband metasurface holograms. Nat. Commun. 6, 8241 (2015).
 28.
Arbabi, A., Horie, Y., Bagheri, M. M. & Faraon, A. Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission. Nat. Nanotechnol. 10, 937–943 (2015).
 29.
Mueller, J. P. B., Rubin, N. A., Devlin, R. C., Groever, B. & Capasso, F. Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization. Phys. Rev. Lett. 118, 113901 (2017).
 30.
Devlin, R. C., Ambrosio, A., Rubin, N. A., Mueller, J. P. B. & Capasso, F. Arbitrary spinto–orbital angular momentum conversion of light. Science 358, 896–901 (2017).
 31.
Wang, Z. J. et al. Circular dichroism metamirrors with nearperfect extinction. ACS Photonics 3, 2096–2101 (2016).
 32.
Jing, L. Q. et al. Gradient chiral metamirrors for spinselective anomalous reflection. Laser Photonics Rev. 11, 1700115 (2017).
 33.
Burch, J. & Di Falco, A. Surface topology specific metasurface holograms. ACS Photonics 5, 1762–1766 (2018).
 34.
Durnin, J., Miceli, J. J. Jr & Eberly, J. H. Diffractionfree beams. Phy Rev. Lett. 58, 1499–1501 (1987).
 35.
Qi, M. Q., Tang, W. X. & Cui, T. J. A broadband Bessel beam launcher using metamaterial lens. Sci. Rep. 5, 11732 (2015).
 36.
Pfeiffer, C. & Grbic, A. Controlling vector Bessel beams with metasurfaces. Phys. Rev. Appl. 2, 044012 (2014).
 37.
Aieta, F. et al. Aberrationfree ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces. Nano. Lett. 12, 4932–4936 (2012).
 38.
Chen, W. T. et al. Generation of wavelengthindependent subwavelength Bessel beams using metasurfaces. Light Sci. Appl. 6, e16259 (2017).
 39.
Heckenberg, N. R., McDuff, R., Smith, C. P. & White, A. G. Generation of optical phase singularities by computergenerated holograms. Opt. Lett. 17, 221–223 (1992).
 40.
Thidé, B. et al. Utilization of photon orbital angular momentum in the lowfrequency radio domain. Phys. Rev. Lett. 99, 087701 (2007).
 41.
Mehmood, M. Q. et al. Visiblefrequency metasurface for structuring and spatially multiplexing optical vortices. Adv. Mater. 28, 2533–2539 (2016).
 42.
Ling, X. H. et al. Recent advances in the spin Hall effect of light. Rep. Prog. Phys. 80, 066401 (2017).
 43.
Xu, H. X., Liu, H., Ling, X. H., Sun, Y. M. & Yuan, F. Broadband vortex beam generation using multimode Pancharatnam–Berry metasurface. IEEE Trans. Antennas Propag. 65, 7378–7382 (2017).
 44.
Yang, Y. J., Thirunavukkarasu, G., Babiker, M. & Yuan, J. Orbitalangularmomentum mode selection by rotationally symmetric superposition of chiral states with application to electron vortex beams. Phys. Rev. Lett. 119, 094802 (2017).
 45.
Liu, S., Cui, T. J., Zhang, L., Xu, Q. & Wang, Q. et al. Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams. Adv. Sci. 3, 1600156 (2016).
 46.
Karimi, E., Schulz, S. A., De Leon, I., Qassim, H. & Upham, J. et al. Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface. Light Sci. Appl. 3, e167 (2014).
Acknowledgements
This work was supported by the National Natural Science Foundation of China (61501499, 11634010); Youth Talent Lifting Project of the China Association for Science and Technology (17JCJQQT003); National Defense Foundation of China (2201078); Key Program of Natural Science Foundation of Shaanxi Province (2017KJXX24); China Scholarship Fund (201703170022); and Aviation Science Foundation of China (20161996009). T.J.C. acknowledges supports from the National Natural Science Foundation of China (61631007 and 61571117), the National Key Research and Development Program of China (2017YFA0700201, 2017YFA0700202, 2017YFA0700201), and the 111 Project (111205). C.W.Q. acknowledges the financial support from the National Research Foundation, Prime Minister’s Office, Singapore under its Competitive Research Program (CRP award NRFCRP15201503).
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Contributions
H.X.X. and C.W.Q. proposed the idea. H.X.X. designed and fabricated the samples and performed the numerical simulations and experiments. G.H. wrote the program code for the coupled mode analysis. G.H., Y.L., and L.H. interpreted the data. J.Z., Y.S., G.M.W., Z.H.J., T.J.C., and X.L. analyzed the results and made additional efforts in preparing the manuscript. F.Y. participated in the experiments. H.X.X., G.H., and C.W.Q. wrote the manuscript with input from all authors. C.W.Q. supervised the project. All authors commented on the manuscript.
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Correspondence to HeXiu Xu or Tie Jun Cui or ChengWei Qiu.
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