Electromagnetic metasurfaces: physics and applications · Electromagnetic metasurfaces: physics and...

Electromagnetic metasurfaces:physics and applicationsSHULIN SUN,1,5 QIONG HE,2,5,6 JIAMING HAO,3 SHIYI XIAO,4

AND LEI ZHOU2,5,6,*

1Shanghai Engineering Research Center of Ultra-Precision Optical Manufacturing,Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Green Photonics,and Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China2State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures(Ministry of Education), and Physics Department, Fudan University, Shanghai 200433, China3State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics,Chinese Academy of Sciences, Shanghai 200083, China4Key Laboratory of Specialty Fiber Optics and Optical Access Networks,Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication,Shanghai Institute for Advanced Communication and Data Science, Shanghai University,Shanghai 200444, China5Academy for Engineering and Technology, Fudan University, Shanghai 200433, China6Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China*Corresponding author: [email protected]

Received December 17, 2018; revised April 9, 2019; accepted April 10, 2019; published June 19, 2019(Doc. ID 355464)

Metasurfaces are ultrathin metamaterials consisting of planar electromagnetic (EM) mi-crostructures (e.g., meta-atoms) with pre-determined EM responses arranged in specificsequences. Based on careful structural designs on both meta-atoms and global sequen-ces, one can realize homogenous and inhomogeneous metasurfaces that can possess ex-ceptional capabilities to manipulate EM waves, serving as ideal candidates to realizeultracompact and highly efficient EM devices for next-generation integration-optics ap-plications. In this paper, we present an overview on the development of metasurfaces,including both homogeneous and inhomogeneous ones, focusing particularly on theirworking principles, the fascinating wave-manipulation effects achieved both staticallyand dynamically, and the representative applications so far realized. Finally, we alsopresent our own perspectives on possible future directions of this fast-developingresearch field in the conclusion.© 2019 Optical Society of America

https://doi.org/10.1364/AOP.11.000380

1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3822. Homogeneous Metasurfaces: Role of Meta-Atoms . . . . . . . . . . . . . . . . . 383

2.1. Phase Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3832.1a. Electric Resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3832.1b. Magnetic Resonance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3852.1c. Dielectric Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

2.2. Amplitude Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

380 Vol. 11, No. 2 / June 2019 / Advances in Optics and Photonics Review

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2.2a. Enhanced Optical Transmission . . . . . . . . . . . . . . . . . . . . . . 3862.2b. Perfect Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390

2.3. Polarization Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3932.3a. Manipulating Polarization in Reflection Mode . . . . . . . . . . . . 3932.3b. Manipulating Polarization in Transmission Mode . . . . . . . . . . 396

2.4. Tunable Homogeneous Metasurfaces. . . . . . . . . . . . . . . . . . . . . . . 3992.4a. Electrically Tunable Metasurfaces . . . . . . . . . . . . . . . . . . . . . 3992.4b. Optically Tunable Metasurfaces . . . . . . . . . . . . . . . . . . . . . . 4022.4c. Mechanically Tunable Metasurfaces . . . . . . . . . . . . . . . . . . . 4022.4d. Thermally Tunable Metasurfaces . . . . . . . . . . . . . . . . . . . . . 4032.4e. Tunable Metasurfaces Based on Other Tuning Mechanisms. . . . 403

3. Gradient Metasurfaces: Principles and Realization . . . . . . . . . . . . . . . . . 4043.1. Generalized Snell’s Law: Metasurfaces for Linearly Polarized EM Waves 4043.2. Geometric-Phase Metasurfaces for Manipulating Circularly Polarized EM

Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4113.3. Linking PWs and SWs with Metasurfaces . . . . . . . . . . . . . . . . . . . 4173.4. Dielectric Metasurfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4243.5. New Mechanisms for Constructing Metasurfaces with Nearly Perfect

Efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4274. Applications of Inhomogeneous Metasurfaces . . . . . . . . . . . . . . . . . . . . 429

4.1. Metalenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4304.2. Metaholograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4364.3. Metasurface-Based Cloaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4404.4. Special Beam Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444

4.4a. Vortex Beam Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4444.4b. Bessel Beam Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4474.4c. Vector Beam Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 447

4.5. Multifunctional Metasurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4484.6. Tunable/Active Inhomogeneous Metasurfaces . . . . . . . . . . . . . . . . . 451

5. Conclusions and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454Funding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456

Review Vol. 11, No. 2 / June 2019 / Advances in Optics and Photonics 381

Electromagnetic metasurfaces:physics and applicationsSHULIN SUN, QIONG HE, JIAMING HAO, SHIYI XIAO, AND LEI ZHOU

1. INTRODUCTION

Manipulating electromagnetic (EM) waves in the desired manners is one of the mostimportant tasks in photonics research, as photons are believed to be alternative infor-mation carriers that may play crucial roles in the next-generation industry revolution.According to Maxwell’s equations, permittivity and permeability of a medium dictatethe behavior of EM waves propagating inside it. However, naturally existing materialsexhibit only limited abilities to control EM waves, since their permittivities lie in anarrow variation range, and, even worse, their permeability is all very close to 1 athigh frequencies (e.g., the visible range), due ultimately to the weak interactions be-tween natural molecules/atoms and the magnetic fields of EM waves. As a result,conventional EM devices typically need to be thick enough (compared to the oper-ation wavelength) and exhibit certain curved shapes to ensure appropriate propagationphases accumulate to realize the desired wave-manipulation functionalities (say, fo-cusing). In addition, efficiencies of conventional devices can also be an issue causedby impedance mismatch between air and natural materials that typically do not exhibitmagnetic responses. Such limitations (i.e., size, shape, and efficiency) significantlyhinder the applications of conventional optical devices in next-generation on-chipphotonics scenarios, which are typically flat, ultracompact, and energy saving.

Metamaterials, artificial composite materials made by subwavelength microstructures(e.g., meta-atoms) with tailored EM properties can in principle possess arbitrary valuesof permittivity ε and permeability μ, and therefore provide a promising platform to solvethe issues mentioned above [1–4]. The much expanded parameter ranges offer meta-materials significantly improved capabilities to control EMwaves in different frequencyregimes, leading to many fascinating new physics and wave-manipulation effects beingproposed and demonstrated, such as optical magnetism, negative refraction, super lens-ing, and even invisibility cloaking [5–7] and optical illusion [8]. However, despite greatsuccesses, metamaterial-based EM devices are still bulky in size since they rely on thepropagation phases of light accumulated inside the devices. More seriously, they sufferfrom grand challenges in efficiency and fabrication, since they are typically constructedby metallic/plasmonic microstructures with complex geometries, which are lossy anddifficult to make, particularly in mass production [9].

Metasurfaces are two-dimensional (2D) versions of metamaterials constructed byidentical or distinct planar meta-atoms with predetermined EM responses arrangedin some specific global orders. They offer a much better platform to overcomethe issues faced by natural materials and bulk metamaterials [10]. In contrast tometamaterial-based EM devices relying critically on the propagation phases of EMwaves, metasurfaces fully exploit the abrupt phase changes of EMwaves at meta-atominterfaces, so they can be much thinner than the working wavelength. Meanwhile,since EM waves do not typically stay inside metallic structures for a long time,the loss issue can be significantly alleviated in metasurface-based devices. Also, theflat configuration makes such systems easy to fabricate. Most importantly, by tailoringthe “order” on which the meta-atoms are arranged, one can realize metasurfaces thatexhibit desired inhomogeneous distributions of amplitude and phase for transmitted/reflected EM waves, enabling diversified fascinating wave-manipulation effects far


beyond those realized with metamaterial-based devices [11–13]. These unique fea-tures make metasurfaces ideal candidates to realize flat and miniaturized metadevicesthat exhibit powerful wave-manipulation capabilities, being particularly suitable foron-chip photonic applications.

In this paper, we present an overview onmetasurfaces, focusing particularly on thework-ing principles, practical realizations, and potential applications of such ultrathin EM sys-tems. This paper contains the following five sections. In Section 2, we review theavailable mechanisms to use homogeneous metasurfaces, constructed by identical sub-wavelength-size planar meta-atoms arranged periodically, to manipulate the key char-acteristics of EM waves, including phases, amplitudes, and polarizations, bothstatically and actively. Understanding these mechanisms not only helps us constructhomogeneous metasurfaces to achieve certain immediate applications (conducting elec-trodes, perfect light absorbers, polarization-control devices, etc.), but more importantly,provides a solid basis for further studies on inhomogeneous metasurfaces that requiremeta-atoms with particular EM properties. Equipped with this basic knowledge, we nextreview in Section 3 the working principles and practical realizations of inhomogeneousmetasurfaces constructed with plasmonic or dielectric materials for controlling EMwaves with different polarizations. In particular, we highlight a very unique role playedby gradient metasurfaces, which is the bridge to link propagating waves and surfacewaves efficiently, as well the latest exciting theoretical developments on new mecha-nisms to achieve extreme-condition anomalous EM wave bending. With these mecha-nisms understood, we then summarize in Section 4 several representative applications ofinhomogeneous metasurfaces, including metalenses, metaholograms, metasurface-basedcloaking, special beam generation, multifunctional metasurfaces, and tunable/activeinhomogeneous metasurfaces. Finally, Section 5 concludes this review, followed byour own perspectives on future directions of this fast-developing research field.

2. HOMOGENEOUS METASURFACES: ROLE OF META-ATOMS

We start from studying metasurfaces constructed by identical meta-atoms arrangedperiodically in a 2D plane. In many cases, the lattice constants of these ultrathin struc-tures are much less than wavelengths of interest, and thus one can consider these sys-tems homogeneous metasurfaces with EM properties determined by constitutionalmeta-atoms. Early efforts along this direction are mainly devoted to using homo-geneous metasurfaces to control the key characteristics of EM waves, such as phases,amplitudes, and polarizations. To achieve these goals, apparently one needs to firstunderstand how different meta-atoms interact with EM waves, based on which onecan choose appropriate meta-atoms to design metasurfaces to realize the desired wave-manipulation functionalities. In this section, we briefly summarize available mecha-nisms to control phases, amplitudes, and polarizations of EM waves, both staticallyand dynamically, based on homogeneous metasurfaces.

2.1. Phase ModulationDramatic phase changes are induced when EMwaves excite certain resonances. Theseresonances can be classified as electric and magnetic ones, depending on the dipolemoments possessed by the structures. On the other hand, systems exhibiting theseresonances can be constructed with metallic/plasmonic or dielectric materials.Here, we summarize the features of these resonances and the typical structures sup-porting them.

2.1a. Electric Resonances

The simplest structure supporting an electric resonance is a metallic bar, as depicted inFig. 1(a). When an EM wave hits the bar with polarization along its long axis, electric


current will be driven to flow along the bar, oscillating back and forth at the drivenfrequency, giving rise to an inductance (L). Meanwhile, because of the finite length ofthe bar, electric charges can be accumulated at two ends of the bar, with magnitudesoscillating with the driven field thus contributing to a capacitance (C). The co-existence of L and C dictates that the structure must resonate at a frequencyωe ∼ 1∕

ffiffiffiffiffiffiffiLC

p. A careful examination of charge/current distribution reveals that the

structure supports an electric dipole moment at resonance. As two typical featuresof a Lorentz-type resonance, the scattered electric field reaches a maximum as fre-quency hits ωe, and its phase undergoes a variation of π as frequency passes throughωe [Fig. 1(a)]. In principle, ωe of different structures can be accurately computed bysolving the charge/current distributions self-consistently [15], but one can alterna-tively use an empirical formula to estimate it, that is, the resonance wavelength isroughly twice of the total length of the bar. The accuracies of such an empirical for-mula are better for metallic thin wires at low frequencies, but get worse at opticalfrequencies, particularly when approaching the plasmon resonance of metals. We note

Figure 1

Phase manipulations with metasurfaces. (a) Metallic electric resonance. Top panel:schematic of a free-standing gold nanorod illuminated by impinging light. Middlepanel: simulated electric field distributions around the nanorod at electric resonancefrequency. Bottom panel: simulated reflection (red solid line)/transmission (reddashed line) amplitudes and reflection phase (black solid line) spectra of the goldnanorod array. (b) Metallic magnetic resonance. Top panel: schematic of oneMIM-type meta-atom consisting of a gold nanopatch and a continuous gold thin film(yellow) separated by theMgF2 spacer (blue). Middle panel: simulated electric currentinduced inside the MIM meta-atom illuminated by the input light at magnetic reso-nance frequency. Bottom panel: simulated reflection (red solid line)/transmission (reddash line) amplitudes and reflection phase (black solid line) spectra of the MIM meta-atom array. (c) Dielectric electromagnetic resonances. Top panel: schematic of a sil-icon (Si) nanosphere resonator. Bottom panel: scattering efficiency versus dielectricpermittivity ε (lossless particle) for plasmonic (ε < 0) and dielectric (ε > 0) materials.Middle panel: simulated electric field distributions of the electric dipole (ed) and mag-netic dipole (md) resonances of the Si nanosphere resonator [14]. (c) From Kuznetsovet al., Science 354, aag2472 (2016) [14]. Reprinted with permission from AAAS.


that the phase tuning enabled by such a single-mode electric resonator is limited by π,which is also tightly connected with amplitude modulation [see Fig. 1(a)]. These re-strictions can be released through designing multimode resonators, as introduced withmore detail in the following subsections.

2.1b. Magnetic Resonance

Quite a few different structures can support magnetic resonance. In fact, optical mag-netism is an important topic in early years of metamaterials research and plays animportant role in achieving negative refraction [16]. For example, a split ring resonator(SRR) [2], a topological variant of a metallic straight wire, exhibits a magnetic res-onance contributed by the currents flowing along the ring. The EM response of a SRRis similar to that of a metallic bar, only with the electric field changed to a magneticone. As a result, phase modulation enabled by an SRR possesses the same restrictionsas an electric resonator. An alternative structure supporting magnetic resonance is themetal–insulator–metal (MIM) structure [17] consisting of a planar metallic micro-structure (say, a metallic bar) and a continuous metal film separated by a thin dielectricspacer [see Fig. 1(b)]. As the MIM structure is illuminated by an EM wave, antipar-allel electric currents can be induced on two metallic layers due to the coupling be-tween them, which forms a magnetic mode with a strongly enhanced magnetic fieldinside the spacer layer. The resonance wavelength is roughly 4 times the bar length,since now the path on which current flows is doubled as compared to that of an electricresonator [see Fig. 1(b)]. Different from a single-mode electric or magnetic resonator,the MIM structure can modulate the phase over a full 2π range, which inherent physicsexplained below. When the frequency of the incident wave is far away from the mag-netic resonance frequency ωm, the resonant response dies off, and thus the EM wave isdirectly reflected back by the metallic ground plane. As a result, the reflection phase is�π. However, when the incident-wave frequency approaches ωm, the magnetic res-onance is strongly excited, making the whole MIM structure behave like a perfectmagnetic conductor (PMC) and exhibiting a divergent effective permeability. TheEM wave is thus reflected by the PMC with a reflection phase of 0. Therefore, asthe frequency passes through ωm, the reflection phase of the whole structure changescontinuously from −π to 0 and then to π, covering the full range of 2π[see Fig. 1(b)].In fact, no matter how complex the top metallic microstructure is, suchMIM structurescan always be modeled by a double-layer system consisting of a homogeneous mag-netic material put on top of a metal plane [18]. Such a theoretical model can welldescribe all EM properties of the MIM structure. At optical frequencies, such a mag-netic resonance is also called gap surface plasmon (GSP) resonance, as proposed inRef. [19], since it can be viewed as a cavity mode of a GSP. In addition to the full-range phase modulation capability, MIM structures also de-link the modulations onphase and amplitude, which is another advantage compared to common electric andmagnetic resonators. Most importantly, the metallic ground plane can ensure totalreflection of EM waves (neglecting material losses), indicating that the reflection am-plitude is always 100% independent of the phase variation. At high frequencies wheremetallic losses are inevitable, reflection amplitude is reduced from 100%, particularlyat the resonance frequency. However, one can still use MIM structures to realizephase-modulation-related applications efficiently, through carefully designing thescattering and absorption quality factors of the MIM structure, as discussed inSubsection 2.3.

2.1c. Dielectric Resonance

The resonators discussed in the previous two subsections are all constructed by metals,inside which electric currents oscillate with frequency and resonate at certain frequen-cies. However, while metals behave as perfect electric conductors (PECs) at low


frequencies, ohmic losses inevitably exist in metals at high frequencies, which cansignificantly degrade the performances of such resonators. Alternatively, one canuse high-index dielectric materials to construct EM resonators to overcome the lossissues [20]. Moreover, since dielectrics are naturally more compatible with currentcomplementary metal-oxide semiconductor (CMOS) technologies, dielectric-reso-nance-based optical devices exhibit further advantages in applications compared totheir metallic counterparts. We choose a spherical nanoparticle (with permittivity ε)as an example to explain the working mechanism of dielectric resonances. Accordingto Mie theory [21,22], we understand that a particle with a given diameter can exhibit aseries of EM resonances at certain frequencies for certain values of ε, evidenced bystrongly enhanced scatterings. Such resonances can happen not only for negative val-ues of ε corresponding to plasmonic resonances, but also for positive values of ε,which are the dielectric resonances that we are discussing. Different from plasmonicresonances where conducting currents are strongly enhanced, dielectric materials donot have free electrons to support conducting currents. Instead, incident electric fieldscan penetrate inside the dielectric medium to induce strong displacement currents,which play similar roles as their conducting counterparts and can resonant under cer-tain conditions. Analyzing the distributions of displacement currents shows that bothelectric and magnetic modes exist in a single particle, but under different conditions[14]. As shown in Fig. 1(c), the magnetic dipole response results from the circulardisplacement currents of the electric field, while the wavelength inside the particleis comparable to the diameter of the particle. Also, the electric dipole response isformed by the straight electric displacement current flowing along the diameter di-rection appearing at higher frequency. Moreover, high-order resonance modes,e.g., magnetic and electric quadrupoles, are also supported by dielectric nanoparticlesat high frequency domains. In principle, such dielectric resonances exhibit similarwave-manipulation properties as their metallic counterparts in terms of both phaseand amplitude modulations, but with significantly reduced losses. However, comparedto metallic resonators, dielectric ones have larger sizes (even comparable to wave-length, depending on the refraction index) in order to achieve the desired opticalmanipulations.

2.2. Amplitude ModulationWe now introduce available mechanisms to control the amplitudes of EM waves usinghomogeneous metasurfaces, at both the transmission and reflection sides.

2.2a. Enhanced Optical Transmission

Making optically opaque media transparent is always fascinating. Understanding suchmechanisms can greatly facilitate designing metasurfaces to manipulate EM waves atthe transmission side. Meanwhile, such effects can find many applications in practice.For example, transparent conducting metals with both high optical transmittance andhigh conductivity are highly desired in optoelectronics. However, while metals exhibitgood static conductivities, they exhibit negative permittivity at frequencies belowplasmon resonance frequency and can strongly reflect EM waves. In 1998, Martín-Moreno et al. reported, rather surprisingly, that an optically thick metal film drilledwith a periodic array of subwavelength air holes can allow extraordinary optical trans-mission (EOT), which is orders of magnitude larger than that predicted by standardaperture theory [see Fig. 2(a)] [23]. Such an unusual effect was tightly associated withthe excitation of surface plasmon polaritons (SPPs) on the metal surfaces, aided byBragg scattering enabled by the air-hole array. Here, SPPs denote EM eigenmodesbounded at dielectric/metal surfaces associated with collective oscillations of freeelectrons, and can be excited when the following momentum matching condition issatisfied: kspp � k0 sin θi � mGx � nGy (k0 is the wavevector in vacuum; Gx,Gy are


the reciprocal wavevectors provided by the periodicity) [27,28]. To understand themicroscopic origin of EOT, Liu and Lalanne proposed a SPP coupled-mode modelconsidering all crucial processes, such as the excitation, propagation, and interferenceof SPP modes [29]. The model can well describe all important features of EOT.However, strictly speaking, such an effect happens only in large systems containing

Figure 2

Enhanced optical transmission (EOT). (a) Top panel: schematic of the surface-plasmon-polariton-aided EOT effect through a structural metal. Middle: sample picture of anoptically thick metal film perforated with a periodic array of subwavelength apertures.Bottom panel: zero-order transmission of 200 nm thick Ag film (periodicity of air holes,900 nm; hole diameter, 150 nm) at normal incidence [23]. (b) Top panel: schematic ofthe localized plasmonic-resonance-aided EOT effect. Middle panel: part of the samplepicture of the random arrays of holes. Bottom panel: normalized transmission amplitudeof the sample at normal incidence [24]. (c) Top panel: schematic of the scattering-cancellation-induced EOT effect through a homogeneous B layer (yellow, ε < 0)sandwiched by two other homogeneous A layers (dark, ε > 0). Middle panel: normal-ized magnetic field distribution inside the ABA structure at the high transmission fre-quency obtained by effective-medium level calculation. Bottom panel: measured(circles) and calculated (lines) transmission spectra of a practical ABA sample.Following the spirit of metamaterials, subwavelength metallic mesh structures andH-shaped resonators (inset) are adopted to realize, respectively, the desired B layer withnegative ε and A layers with positive ε at the working frequencies [25]. (d) Top andmiddle panels: interference model and practical design of the metamaterial antireflec-tion coating. Middle panel: experimentally measured reflectance and transmittancespectra for the normal incidence case. The solid and dashed lines represent the reflec-tance and transmittance of a bare GaAs surface [26]. (a) Figure 1 reprinted with per-mission from Martín-Moreno et al., Phys. Rev. Lett. 86, 1114–1117 (2001) [23].Copyright 2001 by the American Physical Society. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.86.1114. (b) Figure 1 reprinted with permission fromLee et al., Phys. Rev. Lett. 99, 137401 (2007) [24]. Copyright 2007 by theAmerican Physical Society. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.99.137401. (c) Figures 2 and 3 reprinted with permission from Zhou et al., Phys.Rev. Lett. 94, 243905 (2005) [25]. Copyright 2005 by the American Physical Society.https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.94.243905. (d) Figures 1 and4 reprinted with permission from Chen et al., Phys. Rev. Lett. 105, 073901 (2010) [26].Copyright 2010 by the American Physical Society. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.105.073901.


https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.86.1114












enough number of apertures, since Bragg scatterings play very important roles. Thisrestriction makes the mechanism difficult to use directly in metasurface design.

Later, scientists discovered that EOT can also happen in metallic films drilled with com-plex-shape apertures, where localized plasmonic resonance (or termed “shape reso-nance” and “waveguide cutoff modes” in different literature) supported by theseapertures play more important roles than the global Bragg scattering [see Fig. 2(b)].For example, in 2013 Wen et al. experimentally demonstrated that a metallic platedrilled with fractal-shape apertures exhibits multiple high-transmission bands in the in-frared (IR) regime, contributed by the self-similar multiple shape resonances supportedby such apertures [30]. Such localized resonances exhibit deep-subwavelength and mul-tiband responses, making them particularly suitable for meta-atom designs [31,32].Later, Huang et al. further utilized the deep-subwavelength responses of such fractalapertures to realize a metadevice that can achieve subwavelength imaging, thanks to thelocal-resonance-enabled EOT effect [33,34]. Apparently, similar high transmission canalso be achieved through apertures with other shapes [35–38]. In addition to thesemechanisms, enhanced transmission can also be induced by the Fabry–Perot (FP) res-onance of waveguide modes inside nanoapertures. For example, in 1999 Porto et al.numerically demonstrated that metallic gratings with very narrow and deep enough slitscan exhibit high transmission resonance via coupling with the waveguide mode in theslits [39]. Ruan and Qiu numerically demonstrated that such a waveguide-mode-aidedhigh-transmission effect is quite independent of the period of the structure, manifestingits nature of localized resonance [40]. Lee et al. experimentally observed the EOTeffectat terahertz (THz) frequencies in random arrays of single rectangular holes [24]. Such aresearch field has become extremely active since 1998, and readers can learn more fromseveral excellent review articles [41–43].

The EOT mechanisms, while being scientifically inspiring, suffer from several issuesin practical applications. For example, SPP-aided EOT is sensitive to both incidenceangle and polarization of the excitation wave, and the apertures inevitably degrade theconductance of metals. In 2005, Zhou et al. proposed a new mechanism to make anopaque slab perfectly transparent [25]. Consider a plasmonic metal slab with a neg-ative permittivity (ε2 < 0). Instead of structuring it by making holes and grooves, theauthors proposed to add two identical layers with positive permittivity (ε1 > 0) toform an ABA structure. Simple calculations show that the whole structure becomesperfectly transparent when the following criterion is met:�

k1k0

− k0k1

�2 tan�k1d1� −

�α2k0

� k0α2

�tanh�α2d2�

−�

k21α2k0

� α2k0k21

�tan2�k1d1� tanh�α2d2� � 0, (1)

where kj � ffiffiffiffiεj

pω∕c, k2 � iα2, and dj denote the thickness of the jth layer. The first

two terms in Eq. (1) are contributed by individual A and B layers, while the third termis a multiple scattering contribution of the whole system. Equation (1) clearly revealsthat the transparency is governed by cancellation of scatterings from two layers. In thelong wavelength limit (kidi → 0), Eq. (1) is reduced to ε � �2ε1d1 � ε2d2�∕�2d1 � d2� � 1, in consistency with the prediction based on effective-medium theory(EMT). Moreover, even k1d1 and α2d2 are not so small; one can still find solutions ofEq. (1) numerically, going beyond the EMT predictions. Such a mechanism was ex-perimentally demonstrated in the microwave regime, with the “plasmonic” metalmimicked by a metallic mesh with subwavelength openings and layer A representedby a metasurface consisting of H-shaped electric resonators. Perfect transmission of


EM waves was found at frequencies where Eq. (1) is met, in excellent agreement withboth full-wave simulations and EMT calculations. Such a mechanism exhibits certainunique features as compared to the SPP-aided ones. First, the perfect transmission islargely governed by the “local” EM properties of the system. Second, the effect isquite insensitive to incident angles, since jεij is very large in both layers so that vary-ing the incidence angles (and thus varying the parallel wavevectors) does not changeEq. (1) significantly. Third, the magnetic field is highly amplified inside the ABAsystem due to the coupling between two metallic layers (as depicted in Fig. 2(c)],which plays a very important role in designing transmissive metasurfaces later(see Subsection 3.2). Soon after such a scattering cancellation mechanism was pro-posed, experiments were performed in different frequency domains to demonstratethis concept [44,45]. For example, Hooper et al. fabricated such an ABA structurein the optical frequency domain, and experimentally demonstrated the desired highoptical transmission [45].

Closely related to the above mechanism, one can also place an antireflection coatinglayer on a target interface to enhance the optical transmission through it. However, it isnot easy to find appropriate coating materials that satisfy the index-matching require-ment in low-frequency domains (e.g., far-IR and microwave), and fabricating suchantireflection layers is also challenging. In 2010, Chen et al. proposed a new strategyto realize antireflection coatings based on metasurfaces [26]. For an optical interfacebetween air and GaAs, the authors designed an antireflection layer consisting of anarray of gold cross-shaped microstructure and a gold mesh separated by a dielectricspacer [see Fig. 2(d)], and then experimentally demonstrated that it can significantlysuppress the reflection and thus enhance the transmission into the GaAs medium. Themeasured maximum transmittance under normal incidence was 90% near 1.2 THz ascompared to 68% through a bare air–GaAs interface [dashed line in Fig. 2(d)].Moreover, the anti-reflection effect is also polarization insensitive even for obliqueincident cases. To elucidate the mechanism, the authors modeled the SRR arrayand the mesh layer as individual metasurfaces with EM characteristics computedas they stand alone, and then calculated the reflection and transmission of the wholesystem by considering the multiple reflection/transmission effects [Fig. 2(d)]. In thelossless case, the total reflection coefficient can be simplified as

er � r21 exp�iϕ12� − r23 exp�i�ϕ12 � ϕ21 � ϕ23 � 2β��1 − r21r23 exp�i�ϕ21 � ϕ23 � 2β�� , (2)

where 2β represents the phase accumulated for a wave traveling inside the dielectricspacer in a round. Clearly, through tuning the spacer thicknesses and the EM char-acteristics of individual layers, one can make r � 0 under certain conditions, yieldingcomplete antireflection. Here, the destructive and constructive interferences areresponsible, respectively, for suppression of reflection and enhancement of transmis-sion. The concept was intimately related to the scattering cancellation mechanism, butwas established here in an asymmetrical scenario. Experiments were performed toverify the idea in different frequency regimes and to significantly enlarge the workingbandwidth [46,47]. For example, Huang et al. report bilayer metasurfaces for accom-plishing dual- and broadband optical antireflection in the THz and mid-IR regimes.The dispersions of individual metasurface layers are carefully tailored to provide sim-ilar reflection amplitudes and opposite phase dispersions to expand the antireflectionoperational bandwidth. By exploiting the self-aligned bilayer metallic metasurfaces,this antireflection scheme avoids the deposition of thick dielectric films and is appli-cable to substrates with arbitrary refractive indices [48].


2.2b. Perfect Absorption

Absorption is another way to control the amplitudes of EM waves. Moreover, effi-ciently absorbing EM waves are important in many applications, such as enhancingthe efficiency of radar detection, photodetectors, and solar cells. However, naturalmaterials cannot efficiently absorb light due to their weak interactions with light.Conventional perfect-absorption devices, such as Dallenbach and Salisbury screens[49,50], are too bulky in size, as they usually consist of resistive sheets placed atquarter-wavelength distances above a metal ground plane. Recently, metasurfaceswere widely used to realize EM absorbers in different frequency domains that areultrathin and highly efficient. Here we briefly review the developments along this line.

To maximize light absorption within a medium, one must simultaneously minimizeboth transmission and reflection from it. Transmittance through an optical materialcan be easily diminished if the system is thick enough and exhibits certain losses.However, eliminating the reflection is not easy. Consider a plane EM wave impingingnormally on an interface between two homogeneous media, the reflection coefficientcan be written as

r � Z2 − Z1

Z2 � Z1

, (3)

with Zi �ffiffiffiffiffiffiffiffiffiffiμi∕εi

pbeing the impedance of the ith medium. Equation (3) shows that

eliminating the reflection requires matching the impedances of two media, namely,Z2 � Z1. Such a condition is difficult to meet based on natural materials that lackmagnetic responses at high frequencies. Metamaterials, which can in principle possessarbitrary values of permittivity and permeability upon design, are the ideal candidatesto realize perfect absorbers [51,52].

The idea of using metasurfaces to design thin absorbers was first proposed in 2002 byEngheta [53], who predicted that combining an MIM structure (also called a “high-impedance surface”) with a resistive sheet can efficiently absorb EM waves underappropriate conditions. In contrast to a Salisbury screen, here the distance betweenthe resistive sheet and the ground plane can be much smaller than the working wave-length. Since an MIM structure exhibits a magnetic mode at resonance, it can reflectEM waves without any phase changes, resulting in a strongly enhanced electric fieldon its surface. As a result, by placing a resistive sheet with proper impedance on top ofsuch a structure the reflected wave can be reduced to zero, leading to perfect EM waveabsorption since there is no transmission through the system [53,54].

In 2008, Padilla’s group experimentally demonstrated the first metasurface-basedabsorber [55], which consists of two metallic layers separated by a dielectric spacer.The top metallic layer is composed of an array of electric ring resonators (ERRs) asshown in Fig. 3(a), which primarily provides electric responses to the system. Thebottom layer contains an array of metallic cut wires, which, coupled with theERR on the top layer, contribute strong magnetic responses to the device. The wholesystem thus possesses both electric and magnetic responses, which can be tuned inde-pendently by varying different structural parameters. Through adjusting geometricalparameters, the authors successfully designed a perfect absorber with impedancematching that of air. Microwave experiments demonstrated that the fabricated deviceexhibits an absorption peak 88% at 11.5 GHz, though theoretical results predicted nearperfect absorption [see Fig. 3(a)].

After such a meta-absorber was demonstrated, follow-up investigations were quicklycarried out in the THz regime [56,61,62]. Compared with microwave absorbers, thedesign presented in Ref. [56] exhibits several new traits. First, the absorber has a


Figure 3

Enhancement of absorption by metasurfaces. (a) Microwave metasurface absorber [55].Left panel: schematics of an electric ring resonator, cut wire, and the unit cell of themicrowave metasurface absorber. Right: simulated (red line) and measured (blue line)absorbance spectra of the microwave absorber. The inset displays the simulated angulardependence of the absorbance at the peak absorption frequency of 11.5 GHz [55].(b) THz metamaterial absorber. Left panel: schematic (top) of the THz absorber, andphotograph (bottom) of a portion of the experimental sample. Right panel: measuredabsorptivity as a function of frequency for TE (top) and TM (bottom) modes at threedifferent incident angles [56]. (c) Mid-IR metasurface absorber. Top-left panel: simu-lated reflection (blue line), transmission (green line), and absorption (red line) of thedevice. Bottom-left panel: a comparison between the experimental absorption (red line)and simulated absorption (dashed gray line). Right panel: simulated energy dissipationin the mid-IR metasurface absorber structure at a wavelength of 6 μm. Energy dissi-pation distribution in cross (upper left corner), dielectric spacer (upper right corner),ground plane (lower left corner), and cross view of the whole structure (lower rightcorner) [57]. (d) and (e) NIR metasurface absorbers [58,59]. Metasurfaces in MIM con-figurations were used in both works, with the top resonator being a gold disk [58][the left of Fig. (d)] or a patch [59] [the left of Fig. (e)], respectively. The maximumabsorptions reported in these twoworks are 99% and 88%, respectively, while the work-ing wavelengths are both roughly at 1.6 μm. (f) Visible metasurface-based absorber.Upper left corner: unit cell of the absorber. Upper right corner: schematic of the device.Lower left corner: scanning electronic microscopy image of the fabricated sample.Lower right corner: experimental reflectance for normal incidence, normalized tothe gold film, for Ag nanocube surface coverages of 7.3% (thin solid line) and17.1% (thick solid line) [60]. (a) Figures 1 and 3 reprinted with permission fromLandy et al., Phys. Rev. Lett. 100, 207402 (2008) [55]. Copyright 2008 by theAmerican Physical Society. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.100.207402. (b) Figures 1 and 4 reprinted with permission from Tao et al., Phys.Rev. B 78, 241103 (2008) [56]. Copyright 2008 by the American Physical Society.https://journals.aps.org/prb/abstract/10.1103/PhysRevB.78.241103. (c) Figures 2 and 4reprinted with permission from Liu et al., Phys. Rev. Lett. 104, 207403 (2010) [57].Copyright 2010 by the American Physical Society. https://journals.aps.org/prb/abstract/10.1103/PhysRevB.78.241103. (d) Reprinted with permission from Liu et al.,








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flexible polyimide substrate with only 16 μm thickness, making it particularly suitablein conformal applications [see Fig. 3(b)]. Second, the device can absorb THz wavesunder a wide range of incidence angles with both transverse electric (TE) and trans-verse magnetic (TM) polarizations [see Fig. 3(b)]. For the TE measurement, the ab-sorption peak is 95% for 30° incidence, reducing slightly to 88% at 60°. For TMradiation, the maximum absorption value reaches 96.8% at 30° and falls by only0.024 upon increasing to 60°. Third, the bottom layer of the absorber is replacedby a continuous metallic film, forming an MIM structure. Such a configuration cutsoff the transmission and thus only the reflection needs to be worried about, whichsimplifies the design process. In addition, the new configuration is also favored infabrications, as precise alignment between top and bottom metallic layers is no longernecessary.

The concept was soon pushed to even higher frequencies, with perfect absorbers de-signed essentially through down-scaling the dimensions of their low-frequency counter-parts predominantly in MIM configuration, only with top resonators replaced by newdesigns. The first mid-IR perfect absorber was again demonstrated by Padilla’s group in2010 [57], with the top resonator being a metallic cross. The group experimentallyachieved an absorbance of 97% at 6 μm and found that the majority of power is dis-sipated by dielectric losses [see Fig. 3(c)]. Still in 2011, two groups independently re-ported near-IR perfect absorbers, again in MIM configurations, with the top resonatorbeing a gold disk [58] [Fig. 3(d)] or a patch [59] [Fig. 3(e)]. The maximum absorptionsreported in these two works are 99% and 88%, respectively, while the working wave-lengths are both roughly at 1.6 μm. The absorption effect is tunable by adjusting thenanostructure dimensions and is robust against varying incident angles. In contrast totheir low-frequency counterparts, Hao et al. revealed that, for the near-IR absorbers, thepower carried by light is predominantly dissipated through ohmic losses in metals ratherthan in a dielectric spacer. Visible absorbers were proposed in 2011 [63–65], but ex-perimental demonstrations are rarely seen mainly due to fabrication challenges,although one theoretical work numerically predicted that the absorbance can be as highas 99% at the wavelength 596 nm. To overcome fabrication challenges in the top-downapproach, researchers turned to using the chemical self-assembly method to realize per-fect absorbers [60,66,67]. In 2012, Moreaus et al. employed a colloidal approach tochemically synthesize silver nanocubes onto a nanoscale-thick polymer spacer layer,which was then put on a metal film, forming a visible metasurface absorber, as shownin Fig. 3(f) [60]. Experimental results showed that measured light reflectance can bereduced to 7% at 637 nm, for a sample with 17.1% Ag nanocube surface coverage.

Finally, we note that MIM metasurfaces were also widely used to control EM polar-izations, which will be discussed in detail in the next subsection. To understand whyMIM metasurfaces can exhibit two such distinct functionalities, Zhou’s group hasestablished a complete phase diagram by considering the intriguing interplays be-tween losses from radiative and absorptive channels [68]. Intuitively, the phase dia-gram reveals that perfect absorption is achieved when the two losses are equal to eachother, which is also known as the critical coupling condition. This actually provides analternative yet more inspiring interpretation on the underlying physics of perfect ab-sorption, which will be discussed with more detail in Subsection 2.3a.

Nano Lett. 10, 2342–2348 (2010) [58]. Copyright 2010 American Chemical Society.(e) Reprinted with permission from Hao et al., Appl. Phys. Lett. 96, 10–13 (2010) [59].Copyright 2010 AIP Publishing LLP. (f) Reprinted with permission from MacmillanPublishers Ltd.: Moreau et al., Nature 492, 86–89 (2012) [60]. Copyright 2012.


2.3. Polarization ControlPolarization is a fundamental characteristic of EM waves, and polarized light is ofgreat importance for various applications, ranging from sensing and photographyto optical communications. In practice, it is greatly desirable to have full controlon polarization. However, conventional devices to manipulate light polarizationare either too bulky in size (say, dichroic crystals) or less efficient (say, optical gra-tings), which limit their application in certain optical scenarios. Metasurfaces providean ultrathin and efficient platform to control EM wave polarization. Here, we brieflyreview the efforts in employing homogeneous metasurfaces to manipulate EM wavepolarizations in both reflection and transmission geometries.

2.3a. Manipulating Polarization in Reflection Mode

We start from studying the reflection property of a homogeneous anisotropicmetasur-face. Suppose a linearly polarized wave is normally incident on a metasurface, withthe E vector lying at an angle ϕ with respect to the x axis. The incident electric fieldcan be written as (the IEEE definition for EM wave phase is adopted in all of theequations in this paper)

~Ei � �cos ϕx� sin ϕy�ei�kz�ωt�: (4)

Assume that ri � jrijeiΦi (i � x, y) denote the complex reflection coefficients of such ametasurface, then the reflected wave can be obtained as

~Er � �jrxjeiΦx cos ϕx� jryjeiΦy sin ϕy�ei�−kz�ωt�: (5)

We see immediately that the polarization state of the reflected wave is determined bythree items, azimuthal angle ϕ, the ratio of jryj∕jrxj, and the phase differenceΔΦ � Φy −Φx. Consider the case of ϕ � 45° and jryj∕jrxj � 1. If the phase differ-ence satisfies ΔΦ � 90°, the polarization state of the reflected wave is circular polari-zation, indicating that the metasurface functions as a quarter-wave plate. Meanwhile,if ΔΦ � 180°, the resultant polarization is still linear polarization (LP), but the polari-zation direction changes to the cross direction of the original one. In such a case, themetasurface is essentially a half-wave plate but with ultrathin thickness. Therefore, thereflection phase difference between two orthogonal polarizations is essential in de-signing metasurfaces for polarization manipulation [69,70].

In 2007, Hao et al. initiated the idea of using anisotropic metasurfaces to manipulateEM wave polarization in reflection geometry [69]. Understanding the difficulties ofusing conventional materials (exhibiting purely electric responses) to modulate theEM wave phases in wide ranges, the authors proposed and then theoretically studiedthe EM properties of a model system consisting of an ultrathin metamaterial slab witha dispersive permeability μ tensor placed on a perfect metal substrate. Theoreticalcalculations predicted that all possible polarization states (circular, linear, elliptic po-larizations) are realizable for a LP wave being reflected by such a model system. Asimple argument was used to understand these unusual phenomena. Since the per-meability is anisotropic (μxx ≠ μyy), the reflection coefficients rx and ry are differentfor incident waves polarized along two directions. In most cases where μxx�μyy� is notlarge, we have φx�φy� ∼�180°, since the top metamaterial layer is transparent andlight can directly “see” the metallic ground plane that is reflecting out of phase.However, at the resonances where μxx�μyy� → �∞, we get φx�φy� � 0 since lightis reflected directly by the opaque metamaterial layer, which possesses infinite imped-ance (the right panel of Fig. 4(b)]. Therefore, in general we can obtain arbitrary valuesfor Δφ by adjusting the geometric and material properties of the metamaterial layer.The authors found that MIM structures are the ideal candidates to realize the proposed


Figure 4

Manipulating polarization in reflection mode. (a) Left panel: polarization conversionratio (PCR) as a function of frequency, obtained by theoretical calculations (solidlines), numerical simulations (solid stars), and experimental measurements (opencircles). The inset shows an image of part of the experimental sample. Right panel:frequency dependences of the reflection phase changes on the metamaterial reflectorsurface for normally incident waves with different polarizations, obtained by theoreti-cal calculations (solid lines) and numerical simulations (solid stars) [69]. (b) The cal-culated PCR as a function of wavelength using the experimental data. The inset showsa SEM image of a part of the experimental sample [71]. (c) Top panel: reflectivity forthree different incident angles. Inset shows SEM image of the fabricated structure.Curves correspond to numerical calculations; markers are experimentally measured val-ues. Bottom panel: reflectivity as a function of analyzer angle measured from the x axiswhen incident angle β � 40°. The legend “Reference” refers to reflection from a 50 nmthick SiO2 layer on top of a gold substrate [72]. (d) Left panel: SEM image of the arrayof gold L patterns fabricated by electron beam lithography. Right panel: experimentallymeasured reflectance of the fabricated broadband half-wave plate [73]. (e) Phase dia-grams of the on-resonance absorption A (left panel) and the span of reflection phaseΔΦ(right panel) versus Qr and Qa calculated with coupled-mode theory for the single-portmodel [68]. (a) Figures 2 and 4 reprinted with permission from Hao et al., Phys. Rev.Lett. 99, 63908 (2007) [69]. Copyright 2007 by the American Physical Society. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.99.063908. (b) Figures 1 and 3 re-printed with permission from Hao et al., Phys. Rev. A 80, 23807 (2009) [71].Copyright 2009 by the American Physical Society. https://journals.aps.org/pra/abstract/10.1103/PhysRevA.80.023807. (c) Reprinted with permission from [72].Copyright 2013 Optical Society of America. (d) Reproduced from [73] under theterms of the Creative Commons Attribution 3.0 License. (e) Figure 1 reprinted withpermission from Qu et al., Phys. Rev. Lett. 115, 235503 (2015) [68]. Copyright2015 by the American Physical Society. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.235503.









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model [69], and they then designed/fabricated an MIM structure in the microwaveregime with the top resonator being a metallic “H” [see the inset of the right panelof Fig. 4(a)]. Microwave experiments show that an LP beam indeed converts its polari-zation completely to the cross direction after being reflected by the metasurface atfrequencies near resonance [see the left panel of Fig. 4(a)]. Both the absolute workingefficiency and the polarization conversion ratio (PCR) of the device are nearly 100%,since here the system has jrxj ≈ jryj ≈ 1 with very weak absorptions. Other predictedpolarization control effects were also experimentally realized by such a MIM device.

Such concept was soon pushed to optical frequencies. The first reflection-type meta-surface half-wave plate was again demonstrated by Zhou’s group in 2009 [71]. Thedevice is also a tri-layer structure consisting of a gold nanorod array and a continuousgold film separated by a SiO2 spacer [see the inset of Fig. 4(b)]. Experimental resultsrevealed that the maximum PCR of such a device can reach 96% at the wavelength of685 nm, as shown in Fig. 4(b). Although the designed structure looks like its micro-wave counterpart [69], in fact the underlying physics is a bit different. In the opticaldesign, the thickness of the continuous gold film is only 15 nm, implying that thebottom metallic layer is no longer perfectively reflective since metal exhibits a finitepenetration length in the optical domain. Therefore, here the couplings between nano-rods and the gold continuous film generate not only magnetic resonance similar to themicrowave case, but also electric resonance that does not exist in the microwave de-vice. With both magnetic and electric modes fully considered, the authors establishedan effective-medium model to quantitatively describe the experimentally observedeffects. The key physics is that the designed metasurface can exhibit desired permit-tivity and permeability (in turn, desired impedance) for light polarized along two prin-ciple axes, resulting in the π phase difference requested by a half wave-plate.However, although possessing an ultrathin thickness, the realized optical device ex-hibits a degraded working efficiency compared to the microwave device, since it al-lows substantial light transmission. Many follow-up works were subsequentlyperformed to demonstrate the polarization conversion effects at optical frequencieswith enhanced working efficiencies. The realized devices either have thicker bottommetallic films, and thus block the transmitted signals [72,74,75], or have top resona-tors taking other shapes [76] or with more carefully tuned space layers [75]. In 2013,Bozhevolnyi’s group utilized a similar MIM-type metasurface [72], but with a thickerbottom gold substrate, to realize a more efficient wave plate [see Fig. 4(c)]. The fab-ricated structure functions as a half-wave plate at the wavelength of 780 nm with arelative bandwidth of 160 nm. A reflectance of 50% is experimentally obtained.

In the THz regime, Chen’s group demonstrated a reflection-type metasurface polari-zation converter in 2013 [77]. The device is similar to the microwave one but withH-shaped top resonators replaced by metal cut wires. An important contribution of thiswork, apart from the actual device realization in the THz regime, is the significantlyenlarged working bandwidth (0.73–1.88 THz). The working principle is slightly dif-ferent from those of the microwave and optical devices, although all of them are inMIM configurations. Here, the authors argued that two metallic layers form an FP-likecavity in which THz waves are multiply reflected before leaving the device. Therefore,THz waves polarized along two orthogonal directions can experience distinct inter-ference upon multiple reflection inside the cavity, generating a significant phase dif-ference for the reflected THz waves. It is such difference in FP modes supported bythe cavity that eventually helps realize the desired half-wave plate functionality.The obtained broadband performance results from the superposition of the multiplepolarization conversion effect [78,79]. In 2014, Jiang et al. introduced a new mecha-nism to construct broadband wave plates. Basically, the designed structure is alsocomposed of a layer of metallic metastructure and a continuous metallic film separated


by a dielectric layer [see Fig. 4(d)] [73]. In contrast to the previous works, here thedielectric layer is dispersive over the region of interest, which can perfectly compen-sate the intrinsic dispersion of the metallic structures. Experimental results demon-strated that, for the half-wave plate sample, the x-polarized (y-polarized) incidentlight is almost entirely converted to its cross polarization after being reflected bythe metasurface in a wide frequency band (70–145 THz) [see right panel of Fig. 4(d)].Very recently, using Jones matrix and Poincaré sphere analyses, Ma et al. derived a setof criteria to help design high-efficiency ultra-wideband THz wave plates using aniso-tropic metasurfaces [80], and further experimentally demonstrated three differentwave plates, all exhibiting excellent polarization manipulation capabilities withinultrawide bandwidths (relative bandwidths larger than 100%).

It is intriguing to note that MIM structures can support distinct resonant modes (e.g.,magnetic resonance or FP modes) and exhibit completely different functionalities (per-fect absorption in Subsection 2.2b and polarization control in this section). One natu-rally asks the question: Why does the same type of structure behave so distinctly andwhat determines their physical behaviors? In a series of works published in 2015–16,Zhou’s group provided answers to these questions [68,81]. In [81], the authors em-ployed a rigorous mode expansion method to analytically study the resonance proper-ties of MIM systems. They found that an MIM system supports magnetic resonantmodes when the spacer is thinner than a critical thickness, while the mode changesto a vertical FP mode as the spacer thickness enlarges. The near-field couplings betweentwo metallic layers play the most important role to differentiate these distinct modes.Furthermore, the authors established a complete phase diagram to fully understand thefunctionalities of MIM structures [68]. They found that all MIM structures can be de-scribed by a one-port cavity with a supported mode described by two factors, i.e., theabsorptive and radiative quality factors defined as Qa � ω0τa∕2 and Qr � ω0τr∕2,where τa and τr denote the mode lifetimes due to absorption and radiation, respectively.Based on such a simple model, the authors found that the optical properties of MIMsystems are fully controlled by the ratio between these two parameters, which is, in turn,dictated by the geometrical or material properties of the underlying structures.Specifically, a MIM metasurface behaves as a perfect absorber when Qr∕Qa � 1,but turns to being a strong reflector (i.e., jrj → 1) when Qr∕Qa is far away from 1,as shown in the left panel of Fig. 4(e). Moreover, in the Qr < Qa region, the MIMstructure represents an underdamped resonator with phase variation covering 2π as fre-quency passes through the resonance, while in the Qr > Qa region, the resonator be-come overdamped with small variation range of reflection phase (i.e., less than 180°)[see the right panel of Fig. 4(e)]. Such a phase diagram can greatly facilitate the designof appropriate metasurfaces with tailored functionalities, demonstrated by experimentalresults on a series of THz MIM metasurfaces realized by the authors. We need to men-tion that several other groups also noted the fascinating interplay between absorptiveand radiative losses in such MIM structures, although presented in different forms[82,83]. Moreover, such a generic phase diagram establishes a solid basis for achievingdynamically tunable metadevices based on MIM systems, as we will discuss inSubsection 2.4.

2.3b. Manipulating Polarization in Transmission Mode

After the first demonstration of polarization manipulation in reflection mode, manyefforts were devoted to extending the concept to transmission mode, which is moredesired in practice. However, such a task is much more difficult to fulfill than that inreflection mode, since now both transmission and reflection need to be considered.

In 2008, Beruete et al. designed a metadevice consisting of multilayers of EOT slabs[see Fig. 5(a)], and experimentally demonstrated that it can select an EM wave with a


Figure 5

Manipulating polarization in transmission mode. (a) Left panel: photograph of thefabricated hole array metasurface plate. Right panel: measured phase for the negativerefractive index (NRI) component, two plates (solid red) and three plates (solid blue),and for the positive refractive index (PRI) component, two plates (dashed red) andthree plates (dashed blue) [84]. (b) Left panel: SEM image of the fabricated L-shapedholes metasurface plate. Right panel: measured transmission spectra with the polari-zation analyzer set at four different angles (upper panel). Phase difference between thedetected phases in the x and y directions as a function of wavelength (lower panel),where insets are the calculated polarization states of the transmitted light at twoeigenfrequencies [85]. (c) Left panel: focused-ion-beam cut of a polymer structurepartially filled with gold (upper left) and oblique view of a left-handed helix structureafter removal of the polymer by plasma etching (upper right); top-view imagerevealing the circular cross section of the helices and the homogeneity on a largerscale (lower panel). The lattice constant of the square lattice is a � 2 mm. Rightpanel: normal-incidence measured transmittance spectra. LCP and RCP are depictedin red and blue, respectively. Pitches of left-handed helices (upper panel) and right-handed helices (lower panel) [86]. (d) Left panel: layer A (upper panel) is periodicallyarranged electric resonators; layer B (lower panel) is metallic mesh. Right panel: si-mulated (solid curves) and measured (circles) spectra of transmission amplitudes andphases for two incident polarizations [87]. (e) Left panel: schematic of the unit cell ofthe broadband THz transmission-type linear polarization converter. Right panel:cross-polarized transmittance obtained through experimental measurements, numeri-cal simulations, and theoretical calculations, and with the numerically simulated co-polarized reflectance [77]. (f) Left panel: experimentally measured degree of linearpolarization (DoLP) and angle linear polarization (AoLP) for circularly polarized ex-citation. The inset is an SEM image of silver nanorods. Right panel: experimentalmeasurement of the transmission coefficients for linearly polarized excitation alongthe two nanorod axes [88]. (a) Reprinted with permission from Beruete et al., J. Appl.Phys. 103, 053102 (2008) [84]. Copyright 2008 AIP Publishing LLC. (b) Reprintedwith permission from Li et al., Appl. Phys. Lett. 93, 021110 (2008) [85]. Copyright2008 AIP Publishing LLC. (c) From Gansel et al., Science 325, 1513–1515 (2009)[86]. Reprinted with permission from AAAS. (d) Reprinted with permission from[87]. Copyright 2011 Optical Society of America. (e) From Grady et al.,


particular polarization to pass through [84]. For an incident wave with arbitrary polari-zation, any type of polarization state can be obtained at the output by simply adjustingthe number of stacked plates. The phase shift between two orthogonally polarizedeigenwaves is dictated by the negative and positive indices for two different modestraveling inside. However, such a device still needs a large enough thickness since itrelies on propagation-phase accumulations, as shown in the right panel of Fig. 5(a),and the working efficiency of the device is quite low. Soon, Li et al. proposed a single-slab polarization-control device that is a silver film drilled with an L-shaped aperturearray [see Fig. 5(b)] [85]. Since the aperture exhibits different “shape resonances” fortwo polarizations controlled by the lengths of two arms of the L [see Subsection 2.2),naturally the EOT through such a device exhibits distinct behaviors for two polariza-tions, which can be fully utilized to control the polarization state of light transmittedthrough it. Indeed, nearly 45° polarization rotation was experimentally observed withrelatively strong transmission for a polarized light with a specific incidence angle atthe wavelength 1200 nm [see Fig. 5(b)]. The optical rotation is high considering thatthe sample is only 80 nm thick. In the same year, Chin et al. demonstrated a micro-wave transmission polarizer based on an anisotropic metasurface [89] consisting of anarray of electric resonators exhibiting designable effective electric permittivity. A de-vice consisting of two layers can function as a quarter-wave plate, while a four-layerdevice functions as a half-wave plate. However, while these devices do not need wave-length-scale thicknesses, their working efficiencies are not perfect, not only due toabsorption, but more importantly, also due to reflection caused by lacking magneticpermeability in the designed systems.

In addition to using anisotropic metasurfaces, researchers also proposed to use chiralmetasurfaces to control EM-wave polarization at the transmission side [86,90,91]. Alsoin 2008, Li et al. investigated the transmission of microwaves through a chiral metasur-face [90], formed by an array of square single SRRs. They found that an ellipticallypolarized transmitted wave was achieved at the resonant frequency of the metasurface,with major polarization axes approximately perpendicular to that of the incident wave.The optical activity of such a medium is due to the hybridization effect of magneticresonances. Such a device can be ultrathin, but both the PCR and the working efficiencyof the device do not approach 100%. In 2009, Gansel et al. investigated the propagationof light through an anisotropic photonic metamaterial [86] composed of a three-dimensional (3D) array of gold helices [see Fig. 5(c)]. For light propagating alongthe helix axis, the circular polarization with the same handedness as that of the helicesis blocked by the structure, whereas light with another circular polarization is transmit-ted. The measured spectra revealed that a large transmittance ratio appears in the wave-length range (3.5–7.5 μm), as shown in the right panel of Fig. 5(c).

In 2011, Zhou’s group proposed a new device configuration to achieve 100% effi-ciency polarization control on a transmitted wave. The device is a tri-layer structurein an ABA configuration [87], where layer A consists of periodically arranged electricresonators, while layer B is a metallic mesh [see Fig. 5(d)]. Such ABA structure sup-ports perfect transmission for an x-polarized EM wave at a frequency interval centeredat 5.1 GHz [see the right panel of Fig. 5(d)], dictated by the scattering cancellationmechanism introduced in Subsection 2.2a. Moreover, the proposed device also allowsperfect transmission for y-polarized EMwaves within the same frequency interval, butwith physics governed by the EOTmechanism assisted by Bragg scatterings. Different

Science 340, 1304–1307 (2013) [77]. Reprinted with permission from AAAS.(f) Reprinted with permission from Zhao and Alù, Nano Lett. 13, 1086–1091(2013) [88]. Copyright 2013 American Chemical Society.


transparency mechanisms generate a π∕2 difference in transmission phases for twopolarizations, making the device an ideal half-wave plate working in transmissionmode. The whole device is much thinner than wavelength but exhibits a nearly100% working efficiency. Extensions to THz frequencies are possible, but with sig-nificantly degraded efficiency due to strongly enhanced material absorptions [92].

However, the proposed device still exhibits a narrow working bandwidth. In 2013, inaddition to realizing a reflection-type THz polarizer, Chen and co-workers [77] alsopresented a scheme to realize a broadband transmission polarization convertor for THzwaves. The fabricated device contains three metallic layers, in which the top and bot-tom ones are orthogonally orientated metallic gratings, which ensure that only cross-polarized THz waves can pass through the whole device. The middle metallic layercontains an array of cut wires oriented at an angle 45° with respect to the two gratings.The role of cut wires is to efficiently convert the energy of an incident wave to that ofthe cross-polarized transmitted wave. The distances between two adjacent metalliclayers are carefully chosen to diminish the reflection (thus to enhance the transmis-sion) based on multiple scatterings. Experimental results revealed that x-polarized in-cident THz waves can be completely converted to y-polarized transmitted waves, witha conversion efficiency exceeding 50% from 0.52 to 1.82 THz, as shown in Fig. 5(e).Such an elegant approach was further used to design high-efficiency inhomogeneousmetasurfaces in transmission mode, which will be introduced with more detail inSubsection 3.1. Inspired by this work, a variety of similar structures have been realizedin other frequency domains to demonstrate broadband, high-efficiency polarizationconverters [93–95]. Also in 2013, Alù’s group realized a broadband optical meta-wave-plate using a single, planar metasurface [88], as shown in the inset of the leftpanel in Fig. 5(f). The device is based on interleaved silver nanorods with properlytailored frequency dispersion that introduces an abrupt flat π∕2 phase shift for twoorthogonal polarizations over an ultrathin thickness. The achieved quarter-wave platecan work in a large frequency portion of the entire visible spectrum.

2.4. Tunable Homogeneous MetasurfacesThe metasurfaces/metadevices introduced in previous subsections are all passive sys-tems, whose fascinating wave-manipulation functionalities are fixed once they arefabricated out. However, in real applications it is more desirable to have tunable de-vices with properties/functionalities controllable by external knobs. Much effort hasbeen devoted to realizing tunable metasurfaces through integrating active elementsinto corresponding meta-atoms, which can thereby be controlled by appropriate ex-ternal stimuli. In this subsection, we briefly summarize the available mechanisms tomake tunable (homogeneous) metasurfaces, classified by different external stimuliadopted to control the EM responses of meta-atoms. We emphasize that the mech-anisms described below actually lay a solid basis for designing functional metadevicesbased on inhomogeneous metasurfaces with individually controlled meta-atoms,which will be introduced in Subsection 4.6.

2.4a. Electrically Tunable Metasurfaces

As a commonly adopted approach, one can integrate electrically sensitive materialsfunctioning at different frequency domains, such as varactor diodes, liquid crystals(LCs), doped semiconductors, and two-dimensional (2D) materials, into the meta-atomdesigns. At microwave frequencies, varactor and PIN diodes are frequently adopted indesigning tunable metasurfaces, since their EM responses (e.g., capacitances) can bedramatically tuned by applying external voltages. For instance, in 2011 Zhu et al. ex-perimentally demonstrated a microwave metadevice composed of MIM meta-atomswith PIN diodes incorporated. By varying the voltage applied across these diodes,


the authors can control the “on” and “off” states of the diodes and thus switch the func-tionality of the device from a reflector to a perfect absorber [96]. Based on similar mech-anisms, many other tunable microwave metadevices were experimentally demonstrated,such as a tunable polarization controller [97,98] and a frequency switchable absorber[99,100]. However, such a scheme cannot be directly extended to frequencies higherthan gigahertz (GHz), where diodes typically do not work.

In the THz and IR regimes, doped semiconductors can be used as the active elementsto design tunable metasystems, since their conductivities (and thus optical responses)can be dramatically modified via electrical gating [101,102]. Such a mechanism fea-tures broad bandwidth and high modulation speed, and is compatible with CMOStechnology. In 2006, Chen et al. experimentally demonstrated the first THz tunablemetasurface, which consists of electrically connected SRRs placed on a semiconduc-tor substrate. By varying the bias voltage applied across the Schotty diode formed atthe metal–semiconductor interface, a modulation of 50% on transmission through thedevice was experimentally realized [101]. Three years later, the authors further real-ized a tunable metadevice based on the same configuration but with optimized designfor SRR resonators, and experimentally demonstrated that it can achieve real-timeactive amplitude (55%) and phase (π∕6) modulation on the transmitted wave at0.81 THz with a speed of up to 2 MHz [see in Fig. 6(a)] [102]. After this work, manyother tunable metadevices were proposed to achieve larger modulation depths, highermodulation speeds, and/or broader tuning ranges, based on a similar mechanism but

Figure 6

Homogeneous tunable metasurfaces. (a) Semiconductor-hybridized electrically tunablemetasurfaces (ETMs) (bottom inset) for THz phase and amplitude modulations. Upperinset: measured transmission spectra at different bias voltages [102]. (b) Measured rel-ative change in transmission and phase change as a function of gate voltage and fre-quency for graphene-based ETMs. Inset: schematic rendering of a gate-controlled activegraphene metamaterial [103]. (c) MIM graphene ETMs for full-range phase modula-tions (inset). Experimental results on relative change in reflection and phase for THzbeams [104]. (d) Optically tunable metasurfaces (OTMs) based on semiconductors forTHz wave modulation. Experimental transmission spectra with different powers ofpump light. Inset: SEM picture of a meta-atom of proposed OTMs [105].(e) Schematic of OTMs based on optically sensitive polymer to manipulate the polari-zation of transmitted light in the optical regime [106]. (f) Right panel: mechanicallytunable metasurfaces (MTMs) based on MEMS technology. Left panel: reflection


with different geometries and active materials [111,112] (e.g., transparent conductingoxides [113–115] and transition metal nitrides [116]).

Graphene, a zero-bandgap 2D material with conductivity tuned efficiently via an ex-ternal gating, is another excellent candidate to help realize tunable devices in the THz ormid-IR regimes [117,118]. In 2011, Ju et al. showed that the plasmon resonance of agraphene ribbon array can be dramatically tuned through gating the graphene [119].However, the graphene alone has weak optical responses, since it is only a single atomiclayer. In 2012, Lee et al. combined gate-controlled graphene with a transmissive meta-surface and experimentally achieved active amplitude (47%) and phase (32.2°) mod-ulations on the transmitted THz wave [103], as shown in Fig. 6(b). Recently, manygraphene–meta-hybridized tunable metadevices were demonstrated in both the THz[120–124] and IR regimes [125–131], which exhibit diversified functionalities, suchas tunable absorbers [120,123,130], phase modulators [128,129], active polarizationcontrollers [124], and beam steering [131]. Unfortunately, the phase tuning rangesof these graphene–metasurfaces are all very limited. Recently, Miao et al. combinedgraphene with a MIM metasurface, and experimentally demonstrated that the wholesystem can modulate the phase of a THz wave in a range much wider than those realizedbefore. The physics is well explained by the coupled mode theory, which shows thatgraphene essentially plays the role of tunable loss, which drives the system to transitfrom an underdamped resonator to an overdamped one as the graphene is gated [see thegeneric phase diagram of MIM systems in Fig. 6(e)]. Wide-range phase changes occurat two different frequencies covering �π. By designing two meta-atoms with slightlydifferent working frequencies, the authors further demonstrated that using two “phase

spectra of a reconfigurable MTM with different applied voltages controlled by MEMS[107]. (g) Microfluidic reconfigurable TiO2 metasurfaces integrated with polydimethyl-siloxane (PDMS) microfluidic chips (top right panel) and bright-field photographs forthe sample in different solvents (top left panel). Bottom: experimentally recorded re-flection colors for 11 TiO2 metasurfaces under a bright-field microscope in differentsolvents and its chromatic coordinates [108]. (h) Thermally tunable metasurfaces(TTMs) based on the incorporation of plasmonic metasurfaces with the VO2 layer.Left panel: DC resistance and SRR resonance frequency as a function of temperature.Right panel: measured transmission spectra at different temperatures. Inset: schematicsof designed memory–oxide hybrid metadevices [109]. (i) TTMs based on dielectricmetasurfaces hybridized with LCs. Right panel: schematics of the silicon nanodiskmetasurface integrated into an LC cell. Left panel: experimental temperature-dependenttransmittance spectrum for one particular sample [110]. (a) Reprinted with permissionfrom Macmillan Publishers Ltd.: Chen et al., Nat. Photonics 3, 148–151 (2009) [102].Copyright 2009. (b) Reprinted with permission from Macmillan Publishers Ltd.: Leeet al., Nat. Mater. 11, 936–941 (2012) [103]. Copyright 2012. (c) Reproduced from[104] under the terms of the Creative Commons Attribution 3.0 License.(d) Reprinted with permission from Macmillan Publishers Ltd.: Chen et al., Nat.Photonics 2, 295–298 (2008) [105]. Copyright 2008. (e) Reproduced from [106] underthe terms of the Creative Commons Attribution NonCommercial-ShareAlike 4.0International License. (f) Reprinted with permission from Macmillan PublishersLtd.: Ou et al., Nat. Nanotechnol. 8, 252–255 (2013) [107]. Copyright 2013.(g) Reprinted with permission from Sun et al., ACS Nano 12, 2151–2159 (2018)[108]. Copyright 2018 American Chemical Society. (h) From Driscoll et al.,Science 325, 1518–1521 (2009) [109]. Reprinted with permission from AAAS.(i) Reprinted with permission from Sautter et al., ACS Nano 9, 4308–4315 (2015)[110]. Copyright 2013 American Chemical Society.


bits” can enable THz phase modulation with a maximum range of 243° at 0.48 THz [seeFig. 6(c)] [104].

LCs are also widely used as “active elements” to help realize tunable metasurfaces.The orientation angles of molecules in an LC can be controlled by external electricfields, leading to significant modulations on the refractive index of the LC. As a result,the resonant properties of metasurfaces with LCs incorporated can be efficiently tunedby applying an electric field across the LC [110,132,133].

Epsilon-near-zero (ENZ) thin films, made by transparent conducting oxide or dopedsemiconductor materials, provide a promising platform to realize ETMs [113,134].Thanks to the strongly enhanced density of the optical mode at the permittivity nearzero regime, the optical properties of ENZ materials can be efficiently tuned withdifferent external stimuli.

2.4b. Optically Tunable Metasurfaces

By hybridizing optically sensitive materials with passive metasurfaces, we then realizeoptically tunable metasurfaces (OTMs), whose properties can be controlled by ultrafastlight pulses. In 2008, Chen et al. experimentally demonstrated that a semiconductor-incorporated OTM, constructed by an SRR array on a silicon-on-sapphire substratecould realize a 20% frequency switching at frequencies around 0.85 THz with an opticalpump fluence of 0.5 mj cm−2 [Fig. 6(d)] [105]. Recently, Gu et al. experimentally dem-onstrated an optically controlled electromagnetically induced transparency with activelytuned EM wave group delay through a carefully designed THz metasurface, which con-sists of a metallic cut wire and two SRRs with photoconductive silicon islands posi-tioned in their gaps [135]. Optically responsible phase change materials [106,136–138]are also good candidates to realize OTMs. Very recently, Ren et al. designed/fabricatedan OTM by combining a plasmonic metasurface (consisting of a periodic array ofL-shaped slits) with an Ethyl Red switching layer, and experimentally demonstratedthat the device can actively modulate the polarization of transmitted light. The tunabilityis achieved by controlling the coupling conditions between the plasmonic resonantmodes and the binary isomeric states of the ethyl polymer switching upon light stimu-lation [see Fig. 6(e)] [106]. Chalcogenide phase-change materials, composed of alloysof germanium (Ge), antimony (Sb), and tellurium (Te), have also been widely used torealize OTMs in the IR regime, through combinations with carefully designed plas-monic meta-atoms [137,139].

2.4c. Mechanically Tunable Metasurfaces

Exerting mechanical forces on a metasurface can also efficiently tune its optical prop-erties, since the meta-atom structure or its local environment can be dramaticallymodified [107,108,140–142]. Micro-electro-mechanical-systems (MEMS) or nano-electro-mechanical-systems (NEMS) are widely used technologies to realize mechan-ically tunable metasurfaces in different frequency domains [107,140,143]. In 2013,Ou et al. experimentally demonstrated an electromechanical light modulation in thenear-IR regime based on an electrically reconfigurable metasurface, which is com-posed of a continuous metallic “meander near the wire” pattern manufactured on agrid of flexible dielectric strings, as shown in Fig. 6(f). With the help of MEMS, theinter-position change of metastructures can lead to a continuous reflection modulationup to 8% at 1500 nm. In addition, the modulation rate of such a 100 nm thick meta-device can reach as high as several megahertz [107]. Very recently, based on thegeneric phase diagram of MIM systems [Fig. 4(e)] [68,81], Cong et al. experimentallydemonstrated wide-range active phase modulation on THz waves based on anMIM metadevice with an inter-layer gap dynamically controlled by MEMStechnology [144].


Microfluidics is another technology widely used to achieve mechanically tunablemetasurfaces at different frequency domains [141,108,145,146]. For instance, Sunet al. experimentally realized real-time tunable colors with all dielectric (TiO2) meta-surfaces embedded in a polymeric microfluidic channel [108]. As shown in Fig. 6(g),the narrowband reflection peaks of the metasurfaces (corresponding to distinct colors)can be well controlled with the injection of different solutions with different refractionindices into the channel. Based on the rapid color transition (less than 16 ms) and highspatial resolution of such an approach, the clearance and restoration of informationand images encoded in the microfluidic reconfigurable metasurfaces was also dem-onstrated experimentally.

Mechanically tunable metasurfaces (MTMs) based on stretchable and flexible sub-strates have been proposed to achieve various dynamic effects (e.g., color tuning[147,148], switchable holograms [149], and varifocal lenses [150]). The tunablecapability of such approach is based on dynamical control on the interspacing dis-tances among meta-atoms with applied force, which can efficiently modify their inter-actions and result in significant modification of the EM properties of the metasurfaces.However, mechanically tunable metadevices usually suffer from the issues of slowspeed, limited device size, and/or restricted tuning range.

2.4d. Thermally Tunable Metasurfaces

Incorporating thermally responsive materials (e.g., phase change materials (PCMs)[109,151], LCs [110], and superconductors [152,153]) into metasurfaces is anotherapproach to realize tunable metasurfaces. Vanadium dioxide (VO2) is a typical PCMthat exhibits a metal–insulator transition at 340 K. In 2008, Driscoll et al. experimen-tally demonstrated a TTM by patterning metallic structures on a VO2 substrate [154].By varying the temperature to induce the phase transition, the authors demonstrated a20% modulation on light transmission through the system at 1.5 THz. As shown inFig. 6(h), they further utilized the hysteresis of such metal–insulator phase transitionto demonstrate a TTM-based memory device [109]. In 2015, Wang et al. experimen-tally demonstrated a switchable quarter-wave plate in the THz regime, based on aVO2-hybridized metasurface [151]. The tunability of such a metadevice arises fromthe effective length change of the designed resonator, induced by the phase change ofthe VO2 inserted inside the meta-atom. Since LCs exhibit temperature-dependent re-fractive indices, many LC-based TTMs were also proposed to achieve different func-tionalities at different frequency ranges, such as tunable absorbers and spatial lightmodulators. For instance, Sautter et al. fabricated a metasurface consisting of siliconnanodisks with LCs incorporated, and demonstrated that its EM resonance can bedynamically tuned at telecom wavelengths by varying the temperature [110]. Asshown in Fig. 6(i), a 40 nm shift in resonance wavelength with a pronounced trans-mittance change was achieved with room-temperature tuning. In addition, supercon-ductors are another intriguing material to realize TTMs, especially in the THz regime[153,155]. Very recently, Ding et al. experimentally demonstrated an electrically andthermally tunable silicon metasurface for broadband THz antireflection application.Composed of interdigitated p–n junctions, such an active metadevice exhibits ther-mally tuned reflection and electrically tuned transmission properties, enabled bythe bias voltages applied across the p-n junctions [156].

2.4e. Tunable Metasurfaces Based on Other Tuning Mechanisms

In addition to the mechanisms introduced above, there are many others that havebeen successfully used to realize tunable metadevices in different frequency ranges.For example, one can incorporate ferroelectric materials into the meta-atom design,which can be tuned by applying a magnetic field [157]. Meanwhile, it is also possibleto use a chemical approach to change certain chemical components of the constituent


materials forming the metadevices, thus yielding the desired tunable optical responses(e.g., hydrogenation-based metadevices [158]).

3. GRADIENT METASURFACES: PRINCIPLES AND REALIZATION

In the last section, we discussed how to employ homogeneous metasurfaces to controlEM waves, where the crucial role played by meta-atoms is highlighted. Recently, sci-entists gradually realized that metasurfaces are not necessarily homogeneous, butrather, the “macro-order” on which meta-atoms are arranged in a specifically designedinhomogeneous metasurface can play an important role. Indeed, such an artificiallydesignable “macro-order” is another important feature of metasurfaces, apparently notbelonging to natural materials, that can significantly expand the capabilities of meta-surfaces to manipulate EM waves. In this section, we summarize the physical prin-ciples established for designing gradient metasurfaces, constructed with metallic ordielectric materials, to control EM waves with linear or circular polarizations, includ-ing recently proposed new mechanisms for designing metadevices with perfect effi-ciencies at extreme conditions.

3.1. Generalized Snell’s Law: Metasurfaces for Linearly Polarized EM WavesGuiding light to propagate along a predetermined direction is always desired in optics.A simple approach is to use a flat mirror to reflect light. Alternatively, the propagationdirection of light can also be bent at an interface between two media with differentrefraction indices. Light reflection/refraction at an interface, the basis for nearly allkinds of optics devices, are governed by Snell’s law [159]:�

sin θr � sin θint sin θt � ni sin θi

, (6)

where θi, θr, θt denote, respectively, the angles of incidence, reflection, and refraction,while ni, nt denote the refraction indices of two media. The physics behind such anelegant law is the conversation of a tangential wave vector of light at the interface,which is ultimately dictated by the translation invariance symmetry of the system.However, such conversation also imposes unavoidable restrictions on light manipu-lation based on reflections/refractions. For instance, the angle of reflection must pre-cisely equal the angle of incidence, implying that one has to vary the orientation angleof a mirror to change the direction of reflected light. While the refraction angle can bedifferent from the incidence one, such difference is tied with the index contrast at theinterface, which significantly limits the light-manipulation capabilities since the indexvariation range of natural materials is quite narrow.

In 2011, Yu et al. proposed a new concept to control the directions of the reflected/refracted light at optical interfaces, which breaks the constraint imposed by the con-ventional Snell’s law [160]. Instead of studying the interfaces with translation invari-ance symmetries, the authors considered an artificial interface exhibiting abrupt phasechanges Φ�x, y� for waves reflected and/or transmitted through the interface at theposition �x, y�. The behavior of light reflection/refraction at such an interface canbe understood based on the Fermat–Huygens principle. As shown in Fig. 7(a), con-sider a light beam traveling from far-field point A at medium 1 to far-field point B atmedium 2 through the artificial interface. According to the Fermat–Huygens principle,the right optical path of light should take a minimized accumulated phase. Therefore,the phase accumulated along an optical path near the right one (the red line inFig. 7(a)] and that along the right path [the blue line in Fig. 7(a)] must be identical.Considering both the propagating phases and the abrupt phase changes at the inter-face, one can easily derive the following equation:


nt sin θt − ni sin θi �λ02π

dΦdx

(7)

to describe light refractions at the interface, with λ0 being the light wavelength. Basedon similar arguments, we have

Figure 7

Generalized Snell’s law. (a) Schematics used to derive the generalized Snell’s law. At theinterface between the two media, an ideal surface structure is adopted to introduce agradient abrupt phase shift in the light path. (b) Illustration of the symmetric (top panel)and antisymmetric (bottom panel) plasmonic modes defined by the induced current pat-terns inside the V-antenna. The angle between the incident polarization and the antennasymmetry axis is 45°. (c) Refraction angle versus incidence angle for the ordinary (black)and anomalous refraction (red) for the V-antenna sample with a periodicity of 15 μm. Thecurves and symbols are the results obtained by the theory [Eq. (8)] and experiments,respectively. (d) The envelope of the scattered waves of the eight V-antennas with anoblique equal phase plane. According to Huygens’ principle, the interference of thesescattered waves will give rise to an anomalous refraction beam. (e) A metasurface com-bining a thin gradient-index metamaterial layer with a PEC. Under illumination of a nor-mally incident wave, the induced currents inside the metasurface will generate anobliquely reflected beam. (f) Measured (circle) and simulated (line) scattering patternsfor the metasurfaces (see inset) with phase gradient of ξ � 0.8k0. (g) Measured scatteredfield intensity profiles for the V-antenna array designed for the NIR regime and illumi-nated with x-polarized light, with the dashed line representing the theoretical predictionbased on the generalized Snell’s law. (h) Schematics of a high-efficiency reflective meta-surface with the unit cell (inset) consisting of an Au nanorod (yellow) and a continuousAu film (yellow) separated by theMgF2 spacer (blue). (i) Measured and simulated scat-tered field intensity for the gradient metasurface depicted in (h) illuminated by y-polarizedlight at λ � 850 nm with different incident angles. (a)–(d) From Yu et al., Science 334,333–337 (2011) [160]. Reprinted with permission from AAAS. (e), (f) Reprinted withpermission from Macmillan Publishers Ltd.: Sun et al., Nat. Mater. 11, 426–431 (2012)[161]. Copyright 2012. (g) FromNi et al., Science 335, 427–427 (2012) [162]. Reprintedwith permission from AAAS. (h), (i) Reprinted with permission from Sun et al., NanoLett. 12, 6223–6229 (2012) [163]. Copyright 2012 American Chemical Society.


ni sin θr − ni sin θi �λ02π

dΦdx

(8)

to describe light reflections at such an interface. Equations (7) and (8) are called thegeneralized Snell’s law for light reflections/refractions, which, compared with theoriginal Snell’s law [Eq. (6)], contain an important new term proportional to the phasegradient dΦ∕dx provided by the artificial interface. Alternatively, we can also rewriteEqs. (7) and (8) as a more physical version:

~krk � ~kik � ∇Φ, ~ktk � ~kik �∇Φ, (9)

which states that the parallel wave vector of light does not conserve at the interfaceafter reflection/refraction, but rather gains an additional term contributed by the ar-tificial interface. Such an additional term significantly expanded our capabilities tocontrol light propagation. For example, even for normally incident light (i.e.,θi � 0°), one can bend the reflected/refracted light to arbitrary directions dictatedby the phase gradient. Moreover, since ∇Φ is solely determined by the artificial inter-face, its direction is not necessarily parallel to ~kik, indicating that off-plane reflection/refraction can easily happen at a carefully designed artificial interface.

The question is then how to realize an interface with a desired phase profileΦ. This is,however, quite nontrivial since any single-mode resonator exhibits a Lorentz-type re-sponse to incident light, and thus can provide a phase modulation only over a π range.Yu et al. proposed to adopt V-shape nanoantennas to modulate the phase over a 2πrange on a subwavelength scale [160,164]. As shown in Fig. 7(b), such V-shape an-tennas consist of two arms with length h joined at their ends, forming an angle ofΔ. Incontrast to a single-mode structure, such antennas naturally support two resonantmodes with different symmetries and at different frequencies. While the effective res-onance wavelength of the symmetric mode is roughly 2h, that of the anti-symmetricone is roughly 4h, dictated by the currents flowing inside the two arms. Therefore, asLP light strikes on the antenna, both modes can be excited, with substantially differentamplitudes, by the electric-field components along the symmetry axis s and the anti-symmetric axis a. A simple calculation shows that the cross-polarization componentof scattered light contains two Lorentz terms exhibiting an additional π phase differ-ence. It is such a unique feature that motivates Yu et al. to use cross-polarized scatter-ings of such V-shape antennas to modulate the phase of incident light over a full 2πrange. By setting the working wavelength to 8 μm, the authors successfully found fourV-shape antennas with different geometrical parameters h and Δ that can scatter in-cident light to the cross-polarization component with nearly equal amplitudes, butwith phases changing linearly over a π range. By simply taking the mirror structureof the existing V-antennas, the authors got another set of four antennas whose cross-polarized radiation have phase shifts covering another π range [Fig. 7(d)]. Yu et al.then fabricated a metasurface consisting of a periodic array of eight such V-shapeantennas, which, as argued before, must exhibit an abrupt phase distribution Φ�x�linearly varying in space. According to the Fermat–Huygens law, light reflection/re-fraction at such an interface must follow the generalized Snell’s law given by Eqs. (7)and (8), which can be understood by the Huygens’ wave interference picture, asshown in Fig. 7(d). Yu et al. performed angle-resolved optical measurements in themid-IR regime to unambiguously demonstrate such unusual behaviors [see Fig. 7(c)].Several months later, Ni et al. fabricated a metasurface through down-scaling the sizesof V-shaped antennas and experimentally demonstrated that the anomalous reflectionand refraction effect held in the near-IR regime [162]. Moreover, the authors showedthat such effect can work within a very broad wavelength region [see Fig. 7(g)],


in sharp contrast to the narrowband resonance-induced effects in periodic metasurfaces/metamaterials. Furthermore, Aieta et al. experimentally demonstrated out-of-planeanomalous reflections and refractions based on a similar metasurface [165] by pur-posely setting ~kik not parallel to ∇Φ.

Despite the great successes achieved, such V-antenna metasurfaces exhibit certain short-comings. First, the working mechanism of a V-antenna dictates that one can utilize onlyits cross-polarized scattered field, which is quite inconvenient for some applications.Meanwhile, since the co-polarized scattered fields do not exhibit the desired phases,they will be normally reflected and refracted governed by the original Snell’s law,as shown in Fig. 7(c) by the black curves. Finally, since V-antennas can radiate to bothsides symmetrically as electric dipoles, so the scattered fields form transmitted and re-flected beams simultaneously. Therefore, there exist altogether four different channelsto scatter light by the V-antenna array, which are normal/anomalous reflection/transmission modes. As a result, the efficiency of the desired anomalous refraction,being only one of these four channels, is quite low (about 10%) [164]. Moreover,in designing such metasurfaces, one needs to choose V-antenna arrays exhibiting nearlyequal amplitudes but different phases for the cross-polarized scattered field. This isagain not a trivial task since one needs to carefully balance the influence of structuraloptimizations on amplitude and phase, which are usually tightly correlated.

Half a year later, Sun et al. [161] proposed an alternative approach that can overcomemost of the deficiencies of V-antenna metasurfaces mentioned above, particularly theefficiency issue. More importantly, the authors also developed a new scheme to couplepropagating waves (PWs) to surface waves (SWs) with nearly 100% efficiency basedon gradient metasurfaces. We will discuss the PW–SW couplings in Subsection 3.3with more detail, and here we focus only on efficiently controlling PWs using meta-surfaces. The new strategy is based on a reflection geometry for which one does notneed to worry about transmission. The key idea can be understood by the followingargument [Fig. 7(e)]. As a plane EM wave strikes on flat metal, electric currents areexcited on different parts of the metal surface, which, in turn, work as secondarysources to radiate to free space. The interference among waves radiated from thosesub-sources form the wavefront of the reflected light. Under normal incidence, thesesub-sources all exhibit the same initial phases and, thus, their interference must formspecular reflection. Suppose we put an ultrathin slab with appropriate ε�x� and μ�x�onto the metal [see Fig. 7(e)], and reconsider the reflection properties of the system.Now the initial phases of sub-sources can be tailored to arbitrary values depending onexact values of ε and μ at each local position. As a result, one can tune the forms ofε�x� and μ�x� to make the reflection phase Φ�x� of the whole device satisfy a lineardistribution. The existence of a metal ground plane ensures that the reflection ampli-tudes at different local positions are all 100%, which already implies the high (nearly100%) efficiency of the device. Indeed, the authors employed a rigorous mode ex-pansion method to calculate the scattering properties of such a model system[161,166], showing that it can inherently support nearly 100% efficiency anomalousreflection. Sun et al. further designed/fabricated two realistic gradient metasurfaceswith different phase gradients based on the effective-medium model, and performedmicrowave experiments to demonstrate that they support nearly 100% efficiencyanomalous reflection to different angles dictated by the designed phase gradients[see Fig. 7(f) for one example). The building block of these metasurfaces is aMIM meta-atom, as was discussed in Subsection 2.2, consisting of a metallic H-shapeantenna and a metal plate separated by a 1 mm thick dielectric spacer. As such a meta-atom is illuminated by an LP wave, anti-parallel currents are induced on two metalliclayers, resulting in magnetic resonance (see Subsection 2.1). The whole structure canbe modeled as a double-layer effective-medium system consisting of a flat metal


capped by a homogeneous layer exhibiting a highly dispersive μ [18]. As argued inSubsection 2.1b, the reflection phase Φ of such a meta-atom can vary in the whole 2πrange as frequency changes, which is highly desired for metasurface designs. By set-ting the working frequency as 15 GHz, the authors carefully tuned the arm length ofthe H to find a set of MIM meta-atoms exhibiting different reflection phases, andadopted them to realize a series of gradient metasurfaces with different phase gradientsξ�� dΦ∕dx�. A picture of a metasurface fabricated with ξ � 0.8k0 (with k0 � ω∕c) isdepicted in the inset of Fig. 7(f). The authors then characterized the scattering patternsof these metasurfaces under illumination of normally incident microwaves. Clearly,the normally incident wave is deflected to a non-specular direction with θr � 53° bythe metasurface with ξ � 0.8k0, which is consistent with the theoretical predictionbased on Eq. (7) [see Fig. 7(f)]. The authors also demonstrated, through both numeri-cal simulations and experiments, the generalized Snell’s law by measuring the relationbetween θr and the incident angle θi on samples with different ξ. The high efficienciesof these metasurface devices can be clearly seen from the measured scattering pat-terns. Several months later, Sun et al. successfully pushed the idea forward, and ex-perimentally demonstrated a highly efficient reflection-type gradient metasurface inthe near-IR regime [163]. The fabricated device is still based on MIM meta-atoms,only with the H resonators replaced by gold nanorods to alleviate the fabrication chal-lenges [Fig. 7(h)]. The authors experimentally characterized the scattering patterns ofsuch a device at different incident angles and wavelengths [Fig. 7(i)], and the resultsobtained show that the anomalous reflections exhibit very high efficiencies (∼80%)and a wide working band (750–900 nm). In addition, such metasurface was also pro-posed as a polarization beam splitter [163], which was soon experimentally realizedby Bozhevolnyi’s group [167]. Compared with the V-antenna metasurfaces, suchMIM metasurfaces exhibit the following apparent advantages: 1) their working effi-ciencies are intrinsically high, since all transmission channels are blocked and thenormal reflection mode can also be suppressed through careful design, 2) the anoma-lous mode exhibits the same polarization as that of the incident light, and 3) they arerelatively easy to design since one does not need to worry about the amplitude fluc-tuation of these meta-atoms.

However, the MIM metasurfaces, although exhibiting high efficiencies, work in re-flection geometry, which is still inconvenient for certain applications. In 2013, basedon the general concept of Huygens’ surfaces, Pfeiffer and Grbic proposed a new strat-egy to design high-efficiency gradient metasurfaces to manipulate the EM wavefrontsat the transmission side [168]. Noting that the V-antennas exhibit purely electric re-sponses and radiate to both sides, the authors proposed to adopt meta-atoms exhibitingsimultaneous electric and magnetic responses, which, through careful structural op-timization, can radiate only to the transmission side after being excited. Equivalently,these meta-atoms can also be viewed to possess impedance matched perfectly withthat of air (through tuning their electric and magnetic responses appropriately), so thatthey can allow perfect transmission of EM waves without reflection. Figure 8(a) de-picts a representative meta-atom adopted by the authors, which consists of a metalliccut wire and an SRR to provide the desired electric and magnetic responses, respec-tively. By carefully tuning the structural parameters, the authors successfully designeda series of meta-atoms with (nearly) 100% transmission amplitudes and linearly vary-ing transmission phases covering the full range of 2π at a target frequency of 10 GHz.By fabricating a gradient metasurface based on these transparent Huygens’ meta-atoms, the authors experimentally characterized the transmission/reflection propertiesof the device under normal-incidence excitation. The results obtained clearly demon-strated the anomalous beam bending effect enabled by the metasurface, as shown inFig. 8(a). In sharp contrast to the V-antenna metasurface, such a Huygens’metasurface


Figure 8

Generalized Snell’s law. (a) Reflectionless Huygens’ metasurface. Left panel: schematicof one representative Huygens’meta-atom. Right panel: simulated magnetic field (Hz) ofa y-polarized plane wave normally illuminated on the gradient Huygens’ metasurface[168]. (b) Schematic (left panel) and simulated beam-refraction effect (right panel)of an optically thin, isotropic Huygens’ metasurface working at telecommunicationwavelengths [169]. (c) Left panel: schematic of the hybrid bilayer plasmonic metasur-face, composed of one layer of gold nanoantennas on the top and its Babinet-invertedpattern at the bottom, separated by conformal dielectric pillars. Right panel: measuredanomalous transmitted field intensity as a function of wavelengths and refraction angle[170]. (d) Transmissive metasurface composed of single layer C-antennas for achievingthe broadband THz wave bending effect. Left panel: optical image of the fabricated sam-ple. Right panel: transmission amplitude and phase shift of the y-polarized component ofthe proposed structure under x-polarized incidence at 0.63 THz [171]. (e) High-efficiencyanomalous refraction effect. Left panel: proposed metasurface composed of eight resona-tors creating a linear phase shift of the cross-polarized transmission over a 2 ≅ rangeand two orthogonal metallic gratings perpendicular to each other. A normally incidentx-polarized wave is deflected to the anomalous refraction channel with the cross-polarization. Right panel: measured cross-polarized transmittance as a function of frequencyand angle, compared to theoretical prediction (dashed curve) [77]. (f) Beam bending bycoding metasurface. Left panel: the 1 bit digital metasurface composed of two types ofelements, “0” and “1”. Right panel: simulated scattered field distribution of the 1 bitmetasurface [173]. (g) Dielectric meta-reflectarray for the beam bending effect. Leftpanel: simulated cross-polarized reflection magnitude and phase maps for resonators withdifferent geometry (bottom) and schematic of eight resonators that provide a phase shiftfrom 0 to 2π (top). Right panel: simulated electric field pattern of the meta-reflectarrayillumined by a normally incident x-polarized Gaussian beam. The wavelength is 1550 nm[174]. (h) Left panel: metasurfaces consisting of trapezoid shaped silver plasmonic an-tenna arrays in an MIM configuration. Right panel: a photograph of various reflectionmodes of the redirected beam [175]. (a) Figure 2 reprinted with permission from Pfeifferand Grbic, Phys. Rev. Lett. 110, 197401 (2013) [168]. Copyright 2013 by the AmericanPhysical Society. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.110.197401.








exhibits a maximum efficiency of 86%, which is even comparable to that of the MIMmetasurface. However, directly scaling down the microwave sample to opticalfrequencies is difficult, since the meta-atoms are complex 3D non-flat structures,which are very challenging to fabricate. Alternatively, Pfeiffer et al. adopted a multi-layer metallic structure as building block to design a Huygens’metasurface working attelecommunication wavelength [see Fig. 8(b)], in which the magnetic response isinduced effectively through the inter-layer couplings [169]. Unfortunately, the work-ing efficiency of the fabricated device is only 18% in experiment and is 30% in full-wave simulation. Compared to early microwave realizations, the low efficiency ofsuch optical Huygens’ metasurface is due to strongly enhanced ohmic losses of plas-monic metals at optical frequencies and fabrication imperfections. New structureshave also been proposed. For example, Monticone et al. proposed a metasurface con-figuration to control the transmission wavefronts efficiently [176]. The meta-atomsproposed are essentially parallel-plate waveguides composed of plasmonic and dielec-tric thin films, which, upon careful optimization, can support high transmission oflight with different transmission phases. Full wave simulations demonstrated that75% of the incident Gaussian beam can be deflected to the off-normal direction aftertransmission.

In 2013, Chen’s group utilized multilayer meta-atoms as building blocks to constructhigh-efficiency transmissive metasurfaces, but working at THz frequencies, as de-picted in Fig. 8(e). Moreover, the newly realized metasurfaces combine the function-alities of wavefront controls and polarization rotation with very high efficiencies andwithin a broad frequency band, which goes a step further over a standard Huygens’metasurface [77]. Such improvement is enabled by a series of smartly designed three-layer meta-atoms, each consisting of two orthogonally placed metallic gratings in-serted with a cut-wire resonator with the symmetric axis lying between two gratings.Based on the mechanism presented in Subsection 2.3, such meta-atoms can allow hightransmission of cross-polarized THz waves with phases tuned by adjusting the struc-tures of the cut-wire resonators. The authors designed and fabricated a gradient meta-surface utilizing such meta-atoms, and experimentally demonstrated that the devicecan enable anomalous refraction and polarization rotation simultaneously for incidentTHz waves, as shown in Fig. 8(e) [77]. The maximum efficiency of the device is 61%at 1.4 THz with an anomalous refraction angle θt � 24°, which is quite remarkableconsidering the non-negligible losses of metals at this frequency domain, not men-tioning the added advantage of polarization-control functionality.

Researchers have continued to report new configurations to achieve anomalousdeflection of light, and these are briefly summarized here. In transmission geometry,Qin et al. proposed a bilayer plasmonic metasurface to enhance the efficiency forreshaping visible light [170]. As shown in Fig. 8(c), the metasurface consists of

(b) Reprinted with permission from Pfeiffer et al., Nano Lett. 14, 2491–2497 (2014)[169]. Copyright 2014 American Chemical Society. (c) From Qin et al., Sci. Adv. 2,e1501168 (2016) [170]. Reprinted with permission from AAAS. (d) Zhang et al.,Adv. Mater. 25, 4567–4572 (2013) [171]. Copyright Wiley-VCH Verlag GmbH &Co. KGaA. Reproduced with permission. (e) From Grady et al., Science 340, 1304–1307 (2013) [77]. Reprinted with permission from AAAS. (f) Reproduced from [173]under the terms of the Creative Commons Attribution NonCommercial-ShareAlike 3.0Unported License. (g) Reprinted with permission from Yang et al., Nano Lett. 14, 1394–1399 (2014) [174]. Copyright 2014 American Chemical Society. (h) Reprinted with per-mission from Li et al., Nano Lett. 15, 1615–1621 (2015) [175]. Copyright 2015American Chemical Society.


two physically separated plasmonic structures, with top layer being a gold V-antennaarray, while the bottom one is its Barbinet-inverted structure. The proposed hybridmetasurface can achieve a high cross-polarization conversion efficiency (36% in sim-ulation and 17% in experiment), with physics governed by strong interlayer couplingsthat can excite both electric and magnetic responses. Zhang et al. utilized C-shapedresonators to construct a gradient metasurface to tailor the wave fronts of THz waves[171]. By varying the radius r and the opening angle α of the split rings, the authorsobtained a series of split rings that can allow cross-polarized transmission with nearlyconstant amplitudes and linearly varying phases, which are used to construct a gra-dient metasurface, as shown in Fig. 8(d). The fabricated device can achieve a broad-band anomalous refraction effect from 0.57 to 1 THz, with a maximum deflectionangle of 84°.

In reflection geometry, Cui et al. extended the concept of gradient metasurface to a“digital” metasurface [173]. The key idea is to use meta-atoms with discretized phasevalues as digital elements to construct metasurfaces. In a 1 bit realization, one needsonly two meta-atoms exhibiting 0 and π reflection phases to construct metasurfaceswith different functionalities. For instance, a metasurface composed of such 2 bitsarranged periodically can deflect the incident wave to two diffraction channels, asshown in Fig. 8(f). By changing the coding sequence or increasing the bit number,the authors realized digital metasurfaces with more functionalities, including beammanipulation and scattering reduction [177]. To reduce the ohmic losses at highfrequencies, Yang et al. proposed to replace plasmonic metals with high-index siliconto construct a reflection-type metasurface [174]. As shown in Fig. 8(g), the buildingblock consists of eight 45° or 135° oriented silicon short wires and a silver backgroundplane with an ultrathin (200 nm) PMMA spacer. Based on the phase diagram shownin Fig. 8(g), the authors sorted out four silicon antennas, all providing high cross-polarization reflection amplitude but with different reflection phases covering a πrange. By rotating those four antennas by 90°, another set of four antennas with re-flection phases covering the remaining π range are obtained, which, together with theoriginal four, are used to construct a gradient metasurface, as shown in Fig. 8(g). Sucha scheme is quite similar to that of the V-antenna metasurface [160], but realized withdielectric materials. Figure 8(g) shows the simulated cross-polarization reflection fielddistribution at the wavelength of 1550 nm for the x-polarization incidence case. Thecalculated working efficiency of such an anomalous deflector is about 83%, which ishigher than its plasmonic counterpart, but with the shortcoming of increased devicethickness. In 2015, Li et al. reported a simple metasurface design to achieve anoma-lous reflection for visible light within a broad band. The device consists of trapezoid-shaped silver antenna arrays and a thick silver mirror separated by the thin SiO2

spacer, as shown in Fig. 8(h) [175]. Compared to metasurfaces composed of multipleantennas, the present design can provide a quasi-continuous local reflection phaseshift covering the full 2π range, due to the continuously varied antenna width in asingle structure. Meanwhile, the reflection amplitude is very high. The device canachieve a broadband co-polarized anomalous reflection effect (450–850 nm) withthe highest measured efficiency of 85%, with loss taken into account.

3.2. Geometric-Phase Metasurfaces for Manipulating Circularly Polarized EM WavesThe metasurfaces described in the last subsection all work for LP EM waves, and areconstructed by planar resonators with different structures [160,162,161,163,165].However, such resonance-based metasurfaces suffer from the following issues.First, the phase profiles provided by such metasurfaces inevitably deviate from thecorrect ones at frequencies away from the working one at which the meta-atomsare designed, due to the intrinsic frequency dispersions of resonant structures, which


ultimately leads to limited working bandwidths. Second, to design such metasurfacesinvolving different meta-atoms with distinct EM responses, one has to perform full-wave simulations to optimize the structures of each meta-atom, which are time con-suming, particularly for metasurfaces exhibiting sophisticated functionalities. Finally,fabrication of such metasurfaces (especially working at optical frequencies) is chal-lenging and requires precise controls on complex structures with fine differences.

Facing these challenges, scientists have continued to search for new mechanisms toconstruct metasurfaces. Pancharatnam–Berry (PB) metasurfaces, built with identicalmeta-atoms oriented with particular angles, thus exhibiting geometry-originatedphases for scattered EMwaves, are an alternative type of metasurface that can manipu-late the wavefronts of circularly polarized (CP) EM waves [178,179]. Because suchmetasurfaces can largely overcome the issues mentioned above, they have quicklybecome a widely studied class of systems in parallel with the resonance-based meta-surfaces. We first briefly describe the origin of such PB phases. Consider an arbitraryanisotropic planar structure (say, a metallic bar) placed on the x–y-plane and illumi-nated by normally incident CP light with a certain spin [spin-up σ � 1, left CP (LCP);spin-down σ � −1, right CP(RCP)]. Upon excitation, the resonator can generate elec-tric currents flowing along the x and y axes with different amplitudes and a 90° phasedifference. Such differences in response along two orthogonal directions, manifestingthe anisotropic nature of the resonator, ensure that the wave scattered by the resonatorcontains both spin-conserved and spin-reversed components. The spin-conservedscatterings are less interesting, but the spin-reversed scatterings are quite non-trivial.In a pioneering work, Pancharatnam first discovered [180] that spin-reversed scatter-ing can possess an additional phase factor ei2θ as the planar structure is rotated by anangle θ with respect to the z axis [see Fig. 9(a)], which was later interpreted as ageometrical phase by Berry in Ref. [184]. The geometrical origin of such an additionalphase can be understood with the help of the Poincaré sphere, as shown in Fig. 9(a).Specifically, the spin-reversed scatterings by two objects in Fig. 9(a) can be interpretedas two lines on the Poincaré sphere that connect the north and south poles, and passthrough the equator at different points separated by an angle θ. The phase differencebetween these two processes is the solid angle surrounded by two curves, which isprecisely twice of θ. Such a phase can be interpreted as a Berry phase carried by aphoton moving in an adiabatic process represented by the closed loop on the Poincarésphere. One unique feature of the PB phase is that it is solely dictated by the orien-tation angle of the scatter, and thus it is frequency non-dispersive. Moreover, the PBphase changes its sign as the incident spin state changes from σ � 1 to σ � −1.Finally, one should bear in mind that the spin-reversed scattering actually contributesto the spin-maintained reflection, since the definition of spin is associated with thewavevector of the EM wave, which is reversed after reflection.

Even before the concept of metasurface appeared, Hasman’s group had already done aseries of pioneering works utilizing such a mechanism to build spin-dependent opticaldevices [178]. As shown in Fig. 9(a), the first device realized in 2002 consists ofsubwavelength dielectric gratings with local periodic direction varying linearly inspace. Because the local period is much smaller than the wavelength, the gratingcan be effectively regarded as a uniaxial crystal at every local point. Now illuminatethe device with CP light with different spin. Since the local uniaxial axis of the systemchanges continuously from 0 to π within one supercell, the spin-reversed wave trans-mitted through the device at a local position must carry a PB phase, which is linearlyvarying in space covering the full 2π range over a supercell [see Fig. 9(a)]. The spatialphase gradients are of opposite signs for incident CP light with different spin. Therefore,the spin-reversed components of waves transmitted through such a device, formed byinterference among those locally transmitted waves possessing different PB phases,


must propagate to two opposite oblique directions depending on the input spin, gen-erating a spin-dependent diffraction, which is now called the photonic spin-Hall effect(PSHE). The authors then fabricated a sample with a periodicity Λ � 3.2 μm and

Figure 9

Pancharatnam–Berry (PB) metasurfaces. (a) PB phase optical elements with computer-generated subwavelength gratings. Left panel: illustration of the origin of PB phasebased on the Poincaré sphere. Right panel: geometry of the subwavelength gratingas well as the PB phase profiles for LCP and RCP illumination [178]. (b) PSHEsin plasmonic chains. Left panel: SEM images of two different plasmonic metasurfacesfor achieving PSHE. Right panel: the spin-dependent momentum deviation for a meta-surface composed of spatially orientated rectangular apertures for different input spinstates at a wavelength of 730 nm [179]. (c) Left panel: SEM image of a PB metasurfacecomposed of gold nanorods fabricated on the SiO2 substrate. Right panel: phase dis-tributions of both incidence and refraction with different spins obtained by full wavesimulations. Here, the wavelength is 1020 nm [181]. (d) PSHE with nearly 100% effi-ciency in reflection geometry. Left panel: schematics of the 100% efficiency PSHErealized at our reflective metasurface. Right panel: measured normalized scattered-fieldintensities versus frequency and reflection angle for one high-efficiency metasurfaceunder different spin polarized illuminations [182]. (e) PSHE with nearly 100%efficiency in transmission geometry. Top: illustration of the principle of the 100% effi-ciency transmissive PB meta-atoms with both electric and magnetic dipolar responses(left panel) and measured electric filed distributions (real part) of the vortex beam withtopological charge of q=1 (right panel) generated by the metasurface depicted in thebottom right panel. Bottom: part of the image of the fabricated high-efficiency vortexbeam metasurface generator (right panel) formed by ABA meta-atoms (left panel)[183]. (a) Reprinted with permission from [178]. Copyright 2002 Optical Society ofAmerica. (b) Reprinted with permission from Shitrit et al., Nano Lett. 11, 2038–2042 (2011) [179]. Copyright 2011 American Chemical Society. (c) Reprinted withpermission from Huang et al., Nano Lett. 12, 5750–5755 (2012) [181]. Copyright2012 American Chemical Society. (d) Luo et al., Adv. Opt. Mater. 3, 1102–1108(2015) [182]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced withpermission. (e) Figures 3 and 7 reprinted with permission from Luo et al., Phys.Rev. Appl. 7, 044033 (2017) [183]. Copyright 2017 by the American PhysicalSociety. https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.7.044033.


https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.7.044033






performed optical measurements at the wavelength 10.6 μm. Experimental resultsclearly verified the predicted effects, showing that spin-reversed diffraction modes ap-pear at the desired angles for RCP and LCP illumination, respectively.

The rapid advances in plasmonics offer abundant choices to design PB optical ele-ments. In 2011, Hasman’s group further demonstrated a plasmonic device that canrealize the PSHE [179]. As shown in Fig. 9(b), the device is a 200 nm thick goldfilm etched with a collection of air holes arranged in a curve such that the directionof the air-hole chain varies spatially as θ � πx∕a. Although every individual nano-aperture possesses an isotropic shape, the transmission spectra at different positionsdo exhibit anisotropic responses, caused by inter-aperture couplings that result in dis-tinct plasmonic coupled modes for transverse and longitudinal excitation. Therefore,the curved plasmonic chain can be regarded as a collection of anisotropic meta-atomswith spatially varying orientations, generating a linearly varying phase profile for thespin-reversed scattered light, which, in turn, results in the PSHE. The authors per-formed optical experiments to clearly demonstrate the desired PSHE enabled bythe fabricated device [see Fig. 9(b)]. In addition to utilizing the coupling-inducedanisotropy, Hasman’s group further directly utilized a nanoaperture with anisotropicshape to generate the desired PB phases. In the same work [179], Hasman’s groupfabricated another plasmonic device consisting of identical rectangular apertures withorientation angles linearly varying in space, arranged in a straight line instead of acurved one [see Fig. 9(b)]. Optical experiments nicely demonstrated the PSHE real-ized by the device. Such an excellent series of pioneering works laid a solid basis forfuture developments along this direction. However, these early-version PB deviceseither exhibit very low efficiencies or have thicknesses comparable to wavelength(the dielectric devices), and exhibit only beam-bending functionalities (i.e., PSHE).

The emergence of the metasurface concept significantly stimulated the developmentof PB metadevices based on geometric phases. In 2012, Li’s group theoretically pro-posed a more efficient PB device utilizing a split-ring slot antenna as the buildingblock to achieve spin-dependent wavefront control [185]. A complex-shape antennacan provide more degrees of freedom to tailor spin-reversed scattering strengths, thusyielding a more efficient wave-control effect. Several months later, Zhang’s groupfurther proposed to use a nanoparticle with anisotropic shape as the building blockto build PB devices, which exhibit further enhanced working efficiencies because lessmetal is adopted as compared to previous devices [181]. Moreover, Zhang’s groupfabricated a device consisting of an array of rectangular patch antennas with orienta-tion angles linearly varying in space [see Fig. 9(c) for the sample picture], and thenexperimentally characterized its angle-resolved transmission properties under theillumination of CP light with spin σ. Indeed, experiments revealed clearly that thespin-reversed transmission modes are refracted to two off-normal directions at twodifferent sides of the surface normal. In fact, within a unified framework developedfor metasurfaces in Subsection 3.1, the anomalous transmission (and reflection) onsuch PB metasurfaces can be described by the following (spin-dependent) generalizedSnell’s law: (

ni sin θr − ni sin θi � σ λ02π

dΦdx

nt sin θt − ni sin θi � σ λ02π

dΦdx

, (10)

where σ dΦdx � σ 2θ

S is the phase gradient with σ denoting the spin of incident light, andθ, S denote, respectively, the orientation-angle difference and spatial distance betweentwo adjacent meta-atoms. Compared to Eqs. (7) and (8) in Subsection 3.1, now σ isanother degree of freedom to control the generated physical effects (e.g., PSHE).


In addition, based on such a unified picture, one can extend the concept developed forLP light to realize similar wave-manipulation effects for CP light, by using PB meta-surfaces designed appropriately. We will describe more applications of PB metasur-faces in Section 4.

Despite the great successes achieved, most PB devices realized in the early days exhibitvery low working efficiencies. In fact, an early theoretical analysis even suggested thatthe highest efficiency achievable in an ultrathin PB transmissive metasurface is boundedby 25% [186], which was later demonstrated experimentally in the microwave regime[187]. Such an efficiency issue, if unsolved, may eventually hinder the real applicationsof these PB devices. In 2015, Zhou’s group theoretically analyzed the problem in detailand discovered that one can realize PB metasurfaces with 100% efficiency [Fig. 9(d)],as long as the adopted meta-atoms exhibit transmission/reflection characteristics satis-fying certain criteria [182]. We now briefly introduce their analyses based on the Jonesmatrix and the Poincaré sphere. Suppose that a generic slab formed by a periodic arrayof PB meta-atoms is placed on the x–y plane. The transmission/reflection properties of

the slab can be generally described by two Jones matrices, T�0� ��tuu tuvtvu tvv

�and

R�0� ��ruu ruvrvu rvv

�, where u, v denote two principle axes of the meta-atoms. By

changing the basis from LP to CP via defining two unit vectors e��0� ��u� iv�∕ ffiffiffi

2p

, one obtains the forms of two Jones matrices in CP bases T�0�, R�0�.Now consider another slab with all meta-atoms rotated by an angle of ϕ with respectto the z axis. One can easily derive its Jones matrices in CP bases as T�ϕ�, R�ϕ�.Interestingly, these Jones matrices can be expanded to linear combinations of four basic2 × 2 matrices, i.e., the unit matrix I and three Pauli matrices fσ1, σ2, σ3g. For example,

R�ϕ�� 1

2�ruu� rvv�I�

i

2�ruv− rvu�σ3

�1

2�ruu− rvv��e−i2ϕσ��ei2ϕσ−��

i

2�ruv� rvu��−e−i2ϕσ�� ei2ϕσ−�, (11)

where σ� � �σ1 � iσ2�∕2 are two spin–flip operators satisfying σ�j�i � 0 andσ�ji � j�i, with j�i denoting the spin-up and spin-down states, respectively.Equation (11) revealed the underlying physics clearly. Obviously, the first two termsin Eq. (11) represent the spin-conserved scattering, while the last two terms change thespin state of incident light. While the spin-conserved scatterings do not carry any addi-tional phase, the spin-flipped ones do carry PB phases e�i2ϕ depending on the incidentspin. Thus, any PB metadevice formed by such a meta-atom must simultaneously con-tribute a normal reflection mode and an anomalous reflection mode, with power effi-ciencies given by Rn ≡ j�ruu � rvv�j2∕4, Ra ≡ j�ruu − rvv�j2∕4, respectively. The sameargument applies to the transmission Jones matrix T�ϕ�, only with fruu, ruv, rvu, rvvgreplaced by ftuu, tuv, tvu, tvvg. Therefore, in pure reflection geometry, the criterion toachieve 100% efficiency PB device is then

ruu � rvv � ruv − rvu � 0, (12)

implying that the normal reflection channel should be terminated, leaving all theincident power transferred to the anomalous reflection channel in the ideal losslesscase.

Based on these criteria, the authors designed two microwave PB metasurfaces, con-structed with meta-atoms either with mirror symmetry or not, but both with Jones’


matrices satisfying the criteria [Eq. (12)]. Designing the symmetric meta-atom isstraightforward, as now the criterion [Eq. (12)] is reduced to ruu � −rvv, implyingthat the desired meta-atom is nothing but an ideal wave plate. Such a task is easy tofinish as one already gained lots of experience in designing polarization-control de-vices using periodic metasurfaces (Subsection 2.3). Indeed, the symmetric meta-atom is just an MIM structure with an anisotropic-shaped top resonator. Such ameta-atom naturally totally reflects EM waves for two polarizations, and one needsonly to carefully adjust the structure to make the reflection-phase difference(ϕuu − ϕvv) stay at ∼π within a wide frequency window. Designing the asymmetricmeta-atom is a bit complicated and will not be described in detail here. With twometa-atoms successfully designed, the authors then fabricated two wave-bending PBmetasurfaces, and performed microwave experiments to characterize their reflectionproperties. Far-field measurements clearly demonstrated that nearly all LCP com-ponents of an incoming wave are reflected to the left side of surface normal, whileall RCP components are reflected to the right side, within a frequency band of10–14 GHz. In particular, the normal reflections are completely suppressed, whichensures the high working efficiency of the device (>90%). The performance ofanother metasurface is similar to that of the symmetric metasurface. Such criteriaare important as they make possible the design of high-efficiency PB metadevices,which are highly desired for future applications. We note that at a similar time,Zhang’s group also independently discovered a similar criterion, and they furtherutilized the criterion to design/fabricate an optical PB metasurface to achieve holo-gram imaging with exceptionally high efficiency (∼80%) [188]. We will discuss itwith more detail in Subsection 4.2.

100% efficiency PB metasurfaces in transmission geometry are even more desirablein applications, but are also more difficult to realize [183]. In 2017, Luo et al.examined the problem and found that 100% efficiency metasurfaces can be ob-tained as long as we get appropriate meta-atoms exhibiting Jones-matrix elementsthat satisfy

ruu � rvv � 0, jtuuj � jtvvj � 1, arg�tuu� � arg�tvv� � π: (13)

However, a single-layer resonator exhibiting an electric response only can never fulfillthe above condition [31], since it will radiate to both sides, and thus we cannot inde-pendently tune the reflected and transmitted waves. Such a constraint can be releasedif the meta-atom exhibits both electric and magnetic responses. As shown in Fig. 9(e),the electric fields radiated from an electric (magnetic) dipole are symmetrical (anti-symmetrical) at two sides of the dipole. Therefore, one can independently control theradiation at two sides of the meta-atom by tuning its electric and magnetic responsesappropriately. In further adding appropriate anisotropy, one thus obtains a transmis-sive meta-atom with Jones-matrix elements satisfying Eq. (13). Inspired by Ref. [25],Luo et al. adopted the ABA structure to design a 100% efficiency PB meta-atom[Fig. 9(e)], in which the magnetic response is induced by the couplings betweentwo metallic layers. Here, layer A contains an array of metallic bars, while layerB is a holey metallic film loaded with metallic bars, and two dielectric spacersare adopted to separate them. Through careful optimization, the authors obtainedan ABA meta-atom with Jones-matrix elements satisfying Eq. (13) within a frequencywindow centered at 10.5 GHz. With such a building block at hand, the authors fab-ricated two microwave PB metasurfaces and experimentally demonstrated that theycan realize PSHE and vortex beam generation [Fig. 9(e)] with very high efficien-cies (∼91%).


Before concluding this subsection, we would like to compare the two widely studiedmetasurfaces:

1) PB metasurfaces work for CP light, while the resonance-phase ones work forLP light.

2) The phase responses of PB metasurfaces are usually non-dispersive, while thosein resonance-phase ones suffer from strong frequency dispersion. However, theworking efficiencies of PB metasurfaces strongly depend on frequency, indicat-ing that such systems still have frequency dispersion.

3) PB metasurfaces usually exhibit correlated functionalities under illuminationwith different spin, while the resonance-phase ones do not have such a constraint.

4) PB metasurfaces are usually easy to design and fabricate, while the same thingsare not true for the resonance-phase metasurfaces.

3.3. Linking PWs and SWs with MetasurfacesMost optical devices are based on manipulating propagating waves (PWs) in the freespace. There is, however, another type of wave propagation mode called “surface wave”(SW), which plays an important role in modern photonics research, particularly foron-chip applications. SWs generally denote fundamental EM eigenmodes, bounded atcertain interfaces between two different optical media, that can transport only on theinterface, with field strength exponentially decaying as they leave the interface. An SPPis an important type of SW, existing on dielectric/metal interfaces at near-IR (NIR) andoptical frequencies typically associated with charge oscillations inside the plasmonicmetal. Because of their extraordinary properties, i.e., subwavelength lateral resolutionand a strongly enhanced near field at the interfaces, SPPs have drawn intensive interestin physics, chemistry, and biology [189], and have been widely used in superresolutionimaging [190,191], biosensing and chemical sensing [192,193], enhanced Raman [194]and nonlinear effects [195], solar cells [196], and so on. In low-frequency domains (e.g.,THz and GHz) where metals usually behave as PECs lacking plasmonic responses, onecan design structured metal surfaces that can support spoof SPPs [197,198], whichexhibit similar wide-range applications as natural SPPs. Although SWs have many im-portant applications, their efficient excitation is challenging, since far-field light cannotcouple directly with SWs due to the inherent momentum mismatch [189]. Many ap-proaches have been proposed to excite SWs, such as using grating and prism couplers.However, these devices are either bulky in size or exhibit intrinsically low frequenciescaused by normal reflection at device surfaces and decoupling effects, making themunfavorable for modern photonic applications [199]. Although metamaterials have beenused to control PWs and SWs separately, based on, say, transformation optics theory, anefficient bridge to link these two wave-propagation modes is still lacking.

In 2012, Sun et al. proposed that gradient metasurfaces are the very bridge to linkthese two important modes with essentially 100% efficiency [161]. The working prin-ciple is schematically depicted in Fig. 10(a), and is closely related to the discussion ofanomalous reflection by MIM metasurfaces in Subsection 3.1. Suppose a reflection-type gradient metasurface is illuminated by a normally incident light. Each meta-atomon the metasurface then radiates to free space as a secondary source with a unitaryamplitude and an initial phase linearly depending on its position. When the phasegradient ξ�� dΦ∕dx� is smaller than k0, interference among these sub-sources cangenerate an obliquely outgoing beam, leading to the anomalous reflection effect[see Fig. 7(f)]. Intriguingly, when ξ > k0, radiation from these sub-sources cannotconstruct any PW with an equal-phase plane [see Fig. 10(a)] [161], but rather forman SW bounded by the metasurface. Such an argument can also be understood fromthe generalized Snell’s law, which is explicitly written as


Figure 10

Gradient metasurface SPP couplers. (a) Schematic of PW–SW conversion processes forgradient metasurfaces with ξ > k0. (b) Left panel: schematic of the near-field scanningtechnique to demonstrate SW generation. Right panel: Ez field (phase information in-cluded) on part of the ξ � 1.14k0 metasurface under x-polarized normal illumination,obtained with experiments (top) and simulations (bottom). (c) Measured [including far-field (FF) and near-field (NF)] and simulated parallel k vectors (krx) of the waves re-flected by the ξ � 0.8k0 metasurfaces, illuminated by x-polarized waves of differentincident angle θi. (d) Top: experimental setup for demonstrating the process of guidingdriven SWs outside the metasurface. Bottom: measured Ez distribution on both themetasurface and the mushroom surface. (e) Left panel: sketch of 1D periodic metasur-face illuminated by a TM-polarized (i.e., x-polarized) normally incident light. Rightpanel: amplitude and phase of reflected light from the metasurface as a function ofstrip width w when λ � 1500 nm, periodicity Λ � 489 nm, and d � t � 50 nm.(f) Simulated Ez field patterns inside the gradient metasurface SPP coupler based onthe unit structures in (g), illuminated by x-polarized normally incident light atλ � 1500 nm. (g) SEM images of the fabricated 1D (left) and 2D (right) SPP metasur-face couplers. (h) Leakage radiation microscopy images showing polarization-controlled SPP excitation inside the 2D SPP coupler at λ � 1500 nm. (i) Left panel:key issues that degrade the efficiencies of conventional SPP couplers (e.g., grating andprism couplers), the initial reflection loss, and the decoupling loss from SPPs to freespace. Right panel: configuration of the SPP metacoupler. A transparent gradient meta-surface is placed at an optimized distance above the plasmonic metal. The incident waveis first converted into a driven SW bound on the metasurface and is then resonantlycoupled to the eigen SPP wave on the plasmonic metal. Neither reflection loss at themetasurface nor decoupling from the SPP to free space occurs. (j) Simulated Hy fielddistribution showing SPP excitation by the effective-medium-based metacoupler with94% efficiency. (k) Left panel: schematic of five designed ABA-type meta-atoms,


krx � k0 sin θi � ξ: (14)

Now, with an additional wavevector ξ provided by the gradient metasurface, the “re-flected wave” exhibits a tangential wavevector larger than k0 even under normal ex-citation, making it an SW bounded at the interface. Different from conventionalPW–SW conversion schemes, here the momentum mismatch between PW and SWis compensated by the phase gradient provided by the metasurface. In addition, thescheme is intrinsically of high efficiency since the SW is the only channel for the waveto go, while there are many channels in other couplers (say, the grating coupler). Indeed,numerical simulations based on an ideal model system (a PEC capped with a thin di-electric layer with continuously varying refraction index) without super-periodicitydemonstrated that the PW–SW conversion efficiency can be as high as 98% [161].

To experimentally demonstrate this prediction, Sun et al. designed and fabricated anMIM metasurface with ξ � 1.14k0 at the frequency 15 GHz, using meta-atoms similarto those described in Subsection 3.1. By shining an x-polarized microwave normallyonto the metasurface, the authors found that no “reflected” far-field signals can be de-tected, verified also by simulations on realistic structures. They next used a monopoleantenna to directly probe the local Ez fields (with both amplitude an phase) on an x–yplane 2 mm above the metasurface [see Fig. 10(b)]. The measured pattern [upper panelin Fig. 10(b)] unambiguously revealed that the SW nature of the generated “reflectedwave,”which has a parallel wavevector larger than k0 (very close to ξ � 1.14k0). Finite-difference time-domain (FDTD) simulations [lower panel in Fig. 10(b)] agree well withexperimental results.

An important feature of such PW–SW conversion is that it is a non-resonant scheme,which can happen at any incident angle exceeding a critical value θi > θc �sin−1�1 − ξ∕k0�, as predicted by Eq. (14). This is quite different from the usualPW–SW conversion processes (say, using grating or prism couplers), which typicallyhappen only at particular incident angles. Taking the ξ � 0.8k0 sample as an example[Fig. 6(f)], the authors experimentally demonstrated that PW–SW conversion can takeplace at oblique angles exceeding a critical value [Fig. 10(c)], demonstrating the validityof Eq. (14). However, one should notice that the SWexcited with this scheme is not aneigenmode as is a usual SPP, but is in fact a “driven” SW, which can exist only under theillumination of an impinging PW. This also explains why such a PW–SW conversionworks for a wide range of incidence angles, since a “driven” SW can take any wave-vector not restricted by the SPP dispersion relation.

Such a new mechanism paves the way to realize many SW-related applications, suchas high-efficiency SPP couplers, anti-reflection coatings, and light absorbers.

consisting of two identical metallic micro-structures and another metallic micro-structure separated by two 1.5 mm thick dielectric spacers. Right panel: measuredand simulated transmission amplitudes and phases of five slabs consisting of periodicarrays of different meta-atoms. (l) Left panel: image of the fabricated SPP metacouplerplaced at an optimized distance (10 mm) above the “plasmonic metal.” Right panel:measured Ez field distribution on part of the “plasmonic metal” when the metacoupleris illuminated by an input propagating wave with a frequency of 9.2 GHz.(a)–(d) Reprinted with permission from Macmillan Publishers Ltd.: Sun et al., Nat.Mater. 11, 426–431 (2012) [161]. Copyright 2012. (e)–(h) Reproduced from [200]under the terms of the Creative Commons Attribution NonCommercial-NoDerivs3.0 Unported License. (i)–(l) Reproduced from [201] under the terms of theCreative Commons Attribution NonCommercial-NoDerivs 4.0 Unported License.


Knowing that the excited SW is still not the desired SPP, Sun et al. designed andfabricated an artificial plasmonic metal (a mushroom structure [202]) supportingan eigen spoof SPP at this frequency, and placed it to the right-hand side of thegradient metasurface to guide the excited “driven” SW out of the metasurface [seeFig. 10(d)] [161]. In their experiments, the authors illuminated only the gradient meta-surface by an x-polarized microwave, and used a monopole antenna to measure the Ez

distribution on the entire x–y plane covering both the metasurface and the “plasmonic”metal. Figure 10(d) depicts the measured Ez distribution, showing clearly that the“driven” SWs on the metasurface are indeed guided out to spoof SPPs on the mush-room structure. Compared to conventional SPP couplers, such a metasurface-basedcoupler exhibits many advantages, such as much enhanced efficiency, unidirectionalexcitation, incidence-angle insensitivity, and a miniaturized device size. One yearlater, Pors et al. pushed the concept forward, demonstrating a unidirectional polari-zation-controlled SPP metacoupler working at telecommunication wavelength [200].The fabricated coupler is constructed by the same type of MIM meta-atoms, only withsizes scaled down for high frequencies. Since metals exhibit finite penetration lengthsand losses for light in this frequency domain, the authors carefully considered thereflection-amplitude fluctuations of meta-atoms in their design [see Fig. 10(e)]. Theyfirst fabricated a one-dimensional (1D) SPP coupler [left-panel in Fig. 10(g)] withphase gradient matching the wavevector of the eigen SPP on the plasmonic metal(without the top metallic patches), and experimentally demonstrated that SPPs canbe excited with an efficiency of 27% (47% in simulations [Fig. 10(f)]). The authorsnext realized a 2D metacoupler exhibiting phase gradients along two orthogonal di-rections [right panel in Fig. 10(g)]. Experiments show that such a device can exciteSPPs flowing along two directions on the plasmonic metal, as illuminated by incidentlight with different polarizations [see Fig. 10(h)]. However, the measured SPP exci-tation efficiency is only 15%, which is possibly caused by fabrication imperfectionsand enhanced material losses at optical frequencies.

In a theory paper, Qu et al. analyzed the key issues that most influence the workingefficiency of such SPP couplers [203]. The authors found that, while an ideal gradientmetasurface (exhibiting continuously varying permittivity/permeability) can indeedyield light-bending effects with nearly 100% efficiency, practically realized metasur-faces are all composed of supercells exhibiting truncated reflection-phase distribu-tions. Therefore, scatterings naturally exist at the boundaries between adjacentsupercells. Such effect is particularly significant for the PW–SW–SPP conversion pro-cess, which can decouple the generated SWs back to PWs, since the generated SWshave to flow on the inhomogeneous metasurface before reaching the homogeneouspart (i.e., the plasmonic metal). Indeed, calculations show that as the coupler’s sizeincreases, the SPP excitation efficiency gradually decreases, caused by the above-mentioned decoupling effects. As a result, while such SPP couplers are particularlyuseful in highly miniaturized applications (say, on-chip photonics devices), they arenot convenient for SPP excitation with incident light with large beam widths.

Facing these challenges, in 2016 Sun et al. discovered a new strategy to realizeSPP metacouplers with very high efficiencies [201]. The authors first sorted outtwo issues that limit the performance of conventional SPP couplers, which are thereflection losses at the devices’ interfaces and the decoupling of SPPs on metasurfa-ces, as shown in Fig. 10(i). Having understood these origins, the authors then proposeda new metasurface-based configuration for PW–SPP conversion, which consists of aperfectly transparent gradient metasurface (with ξ > k0) placed at an optimized dis-tance above the target plasmonic metal. The working principle can be described as fol-lows: the metasurface first converts an incident PW to a driven SW bounded at themetasurface, which is then resonantly coupled to an eigen SPP on the plasmonic metal.


The efficiency of such a coupler must be very high since the metasurface is perfectlytransparent without reflection, and more importantly, the generated SPP cannot decou-ple back to a PW due to the broken inversion symmetry of the system. Full-wave sim-ulations on an ideal system verified the concept, showing that the SPP couplingefficiency reaches 94% as the gap distance takes an optimized value, as shown inFig. 10(j). Such a distance plays a dual role in affecting the conversion efficiency—decreasing it can enhance the efficiency of the PW–SW coupling process but diminishthat of the SW–SPP conversion process—and thus one must carefully optimize it tobalance the two effects. The authors experimentally demonstrated the concept by mak-ing a transparent microwave metacoupler at the frequency 9.2 GHz, based on ABA-typeof meta-atoms. Aided by effective-medium analyses, the authors successfully designedfive different ABA structures, all allowing high transmission for EM waves but exhib-iting different transmission phases covering the entire 2π range [Fig. 10(k)]. The authorsthen fabricated a transparent gradient metasurface and put it at 1 mm (an optimizedvalue obtained via full wave simulations) above an artificial plasmonic metal (a mush-room structure), as shown in Fig. 10(l). Illuminating the metacoupler by an x-polarizedmicrowave at 9.2 GHz, the authors performed near-field scanning experiments to dem-onstrate that the incident PW has indeed been successfully converted to an SPP flowingon the “plasmonic”metal [see the well-defined SPP field pattern depicted in Fig. 10(l)].Far-field experiments further indicate that the SPP conversion efficiency of the devicereaches 73%, which is the highest among all SPP couplers available in this frequencydomain. These findings point out a new direction to design high-performance SPP cou-plers, but realizing them is challenging in high-frequency domains.

We note that the SPP excitation directions are fixed (dictated by the signs of phasegradients) once the metacouplers mentioned above are fabricated. Meanwhile, PBmetasurfaces can exhibit helicity-controlled phase profiles, which offer the possibilityto realize unidirectional SPP excitation. Two papers independently demonstrated thisidea at a similar time. In 2013, Huang et al. proposed a spin-controlled directional SPPcoupler based on a PB metasurface [204]. As shown in Fig. 11(a), the fabricated de-vice is a gold film drilled with an array of rectangular air holes with orientation angle αlinearly varying as a function of x, thus providing a PB phase φσ�x� � σ2θ�x� forincident CP light with spin-σ. However, the gradients on PB phases are not largeenough to convert a PW to a SPP, and the authors have to seek help from Bragg scat-terings, which provide reciprocal wavevectors G � �m2π∕s for the impinging light,with m being the diffraction order and s being the inter-hole distance. Therefore, as thewavevector matching condition

m · 2π∕s� ∇Φσ � �ksppx (15)

is satisfied, with ksppx being the wavevector of the eigen SPP, an SPP mode can beexcited on the metal surface. Suppose for the σ � 1 (LCP) excitation, one can adjustthe structural details (i.e., the θ�x� distribution) to make Eq. (15) satisfied withm � �1, then naturally the combination of fσ � −1,m � −1g is also the solution ofEq. (15), only with the sign in front of ksppx changed. Therefore, such a device naturallysupports spin-controlled unidirectional SPP excitations, which is an advantage incomparison with previously realized SPP metacouplers. The authors performed bothexperiments and simulations to demonstrate spin-controlled unidirectional SPPexcitation at the desired wavelength [see Fig. 11(b)]. At a similar time, Lin et al.demonstrated that a metal film drilled by two arrays of air apertures with orthogonalorientations can achieve similar spin-controlled directional SPP excitations [see inFig. 11(c)] [205]. The key idea is quite similar to that adopted in Ref. [204], butis now demonstrated in a simpler structure. When illuminated by normally incidentCP light, the single aperture array can selectively couple with the component polarized


Figure 11

Gradient metasurface SPP couplers. (a) Top panel: schematic of a unidirectional SPP cou-pler consisting of an array of rectangular apertures with spatially varying orientations on ametal film. Bottom panel: ordinary and anomalous refraction and diffraction illuminatedby the normally incident spin state σ � 1. (b) Experimental observation of the SPP ex-citation along the right direction inside the metacoupler for an incident beam with σ � 1

[204]. (c) Configuration of the polarization-controlled directional SPP coupling. The unitcell consists of two columns of apertures with orientations of θ1 � 45° and θ2 � 135° anda spacing S. (d) SEM image of a circular coupler (top left panel) based on the design shownin (c). The measured NSOM images of the coupler under RCP (top right panel), LCP(bottom left panel), and linearly polarized (bottom right panel) illumination, resulting inradially inward, outward, and both inward and outward couplings, respectively, of SPPs[205]. (e) Top panel: picture of the fabricated chirality-modulated spoof surface plasmonmetacoupler and experimental setup to demonstrate the SPP excitation performance.Bottom panel: measured electric (Ez) and magnetic (Hz) field patterns above PB metacou-pler under LCP illumination at frequency of 10 GHz [206]. (f) The schematic (top panel),sample image (middle panel), and measured electric field (bottom panel) for the high-efficiency and broadband converter linking a conventional coplanar waveguide and an ultra-thin corrugated metallic strip (the plasmonic waveguide) [207]. (g) Left panel: schematicand sample picture (inset) of the plasmonicmetaslit for achieving asymmetric SPP focusing.Middle and right: NSOM images of surface fields generated from the metaslit for LCPand RCP illumination [208]. (h) Top panel: conceptual schematic of a 1D PEC wave-guide covered by a gradient-index metasurface (gradually changing blue regions) forasymmetric transportation of light. Middle and bottom panels: numerical demonstration ofthe asymmetric propagation for an EM wave incident from the left and right sides [209].(a), (b) Reproduced from [204] under the terms of the Creative Commons AttributionNonCommercial-NoDerivs 3.0 Unported License. (c), (d) From Lin et al., Science 340,331–334 (2013) [205]. Reprinted with permission from AAAS. (e) Reproduced from[206] under the terms of the Creative Commons Attribution 4.0 License. (f) Ma et al.,Laser Photon. Rev. 8, 146–151 (2014) [207]. Copyright Wiley-VCH Verlag GmbH & Co.KGaA. Reproduced with permission. (g) Reprinted with permission from [208]. Copyright2015 Optical Society of America. (h) Reprinted with permission from MacmillanPublishers Ltd.: Xu et al., Nat. Commun. 4, 2561 (2013) [209]. Copyright 2013.


along the short axis and excite the SPPs on both sides of the array. By carefully choos-ing the separation distance and the orientation angles of the double-aperture arrays[Fig. 11(c)], the SPP beams emitted from the two aperture arrays can constructivelyinterfere at one side and destructively interfere at the other side, leading to a direc-tional SPP excitation. Furthermore, as the helicity of incident CP light changes, theinterference conditions are changed accordingly, thus switching the SPP excitationdirection. Near-field experiments nicely demonstrated the predicted effects, in goodagreement with theoretical results based on a dipolar model. Moreover, such an effectcan be extended to cylindrical SPP excitations, as shown in Fig. 11(d), where thedouble-aperture arrays are now arranged on a circle. As the spin of incident CP lightis flipped, SPP beams can be excited to propagate either inward or outward on theplasmonic metal. Recently, Zhang et al. modulated the orientation angles of the nano-apertures inside the array along the y direction, giving rise to a phase profile to furthercontrol the wavefront of the excited SPP beam, achieving oblique SPP excitations andSPP focusing [210].

Although these PB couplers enable spin-controlled SPP excitations, their workingefficiencies are unfortunately quite low. Recently, Duan et al. theoretically analyzedthe inherent issues limiting the performance of these PB couplers: (i) the adoptedmeta-atoms do not satisfy the 100% efficiency criterion [Eq. (12)], so that normalmodes inevitably exist to degrade the device performance; and (ii) while the incidentCP light contains both TE and TM components, the converted SPP modes usually takeonly a TM polarization, and such polarization mismatch further decreases the SPPconversion efficiency [206]. The authors then proposed a new scheme to design high-efficiency PB metacouplers, consisting of the following two steps. First, they designeda high-efficiency PB meta-atom based on the criterion in Eq. (12), so that it can per-fectly convert incident CP waves to driven surface waves with nearly 100% efficiency.Second, they designed an artificial metal supporting both TE- and TM-polarized eigenSPPs so that it can efficiently guide out SPPs with two polarizations. Based on thisscheme, the authors successfully constructed a high-efficiency PB metacoupler formicrowave frequencies, and experimentally demonstrated that both TE- and TM-polarized SWs are efficiently guided out as eigen SPPs [see Fig. 11(e)]. Far-fieldmeasurements further demonstrated that the realized coupler exhibits a very high con-version efficiency (78%), which can be further enhanced based on careful optimiza-tion. Although so far the concept has been demonstrated only in the microwaveregime, we expect that extending it to high-frequency domains is possible.

The concept of using metasurfaces to link far-field and near-field can find many ap-plications. In 2014, Ma et al. utilized a gradient metasurface as a bridge to link a trans-mission line and a plasmonic waveguide in the microwave regime [207]. Usually,guided-wave (GW) modes in the transmission line possess smaller wavevectors com-pared to spoof SPP modes in the plasmonic waveguide. Such wavevector mismatchcauses significant scattering losses at the junction of these two systems. To solve thisissue, the authors designed a gradient metasurface that possesses an effective wavevec-tor smoothly varying in space, to link the two systems as a convertor. Microwave experi-ments demonstrated a broadband and high-efficiency conversion between GW andspoof SPP, as depicted in Fig. 11(f). Lee’s group proposed several plasmonic nanoslitstructures, composed of single or double arrays of nanoslit segments with specific tiltingangles, to manipulate the SPPs. By designing the focal lengths of two nanoslits differ-ently, such plasmonic device can achieve the asymmetric SPP focusing effect, as de-picted in Fig. 11(g). Such a concept can also be applied to more complex SPPmanipulation, such as multiple focusing, arbitrary beam shaping, or plasmonic vortexgeneration [208]. Meanwhile, Xu et al. proposed to cap a gradient-index metasurfaceon one sidewall of a waveguide to achieve an asymmetric waveguiding effect [209].


As shown in Fig. 11(h), a mode transporting along the �x direction obtains an addi-tional wavevector (ξ � dΦ∕dx > 0) from each reflection at the metasurface, and finallyturns to a SW propagating through the device. Conversely, a mode transporting alongthe −x direction is reflected back because its wavevector continuously decreases afterreflection and finally changes sign. Clearly, the phase gradient breaks the lateral inver-sion symmetry leading to the fascinating asymmetric waveguiding effect. Microwaveexperiments nicely demonstrated this concept. Several years later, Li et al. adopted asimilar idea to realize asymmetric transmission, but for dielectric waveguide modes inthe IR regime [211]. Moreover, the authors also experimentally demonstrated that suchgradient metasurfaces can work as mode converters in the dielectric waveguide, and aremore miniaturized in size and/or efficient than other mode converts. These excellentexamples revealed the strong potential of integrating metasurfaces with conventionalEM devices, which are highly desired for future applications.

3.4. Dielectric MetasurfacesWhile metals behave as PEC in the GHz regime, they become lossy as frequency in-creases particularly to the visible regime. As a result, ohmic losses can significantlydegrade the performance of metasurfaces constructed with plasmonic metals, especiallyfor those working in the transmission mode at optical frequencies. On the other hand, atoptical frequencies dielectrics exhibit much smaller losses than metals, which stimu-lated rapid developments of dielectric metasurfaces with high performance. As pre-sented in Subsection 2.1, dielectric nanoparticles support both electric and magneticresonances [212–214]. In 2013, Staude et al. [215] demonstrated that disk-shaped di-electric resonators can select either electric or magnetic mode as their lowest-order res-onances, and the spectral positions of these two modes can be tuned in dramaticallydifferent ways through changing the geometry of the disk array [see Fig. 12(a)]. Thisallows us to achieve a spectral overlap between electric and magnetic resonances, lead-ing to a suppression of backward scattering and a high optical transmission [222].Moreover, the phases of light transmitted through such transparent nanoparticlescan be continuously tuned to cover the whole 2π range, through careful structural ad-justments. In addition, dielectric resonators with complex geometries exhibit expandeddegrees of freedom to modulate light in terms of both amplitude and phase. Thus, suchdielectric nanoparticles are the best candidates to build meta-atoms for designing func-tional metasurfaces with high efficiencies and broad operating bandwidths. Many di-electric metasurfaces were recently realized to manipulate light in both transmission andreflection geometries for LP and CP excitations, which will be briefly reviewed here.

In reflection geometry, a simple approach to achieve dielectric-based metasurfaces isto replace the top metallic resonators in plasmonic MIM metasurfaces with dielectricMie resonators. In 2014, Yang et al. fabricated a dielectric metasurface, consisting of aperiodic array of high-index silicon cut wires and a metallic ground plane separated bya low-index polymer spacer, and experimentally demonstrated that it can achievehigh-efficiency LP conversion over a 200 nm bandwidth around 1550 nm. They fur-ther used such meta-atoms to design another metasurface exhibiting an azimuthallyvaried phase profile [see Fig. 12(b)], and demonstrated that it can generate an opticalvortex beam efficiently within a wavelength range of 1500–1600 nm [174]. Based ona similar idea, Sun et al. fabricated a reflective metasurface based on TiO2 nanoblockswith aspect ratio around 1–1.5, and demonstrated that it can achieve efficient cross-polarized anomalous reflection at 632 nm (with conversion efficiency around 50%)and holograms in red, green, and blue with absolute efficiencies of 36.7%, 24.5%, and13.9%, respectively [223].

To manipulate light wavefronts at the transmission side, Mie-resonant meta-atoms (with tailored electric and magnetic resonances) were widely used to construct


Figure 12

Inhomogeneous dielectric metasurfaces. (a) Simulated transmittance spectra for arraysof embedded silicon disks (inset) with different radii, illustrating mode crossing withspectrally separate electrical and magnetic resonances [215]. (b) Polarization conver-tor and vortex beam generation with meta-reflectarray based on silicon cut wirehybridized with a metallic reflector. Bottom panel: experimental results of polariza-tion conversion in the NIR regime. Top panel: SEM image of the vortex beam gen-erator and experimental result at 1600 nm [174]. (c) Beam deflector with Huygenssilicon metasurfaces. Inset: SEM image of a 130 nm thick gradient resonant metasur-face [216]. (d) Gray-scale transparent metasurface holograms with extra high effi-ciency. Experimental holographic images from two holograms at 1600 nm [217].(e) Polarization beam splitter based on Huygens dielectric metasurface. Left panel:schematics of a-Si meta-atom and polarization beam splitter. Right panel: experimen-tal results of a polarization beam splitter at 915 nm, with a SEM image of fabricatedmetasurfaces in the inset [218]. (f) Measured chiral hologram illuminated by RCP andLCP light at λ � 1350 nm. Inset: a false-colored SEM image of four pixels of thehologram [219]. (g) Schematics of reconstruction of three holographic images at threeseparate planes based on silicon PB metasurfaces for broadband visible light [220].(h) Top panel: schematic of the working principle of a spin-to-orbital angular momen-tum converter. Bottom panel: SEM image of a TiO2-based spin–orbital angularmomentum converter with q � 0.5 observed in cross polarization and transverse in-tensity distribution of the vortex beam at λ � 532 nm [221]. (a) Reprinted with per-mission from Staude et al., ACS Nano 7, 7824–7832 (2013) [215]. Copyright 2013American Chemical Society. (b) Reprinted with permission from Yang et al., NanoLett. 14, 1394–1399 (2014) [174]. Copyright 2015 American Chemical Society.(c) Yu et al., Laser Photon. Rev. 9, 412–418 (2015) [216]. Copyright Wiley-VCHVerlag GmbH & Co. KGaA. Reproduced with permission. (d) Reprinted with permis-sion from [217]. Copyright 2016 Optical Society of America. (e) Reprinted withpermission from Macmillan Publishers Ltd.: Arbabi et al., Nat. Nanotechnol. 10,937–943 (2015) [218]. Copyright 2015. (f) From Khorasaninejad et al., Sci. Adv. 2,e1501258 (2016) [219]. Reprinted with permission from AAAS. (g) Huang et al.,Laser Photon. Rev. 10, 500–509 (2016) [220]. Copyright Wiley-VCH VerlagGmbH & Co. KGaA. Reproduced with permission. (h) Reprinted with permissionfrom [221]. Copyright 2017 Optical Society of America.


dielectric metasurfaces exhibiting desired phase profiles [216,224–226]. For example,in 2015, Yu et al. reported that dielectric metasurfaces constructed by supercells con-sisting of eight silicon nanodisks with tailored sizes can efficiently deflect arbitrarilypolarized incident light into the desired diffraction order. As shown in Fig. 12(c), thedeflection efficiency can reach ∼45% over the wavelength range of 665–755 nm[216]. Similar configurations were also implanted to achieve efficient vortex beamgeneration in transmission geometry at the NIR regime [224,225].

A related yet slightly different approach to construct dielectric metasurfaces is to uti-lize upright dielectric nano/micro-post/pillars with high aspect ratios, which operate aslow-Q FP resonators. By adjusting the cross sections of such dielectric waveguides,one can tune the effective indices of the waveguide modes to obtain the desired phaseshifts for the transmitted light. Many fascinating effects and functional devices wererealized based on such a scheme, such as metaholograms [217], metalenses [227,228],and vortex beam generators [229]. For instance, Wang et al. experimentally demon-strated high-efficiency transparent holograms based on dielectric metasurfaces formedby silicon nanopillars. The achieved metaholograms can produce high-resolutiongrayscale images and transmit over 90% of light with diffraction efficiency over99% at 1600 nm, and operate with a working bandwidth of 375 nm [Fig. 12(d)][217]. Very recently, Fan et al. experimentally demonstrated a divergent metalenswith near-unity numerical aperture (NA) based on a dielectric metasurface constructedby SiN hexagonal nanopillars [227]. High transmission (about 80%) and subwave-length resolution were achieved by the metalens over the wavelength range of480–780 nm. Moreover, polarization-dependent phase shifts can be achieved in di-electric waveguides with asymmetric cross sections, which provide an ideal platformto realize polarization-dependent light manipulation [218]. Recently, Faraon’sgroup experimentally demonstrated several polarization-dependent metadevices basedon elliptical-cross-section high-contrast dielectric nanoposts, functioning as waveplates, polarization beam splitters [Fig. 12(e)], metalenses, and metaholograms.These metadevices typically work in the NIR regime and exhibit relatively highefficiencies [218].

Meanwhile, the PB mechanism has also been widely employed in designing dielectricmetasurfaces to manipulate CP light with high efficiencies [219–221,230–233]. Thekey step is to design dielectric meta-atoms exhibiting high PCR according to the cri-teria introduced in Subsection 3.2. For instance, Capasso’s group experimentally dem-onstrated that PB metasurfaces consisting of rotated silicon nanofins can producechiral holograms with chirality-dependent functionalities in the NIR regime. Eachpixel of such a metadevice is composed of two phased arrays (arranged along they-axis direction, as shown in Fig. 12(f)] that couple to CP light with different chirality,thanks to the PB phases introduced by the rotated nanofins [219]. In addition, such ametadevice exhibits an absolute efficiency of ∼20% and extinction ratio of ∼10 at1350 nm, with working bandwidth of ∼200 nm. Recently, based on a transmissivemetasurface with eight-level modulation on geometric phases by precisely controlof the geometries and orientations of the constituted Si nanorods, Huang et al. ex-perimentally realized multiple holographic images at three different z-planes excitedwith spin-polarized light in the visible regime, as shown in Fig. 12(g) [220]. Althoughthe working efficiency of such a device is quite low (about 3%), it exhibits a wideworking band ranging from 480 to 680 nm, and does not suffer from high-order dif-fraction and twin-images issues. In a parallel line, Capasso’s group experimentallydemonstrated that PB metasurfaces constructed with high-aspect-ratio TiO2 nanofinscan realize metalenses [231], chirality-distinguishable beam splitters [232], andvortex beam generators [Fig. 12(h)] [221], all working in the optical regime with highefficiencies.


3.5. New Mechanisms for Constructing Metasurfaces with Nearly Perfect EfficiencyIn previous subsections, we have introduced several mechanisms to design gradientmetasurfaces for manipulating EM waves with different polarizations. These mech-anisms are all based on Huygens’ principle. However, while metasurfaces designed insuch a way work very well in most cases, severe problems exist in certain limitingconditions. Let us take a beam-bending reflective metasurface as an example to ex-plain the physics. According to the common design strategy, ideally such a metasur-face should be designed to exhibit a linearly changing reflection-phase profileΦ�x� � Φ0 � ξ · x to achieve the desired anomalous reflection to an angle determinedby ξ. However, while metasurfaces designed following this criterion do exhibit nearly100% efficiencies (efficiency drops a bit in plasmonic cases due to absorption) when ξis small, the efficiency of the metasurface drops significantly when the designed bend-ing angle is large (typically larger than 70°) [161,163]. Such an issue intrinsicallyexists in all metasurfaces designed with the common Huygens’ principle, which posesan obstacle for using metasurfaces in those applications that need large-angle bending,such as blazing gratings and interferometers. In fact, it was theoretically analyzed[161,166] that the metasurface needs to provide appropriate perpendicular electricor magnetic responses to perfectly construct the desired redirected beam when thebending angle is different from the incident one. Unfortunately, usually metasurfacesare ultrathin and exhibit only in-plane EM responses. It is clear that the large-angleefficiency issue is an inherent limitation of metasurfaces designed with a commonapproach, which exhibit local, passive, and in-plane EM responses.

Recently, many new design schemes have been proposed to solve the issue. In 2016,Mohammadi Estakhri and Alù [234] re-analyzed the correct boundary conditions im-posed on a metasurface to yield a perfect wave bending effect. They pointed out thatthe EM properties of a local part on the metasurface should be governed by total (orlocal) EM fields, including both the incident and the out-going waves, rather thanconsidering only the incident wave, as in the common design approach.Specifically, now the boundary conditions at each point on the metasurface (S) shouldbe expressed as

n × � ~H2S − ~Hi − ~H1S�jS �1

2Ye��~E2S � ~Ei � ~E1S� · t�j

S,

n × �~E2S − ~Ei − ~E1S�jS � − 1

2Zm�� ~H2S � ~Hi � ~H1S� · t�j

S, (16)

where Ye and Zm denote the desired admittance and impedance of this local part; and

�~Ei, ~Hi�, �~E1S, ~H1S�, and �~E2S, ~H2S� denote the incident wave and the scattered waves

in regions I and II, respectively. Assuming that �~E1S , ~H1S� and �~E2S, ~H2S� can be rep-resented by the desired outgoing waves that are already known, solving Eq. (16) canthus yield the exact material properties (i.e., impedance profile) of the metasurfaceunder design. In reflection geometry, Eq. (16) can be analytically solved. In general,suppose that the metasurface is designed to perfectly reflect an incident wave withparallel wavevector kix to a non-specular direction with parallel wavevector krx.The surface impedance and admittance profiles are then retrieved as

Zm � 4

Ye� 2η0

e−ikixx � Are−ikrxx

cos θie−ikixx − Ar cos θre

−ikrxx (17)

through solving Eq. (16), where θi and θr denote the incident and reflection angles,η0 �

ffiffiffiffiffiffiffiffiffiffiffiμ0∕ε0

pdenotes the wave impedance of vacuum, and jArj �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficos θr∕ cos θi

pis

the amplitude of the perfectly reflected wave. Equation (17) states clearly that, in orderto achieve perfect anomalous reflection, the metasurface must involve local losses in


some parts (RefZm�x�g � Ref4∕Ye�x�g < 0) and gains in some other parts(RefZm�x�g � Ref4∕Ye�x�g > 0). This is expected, as the impedance of the incidentwave and the outgoing wave cannot be matched in a passive metasurface due to theirdifferent parallel wavevectors [see Eq. (17)], while with gain and loss on the metasur-face, such an issue can be solved. The authors numerically demonstrated that indeed again–loss metasurface designed with Eq. (3) can indeed reflect an incident wave to anextreme oblique angle with 100% efficiency [see Fig. 13(a)].

While the idea proposed by Estakhri and Alù is inspiring, it has several intrinsic lim-itations. First, gain–loss metasurfaces are difficult to realize in practice, and a simplifieddesign (say, dropping the gain parts in metasurfaces) does not yield the desired 100%working efficiency [234,236,239,240], which is expected since gain material plays acrucial role here. Second, it is not entirely convincing to represent the local EM fieldsby the sum of the incident and far-field forms of the reflected waves in Eq. (16), whichcompletely neglects the contribution of non-radiative near-field components. Inspiredby this work, scientists continued to explore other approaches that are more practicallyrealizable. In 2017, Epstein and Eleftheriades noticed that the non-radiative evanescentwaves on the surface can actually help match the local impedance without necessarilyinvolving gain and loss in the design. Using evanescent waves as auxiliary fields to helpachieve local power conservation, the authors proposed a new scheme to design passiveand lossless metasurfaces that can realize 100% efficiency large-angle wave bending[see Fig. 13(b)] [235]. On the other hand, Tretyakov’s group fully utilized the guidedsurface waves trapped on the metasurface to help design passive metasurfaces thatexhibit nonlocal responses to achieve the 100% efficiency large-angle anomalous re-flection [see Fig. 13(c)]. Such a nonlocal metasurface can well mimic a gain–loss meta-surface as seen at a plane above the metasurface, solving the impedance mismatch issue.

Figure 13

New mechanisms for constructing metasurfaces with nearly perfect efficiencies.(a) Design scheme with distribution of loss and gain [234]. (b) Auxiliary-field-enableddesign scheme with gain/loss free media [236]. (c) Experimental verification ofauxiliary-field-enabled high-efficiency beam steering [237]. (d) Metagrating approachto achieve 100% efficiency large-angle diffraction [238]. (a) Reproduced from [234]under the terms of the Creative Commons Attribution 3.0 License. (b) Reprinted withpermission from [235]. Copyright 2016 Optical Society of America. (c) From Díaz-Rubio et al., Sci. Adv. 3, e1602714 (2017) [237]. Reprinted with permission fromAAAS. (d) Figure 1 reprinted with permission from Ra’di et al., Phys. Rev. Lett.119, 067404 (2017) [238]. Copyright 2017 by the American Physical Society.https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.067404.








The authors fabricated a microwave sample based on MIM meta-atoms and experimen-tally verified its ability to achieve nearly perfect anomalous reflection [237]. Such con-ceptually new mechanisms for high-efficiency wavefront manipulation allows thedesign of thin perfect reflectors, offering versatile design methods applicable to otherscenarios, such as focusing reflectors, surface wave manipulation, or metasurface holo-grams, extendable to other frequencies.

Despite the several mechanisms proposed, challenges still exist in realizing wide-anglehigh-efficiency metadevices in practice. For example, in all these mechanisms, inter-particle near-field couplings are completely overlooked, and, thus, applying such strat-egies in practical design still needs large-scale numerical optimization. Very recently,Ra’di and co-workers proposed a new concept—the metagrating—to realize metasur-faces that achieve 100% efficiency large-angle anomalous reflection, in which a super-cell contains only one resonator that exhibits in-plane and/or perpendicular responses[see Fig. 13(d)] [238]. Almost at the same time, Wong and Eleftheriades proposed amore practical design approach to realize metagratings with a supercell consisting oftwo resonators with different reflection phases [241]. They demonstrated that a fine-tune of the reflection response of two planar resonators can also approach unitary effi-ciency under certain conditions, and they verified this concept experimentally in themicrowave regime [241]. Later on, Shvets’ group brought the concept to transmissiongeometry and the high-frequency domain. They used a bianisotropic metamolecule sup-porting four different types of resonance as a building block to construct a metagratingat mid-IR wavelengths. As the result of destructive interference of these four modes,only one diffractive order is expressed in transmission, while all reflections are stronglysuppressed, leading to nearly 100% efficiency anomalous transmission [242]. Sell et al.demonstrated that silicon-based metagratings capable of large-angle deflection withmultifunctional performance can be realized. Such metagratings contain non-intuitivenanoscale patterns and support a large number of spatially overlapping optical modesper unit area. The quantity of modes, combined with their optimized optical responses,offers enough degrees of freedom to design high-efficiency metadevices [243]. Packoet al. described an inverse design approach to construct a metagrating that can channelthe incident energy toward the desired direction [244]. The grating is composed of acluster of resonators whose properties can be derived by the inversion of a given matrix.Using this design strategy, the authors numerically demonstrated an anomalous refractorand an anomalous reflector, both exhibiting very high efficiencies [244]. In addition tosuch theoretical approaches, numerical optimization is also frequently used to help findoptimized metastructures with high working efficiencies [237]. Based on numericaloptimization, Lin et al. have demonstrated metasurfaces working both in transmissionand reflection modes based on conventional thin-film silicon processes that are suitablefor the large-scale fabrication of high-performance devices [245]. All these newly pro-posed mechanisms share the same key physics. First, the systems are purposely de-signed (via varying the incident angle or lattice constant) in such a way that only asmall number of diffraction channels are “alive” while all others are evanescent.Then, by fully exploiting the differences in radiation symmetries of different resonantmodes, one can “tune” the EM responses of the meta-atom to completely suppress theradiation to all channels except the desired one, resulting in a 100% efficiency extremewave control. These newly proposed strategies can significantly simplify the designingprocesses to realize large-angle bending metasurfaces with nearly 100% efficiencies,which may stimulate much follow-up work in metasurface research.

4. APPLICATIONS OF INHOMOGENEOUS METASURFACES

Having understood different working principles of using metasurfaces to control EMwaves, we turn to describe the key applications of metasurfaces, including metalenses,


metaholograms, metacloaking, special-beam generation, and multifunctional and tun-able metadevices.

4.1. MetalensesLenses play important roles in optics as they are the most crucial components in nearlyall complex optical systems. Conventional lenses are usually made of transparent di-electric materials (say, glass). To realize the desired functionality, a conventional lensmust exhibit a certain curved shape so that waves transmitted through (or reflected by)it at different local positions can gain required phases. Such strict requirements makethem bulky in size, difficult to make, and possess only limited functionalities, whichhampers their application in modern integrated-optics applications.

Metamaterials can partially resolve the above issues [246–250]. In 2008, Lin et al.proposed a flat metamaterial slab, with effective refraction index varying in space togenerate the desired phase for a locally transmitted wave, to realize the same focusingfunctionality as a conventional lens. The building block of such a metamaterial lens isa metallic rod embedded inside a high-index dielectric block [246], which can exhibitboth electric and magnetic resonance upon excitation, yielding an effective index thatcan be tuned by varying the height of metallic rods. Two years later, Paul et al. pro-posed a gradient-index metamaterial lens for THz waves [247], using an annular slotaperture as a building block with effective refractive index dictated by the slot radius.Broadband focusing that is insensitive to polarization and incident angle of externalradiation was experimentally demonstrated. In 2009, Verslegers et al. demonstrated aplasmonic flat lens for visible light. The device is a 400 nm thick metallic film perfo-rated with nanoslits with appropriate widths [see Fig. 14(a)] [248] that can control thewaveguide cut-off frequencies to yield different transmission phases for light passingthrough them. However, this metalens can focus incident light with only one particularpolarization to a focal line (i.e., a 2D focusing). Such an issue was soon solved by Linet al., who fabricated a plasmonic lens based on 2D cross-shaped apertures [249] thatcan realize a polarization-insensitive 3D focusing effect at the 850 nm wavelength.Compared to conventional lenses, all these metamaterial lenses are flat and can exhibitreduced thickness. However, since these devices still exploit the propagation phasesinside the metamaterials, they are inevitably bulky and complex and/or exhibit lowworking efficiencies.

Metasurfaces that exploit interfacial phase changes, rather than propagating phases,provide an excellent platform to overcome the issues mentioned above, boosting thefast development of metalenses. The key idea is to arrange meta-atoms in such a waythat the transmission/reflection phase profile on the metasurface satisfies

ΦLens�r� � k0

� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiF2 � r2

p− F

�, (18)

which can ensure waves transmitted through (or reflected by) the metalens can con-structively interfere at the designed focal point. Here F is the designed focal length.Readers should distinguish these two different definitions clearly in all metadevices toprevent achieving the opposite functionalities. In 2012, Li et al. experimentally dem-onstrated a high-efficiency reflective metalens in the microwave regime [253] basedon MIM meta-atoms with H-shaped top resonators [see Fig. 14(d)]. By tuning thestructural details of the H structures, the authors found a set of meta-atoms yieldingthe desired reflection phases, and then assembled them to construct a 2D metalenswith a focusing length of 100 mm at frequency 10 GHz. Similar to other MIM meta-surfaces, such a device is ultrathin (∼λ∕12 thickness) and exhibits nearly 100% effi-ciency. Nearly at the same time, Bolzhevolnyi’s group realized a broadband reflective


Figure 14

Flat metalenses based on metasurfaces. (a) Planar lens based on a nanoscale slit arrayin metallic film. Left panel: geometry and SEM image of the lens, consisting of a400 nm optically thick gold film with air slits of different widths (80–150 nm) milledtherein on a fused silica substrate. Middle and right panels: focusing patterns mea-sured by confocal scanning optical microscopy and FDTD simulation [248].(b) Focusing flat mirrors based on plasmonic metasurfaces. Left panel: SEM imageof a part of a fabricated metalens designed for 800 nm wavelength, with the buildingblock shown in the inset. Right panel: optical focusing image obtained for the sampleilluminated by light at 800 nm [251]. (c) Metasurface-based terahertz flat lens. Leftpanel: schematic of light focusing analysis by the metasurface. Right panel: schematicof the desired metasurface lens and the imparted phase distribution. Bottom: partialoptical image of the proposed metalens [252]. (d) Flat microwave metalens in reflec-tion geometry with the building block shown in the inset [253]. (e) Babinet-invertedplasmonic metalenses. Left panel: SEM image of the fabricated plasmonic metalenswith a focal length of 2.5 mm at wavelength of 676 nm. Right panel: measured cross-polarized focusing field patterns on the transmission side of the metalens [254].(f) Schematic of a dielectric metalens operating in transmission mode with its build-ing block (a TiO2 nanopillar on a glass substrate) shown in the insets [231]. (g) Dual-polarity plasmonic metalens for visible light. The lens consists of an array of plasmonicdipole antennas (S � 400 nm) on a glass substrate with orientations varied along thex direction [255]. (h) SEM image of the fabricated dielectric metalens based on a siliconnanobeam with a focal length of 100 ≅ m at λ � 550 nm. The insets depict the mea-sured field intensity profiles in the focal plane and along the optical axis [256].(i) Metasurface based on high-aspect-ratio TiO2 metasurfaces. Left panel: SEM imageof the metalens edge. Right panel: focal spot intensity profiles at λ � 532 nmmeasuredby a metalens (top) and a conventional commercial optical lens (bottom) [257].(a) Reprinted with permission from Verslegers et al., Nano Lett. 9, 235–238 (2009)[248]. Copyright 2009 American Chemical Society. (b) Reprinted with permissionfrom Pors et al., Nano Lett. 13, 829–834 (2013) [251]. Copyright 2013 AmericanChemical Society. (c) Wang et al., Adv. Opt. Mater. 3, 779–785 (2015) [252].Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.(d) Reprinted with permission from [253]. Copyright 2012 Optical Society ofAmerica. (e) Reproduced from [254] under the terms of the Creative CommonsAttribution NonCommercial-NoDerivs 3.0 Unported License. (f) Reprinted with per-mission from Khorasaninejad et al., Nano Lett. 16, 7229–7234 (2016) [231].


metalens in the NIR regime [251]. The meta-atoms that they adopted are also MIMstructures [Fig. 14(b)] with the top resonator being gold patches with different lateralsizes, yielding the desired parabolic reflection phase profile. The authors fabricated ametalens with a size of 17.3 ≅ m × 17.3 ≅ m and experimentally characterized the 2Dfocusing functionality of the metalens. Their experiments revealed that the focal lengthof the device changes from 15 to 11 ≅ m as wavelength varies from 750 to 950 nm, withexperimental (theoretical) efficiency lying in the range of 14%–27% (50%–78%).Compared to its microwave counterpart, such an optical metalens has relatively lowerefficiency, which is mainly due to fabrication errors and material losses.

However, reflective lenses are inconvenient in certain applications where transmissivemetalenses are more desired. Soon after V-shaped metasurfaces were proposed, Ni et al.demonstrated a Babinet-inverted plasmonic metalens working in transmission mode atthe NIR regime [254]. The building meta-atom is a V-shaped aperture on a 30 nm thickgold film, which, based on Babinet’s principle, can control transmitted light (includingboth amplitude and phase) in the same way as a V-shaped antenna controls reflectedlight. Figure 14(e) shows an SEM image of one of the fabricated metalenses, with F �2.5 μm for λ � 676 nm. An optical microscope connected with a CCD was adopted tomap the field distributions for the cross-polarized light transmitted through the sample,clearly demonstrating the focusing effect [Fig. 14(e)]. Similarly, Wang et al. proposedto use C-shaped split ring resonators (CSRRs) [252], being topological equivalents ofV-shaped antennas, to build THz metalenses, as depicted in Fig. 14(c). They demon-strated a 5.52 mm diameter metalens with an NA of 0.27, exhibiting nice focusing ef-fects within the frequency range of 0.5–0.9 THz. Moreover, the authors also fabricated a5 × 5 metalens array to quantify the wavefront aberrations of impinging THz beams.When the device is illuminated by a THz beam with a distorted wavefront, the metal-enses in the device can create a series of focal points located at different planes, based onwhich one can retrieve the wavefront distortion of the incident beam. However, theworking efficiencies of these metalenses are very limited, due ultimately to the commonissues existing in such single-layer ultrathin metasurfaces [186]. In principle, a metalensbased on a Huygens metasurface [168] can achieve high-efficiency focusing effects intransmission mode. However, it is difficult to scale down such metasurfaces with com-plicated structures to high-frequency regimes.

Understanding the difficulties in enhancing the working efficiencies of plasmonicmetalenses at high frequencies, scientists turned to studying dielectric metalenses.In 2016, Capasso’s group demonstrated high-efficiency transmissive metalenses forvisible light [231], with meta-atoms being nanopillars made by high-index TiO2 on aglass substrate [Fig. 14(f)]. By varying the diameters of nanopillars with tall-enoughheight, the authors can control the phases of transmitted light within the full 2π range,yet with transmission amplitudes remaining at reasonably high values, based on thedielectric-resonance mechanism introduced in Subsection 2.1. Three different metal-enses were fabricated, working respectively at 405, 532, and 660 nm, all exhibitinga diameter of 300 ≅ m and focal length of 200 ≅ m and thus an NA of ∼0.6.Experiments demonstrated the excellent focusing performance of these metalenses,exhibiting efficiencies of 30%, 70%, and 90%, respectively. Metalenses with evenhigher NAs (0.85) were also fabricated, and they exhibit slightly decreased working

Copyright 2016 American Chemical Society. (g) Reproduced from [255] under theterms of the Creative Commons Attribution NonCommercial-NoDerivs 3.0 UnportedLicense. (h) From Lin et al., Science 345, 298–302 (2014) [256]. Reprinted with per-mission from AAAS. (i) From Khorasaninejad et al., Science 352, 1190–1194 (2016)[257]. Reprinted with permission from AAAS.


efficiencies due to increased fabrication errors in such high-NA metalenses. One ad-vantage of such metalenses is that their performance is essentially independent of theincident polarization. However, it is very challenging to make such metalenses, whichinvolve nanostructures with very high aspect ratio.

Alternatively, the PB mechanism has also been widely employed to design metal-enses. Such PB metalenses are sensitive to excitation light with CP instead of LP,and the phase distribution, designed for a particularly spin-polarized light, may changeto a defocusing profile yielding a virtual image, when the excitation field changes itschirality. The latter naturally offers the PB metalens an attractive property of bifunc-tionality. In 2012, Chen et al. fabricated a PB metalens [see Fig. 14(g)] consisting ofplasmonic dipole antennas with orientation angles designed to realize a 1D focusingphase profile with F � 60 ≅ m at λ � 740 nm [255] for excitation light with RCP.Optical measurements demonstrated that the device realizes a real and a virtual imagesas the incident light changes its chirality from RCP to LCP. However, such a metalensexhibits very low efficiency, since the meta-atom is not designed to satisfy the cri-terion in Eq. (13). In fact, it was theoretically predicted that such a single-layerPB meta-atom cannot exhibit working efficiency higher than 25% [186], whichwas proved experimentally by Ding et al., who demonstrated a transmissive PB metal-ens in the microwave regime, with efficiency approaching the 25% limit [187].Although one can use the high-efficiency trilayer PB meta-atom [183] to design trans-mission-mode microwave PB metalenses with very high efficiencies, such structuresare very difficult to fabricate at optical frequencies, and the enhanced metallic losseswill also diminish the devices’ efficiencies. Alternatively, Lin et al. demonstrated adielectric metalens with an NA of 0.43 working at λ � 550 nm [Fig. 14(h)] [256]. Theauthors employed a 100 nm high Si-nanobeam antenna (put on a quartz substrate) as abasic PB meta-atom, which is carefully designed to possess a π phase difference fortransmitted light with two perpendicular polarizations and thus exhibit a high PCR.However, substantial difference in the transmission amplitudes for the two polariza-tions still limits its working efficiency. Very recently, Khorasaninejad et al. reportedhigh-NA and high-efficiency dielectric metalenses working in the visible, based on a PBmeta-atom being a high-aspect-ratio TiO2 nanofin [see Fig. 14(i)] [257]. The highlytransparent nature of TiO2 and excellent sample quality significantly reduce the lossesof the devices and boost the efficiencies. More importantly, the meta-atom is designed toyield a very high PCR and thus a high working efficiency. Three metalenses workingrespectively at the wavelengths of 660, 532, 405 nm were fabricated, exhibiting focallengths of 90 ≅ m and high NA of 0.8. The metalens designed at 405 nm shows thehighest efficiency of 86%. The authors experimentally compared the performance oftheir metalens with a commercial one and found that the metalens shows a better res-olution at the central wavelength. However, in contrast to a commercial lens exhibitingbroadband performance, the metalens has a relatively narrow bandwidth.

Although metalenses exhibit many attractive properties, they unfortunately sufferfrom severe chromatic responses that are unfavorable for applications. One can under-stand the origin of such chromatic responses by analyzing Eq. (19). Suppose twoadjacent meta-atoms on a metalens are separated by a distance d. Then, the differencein the abrupt phase shifts provided by them should be

Φ1 −Φ2 �dΦLens

dr· d, (19)

where ΦLens is the desired phase profile of the metalens described by Eq. (18) and d isthe periodicity of the metasurface. While one can easily design a metalens to Eq. (18)for a particular wavelength λ0, it is not easy to satisfy Eq. (19) at all wavelengths.


Obviously, the right-side term in Eq. (19) exhibits linear wavelength dependence(∝ k0) due to its propagating-wave nature. However, Φ1 and Φ2, being the abruptphase changes of the two adjacent meta-atoms on the surface, exhibit eitherLorentz-type dispersions (for resonance-phase meta-atoms) or are totally dispersion-less (for PB meta-atoms), both of which cannot compensate for the dispersion of theright-side term. Note that such chromatic responses exist in all metasurface-baseddevices, which can be understood from Eq. (19) only with its left-side term changedaccordingly to enable the meta-atoms to exhibit different linear phase retardations. Torealize achromatic metadevices, the key issue is then to design meta-atoms with en-gineered dispersions that can precisely compensate for the dispersions of propagatingphases, so that Eq. (19) can be satisfied in a wavelength range as wide as possible.

In 2015, Capasso’s group proposed a scheme to realize multiwavelength achromaticmetadevices (including metalenses), as depicted in Fig. 15(a) [258]. They proposed touse multimode composite meta-atoms that exhibit frequency dispersions differentfrom the Lorenz form of a single-mode resonance to compensate for the propagat-ing-phase dispersions at three discrete wavelengths. The composite meta-atoms con-sist of two coupled dielectric resonators with different widths w1,w2. By sweepingw1,w2 and the separation g between two resonators, the authors sorted out a series ofmeta-atoms exhibiting correct phases at three discrete wavelengths, yet with nearlyuniform transmission amplitude. They first demonstrated a metasurface that can bendincident light to the same deflection angle θ � −17°, at three wavelengths (1330,1550, and 1800 nm) [see Fig. 15(a)]. They further demonstrated a 2D multiwave-length achromatic metalens exhibiting an NA of 0.05 and identical focal length F �7.5 mm [see Fig. 15(a) for measured field patterns at three wavelengths]. However,such a scheme can realize achromatic functionalities only at several discretized wave-lengths, and the design strategy relies on brute-force simulations to construct a fullmeta-atom database, which is quite low efficiency.

Such a pioneer work stimulated numerous studies on achromatic metadevices. Forexample, Hu et al. demonstrated a multiwavelength achromatic metalens [264] basedon plasmonic meta-atoms consisting of several nanoparticles with different sizes andshapes. Different from the design strategy based on brute-force simulations [258], thelattice evolution algorithm was adopted to efficiently design a flat optics device. Withmore degrees of freedom added in the design, such metadevice can help produce de-sired frequency dispersions for multiwavelength achromatic focusing. Avayu et al.integrated three plasmonic metalenses, individually designed to focus red, green,and blue light to nearly identical focal points, to form a single device that can realizean achromatic focusing effect [Fig. 15(b)] [259]. Such an idea is simple and straight-forward, similar to the traditional method based on an optical-element array. The real-ized metasystem also possesses the advantages of a flat configuration and easyintegration.

The next task is to realize broadband achromatic metalenses, which are more useful inpractical applications. In 2017, Khorasaninejad et al. proposed a 3D achromatic met-alens working in a continuous frequency band [260], as shown in Fig. 15(c). Thebuilding block consists of a single 600 nm high square TiO2 nanopillar on anSiO2 substrate with an alumina film at the bottom. Such a phase shifter can providemultiple 2π phase modulation and anomalous phase dispersion, both of which offerextra degrees of freedom for designing achromatic lenses. By optimizing the widths oflocal nanopillars, the authors designed a metalens satisfying Eq. (18) at several dis-cretized wavelengths within a continuous band (490–550 nm). A 200 ≅ m diameterachromatic metalens with an NA of 0.2 was experimentally demonstrated to focus LPlight to the same focal length of 485 ≅ m within a 60 nm working band. To further


Figure 15

Achromatic metalenses based on dispersion engineering. (a) Multiwavelength achro-matic dielectric metadevices. Left panel: mechanism for achromatic focusing lens atthree different wavelengths. The phase shifts φm,i and φm,j imparted by the metasur-face at points ri and rj of the interface are designed so that the paths li (ri) and lj (rj) areoptically equivalent at different wavelengths. Right panel: side view of the metasur-face for achromatic deflection. The building block consists of two coupled rectan-gular dielectric resonators of fixed height t and varying widths w1 and w2 [258].(b) Multispectral achromatic metalens composed of three closely stacked metasurfa-ces designed individually at wavelengths of 650, 550, and 450 nm, respectively [259].(c) Schematic of an achromatic metalens over 60 nm bandwidth in the visible (leftpanel) and the measured intensity profiles of the reflected beam by the metalens atthe main-axis plane for different wavelengths (right panel) [260]. (d) Schematic forbroadband reflective achromatic metalenses (left panel). The unit elements are singleor multiple metallic nanorods with different linear phase profiles [261]. (e) Broadbandtransmissive achromatic metalens aiming for providing spatially dependent group de-lays such that wavepackets from different locations arrive simultaneously at the focuspoint. The building block is composed of one or more TiO2 nanopillars with differentdimensions [262]. (f) Macroscopic optical image (left panel) and local SEM image(middle and right panels) of the broadband transmissive achromatic metalens com-posed of the GaN nanopillars and the Babinet nanostructures [263]. (a) FromAieta et al., Science 347, 1342–1345 (2015) [258]. Reprinted with permission fromAAAS. (b) Reproduced from [259] under the terms of the Creative CommonsAttribution 4.0 License. (c) Reprinted with permission from Khorasaninejad et al.,Nano Lett. 17, 1819–1824 (2017) [260]. Copyright 2017 American ChemicalSociety. (d) Reproduced from [261] under the terms of the Creative CommonsAttribution 4.0 License. (e) Reprinted with permission from Macmillan PublishingLtd.: Chen et al., Nat. Nanotechnol. 13, 220–226 (2018) [262]. Copyright 2018.(e) Reprinted with permission from Macmillan Publishing Ltd.: Wang et al., Nat.Nanotechnol. 13, 227–232 (2018) [263]. Copyright 2018.


expand the bandwidth, Wang et al. employed integrated-resonant unit elements, withphases contributed by both resonant and PB mechanisms, to design broadband achro-matic optical components [261]. Specifically, a metallic nanorod can support multipleplasmonic resonances including fundamental and high-order modes. The authors no-ticed that the phase distribution between two resonances exhibits a nearly linear profileagainst 1∕λ, and such slope can be tuned via changing the inter-mode wavelength orintroducing more resonances, as shown in Fig. 15(d). Meanwhile, the PB mechanism isalso utilized to provide a basic phase profile at the boundary of the wavelength band.Using such a design strategy, the authors experimentally demonstrated a metalens withan NA of 0.268, exhibiting achromatic focusing functionality in a wide wavelengthband (1200–1680 nm). However, such a metalens does not exhibit a high working ef-ficiency (∼12%), simply because, to achieve achromatic functionality, the authors haveto purposely avoid using the high-efficiency meta-atoms, which inevitably exhibit thestrongest resonance-induced dispersion. Soon, Wang et al. also demonstrated a trans-mission-type achromatic metalens working in 400–660 nm [263], as shown inFig. 15(f). The adopted meta-atoms are solid or inverse GaN nanopillars, which, uponcareful design, can support multiple waveguide-like modes, which can be fully utilizedto realize dispersion compensation. Aided by brute-force simulations, the authors finallyrealized a metalens with an NA of 0.106 to achieve achromatic focusing and full-colorimaging. Meanwhile, Chen et al. also reported a broadband achromatic metalens intransmission mode for visible light [262]. The involved meta-atoms consist of oneor more 600 nm high TiO2 nanofins standing on a SiO2 substrate, as shown inFig. 15(e). By carefully choosing the dimensions of those nanofins, the authors founda series of meta-atoms that yielded linear phase profiles with different slopes for build-ing up the achromatic metalens. The achromatic focusing effects in the wavelengthrange of 470–670 nm were experimentally demonstrated by two fabricated metalenseswith NAs of 0.2 and 0.02.

Although metalenses working at different frequencies using distinct materials[265–273] have already been demonstrated, research along this line is still underway,since many issues need to be solved before such devices can finally replace currentlyavailable commercial counterparts.

4.2. MetahologramsHolography denotes such a technique that one encodes the information of a target imageinto an optical medium (i.e., hologram), which later, upon excitation, can reconstruct theoriginal image. In a conventional approach, a reference beam is used to interfere withthe light emitted from the target object, generating an interference pattern that is thenrecorded as the permittivity distribution on a holographic plate [274,275]. As the plate isilluminated by the same reference beam, scatterings can reconstruct the desired image.Alternatively, one can also employ a computer-generated-hologram (CGH) technique tonumerically design a holographic plate without necessarily performing the interferenceexperiment [276]. The key step in CGH is to determine the requested transmission/reflection amplitude/phase distributions at a holographic plate by solving an inverseproblem with both the incident field and final image fixed. However, although holo-grams have found many applications in practice (display [277], optical detection [278],beam shaping [279], etc.), holographic plates made by conventional materials sufferfrom the issues of bulky size, less efficiency, the twin-image effect, and limited reso-lution, due ultimately to the narrow permittivity range of naturally existing materials andlarge (wavelength scale) pixel size. Recently, metamaterials/metasurfaces have offeredus an ideal platform to overcome these challenges, thanks to their powerful abilities tocontrol the local transmission/reflection properties at the subwavelength scale. In thissubsection, we briefly review the development of metaholograms.


In 2012, Smith’s group demonstrated the first metamaterial-based hologram in the IRregime [280]. At a working wavelength of 10.6 ≅ m, the authors designed a set ofmetallic structures that exhibited different values of effective refraction indices, whilethe multilayer configuration can further enhance the variation range of transmissionphases through these structures. Fifteen distinct meta-atoms were designed to yield therequested transmission phases, aided by full wave simulations. The final sample wasformed by assembling an array of phase pixels, each consisting of 5 × 5 meta-atoms,selected to exhibit the desired transmission phases based on a CGH phase distributioncalculated for a target hologram image. Optical experiments were performed to dem-onstrate the desired holographic image [Fig. 16(a)]. While this work paves the way tousing metamaterials for hologram applications, it exhibits several limitations. For ex-ample, the multilayer metamaterial is quite complicated and thus difficult to fabricate.In addition, the device is still thick and exhibits very low efficiency.

Metasurfaces can largely overcome the issues mentioned above, and many metasur-face-based holograms appeared soon after this pioneering work. In 2013, Shalaev’sgroup experimentally demonstrated a metahologram in the visible regime, as shown inFig. 16(b) [281]. Here, the metasurface consists of V-shaped apertures perforated in ametallic thin film. Through geometry sweeping, the authors first numerically obtaineda database for designing meta-atoms with desired transmission amplitudes and phases,based on which they then successfully designed a holographic plate for creating adesired image according to the CGH-calculated phase distribution. The workingprinciple of such V-shaped apertures is essentially the same as that discussed inSubsection 3.1 for the V-shaped antenna, according to Babinet’s principle. Therefore,only the cross-polarized component of the scattered field can form the desired image,which is an apparent shortcoming. In addition, the efficiency is still low, persisting inall V-antenna-based metasurfaces due to the inevitable multimode generation. Almostat the same time, Tsai’s group presented a reflection-type metahologram for visiblelight that can overcome the issues mentioned above [282]. The basic meta-atoms areMIM structures with the top resonators being gold nanocrosses, which inherently pos-sess much higher efficiencies than the V-antennas, as discussed in Subsection 3.1. Bytuning the structural details, one can easily obtain a set of meta-atoms that yield differ-ent reflection phases to cover the full 2π range, yet with reflection amplitudes stayingat high values. Moreover, the lengths of two orthogonal nanorods are free parametersto independently control the reflection phases for two LPs, which allowed the authorsto design a single metasurface encoding two distinct hologram images (i.e., “NTU”and “RCAS”) when illuminated by light with different polarizations [see Fig. 16(c)].The realized metaholograms can work within a broad band (width ≅ 880 nm) under awide range of incident angles. The measured efficiency of the device is about 18% atthe wavelength of 780 nm, while the simulated value is even higher (28%). Comparedto the transmission-type metaholograms [281], this scheme yields a much higherefficiency and does not require polarization conversion for detection. The workingefficiency can be further improved by introducing more phase levels and reducingthe material losses. For instance, Yifat et al. later demonstrated a high-efficiencyand broadband metahologram at telecommunication wavelength by adopting MIMmeta-atoms with the top structures being patch-dipole nanoantennas [see Fig. 16(d)[283]. Here, each meta-atom consists of two nanostructures (i.e., a nanopatch anda nanodipole), providing more freedom to tailor the reflection coefficients. Viageometric-parameter sweeping, the authors sorted out six different meta-atoms withreflection phases varying from 0° to 360° with a constant step, yet exhibiting quiteuniform and high reflection amplitude, thanks to the expanded design freedom.These meta-atoms were used to construct a metasurface that can generate the samehologram image at two different detecting angles (20° and 45°). Optical measurements


Figure 16

Metaholograms based on (a)–(d) resonance phase or (e)–(h) geometric phase.(a) Schematic of the IR multilayer phase holograms (left) and the reconstructed holo-graphic image of “DUKE” (right panel) [280]. (b) Holographic images of “PURDUE”produced by the metasurface hologram (see inset) illuminated by a 676 nm laser [281].(c) SEM image (left panel) of the metahologram for projecting the polarization-controlled dual images of “NTU” and “RCAS” [282]. (d) Left panel: schematic ofthe structure and experimental concept of the highly efficient and broadband wide-angle hologram projected to an angle θ in the far field [283]. (e) Left panel: hologramstructure and reconstruction procedure for projecting a 3D optical image of a jet. Rightpanel: measured holographic images of a 3D helix at different focal planes [285].(f) Left panel: illustration of the reflective nanorod based high-efficiency metahologram.Right panel: experimentally obtained optical efficiency for both the image and thezeroth-order beam, showing a maximum efficiency of 80% at 825 nm [188]. (g) Helicitymultiplexed hologram composed of two different sets of metasurface patterns, operatingwith opposite incident helicities and merged together with a displacement vector of (d/2,d/2) [286]. (h) Left panel: SEM image of the fabricated high-efficiency broadband di-electric metahologram. Right panel: holographic images covering the visible spectrumwith the input wavelengths being 480, 520, 540, 600, 620, and 640 nm [287].(a) Reprinted with permission from Macmillan Publishing Ltd.: Larouche et al.,Nat. Mater. 11, 450–454 (2012) [280]. Copyright 2012. (b) Reprinted with permissionfrom Macmillan Publishing Ltd.: Ni et al., Nat. Commun. 4, 2807 (2013) [281].Copyright 2013. (c) Reprinted with permission from Chen et al., Nano Lett. 14,225–230 (2014) [282]. Copyright 2014 American Chemical Society. (d) Reprinted withpermission from Yifat et al., Nano Lett. 14, 2485–2490 (2014) [283]. Copyright 2014American Chemical Society. (e) Reprinted with permission from Huang et al.,Nat. Comm. 4, 2808 (2013) [284]. Copyright 2015 American Chemical Society.(f) Reprinted with permission from Macmillan Publishing Ltd.: Zheng et al., Nat.Nanotechnol. 10, 308–312 (2015) [188]. Copyright 2015. (g) Reproduced from[286] under the terms of the Creative Commons Attribution 4.0 License. (h) Devlinet al., Proc. Natl. Acad. Sci. USA 113, 10473–10478 (2016) [287].


demonstrated that the generated holographic image has high fidelity, high efficiency(40%–50%), and works in a wide wavelength range (180 nm).

After the PB mechanism was identified, many groups soon realized metahologramsbased on PB metasurfaces. By using a plasmonic nanobar as a meta-atom, Huanget al. demonstrated the first PB metahologram on which each nanorod is orientatedto achieve the local phase desired for creating 3D holography, as shown in Fig. 16(e)[285]. Note that rotating a nanorod changes only the local phase (without affecting theamplitude) of the transmitted CP light, which is an important advantage of such ascheme. As a proof of concept, the authors designed/fabricated a metahologram en-coding the image of a 3D jet with a size of hundreds of micrometers, at the wavelengthof 810 nm. Under illumination of CP light with the correct spin (RCP light), a 3Dimage was formed, which was carefully captured by a CCD by tuning the distancebetween the sample and objective. In addition, by tuning the observation plane and theangle of view, the authors clearly demonstrated the 3D nature of the formed holo-graphic image experimentally [see Fig. 16(e)]. We should emphasize that only theLCP components of scattered waves can form a real image, dictated by the PB mecha-nism working only for spin-reversed mode (see Subsection 3.2). Interestingly, revers-ing the spin of excitation light may add a minus sign [see Eq. (11)] to the encodedphase profile, which creates a virtual image at the reflection side. Real and virtualimages were successfully observed, located symmetrically on two sides of the sample,as the sample is illuminated by RCP and LCP light, respectively.

However, low efficiency is still a bottleneck issue of PBmetaholograms. In addition, thecreated holographic image in such PB scheme can be “seen” only by spin-sensitivedetectors, while the scattered field with another CP contributes to “background noise,”which is very inconvenient in realistic applications. In a work parallel to Ref. [182],Zhang’s group independently discovered the criterion to make high-efficiency PBmeta-atoms in reflection geometry. They further experimentally demonstrated a PBmetahologram with high efficiency (∼80%) in optical wavelengths [see Fig. 16(f)][188]. The adopted meta-atom is a MIM structure with the top resonator being a simplenanorod, which, upon careful structural optimization, can function as a half-wave plateas desired [see Eq. (12)]. The PCR of the designed PB meta-atom stays at over 80%within a broad wavelength range (550–1000 nm). The authors utilized such a PB meta-atom to construct a hologram that encoded the image of Einstein’s portrait, in which theorientation angles of PB meta-atoms are determined by CGH-calculated phase distri-bution. In contrast to metaholograms based on resonant meta-atoms [280–282], here thelocal phases can be precisely and continuously controlled, an important advantage ofthe PB scheme that also partially explains why it can exhibit high performance.Experiments verified high-efficiency and high-fidelity holographic imaging within awide wavelength range. Wen et al. further experimentally demonstrated helicity-modulated multiplexed holography based on a high-efficiency PB metasurface [286].As shown in Fig. 16(g), the sample was made by two sets of MIM meta-atoms, withorientations independently controlled to encode two different holographic images (i.e., aflower and a bee), for excitation of LCP or RCP light [Fig. 16(g)]. Therefore, the imageprojected can be switched between flower and bee, as the chirality of incident light istuned. Such chirality-multiplexed holography was experimentally verified in the wave-length range of 475–1100 nm, with maximum efficiency reaching 40% at 960 nm.In addition to metallic losses, cross talk between two sets of nanorods is another factorto affect the device’s performance, which is the key issue persisting in all bifunctionaldevices based on such a “merging” concept (see also Subsection 4.5).

However, the high-efficiency metaholograms mentioned above are all for reflectiongeometry, which is sometimes inconvenient for realistic applications. To realize


high-efficiency metaholograms in transmission geometry, we need to first designa transmissive PB meta-atom exhibiting a high PCR, which is, unfortunately,not an easy task, particularly at optical frequencies when using plasmonic metals(see Subsection 3.2). Meanwhile, researchers have found that dielectric meta-atomscan exhibit high working efficiencies at optical frequencies. In 2016, Capasso’s groupreported a high-performance dielectric PB metahologram working at visible wave-lengths [287] soon after their seminal work on dielectric metalenses [257]. The build-ing block is essentially the same high-aspect-ratio TiO2 nanofin, which, owing to itsgeometric anisotropy and wavelength-scale height, can generate a phase difference ofπ for waves passing through it with two orthogonal polarizations. Three metaholo-grams were designed and fabricated, working at wavelengths of 480, 532 and 660 nm[Fig. 16(h)]. The maximum working efficiencies of these devices are measured as82%, 81%, and 78%, respectively, which is quite remarkable.

With physical mechanisms clearly established, researchers continued to explore moreapplications of metaholograms. Huang et al. reported a plasmonic metahologram thatcan reconstruct a multicolor image under the illuminations of white light [285]. Toensure the device worked in the whole visible regime, the authors purposely selectedaluminum, which has an exceptionally high plasmon frequency, as the material tobuild the metahologram. The device consists of three different sets of nanoantennasthat carry desired phase distributions responsible for holographic images in the threeprimary colors. Wavelength-dependent diffractions are utilized to project images withdifferent colors to specific locations. Soon, Wan et al. fabricated a plasmonic metasur-face composed of subwavelength nanoslits and demonstrated that it can construct 2Dand 3D full color images [288]. Wavelength-multiplexed metasurface holograms withboth amplitude and phase modulations can faithfully produce not only the three primarycolors, but also their secondary colors. Full-color holographic images were successfullyreconstructed, but with relatively low efficiencies (∼2%) caused by the low transmissionthrough the subwavelength nanoslits. Deng et al. proposed a diatomic metasurface toachieve vectorial optical metaholograms [289]. The building block is based on an MIMtrilayer design consisting of two orthogonal silver nanorods. Both the spatial displace-ment and orientation angle of the two nanorods in each metamolecule are modified forachieving full and dispersionless phase and polarization control. Active reconstructionof vectorial holographic images was experimentally demonstrated, and was found to berobust against both incident angles and wavelengths. Recently, Yue et al. extended themetahologram concept to use Sb2TE3 (a topological insulator material) to build a 60 nmthick metahologram [290]. Since Sb2TE3 thin film has different refractive indices at thesurface and in the bulk, it can serve as an intrinsic cavity for large phase tuning throughmultiple reflections. Such mechanism explains why Sb2TE3-based metaholograms canwork in the deep-subwavelength scale. The fast development of this field [291] hasopened up a new direction for complicated wavefront control, which has great potentialin future applications.

We believe that metasurfaces can potentially be very useful in display applications inthe future, based on the promising progress already achieved on metaholograms.However, many practical issues (cost, tuning speed, mechanical stability, etc.) needto be addressed from the application point of view, before such technologies and prod-ucts can finally be accepted by the industry.

4.3. Metasurface-Based CloakingRendering an object invisible to external observers is always fascinating and has im-portant applications in practice. Such a goal can be achieved if the object is surroundedor covered by an invisible cloak that can redirect impinging light to the desired di-rections, as if the object does not exist for an observer in the far field. Obviously, such


a cloak cannot be made by natural materials that exhibit very limited capabilities tocontrol light. In 2006, Pendry [5] and Leonhardt [6] independently proposed a frame-work based on transformation optics (TO) theory to design invisibility cloaks, whichwere soon implemented in different frequency domains [7,292,293]. In a parallel fash-ion, many other schemes were also proposed to achieve invisibility, such as perfectabsorption [55,58,59] and scattering cancellation [294]. However, these schemes havetheir own disadvantages. For example, TO-based cloaks are bulky in size and requirecomplicated metamaterials with extreme EM parameters, and the invisibility achievedby scattering cancellation sensitively depends on the shape of the object being hidden.

Metasurfaces offer a new platform to achieve optical invisibility. In 2013, Zhang et al.proposed a microwave carpet cloak based on a reflective metasurface built with MIMmeta-atoms with H-shaped top structures [295]. The metasurface is placed at a tiltangle θ with respect to the ground plane, below which an object can be hidden[see Fig. 17(a)]. The device is essentially a gradient metasurface with an appropriatereflection-phase gradient so that it can reflect normally incident EM waves back to thenormal direction, according the generalized Snell’s law [160,161,163]. In such a way,an object hidden inside the triangle region below the device cannot be detected byexternal observers, since the reflected wave is identical to that reflected from theground plane. Microwave experiments demonstrated that such a metasurface carpetcloak can work within the frequency band 9.9–10.6 GHz and for incident angles <5°.In principle, the concept of the metasurface-based carpet cloak is quite generic and canbe realized in different frequency domains for objects with arbitrary shapes. In 2015,Ni et al. demonstrated an ultrathin carpet cloak for visible light based on a reflection-type metasurface [296]. As shown in Fig. 17(b), a skin-level conformal metasurfacemade by MIM meta-atoms is used to cloak an arbitrarily shaped object hidden below.By carefully tuning the geometrical parameters, each local part of the metasurface canpossess an appropriate phase gradient that can help reflect normally incident lightback to the normal direction, no matter how this local part is tiled against the groundplane. As a result, the reflected light is the same as that reflected from a flat groundplane so that the object cannot be discovered. The authors performed optical experi-ments to nicely demonstrate the carpet cloaking effect, with several macroscopic 3Dbumps and dents hidden in the region below the cloak. The cloaking effect persistswithin a wide wavelength band (710–810 nm) and for a wide range of incident angles(0–30°). The total thickness of the cloak is only 80 nm (λ∕8), which is a huge ad-vantage of the present scheme. After this work, a series of studies [297,300–306] havebeen conducted to realize polarization-independent, wide-incidence-angle, and/orbroadband carpet cloaks based on metasurfaces. For example, Chen’s group exper-imentally demonstrated a full-polarization arbitrarily-shaped 3D metasurface cloak inthe microwave regime [297], as shown in Fig. 17(c). Both simulations and experi-ments show that such a cloak can completely restore the polarization, amplitude,and phase of input light as if the light was incident on a flat mirror.

Despite great successes achieved along this direction, we note that these metasurface-based cloaks are all in reflection geometry, which makes them inconvenient to imple-ment in certain application scenarios (say, without a ground plane). However, makinga transmissive metasurface cloak is very challenging, as the cloak should not onlyprevent reflection but also redirect the incident wave to pass around the hidden objectwithout touching it. Recently, Chu et al. proposed a new device configuration thatintegrates a transparent gradient metasurface with an ultrathin zero-index material(ZIM) as a cloak working in transmission geometry [298]. The cloaking effect is real-ized through the following three steps, enabled by the metasurfaces and the ZIM[Fig. 17(d)]. First, the gradient metasurface at the device entrance can redirect thelocally incident light to propagate along the normal direction after transmission.


Figure 17

Metasurface based cloaking. (a) An ultrathin directional carpet cloak based on gen-eralized Snell’s law. Left panel: schematic of the directional carpet cloak composed ofmetasurfaces with the whole structure shown in the inset. Right panel: simulated totalelectric field for the tilted metasurface illuminated by a normal incident wave [295].(b) A skin level invisibility cloak for visible light. Left panel: illustration of a metasur-face skin cloak made of nanoantennas covering the arbitrarily shaped object. Rightpanel: simulated scattering electrical field distributions for an object without (top) orwith (bottom) a metasurface skin cloak at normal incidence [296]. (c) Schematic of afull polarization 3D metasurface cloak in THz regime (left panel, whole structure;right panel, building block) [297]. (d) Hybrid invisibility cloak in transmission mode.Left panel: conceptual illustration of the cloak based on the integration of metasur-faces and ZIM. The black lines indicate the ray paths of light and the red arrows in-dicate the flow of electromagnetic flux inside the ZIM. Right panel: electric fielddistribution for the case with the cloaking shell (green rectangle region, experiments;outside region, simulations) [298]. (e) Diffusion-induced cloak with coding metasur-faces. Left panel: schematic of a coding metasurface for achieving THz diffusion (in-set: simulated 3D scattering pattern) in reflection mode. Right panel: measured andsimulated backward reflection spectra of the metasurface [173]. (f) A deterministicapproach to achieving broadband polarization-independent diffusive scatterings.Left panel: three key design steps are (i) design a reflective PB meta-atom with nearly100% efficiency, (ii) form a set of subarrays providing focusing phase profiles but withdifferent initial phases, and (iii) arrange these subarrays based on a certain codingsequence. Inset shows a typical Fourier-transform spectrum of a subarray. Right panel:the wave-diffusion behaviors achieved by such metasurface [299]. (a) Reprinted withpermission from Zhang et al., Appl. Phys. Lett. 103, 151115 (2013) [295]. Copyright2013 AIP Publishing LLC. (b) From Ni et al., Science 349, 1310–1314 (2015) [296].Reprinted with permission from AAAS. (c) Yang et al., Adv. Mater. 28, 6866–6871(2016) [297]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced withpermission. (d) Reproduced from [298] under the terms of the Creative CommonsAttribution 4.0 License. (e) Reproduced from [172] under the terms of theCreative Commons Attribution NonCommercial-ShareAlike 3.0 Unported License.(f) Reprinted with permission from Xu et al., ACS Photon. 5, 1691–1702 (2018)[299]. Copyright 2018 American Chemical Society.


Second, the ZIM is designed such that it can redirect any normally incident light toflow around it, due to the wave-tunneling effect [307]. Finally, the tunneled wave isthen bent back to the original direction after passing through the metasurface at theexit side. This way, the incident wave can never touch the central region, where anarbitrary object can be hidden, and pass through the whole device as if the hiddenobject does not exist at all. The authors first numerically validated such idea basedon an effective-medium model system. They next designed and fabricated a ZIMbased on a photonic crystal with a Dirac-cone-like dispersion following Ref. [308],and a transparent gradient metasurface based on ABA meta-atoms that exhibits aphase gradient to refract a normally incident wave to an angle 45° after transmissionfollowing Ref. [201], both working at the frequency of 10.2 GHz. Figure 17(d) depictsthe electric field distribution inside the rhombic cloak device illuminated by a planewave at 10.2 GHz, verifying the nice EM wave cloaking effect. While this work pro-vides a new concept for realizing skin-level cloak devices in transmission geometry,many problems need to be solved in future studies. For example, although the de-signed metasurface has a subwavelength thickness, the ZIM made of photonic crystalis still bulky, leading to a wavelength-scale hybrid cloak device. Also, the device ex-hibits a limited bandwidth and is quite sensitive to the incidence angle of externalillumination. Such issues can possibly be solved later by employing recently devel-oped coding/programmable metasurfaces [173] or nonlocal metasurfaces [309].

Other mechanisms have also been proposed to achieve invisibility based on metasur-faces. In 2014, Cui’s group proposed a coding metasurface that possesses a signifi-cantly reduced radiation cross section (RCS) for EM waves within a broad frequencyband [173], which is an ideal cover layer to hide an object. As shown in Fig. 17(e), themetasurface is composed by two distinct types of MIM meta-atoms, which are de-signed to have nearly 100% reflection amplitudes, but with reflection phases 0and ≅, denoted as “0” and “1” particles, respectively. By optimizing the arrangingsequences of these two meta-atoms in an N × N lattice, the authors designed a meta-surface that can redirect the normally incident EM wave to many different directionsin 3D space, leading to significant RCS reductions, particularly for specular reflection.The reported device exhibits a −10 dB level RCS reduction within a relatively broadbandwidth (7.8–12 GHz). Such diffusive metasurfaces can be realized with moremeta-atoms exhibiting finely discretized phase levels working in different frequencydomains [172–313]. Despite significant progress achieved in this field, the realizeddiffusive metasurfaces suffer from the following key issues: 1) the RCS reduction isachieved mainly for the specular reflection but not for all directions, and 2) the designprocess involves optimization that is very time-consuming and non-reproducible. Veryrecently, Zhou’s group proposed a deterministic and straightforward method to designdiffusive metasurfaces to achieve full diffusion of incident EM waves to all angles,within an ultrawide frequency band and independent of incident polarization [299].The design strategy consists of three key steps, which are adopted to overcome theissues mentioned above [Fig. 17(f)]. The authors first design an MIM PB meta-atomthat exhibits high-efficiency PCR within an ultrawide band. They then use such ameta-atom to construct a set of subarrays (i.e., bits) that exhibit the same parabolicphase distributions but with different initial phases. Finally, the bits are arranged in anarbitrary coding order to form a diffusive metasurface. The most important improve-ment is that the present design strategy combines the advantages of different mech-anisms, i.e., PB phase, focusing, and coding metasurfaces. Specifically, using a PBmechanism can make the device insensitive to incident LP, while a metalens can nat-urally diffuse an incident EM wave to difficult directions. In addition, adopting anarbitrary coding sequence can further enhance the performance and make the devicecompatible with complex shapes, as requested in practice. The authors performed


extensive numerical and experimental studies to demonstrate the robustness of theirnewly proposed approach. In particular, their experiments show that a metasurfacedesigned with such an approach can reduce the RCS for all directions by more than10 dB within an ultrawide band (6–18 GHz) for incident EM waves with arbitrarypolarizations. Recently, Liu et al. proposed a new approach for designing externalcloaks through combining a surface admittance approach and a TO approach withcomplementary media as a seed simulation. The metadevice can hide an object ontop of a reflective metasurface, mimicking a flat mirror, which is similar to a TO-basedexternal cloak that uses a negative index medium to cancel out the scattering field ofthe object. Here, a metasurface is used to replace the negative index medium [314].

Except for EM cloaking, conformal metasurfaces can be utilized to achieve other fas-cinating physical effects, which form important research directions [315–320]. For in-stance, Faraon’s group proposed to decouple the optical properties of an object from itsphysical shape by capping a thin and flexible metasurface on the object conformally.Such a conformal metadevice is composed of silicon nanoposts embedded in a polymersubstrate that are able to tailor the local wavefront of impinging light. As a proof ofconcept, the authors experimentally demonstrated that a cylindrical lens covered with acarefully designed conformal metasurface can effectively function as a spherical lens[315]. Recently, Genevet’s group proposed the concept of “conformal boundary optics,”which is an analytical method based on first-principle derivation that can help tailor thereflection and transmission fields at will. For any given object, one can use the devel-oped theory to design an appropriate metacoating to cover it, in order to achieve thedesired optical effects, such as anomalous diffraction and optical illusion [316].Moreover, conformal metasurfaces can also be employed to realize even more complexfunctionalities, such as displays [317] and holograms [318,319].

4.4. Special Beam GenerationBeams with special patterns (e.g., vortex beams, Bessel beams, vector beams) can findmany applications in applied optics, but conventional devices to generate them (e.g.,spiral phase plates and light modulators) are either too bulky and/or have low efficien-cies, which makes them unfavorable for integration-optics applications. Metasurfacesprovide new opportunities to design optical devices to generate these special beams.These devices are flat and of subwavelength sizes, which may find important applica-tions in integration optics. In this subsection, we briefly review the development alongthis direction.

4.4a. Vortex Beam Generation

The field profile of a vortex beam can be simply described by ~E�~r� �~E0 exp�−ikz� exp�−imφ�, with k being the wavevector in a background medium.Because of the azimuthally dependent phase factor exp�imφ�, a vortex beam can carryan optical angular momentum (OAM) with a topological charge m�� 0, �1,�2,…� and, hence, can increase the channels for information communication. In ad-dition, the doughnut-like intensity profile of vortex beams is highly desired for nu-merous applications, such as stimulated emission depletion microscopy [321] andoptical tweezers [322].

Along with their pioneering work on establishing the generalized Snell’s law, Yu et al.[160] and Genevet et al. [323] already utilized V-shaped nanoantennas to build meta-surfaces that serve as optical vortex beam generators. As shown in Fig. 18(a), the fab-ricated device consists of eight different types of V-shaped antennas that can scatter lightwith different phases, arranged in different azimuthal angle regimes, to finally create aspiral-like phase profile on the metasurface. As incident light strikes the metasurface,light transmitted through different local parts can gain phases, and the interference


Figure 18

Special beam generation with metasurfaces. (a) Plasmonic optical vortex plate based on ametasurface. Left panel: SEM image of such metasurface. Right panel: measured vortexpatterns created by the interference of the vortex beam and a co-propagating Gaussian beam[323]. (b) Vortex beam generator based on a plasmonic waveguide. Top panel: schematic ofa nanowaveguide array that induces a vortex wavefront. Bottom: SEM picture of the fab-ricated nanowaveguide array (left panel) and the spiral interference pattern for a LP illu-mination case (right panel) [324]. (c) Vortex beam generation based on a PB metasurface(left panel, SEM image of the sample; right panel, measured field patterns of the vortexbeams for different wavelengths [181]. (d) Left panel: schematic of an aberration-free ultra-thin flat axicon for generating Bessel beams at telecomwavelengths. Right panel: measuredfield patterns along the main-axis plane of the generated Bessel beam [325]. (e) Catenarynanostructures for Bessel beam generation. Sketch of the Bessel beam generators for l � 2

and 3with the measured interference patterns depicted in the insets [326]. (f) The plasmonicmetasurface (right panel) used to generate radially polarized beams combines subwave-length apertures for polarization control (left panel) and wavelength-scale diffracting aper-tures (middle panel) [327]. (g) Schematic of a high-efficiency anisotropic Huygens’metasurface for converting a circularly polarized Gaussian beam into a vector Bessel beam[328]. (h) Left panel: schematic of vector vortex beam generation through a single metasur-face. Right panel: polarization and phase distributions of the normal mode (bottom panel),anomalous mode (middle panel), and the interfered vector vortex beam (top panel). Theanomalous mode has the same circular polarization as that of the incident beam and a spiralphase changewith the topological charge of 2, while the normal mode has opposite helicitybut no phase change, upon illumination by RCP light. The interference of two modes givesrise to radial polarization distribution with the topological charge of l � 1 [329].(a) Reprinted with permission from Genevet et al., Appl. Phys. Lett. 100, 013101(2012) [323]. Copyright 2012 AIP Publishing LLC. (b) Reprinted with permission fromSun et al., Nano Lett. 14, 2726–2729 (2014) [324]. Copyright 2014 American ChemicalSociety. (c) Reprinted with permission fromHuang et al., Nano Lett. 12, 5750–5755 (2012)[181]. Copyright 2012 American Chemical Society. (d) Reprinted with permission fromAieta et al., Nano Lett. 12, 4932–4936 (2012) [325]. Copyright 2012 American ChemicalSociety. (e) Reproduced from [326] under the terms of the Creative Commons Attribution4.0 License. (f) Reprinted with permission from Lin et al., Nano Lett. 13, 4269–4274(2013) [327]. Copyright 2013 American Chemical Society. (g) Figure 1 reprinted withpermission from Pfeiffer and Grbic, Phys. Rev. Appl. 2, 044012 (2014) [328]. Copyright2014 by the American Physical Society. https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.2.044012. (h) Reprinted with permission from Yue et al., ACS Photon. 3,1558–1563 (2016) [329]. Copyright 2016 American Chemical Society.









among them can generate a vortex beam with a topological charge of m � 1. In theirexperiments, the authors utilized a co-propagating Gaussian beam to interfere with thetransmitted beam, generating a spiral-like interference pattern [see Fig. 18(a)], which isdirect evidence of vortex beam generation. In 2014, Sun et al. proposed a differentmetasurface to generate a vortex beam [Fig. 18(b)] [324]. The device is a plasmonicmetal drilled with circular nanowaveguides with appropriate sizes located at differentazimuthal positions on a circle. By varying the radii of the waveguides, the authors canprecisely control the phases of light transmitted through the apertures to make themfollow the equation eimϕ, thus providing an OAM to the incident light. An optical vortexbeam was produced experimentally at the wavelength of 532 nm. The structural sym-metry guarantees that the present OAM generator is polarization independent, which ishighly desired in applications.

PB metasurfaces can generate spin-polarized vortex beams with both spin and orbitalmomentum. In 2012, Huang et al. fabricated a PB metasurface to generate an opticalvortex beam [181]. A helical phase front carrying an OAM can be produced uponillumination by a normally incident CP Gaussian beam. Thanks to the non-dispersivenature of the geometric phase, the metasurface can work within a broad band rangingfrom the visible to NIR regimes, as shown in Fig. 18(c). Similar vortex beam generatorsbased on different PB meta-atoms were subsequently proposed in various frequencydomains [330,331]. Since most PB metasurfaces are constructed by meta-atoms witha finite number of orientations, they can provide discretized phase shifts only for theinput light, which limits the performance of vortex beam generation. To solve this issue,scientists proposed certain plasmonic structures that can provide phase shift continu-ously in space to generate optical vortices with better qualities. For example, Chimentoet al. proposed a vortex generator that is a metal film etched with a circular subwave-length nanoslit [332]. Upon illumination with CP light, a straight slit allows only LPlight with a particular polarization to pass through, thus acting as an effective quarter-wave plate. Thanks to the circular configuration, the orientation of the local wave platechanges from 0 to 2π along the curved slit, thus providing a phase of the form e�i2ϕ,which helps generate vortex beams with topological charges �2. Based on similarstructures, Guo et al. proposed to utilize another freedom, i.e., the local aperture’s width,to provide an additional continuous phase shift to the incident light, resulting in vortexbeams with integer or fractional topological charges [333].

However, these PB devices all exhibit very low efficiencies, since their PB meta-atomscan support both normal and anomalous modes. As a result, the desired anomalousOAM pattern may interfere with the undesired normal mode, causing the vortex beamsto blur. To enhance the working efficiency, Yang et al. used a high-index silicon nano-wire on a silver ground plane as a PB meta-atom to build vortex generators [174].Their experiments demonstrated that such dielectric vortex beam generators, with sig-nificantly reduced ohmic losses, do show enhanced working efficiencies within thewavelength range of 1500–1600 nm. The efficiency can be further enhanced by care-fully designing the PB meta-atom following the criterion of Eq. (13). Indeed, usingthe ABA-type PB meta-atom designed according to Ref. [25], Luo et al. fabricatedthree transmissive vortex beam generators, and experimentally demonstrated their ex-cellent ability to generate vortex beams with topological charges m � 1, 2, 3 at10.5 GHz [183]. Field-mapping measurements demonstrated pure OAM beam pat-terns immune from normal background interference, with a maximum efficiencyof ∼91%. Lu et al. experimentally demonstrated a broadband high-efficiency opticalvortex beam generator in the visible regime. A systematic study based on Jones matrixanalysis and full wave simulations reveals the relationship between the conversionefficiency and the antenna nature, enabling the realization of a high-performancedevice [334].


4.4b. Bessel Beam Generation

Bessel beams are a special type of EM radiation with transverse field amplitudes de-scribed by Bessel functions of the first kind. In cylindrical coordinates, we can describea Bessel beam by E�r,ϕ, z� � A · exp�−ikzz� · Jn�krr� · exp��imϕ�, where kz, kr arethe longitudinal and transverse wavevectors, respectively, and m is the order of theBessel function. It is clear that the amplitude of an ideal Bessel beam is independentof z, revealing its non-diffraction property. In addition, high-order Bessel beams cancarry OAMs determined by the mode order m. The non-diffraction property meansBessel beams have numerous applications in practice, such as particle trapping,near-field probing, and photolithography [335–338]. In traditional approaches, one usescertain devices (such as an annular slit [339] and axicon lens [340]) to diffract or refractthe impinging light symmetrically to the main axis, generating the desired Bessel beamsthrough interference. However, such devices are bulky and of low efficiency.

In 2012, Aieta et al. proposed to use V-shaped meta-atoms to construct a Bessel beamgenerator at the telecommunication wavelength [325]. As shown in Fig. 18(d), thedevice is essentially a flat version of an axicon with a linearly increasing phase dis-tribution along the radial direction. Specifically, the metasurface is designed to possess

a phase distributionΦ�x, y� � 2πλ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2 � y2

psin β, with β being the angle of the axicon.

Optical measurements clearly revealed a centimeter-scale non-diffraction field patternalong the propagation direction generated by such a flat meta-axicon. However, such adevice has a low working efficiency (about 1%). Many different Bessel beam gen-erators were subsequently proposed. For example, Li et al. proposed a compact cat-enary-shaped nanostructure as a Bessel beam generator [326]. As shown in Fig. 18(e),such a nanoarray behaves like a grating structure with a period p, which determines theradial wavevector kr � 2π∕p of the Bessel beam. By arranging the nanostructure intoa ring or spiral shape, such metasurfaces can generate second-order or third-orderBessel beams, as depicted in Fig. 18(e). Bessel beams with different orders were ex-perimentally created within a broad frequency band.

Much effort has also been devoted to increasing the efficiency of Bessel beam gen-eration [341–343]. Recently, Wang et al. designed and fabricated an ultrathin (λ∕6)transmissive PB metasurface, constructed with the high-efficiency ABA-type PBmeta-atom designed following the criterion in Eq. (13). The authors experimentallydemonstrated that this metasurface can generate spin-polarized Bessel beams at a fre-quency window of 10.7–12.3 GHz [341]. The measured maximum efficiency of thedevice reaches 91%, in consistency with the simulated result (∼92%). The self-healingproperties of the generated Bessel beam were well demonstrated in experiments with ametallic object purposely put on the propagation path of the beam. In the visible re-gime, Khorasaninejad et al. fabricated a dielectric PB meta-axicon based on similarTiO2 meta-atoms adopted in constructing metalenses [257], and experimentally dem-onstrated its capability of generating spin-polarized Bessel beams [344]. Thanks to thehigh NA (about 0.9) of the fabricated metasurface, the full width at half-maximum ofthe generated zeroth-order and first-order Bessel beams are as small as ∼160 and130 nm at the central wavelength λ � 405 nm, with diffraction-free field patternsmaintaining for a large distance (150λ). Bessel beam generators can also be integratedwith other functional devices. For instance, Mehmood et al. proposed to combine twodistinct functional devices, i.e., a lens and a spiral phase plate, into a single metasur-face that can generate Bessel beams with different topological charges focused atdistinct focal planes [342].

4.4c. Vector Beam Generation

Polarization, an important characteristic of light wave, plays a vital role in light–matterinteraction. Such a degree of freedom has been widely used in many applications, such


as optical detection, displays, and data storage. Different from special beams thatpossess uniform polarization, vector beams—optical beams with spatially variantpolarizations—exhibit expanded degrees of freedom, making them useful in manyapplications. Recently, much effort has been devoted to designing metasurfacesfor generating vector beams, which will be briefly summarized in the following.

In 2013, Lin et al. reported a metadevice to achieve broadband manipulation of vectorbeams [327]. As shown in Fig. 18(f), such a device consists of a radial polarizer andfork diffraction hologram. Here, the radial polarizer can convert input CP light toradially polarized light with an additional spiral phase exp�iθ�, while the fork holo-gram can diffract an incident CP Gaussian beam to a vortex beam with an oppositespiral phase exp�−iθ�. The whole device can thus be regarded as a combination of twoindependent structures, owing to their very different length scales, that cooperativelygenerate the desired radially polarized beams. The fabricated sample was tested at twodifferent wavelengths (633 and 850 nm), exhibiting a conversion efficiency of 3.9%.Vectorial Bessel beams can also be generated with a single device. For instance,Pfeiffer et al. proposed a multilayer metasurface to efficiently generate a vectorialBessel beam in transmission mode [see Fig. 18(g)] [328]. The adopted meta-atomconsists of three cascaded anisotropic sheets that can manipulate the polarizationand phase profiles simultaneously. Owing to the air-matched impedance, the effi-ciency of the device is very high. Two different metasurfaces were demonstrated ex-perimentally to transform linearly and circularly polarized Gaussian beams tovectorial Bessel beams at a frequency of 9.9 GHz [328]. Based on the PB mechanism,Yue et al. proposed to realize a single plasmonic PB metasurface to generate vectorialvortex beams [329]. Since the adopted MIM meta-atom is not an ideal half-wave plate(see Subsection 3.2), the device can generate both the desired anomalous mode andthe undesired normal one, which may affect the final performance of the beam gen-eration. As shown in Fig. 18(h), the resultant beam transmitted through the PB meta-surface is a superposition of the co-polarized normal reflection mode with a phase of0 and the cross-polarized anomalous reflection mode with a PB phase of exp�i2φ�,giving rise to a radially polarized l � 1 vortex beam with spiral phase of exp�iφ�.Finally, we would like to mention that metasurfaces also provide an ideal platform togenerate other types of optical beams, such as Airy beams. These receive intensiveresearch interest because of their unique properties, which include that they are self-accelerating, diffraction-free, and self-healing. Recently, various types of Airy beams,such as plasmonic Airy beams, Airy vortices, and vector beams, have been generatedbased on plasmonic metasurfaces [345–348], which will not be discussed in detaildue to the space limitation of this review.

4.5. Multifunctional MetasurfacesFacing increasing demands on the speed and memory of EM devices, EM integration ishighly desired in modern science and technology. Metasurfaces are ideal candidates tointegrate multiple diversified functionalities into single devices with deep-subwavelengththickness and high efficiencies [349]. Various approaches have recently been proposed toachieve this goal, which will be briefly summarized in this subsection.

Polarization is one important degree of freedom that can be used to realize multifunc-tional metadevices. Based on anisotropic meta-atoms with polarization-sensitive EMresponses, various metadevices were realized at different frequencies, exhibiting multi-ple functionalities triggered by incident EM waves with different LPs [350–356]. In2014, Chen et al. experimentally demonstrated a metahologram based on anisotropicMIM meta-atoms for achieving polarization-modulated dual holographic images [282].However, the device still exhibits similar functionalities (e.g., hologram) for two


incident polarizations. In 2016, Cai et al. proposed a general strategy to design bifunc-tional metadevices that exhibit distinct functionalities with very high efficiencies [350].They demonstrated two microwave bifunctional metadevices, working in transmissionand reflection geometries, respectively, each exhibiting two distinct functionalities [e.g.,focusing and beam bending (or even PW-SW conversion)] with very high efficiencies(90% and 72% for reflection and transmission geometries). The adopted meta-atoms areMIM (reflection) and multilayer structures (transmission), both exhibiting anisotropicshapes and thus polarization-dependent responses. Very recently, Ding et al. extendedsuch a concept to the optical regime, demonstrating a bifunctional reflective metadevicethat can achieve two distinct functionalities (surface plasmon excitation and beam steer-ing) as being excited by incident lights with two orthogonal polarizations. The deviceworks in a broad band (580–700 nm) and is constructed by anisotropic MIM meta-atoms [see Fig. 19(a)] [352]. In addition to using multilayer meta-atoms, one can alsoadopt Huygens’ meta-atom and dielectric meta-atoms to construct transmissive multi-functional metadevices. For instance, Arbabi et al. experimentally demonstrated thatdielectric metasurfaces constructed by silicon elliptical nanoposts are the ideal platformto design bifunctional metadevices achieving high-efficiency (>72%) polarization-switchable functionalities (imaging, hologram, etc.) in the NIR regime [218].However, the above-mentioned metadevices work either in pure reflection or pure trans-mission mode, leaving half of the EM space completely unexplored. To expand thewave manipulation capabilities of metasurfaces, Zhou’s group recently proposed a newtype of multifunctional metasurface to manipulate EM waves in the full space [351].The key improvement is that the designed meta-atoms, consisting of carefully designedmultilayers of metastructures so that the whole system can be perfectly transparent orreflective for two polarizations. Using these unique meta-atoms, the authors fabricatedseveral bifunctional microwave metadevices, and experimentally demonstrated thatthese devices can manipulate EM waves with different functionalities at two sides ofthe metasurface with very high efficiencies (>85%). As shown in Fig. 19(b), one fab-ricated metadevice can achieve anomalous reflection for an x-polarized incident wave,and can focus the incident EMwave at the transmission side as the polarization directionchanges to the y direction. Employing the same idea, Zhang et al. experimentally dem-onstrated that a single microwave metasurface can exhibit three different functionalities(beam bending, reducing the radar cross section, and vortex beam generation) and con-trol transmitted and reflected wavefronts simultaneously [363].

Helicity is another degree of freedom frequently exploited to design multifunctionalmetadevices based on the PB mechanism [357–359,364–368]. A commonly appliedscheme is to merge several different PB metasurfaces, each exhibiting a certain func-tionality as the incident CP light takes a particular helicity, into one single device[365,366]. Although such “merging” strategy is physically straightforward, realized de-vices exhibit limited working efficiencies and suffer from the issue of functionality crosstalk. In 2015, Huang et al. proposed to use PB metasurfaces to record various hologrampatterns into helicity-multiplexing channels, as shown in Fig. 19(c) [357]. Although abroadband hologram ranging from 633 to 1000 nm was experimentally achieved, themeasured working efficiency was only 4.5% at 810 nm (0.65% at 1000 nm). Recently,Hasman’s group experimentally demonstrated that the alliance of spin-enabled geomet-ric phase and shared-aperture concepts can open a new pathway to implement photonicspin-controlled multifunctional metasurfaces [358,368,369]. Helicity-controlled multi-ple wavefronts such as vortex beams carrying different OAMs, were demonstrated in thevisible regime (780 nm), as shown in Fig. 19(d) [358]. In 2017, Mueller et al. proposeda new approach that combines geometric and propagating phases to encode arbitraryphase profiles on any two orthogonal polarization states (linear, circular, or elliptical),and experimentally demonstrated chiral holograms based on transmissive dielectric


Figure 19

Multifunctional metasurfaces. (a) Bifunctional gap-plasmon metasurfaces for visible light:polarization-controlled unidirectional surface plasmon excitation and beam steering atnormal incidence. Left panel: schematic of the working principle of this metadevice.Right panel: measured coupling efficiencies of SPP and extinction ratio with an optimallypositioned incident laser beam. Inset: SEM photo of the fabricated sample [352].(b) Polarization-dependent high-efficiency bifunctional metasurfaces for full-space EMwavefront manipulation. Left panel: measured reflected beam distribution for an x-polarizedwave. Right panel: measured field distribution of transmitted focused beam for y-polarizedwave. Inset: schematic of one particular meta-atom design [351]. (c) Schematic illustrationof the hybrid multiplexing holograph based on PB metasurfaces 357]. (d) Schematic of PBmetasurfaces combined with shared-aperture concepts for multifunctional helicity-controlled wavefront manipulation [358]. (e) Experimental demonstration of chiral holo-grams realized with a single metasurface encoding two independent hologram phaseprofiles for left (dog) and right (cat) circular polarization at 532 nm. Inset: SEM photo offabricated metasurfaces [359]. (f) Multicolor 3D metaholography by broadband plasmonicmodulation. Left panel: schematic diagram of the off-axis illumination method for a meta-hologram with unit cell design. Right panel: seven-color metaholography [360]. (g). Rightpanel: wavelength-multiplexed metasurfaces for achromatic and dispersive holograms. Leftpanel: SEM image of the fabricated metadevice and schematics of multiplexed meta-atoms[361]. (h) Angle-multiplexed metasurfaces for independent wavefront control under differ-ent incident angles. Left panel: SEM photo of fabricated metasurfaces and schematics ofdielectric U-shaped meta-atoms. Right panel: schematics of measurement setups under nor-mal and 30° illumination angles for angle-multiplexed holograms [362]. (a) Reproducedfrom [352] under the terms of the Creative Commons Attribution 4.0 License.(b) Figures 2 and 7 reprinted with permission from Cai et al., Phys. Rev. Appl. 8, 034033(2017) [351]. Copyright 2017 by the American Physical Society. https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.8.034033. (c) Huang et al., Adv. Mater. 27,6444–6449 (2015) [357]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA.Reproduced with permission. (d) From Maguid et al., Science 352, 1202–1206 (2016)[358]. Reprinted with permission from AAAS. (e) Figure 2 reprinted with permission fromBalthasar Mueller et al., Phys. Rev. Lett. 118, 113901 (2017) [359]. Copyright 2017 bythe American Physical Society. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.113901. (f) From Li et al., Sci. Adv. 2, e1601102 (2016) [360]. Reprinted with per-mission fromAAAS. (g) Reprinted with permission fromWang et al., Nano Lett. 16, 5235–5240 (2016) [361]. Copyright 2016 American Chemical Society. (h) Reproduced from[362] under the terms of the Creative Commons Attribution 4.0 International License.











metasurfaces, which can efficiently generate independent far-field images for RCP andLCP excitations at λ � 532 nm [see Fig. 19(e)] [359].

Wavelength multiplexing is also widely exploited to realize multifunctional metasur-faces. In 2016, Li et al. proposed an approach to realize multicolor metaholographywith a single type of plasmonic pixel, based on an off-axis illumination method [360].As shown in Fig. 19(f), a seven-color metahologram with remarkable image qualitywas experimentally demonstrated in the optical regime, as well as multicolor 3D meta-holography. In a parallel line, dielectric metasurfaces are used to build high-efficiencywavelength-multiplexing metadevices at optical frequencies. As shown in Fig. 19(g),Wang et al. experimentally demonstrated that a metasurface formed by three kinds ofsilicon nanoblocks multiplexed in a subwavelength super-unit can achieve wavefrontmanipulations for red, green, and blue light, simultaneously [361]. Again, the exper-imentally achieved efficiencies of the reconstructed images for highly dispersive colorholograms are limited due to the intrinsic issue of the “merging” concept.

Recently, incidence angle was found to be another degree of freedom that has not yetbeen fully exploited. In 2017, Kamali et al. proposed an angle-multiplexed metasurfacecomposed of reflective high dielectric contrast U-shaped meta-atoms with incidence-angle-sensitive responses, and experimentally demonstrated that it can realize high-efficiency angle-multiplexed diffractions and holograms at the working wavelengthof 915 nm, as shown in Fig. 19(h) [362]. Very recently, Zhou’s group established atheory to quantitatively describe the angular dispersion behaviors in metasurfaces [370]and experimentally demonstrated that the angular dispersion is dictated by the plas-monic coupling among meta-atoms inside metasystems. Via “designing” the plasmoniccouplings within particles inside composite meta-atoms, the authors proposed a newstrategy to design metadevices that exhibit incidence-angle-dependent multifunctional-ities, which can possibly stimulate many experimental realizations in the future.

4.6. Tunable/Active Inhomogeneous MetasurfacesThe fascinating effects described above are all based on passive metasurfaces, whichcannot be changed once the metasurfaces are fabricated. In practical applications, itis highly desired to achieve dynamically tunable manipulation of EM waves. InSubsection 2.4, we have summarized the available schemes to dynamically tune theEM properties of homogeneous metasurfaces in which meta-atoms are controlled uni-formly.With the fast developments on inhomogeneous metasurfaces, one can now utilizethose schemes to independently control the EM properties of individual meta-atoms ininhomogeneous metasurfaces, thus equipping metadevices with the capabilities todynamically control EM waves, yielding fascinating applications, such as beam steeringand programmable holograms and imaging. This is, however, highly challenging, par-ticularly for frequencies higher than THz. In this subsection, we briefly introduce recentefforts devoted to this field, focusing on both the achievements and challenges.

In the microwave regime, a frequently adopted scheme is to incorporate voltage-drivenelements such as diodes and varactors into the meta-atom design. By assembling thesemeta-atoms to form a metasurface, each meta-atom can be efficiently and independentlytuned by the diode/varactor inside its structure, thus offering the whole device desireddynamical wave-manipulation functionalities. Much fascinating progress has beenachieved based on such a scheme [371–376]. In 2012, Shadrivov et al. realized a micro-wave light-tunable metadevice, which consists of arrays of broadside-coupled SRRs,each loaded with a varactor diode connected with a light emitting diode (LED) [371].By reconfiguring the LED pattern with external light radiation, the authors can indi-vidually control the voltages supplied to different varactor diodes, which, in turn,dynamically modulates the responses of those different meta-atoms in the device, finally


resulting in active switching between focusing and defocusing functionality for the fab-ricated device [see Fig. 20(a)]. Recently, to solve the issue of the chromatic response ofall metadevices based on resonant mechanisms, Xu et al. proposed to make tunablemetadevices in which the dispersion-induced phase distortion in each meta-atom is pre-cisely rectified by changing the individual external voltage imparted on the varactordiode incorporated in that very meta-atom. A tunable gradient metasurface exhibitingsingle-mode high-efficiency operation within a wide frequency band was experimen-tally demonstrated in the microwave regime, as well as a metadevice exhibiting dynami-cally switchable functionality from a specular reflector to a surface wave convertor[372]. Based on such an approach, the authors further experimentally demonstrateda tunable microwave metalens that can exhibit aberration-free focusing or dynamicallyswitchable focusing performance depending on the gating voltages applied, as shown inFig. 20(b) [373]. These metadevices are all based on reflection geometry and are rel-atively easy to realize since one needs to consider only the phase tuning in practicaldesigns. Meanwhile, metadevices working in transmission mode are more difficult tomake, as they require precise control of both amplitude and phase of locally transmittedwaves. More recently, Feng’s group experimentally demonstrated a reconfigurableHuygens’ metalens working at 6.9 GHz, which exhibits controllable multiple and com-plex focal spots by reprogramming the input voltages applied on the loaded dipoles, asshown in Fig. 20(c). The experimentally achieved focusing efficiency is about 36%,with a modulation speed reaching the order of 105 switches∕s [374]. In a parallel line,Cui’s group also demonstrated a series of reprogrammable microwave metasurfaces toachieve different EM wave manipulations [375,376]. Figure 20(d) illustrates one fab-ricated device that which can achieve multiple holographic images in real time throughdynamically tuning the voltages applied on loaded diodes [375]. Recently, microfluidicstechnology has also been widely used to achieve tunable microwave metadevices, suchas tunable metalenses [377], dynamic beam deflectors [145], and tunable polarizationconvertors [382]. In 2015, Zhu et al. experimentally demonstrated a reconfigurablemetadevice formed by casting microwave resonators through microfluidic channels,which exhibits dynamically switchable focusing functionalities [see Fig. 20(e)], asthe EM responses of those resonators were continuously and individually tuned bymicrofluidic technology [377].

However, these techniques are difficult to implement at frequencies higher than GHz, asno voltage-driven elements work at those frequencies. Much effort has been devoted toexploring new tuning techniques in both the THz and optical regimes, thanks to rapidadvances in nanofabrication and material sciences. In 2014, Watts et al. experimentallydemonstrated THz compressive imaging based on a metadevice that consisted of 8 × 8

dynamic, polarization-sensitive metaspatial light modulators (SLMs). As shown inFig. 20(f), each meta-SLM is essentially an MIMmeta-atom incorporated with n-dopedGaAs whose absorption can be actively controlled by the applied voltage. The individ-ual and dynamic control on each pixel makes such metadevice function as a real-timespatial mask for THz radiation [378]. In 2016, Wang et al. proposed a novel approach torealize reconfigurable optical devices based on phase-change materials (Ge–Sb–Te) byinducing a refractive-index-changing phase transition with a diffraction-limited opticalwriting process. Avariety of reversible devices were experimentally demonstrated, suchas reconfigurable bichromatic and multifocus Fresnel zone plates for visible light and agray-scale hologram [see in Fig. 20(g)]- [379]. In a parallel line, Huang et al. exper-imentally demonstrated an electrically tunable MIMmetasurface that allows both phase(184°) and amplitude (30%) modulation on the reflected beam at telecommunicationwavelength. The tunability arises from the field-effect modulation on the refraction in-dex of conducting oxide layers incorporated into MIM metasurfaces. In addition, theyalso experimentally demonstrated a dynamically controlled diffraction effect through


Figure 20

Inhomogeneous tunable metasurfaces. (a) Illustration of light-tunable metamaterials.EM wave incident on a metamaterial is reflected at different angles depending on thecontrol light illumination [371]. (b) Aberration-free and functionality-switchablemicrowave metalenses. Top panel: picture of a fabricated microwave metalens sampleand schematics of a tunable meta-atom. Bottom panel: experimental results ofachieved metalens with tunable focus length at 5.5 GHz [373]. (c) ReconfigurableHuygens’ metalens and characteristics of a meta-atom. Left panel: active Huygens’metalens for dynamic EM wave focusing, of which meta-atoms are biased bycomputer-controlled multichannel DC voltage sources. Right panel: capacitance-dependent phase and amplitude responses of the tunable meta-atom for the transmittedEM wave at 6.9 GHz [374]. (d) EM reprogrammable coding-metasurface hologramsin the microwave regime. The metasurface is formed by an array of meta-atoms in-tegrated with a PIN diode independently controlled by a DC voltage. A computerdigitally controls the metasurface by dynamically changing the phase distributionfor holograms 1, 2, 3,…. Under the illumination of a feeding antenna, the metasurfacehologram can successively project the holographic images (frames 1, 2, 3, …) at theimaging plane [375]. (e) Microwave metalens with switchable focal length achievedwith random access reconfigurable metamaterial formed by loading liquid metal intothe ring microcavities based on microfluidic technology. Bottom panel: fabricatedsample with schematics of a microcavity filled with liquid metal. Inset: measured fieldpatter of the focusing effect realized [377]. (f) THz SLM with 8 × 8 pixels with indi-vidual voltage bias for compressive imaging. Frequency-dependent absorption ofa single pixel (referenced to a gold mirror) for two bias voltages of 0 and 15 V.Inset: photograph of the SLM [378]. (g) Optically reconfigurable meta-devices basedon phase change materials. Top panel: writing of reconfigurable photonic devices in aphase-change film. Bottom panel: image of the fabricated eight-level gray-scale holo-gram (left) generating a V-shaped five-spot pattern (right) [379]. (h) Schematic ofgate-tunable conducting oxide metadevices based on the MIM metasurfaces incorpo-rated with a thin indium–tin oxide film [380]. (i) Adaptive metalens with simultaneouselectrical control of focal length, astigmatism, and shift. Measurement of focal lengthtuning using the center electrode V5 for double layered devices. Inset: schematic of


electrically controlling different subgroups of meta-atoms in the metasurface[Fig. 20(h)] [380], based on the mechanism described in [68,104]. In the optical regime,researchers also made tunable metasurfaces based on stretchable substrates, which canenable tunable color generation [383] and imaging [381]. In 2018, Capasso’s groupexperimentally demonstrated electrically tunable large-area metalenses controlled bydielectric elastomer actuators (DEAs), which exhibit tunable focal length and astigma-tism and image shift corrections. The achieved adaptive metalens (with a double-layerconfiguration) working at 1550 nm exhibits focal length modulation of 30% with a highfocusing efficiency (62.5%) over the whole tuning range, as shown in Fig. 20(i) [381].

While the past decade has witnessed rapid development in active and tunable meta-surfaces, several major challenges need to be overcome before such devices can beused in practice [384]. For instance, most tuning mechanisms simultaneously modu-late the amplitude and phase responses of the involved meta-atom, which significantlyrestricts the achievable functionality. Thus, finding a new tuning mechanism that sup-port wide range but completely decoupled modulation of amplitude and phase remainsone of these challenges. In addition, the trade-off between modulation depth and speedis another factor that limits the realizations of high-performance devices. In the matterof material concerns, most tunable metasurfaces realized so far are incompatible withcurrent CMOS technology and exhibit relatively poor chemical and physical stabil-ities, which could be an obstacle to prevent them from integrating into realistic pho-tonic systems. Despite these challenges, however, we still expect that tunable/activemetasurfaces have a promising future that might provide an excellent platform to real-ize functional photonics devices.

5. CONCLUSIONS AND PERSPECTIVES

We have presented in this paper an overview on metasurfaces, including both homo-geneous and inhomogeneous ones, focusing particularly on their working principles,practical realization, and potential application. We started in Section 2 with introduc-ing how to construct homogeneous metasurfaces to control all important character-istics of EM waves, including their phase, amplitude, and polarization, bothstatically and dynamically, at frequencies ranging from the microwave to the visible.We next discussed in Section 3 how to build inhomogeneous metasurfaces in which

the adaptive metalens combining a metalens and a DEA with five addressableelectrodes for electrical control over the strain field of the metasurface [381].(a) Figure 1 reprinted with permission from Shadrivov et al., Phys. Rev. Lett.109, 083902 (2012) [371]. Copyright 2012 by the American Physical Society.https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.083902. (b) Reprintedwith permission from Xu et al., Appl. Phys. Lett. 109, 193506 (2016) [373].Copyright 2016 AIP Publishing LLC. (c) Chen et al., Adv. Mater. 29, 1606422(2017) [374]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced withpermission. (d) Reproduced from [375] under the terms of the Creative CommonsAttribution 4.0 License. (e) Zhu et al., Adv. Mater. 27, 4739–4743 (2015) [377].Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.(f) Reprinted with permission from Macmillan Publishers Ltd.: Watts et al., Nat.Photonics 8, 605–609 (2014) [378]. Copyright 2014. (g) Reprinted with permissionfrom Macmillan Publishers Ltd.: Wang et al., Nat. Photonics 10, 60–65 (2016) 379].Copyright 2016. (h) Reprinted with permission from Huang et al., Nano Lett.16, 5319–5325 (2016) [380]. Copyright 2016 American Chemical Society.(i) Reproduced from [381] under the terms of the Creative Commons AttributionNonCommercial License.








meta-atoms with specific EM responses are arranged in certain pre-designed sequences,which can be used to efficiently manipulate the global wavefronts of incoming EMwaves with different polarizations and at different sides of the metasurfaces. Theworkingprinciples established in Sections 2 and 3 related, respectively, to “local meta-atoms” and“global orders,” and offer researchers powerful capabilities to make metadevices thatexhibit diversified functionalities, which were then summarized in Section 4, includingmetalenses, metaholograms, metacloaking, special beam generation, and multifunctionaland tunable/active metadevices. We hope that this review paper can convince the readerthat metasurfaces can indeed provide a promising platform to face the challenges ofultracompact, highly efficient, and flat EM devices raised in future applications, andcan help the reader to quickly jump into this field without much difficulty. However,due to the restriction on paper length and our limited knowledge, we were not ableto cover several interesting sub-branches in metasurfaces, such as nonlinear metasurfaces[385–388], parity-time metasurfaces [389,390], and computing metasurfaces [391–393].Before concluding this review, we would like to mention some promising future direc-tions for metasurface research, based on our perspectives.

A. Active/tunable metasurfaces. While remarkable progress has been achievedalong this direction, great challenges exist that also provide opportunities for futurestudies [384]. For instance, most tuning mechanisms simultaneously modulate theamplitude and phase responses of the involved meta-atom, which significantly re-stricts the achievable functionality. Thus, to achieve fully free and active manipu-lation of EMwaves, one needs to realize independent and full-range control of boththe amplitudes and phases of EM waves at any desired working frequency. In ad-dition, the trade-off between modulation depth and speed is another factor to limitthe realization of high-performance devices. Regarding material concerns, mosttunable metasurfaces realized so far are incompatible with current CMOS technol-ogy and exhibit relatively poor chemical and physical stability, which could be anobstacle to integrating them into realistic photonic systems. Another major chal-lenge is how to independently modulate the EM responses of individual meta-atoms inside arbitrary metasurfaces, at frequencies higher than THz. Existingdemonstrations were mostly in the GHz regime, and several trials in the THzand NIR regimes cannot be easily extended to the general cases required in realisticapplications. New technologies and materials are needed to overcome this issue.Finally, how to deal with high-degree integration to modulate billions of activeelements inside a single device is also a great challenge. New technologies,new design concepts, and new tunable materials are needed to address these issues.

B. Nonlocal metasurfaces. Chromatic and angular dispersion can both degrade theperformance of optical devices, and therefore are two issues that must be addressedbefore metadevices can find any meaningful application. While many recent pro-posals appear to have overcome the chromatic dispersion issue of metasurfaces, theprogress on the angular dispersion issue is relatively slow. Recently, Qiu et al.established a theory to uncover the origin of such intriguing effect and further pro-vided a useful tool to control it [370]. Based on this approach, one can not onlysuppress the angular dispersion of metasurfaces, but can also use the angle as a newdegree of freedom to realize multifunctional metadevices (e.g., polarizer or meta-hologram [362]). We expect that studies on angular dispersion form a very activefuture direction of metasurface research and can stimulate functional devices fordiversified applications.

C. Tailoring light emission by metasurfaces. Atoms or molecules, after being ex-cited, can relax to their ground states by emitting photons. In practice, it is highlydesired to have control of such optical processes, and studies along this line al-ready form an extremely active sub-field following the seminal work of Purcell.


Metasurfaces provide an excellent platform to achieve this end, as they alreadydisplay great potential to control both the local EM environments for emitters andthe far-field channels for the radiation to go. For example, thermal emission of anobject can be strongly modified after surrounding it by a carefully designed meta-surface that exhibits a desired radiation-absorption spectrum, yielding an amaz-ing energy-saving radiation cooling effect [394,395]. More interestingly, bycoupling light to horizontally propagating surface modes, the direction of thermalemissivity can be well controlled [396]. Meanwhile, different metastructures[397–399] have already been used to control the fluorescence of molecules.We expect that more interesting work may appear in this sub-branch, sinceexisting efforts are far from exhausting the full potential of metasurfaces in con-trolling EM waves.

D. Metasystems. We already see from this review paper the strong potential of sin-gle metasurfaces in controlling EM waves. However, in practice facing morecomplicated application requests, metasystems that integrate several metasurfa-ces might be required, which is another promising direction in this field. Indeed,several groups have done interesting work along this direction. Faraon’s groupproposed a metasystem composed of two cascaded metasurfaces to realize retro-reflection it the IR regime [400]. In addition, a metasystem combining functionalmetasurfaces (e.g., metalens) with conventional optical elements (fiber, conven-tional lens, etc.), may possess the advantages of both devices and thus achieveunusual physical effects and functionalities [401–403]. We expect that there willbe plenty of room for researchers working along this direction.

E. Metasurfaces for other waves. The concept of metasurfaces can be extended tomanipulate other types of waves in addition to propagating EM waves. For ex-ample, Lee’s group experimentally demonstrated the generation of surface plas-mon vortices based on plasmonic metasurfaces [404]. Dong et al. experimentallydemonstrated anomalous reflection, focusing, and even Bessel beam generationof SWs, based on dielectric metawalls [405,406]. Sheng’s group experimentallydemonstrated an acoustic metasurface to achieve robust impedance matching andperfect absorption of acoustic waves [407]. Cummer’s group utilized gradientmetasurfaces to realize anomalous refraction and SW conversion of acousticwaves [408]. We believe that research along this direction has great potentialto explore new physics and applications in the future.

FUNDING

National Key Research and Development Program of China (2017YFA0303500,2017YFA0700201, 2017YFA0205800); National Natural Science Foundation ofChina (NSFC) (11874118, 91850101, 11734007, 11674068, 61471345, 11474057,11704240); Science and Technology Commission of Shanghai Municipality (STCSM)(16ZR1445200, 16JC1403100, 16JC1403500, 18ZR1403400, 17ZR1409500,18QA1401800); Shanghai East Scholar Plan; National Young 1000 Talent Plan;Fudan University-CIOMP Joint Fund.

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Shulin Sun received his Ph.D. degree in the Physics Departmentof Fudan University in 2009. From 2010 to 2013, he was a post-doctoral fellow of the Physics Division of the National Center forTheoretical Sciences (NCTS) at National Taiwan University. In2013, he joined the Department of Optical Sciences & Engineeringof Fudan University as an associate professor. He has coauthoredmore than 50 publications in international journals, includingNature Materials, Nano Letters, Light: Science and Applications,

and Physical Review Letters. His research fields include metamaterials/metasurfaces,plasmonics, and photonic crystals.

Qiong He received his Ph.D. degree in Physics from the ParisInstitute of Optics in Paris-Sud University (Orsay, France) in2008. From 2009 to 2013, he was a postdoctoral fellow in thePhysics Department of Fudan University. He is currently an asso-ciate professor in the Physics Department of Fudan University(Shanghai, China). His research interests focus on metamaterialsand plasmonics. He has coauthored more than 40 publications inscientific journals.

Jiaming Hao received his Ph.D. degree in the Physics Departmentof Fudan University, China, in 2008. From 2008 to 2010, he was apostdoctoral fellow in the Department of Photonics and MicrowaveEngineering, Royal Institute of Technology (KTH), Sweden. In2011-2013, he was a postdoctoral researcher at the Laboratory ofElectrical Engineering Paris, Institute of Fundamental Electronics,University Paris Sud XI, France. Currently he is a professor in theShanghai Institute of Technical Physics, Chinese Academy of

Sciences. His research interests are in the fields of metamaterials, plasmonics, and infra-red physics. He has coauthored more than 40 publications in scientific journals.

Shiyi Xiao received his Ph.D. degree from the Physics department,Fudan University in 2013, and then worked as a research fellow inthe School of Physics and Astronomy at University of Birminghamfrom 2014 to 2016. He is currently a professor in the School ofCommunications and Information Engineering, Shanghai University.His research interests cover metamaterials, nanophotonics, andplasmonics. He has published more than 30 papers in scientific jour-nals including Nature Materials, Nature Communications, Physical

Review Letters, and Nano Letters.


https://doi.org/10.1209/0295-5075/122/67002




Lei Zhou received his Ph.D. in Physics from Fudan University,China, in 1997. From 1997 to 2000, he was a postdoctoral fellowof the Institute for Material Research in Tohoku University(Sendai, Japan). In 2000–2004, he was a visiting scholar in thePhysics Department of the Hong Kong University of Scienceand Technology. He joined the Physics Department of FudanUniversity in 2004 as a professor, and has been a “Xi-De” chairprofessor since 2013. He has been working in the fields of

magnetism, metamaterials, photonic crystals, and plasmonics, and has published morethan 160 papers in scientific journals. He was elected as a fellow of The OpticalSociety (OSA) in 2019.


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