arxiv:1605.07672v1 [physics.optics] 24 may 2016 research eld

Review Article

A review of metasurfaces: physics and applications

Hou-Tong Chen1, Antoinette J Taylor2 and Nanfang Yu3

1Center for Integrated Nanotechnologies, Los Alamos National Laboratory, LosAlamos, NM 87545, USA2Associate Directorate for Chemistry, Life, and Earth Sciences, Los AlamosNational Laboratory, Los Alamos, NM 87545, USA3Department of Applied Physics and Applied Mathematics, ColumbiaUniversity, New York, NY 10027, USA

E-mail: [email protected], [email protected], [email protected]

26 May 2016

Abstract. Metamaterials are composed of periodic subwavelength metal/dielectricstructures that resonantly couple to the electric and/or magnetic components ofthe incident electromagnetic fields, exhibiting properties that are not found in na-ture. This class of micro- and nano-structured artificial media have attracted greatinterest during the past 15 years and yielded ground-breaking electromagnetic andphotonic phenomena. However, the high losses and strong dispersion associatedwith the resonant responses and the use of metallic structures, as well as the dif-ficulty in fabricating the micro- and nanoscale 3D structures, have hindered prac-tical applications of metamaterials. Planar metamaterials with subwavelengththickness, or metasurfaces, consisting of single-layer or few-layer stacks of planarstructures, can be readily fabricated using lithography and nanoprinting methods,and the ultrathin thickness in the wave propagation direction can greatly suppressthe undesirable losses. Metasurfaces enable a spatially varying optical response(e.g., scattering amplitude, phase, and polarization), mold optical wavefronts intoshapes that can be designed at will, and facilitate the integration of functionalmaterials to accomplish active control and greatly enhanced nonlinear response.This paper reviews recent progress in the physics of metasurfaces operating atwavelengths ranging from microwave to visible. We provide an overview of keymetasurface concepts such as anomalous reflection and refraction, and introducemetasurfaces based on the Pancharatnam-Berry phase and Huygens’ metasur-faces, as well as their use in wavefront shaping and beam forming applications,followed by a discussion of polarization conversion in few-layer metasurfaces andtheir related properties. An overview of dielectric metasurfaces reveals their abil-ity to realize unique functionalities coupled with Mie resonances and their lowohmic losses. We also describe metasurfaces for wave guidance and radiationcontrol, as well as active and nonlinear metasurfaces. Finally, we conclude byproviding our opinions of opportunities and challenges in this rapidly developingresearch field.

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A review of metasurfaces: physics and applications 2

Contents

1 Introduction 3

2 Anomalous reflection and refraction 42.1 Generalized laws of reflection and refraction . . . . . . . . . . . . . . . 42.2 Demonstration of generalized optical laws . . . . . . . . . . . . . . . . 5

3 Arbitrary phase gradient and beam forming 63.1 Metasurfaces based on Pancharatnam-Berry phase . . . . . . . . . . . 63.2 Huygens’ surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3 Wavefront shaping and beam forming . . . . . . . . . . . . . . . . . . 9

4 Polarization conversion 124.1 Linear-to-circular polarization conversion . . . . . . . . . . . . . . . . 134.2 Linear polarization rotation . . . . . . . . . . . . . . . . . . . . . . . . 154.3 Asymmetric transmission . . . . . . . . . . . . . . . . . . . . . . . . . 17

5 Dielectric metasurfaces 185.1 Dielectric resonators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.2 Directional scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 195.3 Beam forming and wavefront control enabled by dielectric metasurfaces 21

6 Metasurfaces for wave guidance and radiation 226.1 Coupling between free space and surface waves . . . . . . . . . . . . . 236.2 Control of surface waves . . . . . . . . . . . . . . . . . . . . . . . . . . 26

7 Active metasurfaces 277.1 Actively switchable and frequency tunable metal/semiconductor hybrid

metasurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287.2 Graphene hybrid metasurfaces . . . . . . . . . . . . . . . . . . . . . . 307.3 Other resonance switchable and frequency tunable metasurfaces . . . 327.4 Nonlinear metasurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

8 Summary and outlook 35


1. Introduction

Optical devices control and manipulate light by alter-ing its amplitude, phase, and polarization states ina desired manner, which result in steering the beampropagation direction, shaping the wavefront (e.g., fo-cusing), and imparting information for applicationssuch as sensing, imaging and communication. Con-ventional optical components are based on refraction,reflection, absorption, and/or diffraction of light, andlight manipulation is achieved via propagation throughmedia of given refractive indices, which can be engi-neered to control the optical path of light beams. Inthis way, phase, amplitude, and polarization changesare accumulated through propagation in optical com-ponents based on refraction and reflection, such aslenses, waveplates, and optical modulators. Ancientpeople already used ice lenses to focus sunlight andstart fires [1], one example of controlling light prop-agation. They still prevail in today’s optical labora-tories and many consumer-based optical products, butare bulky and heavy, unsuitable for the increasingly de-manding requirements of integration and miniaturiza-tion in modern electromagnetic and photonic systems.The propagation effect is also used in transformationoptics [2,3], which utilizes optical materials structuredon a subwavelength scale to produce spatially varyingrefractive indices that can range from positive to neg-ative.

Metamaterials are composed of periodic subwave-length metal/dielectric structures (i.e., meta-atoms)that resonantly couple to the electric or magnetic orboth components of the incident electromagnetic fields,exhibiting effective electric (represented by electric per-mittivity ε) and/or magnetic (represented by magneticpermeability µ) response not found in nature. Thisclass of micro- and nano-structured artificial mediahave attracted great interest during the past 15 yearsand yielded ground-breaking electromagnetic and pho-tonic phenomena [4, 5]. Their electromagnetic proper-ties are mainly determined by the subwavelength struc-tures together with the integrated functional materials,therefore, producing the desirable electromagnetic re-sponse and device functionalities by structural engi-neering. The initial overwhelming interest in metama-terials lies in the realization of simultaneously negativeelectric and magnetic responses and, thereby, negativerefractive index [6,7], which can be used to accomplishsuperresolution in optical imaging [8,9]. The capabilityof tailoring inhomogeneous and anisotropic refractiveindex resulted in electromagnetic invisibility [10], an-other hallmark accomplishment using metamaterials.These promising potential applications are, however,hindered in practice due to the high losses and strongdispersion associated with the resonant responses andthe use of metallic structures.

Another challenge in metamaterials is the difficultmicro- and nano-fabrication of the required three-dimensional (3D) structures [11], as permittivity,permeability and refractive index are essentiallyproperties of bulk materials. Planar metamaterials,however, can be readily fabricated using existingtechnologies such as lithography and nanoprintingmethods, driving many metamaterial researchers tofocus on single-layer or few-layer stacks of planarstructures that are more accessible particularly in theoptical regime. They are called metasurfaces and canbe considered as the two-dimensional (2D) equivalentof bulk metamaterials. Because the subwavelengththickness introduces minimal propagation phase, theeffective permittivity, permeability and refractiveindex are of less interest in metasurfaces. In contrast,of significant importance are the surface or interfacereflection and transmission resulting from the tailoredsurface impedance, including their amplitude, phase,and polarization states. The ultrathin thickness inthe wave propagation direction can greatly suppressthe undesirable losses by using appropriately chosenmaterials and metasurface structures. Overall,metasurfaces can overcome the challenges encounteredin bulk metamaterials while their interactions with theincident waves can be still sufficiently strong to obtainvery useful functionalities. For this reason, we envisionthat metasurfaces will dominate the general field ofmetamaterials research given their high potential inapplications.

Metasurfaces diminish our dependence on thepropagation effect by introducing abrupt changesin optical properties [12–14]. At microwave andterahertz (THz) frequencies, one can take advantageof subwavelength metallic resonators such as split-ringresonators (SRRs) [15, 16] and a variety of elementstypically used in frequency selective surfaces [17].Abrupt and controllable changes of optical propertiesare achieved by engineering the interaction betweenlight and an array of optical scatterers called “opticalantennas” [18, 19], which can take a variety offorms, including metallic or dielectric micro/nano-particles [20,21], apertures formed in metallic films [22,23], and their multi-layer structures [24]. The mostcritical feature of metasurfaces is that they providedegrees of freedom in designing spatial inhomogeneityover an optically thin interface. Arrays of antennaswith subwavelength separation between adjacentelements can have spatially varying structural featuresor material compositions. Thus, metasurfaces are ableto introduce a spatially varying electromagnetic oroptical response (i.e., scattering amplitude, phase, andpolarization), and mold wavefronts into shapes thatcan be designed at will.

As metasurfaces comprise a rapidly growing field


of research, there have been a few good reviewarticles focusing on different areas [25–31]. Herewe provide our perspective on this research field byreviewing the progress during the past few years,where metasurfaces are broadly defined as planarmetamaterial structures with subwavelength thickness,operating at wavelengths ranging from microwave tovisible. The paper is organized as described below.In section 2 we overview the concept and providedemonstrations of anomalous reflection and refraction,which have largely stimulated and reformed worldwideresearch interest in metasurfaces. In section 3 weintroduce metasurfaces based on the Pancharatnam-Berry phase and Huygens’ metasurfaces, as well astheir use in wavefront shaping and beam formingapplications. In section 4 we review polarizationconversion in few-layer metasurfaces and their relatedproperties. This section is followed by an overviewin section 5 of dielectric metasurfaces that not onlyreduce the ohmic losses in metallic metasurfacesbut also realize some other unique properties andfunctionalities. In section 6 we describe metasurfacesfor wave guidance and radiation control. Wealso summarize active and nonlinear metasurfaces insection 7, and in the last section we provide concludingremarks and an outlook on future research directions.

2. Anomalous reflection and refraction

2.1. Generalized laws of reflection and refraction

When a plane electromagnetic wave encounters aboundary between two homogeneous media withdifferent refractive indices, it is split into a reflectedbeam that propagates back to the first mediumand a transmitted beam that proceeds into thesecond medium. The reflection and transmissioncoefficients and their directions are determined bythe continuity of field components at the boundary,and are given by the Fresnel equations and Snell’slaw, respectively. If we add to the interfacean array of subwavelength resonators of negligiblethickness forming a metasurface, the reflection andtransmission coefficients will be then dramaticallychanged because the boundary conditions are modifiedby the resonant excitation of an effective current withinthe metasurface. The reflection and transmissionwaves carry a phase change that can vary from −πto π, depending on the wavelength of the incidentwave relative to the metasurface resonance. Whenthe resonators are anisotropic, the polarization statemay be also altered. When the phase change isuniform along the interface, the directions of reflectionand refraction are unaltered; in contrast, one of themerits provided by metasurfaces is that we can createspatial phase variation with subwavelength resolution

to effectively control the direction of wave propagationand the shape of wavefront.

Figure 1. A gradient of interfacial phase jump dΦ/dr providesan effective wavevector along the interface that can bendtransmitted and reflected light into arbitrary directions.

We can understand quantitatively the control ofwave propagation direction using Fermat’s principle,which states that the route for the propagationof a light beam should be stationary in the totalaccumulated phase with respect to small variationsof the route. Now we consider a specific case wherea metasurface introduces a spatial distribution ofphase jumps due to electromagnetic scattering at itsconstitutive antennas. The actual optical path in thepresence of these phase jumps should be stationaryin the total accumulated optical phase. This law ofstationary phase ensures that wavelets starting froma source point with the same initial phase will arriveat the point of destination in phase after reflectingfrom or transmitting through the metasurface, andthus constructively interfere, which makes the routea physical path of optical power. A set of generalizedlaws of refraction and reflection can be derived fromFermat’s principle of stationary phase [12,13,32]:{

nt sin(θt)− ni sin(θi) = 1k0

dΦdx

cos(θt) sin(ϕt) = 1ntk0

dΦdy

(1)

{sin(θr)− sin(θi) = 1

nik0

dΦdx

cos(θr) sin(ϕr) = 1nrk0

dΦdy

(2)

where the definition of angles is shown in figure 1, anddΦ/dx and dΦ/dy are, respectively, the components ofthe phase gradient parallel and perpendicular to theplane of incidence. Looking at the problem from analternative point of view, the interfacial phase gradient


functions as an effective wavevector along the interface,and is imparted to the transmitted and reflected waves.The above generalized laws can thus be derived byconsidering the conservation of wavevector along theinterface. These generalized laws indicate that thetransmitted and reflected light beams can be bentin arbitrary directions in their respective half space,depending on the direction and magnitude of theinterfacial phase gradient, as well as the refractiveindices of the surrounding media.

2.2. Demonstration of generalized optical laws

To experimentally demonstrate the generalized laws,one has to devise miniature scatterers that are able tocontrollably change the phase of the scattered wavesand to place such scatterers into an array, forming anartificial interface. The scattering amplitudes shouldbe the same for all scatterers and the spacing betweenneighboring scatterers in the array should be much lessthan the wavelength. These conditions ensure that thesuperposition of spherical waves emanating from thescatterers gives rise to refracted and reflected waveswith planar wavefronts, following Huygens’ principle.

One approach to design the phase response ofscatterers is to use antenna dispersion. That is, fora fixed electromagnetic wavelength and a variation ofantenna geometries, or for a fixed antenna geometryand a variation of excitation wavelengths, there is anassociated phase variation of the waves scattered fromthe antenna (there are also associated amplitude andpolarization changes that can be utilized or otherwisemanaged for designing metasurfaces). For example,when a beam of light impinges on a metallic opticalantenna, the optical energy is coupled into surfaceelectromagnetic waves propagating back and forthalong the antenna surface. These are accompaniedby charge oscillations inside the antenna. Thesecoupled surface electromagnetic waves and oscillatingcharges are known as surface plasmons. For a fixedexcitation wavelength, the antenna resonance occurswhen the antenna length Lres ≈ λ/2, where λ is thesurface plasmon wavelength; under this condition theincident electromagnetic wave is in phase with theexcited antenna current. When the antenna lengthis smaller or larger than Lres, the current leads orlags the driving field. Therefore, the phase of theantenna current and the phase of electromagneticwaves created by the oscillating current (i.e., scatteredwaves from the antenna) can be controlled by choosingthe appropriate antenna length. The tuning rangeof phase is up to π if a single antenna resonance isinvolved. Multiple independent resonances, coupledantenna resonances, or geometric effects (see discussionof the Pancharatnam-Berry phase in section 3.1) areable to extend the phase response to cover the entire

2π range, which is necessary for complete control of thewavefront. In addition to metallic antennas, dielectricones are also able to introduce phase variations tothe scattered light associated with Mie resonances(i.e., establishment of standing wave patterns in thedielectric antennas, see the discussion of dielectricmetasurfaces in section 5).

Generalized optical laws were first demonstratedusing V-shaped optical antennas in the mid-infraredspectral range [12] and later confirmed in the near-infrared [13] (see figure 2). Such optically anisotropicantennas support two plasmonic eigenmodes withdifferent resonant properties. The geometry andorientation of antennas in the array are properlychosen so that for an incident wave at around 8 µmwavelength, over a wide range of incident angles,and polarized along the x -axis (see figure 2(a)), thecomponent of the scattered wave polarized along the y-axis has an incremental phase of π/4 between adjacentV-antennas in the unit cell of the metasurface. Theamplitude of the component polarized along the y-axisis also tuned to be uniform across the antenna array.The antenna spacing is between one tenth and onefifth of the free space wavelength. The metasurfacecreates anomalously refracted and reflected beamssatisfying the generalized laws over a wide wavelengthrange, with negligible spurious beams and opticalbackground, as shown in figure 2(b) and (d). Thebroadband performance is due to the fact that thetwo eigenmodes supported by the V-antennas forma broad effective resonance over which the scatteringefficiency is nearly constant and the phase responseis approximately linear [33, 34]. The scalability ofmetasurfaces allows the extension of this concept toother frequency ranges, e.g., broadband anomalousrefraction was also demonstrated at THz frequenciesusing C-shaped metallic resonators [35]

The generalized law of reflection has also beendemonstrated using reflect-arrays [14, 36, 37], whichconsist of metallic antennas separated from a backmetallic plane by a thin layer of dielectric material (seefigure 3). Such reflect-array metasurfaces are inspiredby initial work on microwave and millimeter wavereflect-array antennas [38, 39]. Figure 3(a) shows anear-infrared reflect-array metasurface based on patchantennas and figure 3(c) shows one that is based onH-shaped antennas for microwaves. The essence ofreflect-arrays is to use antennas coupled with theirdipolar images in the back mirror to achieve a phasecoverage of 2π. Ideally, all incident power will becoupled into anomalous reflection, which will have thesame polarization as that of the incident light; thetransmission and specular reflection will be absent.Experimentally demonstrated efficiency in generatinganomalous reflection in reflect-array metasurface is as


(c)

(b)(a)

(d)

Figure 2. (a) SEM image of a mid-infrared metasurface consisting of an array of V-shaped gold optical antennas patterned on asilicon wafer, with the unit cell highlighted and Γ = 11 µm. It creates a constant gradient of phase jump along the metasurfacefor the control of the propagation direction of light transmitted through or reflected from the metasurface. (b) Under normalincidence, measured far-field intensity profiles show the ordinary (co-polarized) and anomalous (cross-polarized) refraction generatedby metasurfaces like the one shown in (a) and with different interfacial phase gradients (from 2π/13-µm to 2π/17-µm). The far-fieldprofiles are normalized with respect to the intensity of the ordinary beams located at θt = 0◦. The arrows indicate the calculatedangular positions of the anomalous refraction according to θt = − arcsin(λ/Γ). (c) A metasurface used to demonstrate generalizedlaws of reflection and refraction in the near-infrared. Upper panel depicts one unit cell of the fabricated structure and lower panelreveals a schematic of the metasurface. (d) Measured far-field intensity profiles of the metasurface in (c) showing reflection angle θrversus wavelength for cross-polarized light with 65◦ incidence angle. (a) used with permission from [12], (b) used with permissionfrom [33], (c) and (d) reproduced with permission from [13].

high as 80%, significantly higher than the initial proof-of-principle demonstrations in figure 2, which are basedon a single antenna layer, rely on polarization rotationto achieve the 2π phase coverage, and have an efficiencyof 10-20%.

Figure 3(b) shows three regimes of operation for areflect-array metasurface: negative angle of reflection(θr and θi of different signs), angle of incidence andangle of reflection of the same sign but not equalto each other, and coupling of incident light intoevanescent waves propagating on the metasurface (θr

beyond 90◦). In the last case, the interaction betweenthe incident light and the metasurface leads to alateral wavevector that is larger than the free spacewavevector; as a result, no reflection exists and theincident optical power can only be coupled into surfacewaves. The work shown in figure 3(c) and (d) confirmsthe existence of such surface waves by experimentallymeasuring their near-field characteristics. A numberof variations of the reflect-array metasurface have

been also demonstrated. For example, birefringentreflect-array metasurfaces that steer incident lightinto different directions according to its polarizationstate have been demonstrated in simulations [37] (seefigure 3(e) and (f)).

3. Arbitrary phase gradient and beam forming

3.1. Metasurfaces based on Pancharatnam-Berryphase

In the previous examples, variations in phase oramplitude response are introduced by the dispersionof antenna resonance. A completely different approachto introducing phase jumps is to use the so-calledPancharatnam-Berry phase [40, 41]. The latteris associated with polarization change and can becreated by using anisotropic, subwavelength scattererswith identical geometric parameters but spatiallyvarying orientations. The recent development of


x

z

y

ξ = 1.14k0

Φ (

°)

180

0

-180

0 20

x (mm)

40

ModelFDTD

(b)

(c) (d)

(a)

2 μmx

y

(e)

(f)

Figure 3. (a) Schematic of a near-infrared reflect-array metasurface consisting of gold patch antennas separated from a gold backplane by a MgF2 spacer with subwavelength thickness. Left inset shows a basic building block, and right inset is an SEM imageof part of the metasurface. (b) Anomalous reflections at different incident angles for the metasurface shown in (a). The shadedquadrant indicates “negative” reflection. (c) Photograph of a fabricated microwave reflect-array consisting of H-antennas separatedfrom a metallic back plane by a dielectric spacer. The reflect-array introduces an interfacial phase gradient ξ = 1.14k0, where k0is the wavevector of the incident beam corresponding to a wavelength of 2 cm. (d) Scattering phase profile from the metasurfacein (c) showing the phase gradient along the x -direction. (e) Schematic of part of a birefringent reflect-array metasurface workingat λ = 8.06 µm. (f) Depending on the polarization of the incident light, the phase gradient is either positive or negative alongthe x -direction for the metasurface in (e), leading to polarization-dependent anomalous reflection. (a) and (b) reproduced withpermission from [36], (c) and (d) used with permission from [14], (e) and (f) used with permission from [37].

metasurfaces based on Pancharatnam-Berry phase hasbeen largely following the innovative early works byHasman and co-workers [42], who used continuousor discrete subwavelength gratings to control thepolarization states for the generation of vector beamsand manipulation of wavefronts. The easiest way toreveal the relation between polarization and phase isto use Jones calculus [43, 44]. In general, the Jonesmatrix of an anisotropic scatterer can be written as

M = R(−α)

(to 00 te

)R(α), (3)

where to and te are, respectively, the coefficients offorward scattering for incident light linearly polarizedalong the two principal axes of the anisotropic

scatterer,

R(α) =

(cos(α) sin(α)− sin(α) cos(α)

)(4)

is the rotation matrix and α is the rotationangle. Given an incident wave of right/left circular

polarization ER/LI , the scattered light from the

anisotropic scatterer in the forward direction ER/LT can

then be written as [45]:

ER/LT = M ·ER/L

I

=to + te

2E

R/LI +

to − te2

exp(im2α)EL/RI . (5)

The first term represents circularly polarized scatteredwaves with the same handedness as the incident


(a) (b)

(c) (d)(e)

Figure 4. (a) Upper panel: schematic of the super-unit-cell of a metasurface consisting of an array of identical U-shaped apertureswith gradually increasing rotation angles. Lower panels: simulation rusults showing that the metasurface in (a) bends a circularlypolarized incident beam under normal incidence into left or right direction according to the handedness of the incident beam. (b)Upper panel: super-unit-cell of a planar cylindrical lens consisting of an array of identical U-apertures with different orientations.Lower panels: schematics and simulation results showing that the lens focuses right-handed circularly polarized transmissioncomponent when the incident light is left-handed circularly polarized, and that the same lens defocuses left-handed circularly polarizedtransmission component when the incident light is right-handed circularly polarized. (c) SEM image of a metasurface consisting ofan array of gold rod antennas with identical geometry but spatially varying orientations, which is designed for generating an opticalvortex beam with L = 1 (incidence: right-handed circularly polarized; detection: left-handed circularly polarized). (d) Measuredintensity distribution of vortex beams generated by the metasurface in (c) at different wavelengths from 670 to 1100 nm. (e) Pioncaresphere used to derive the phase difference between scattered waves of left-handed circular polarization from rod antennas located atpoints A and B in (c), with right-handed circularly polarized incident light. (a) and (b) reproduced with permission from [45], (c)and (d) reproduced with permission from [46].

light, and the second term represents circularlypolarized scattered waves with opposite handednessand an additional Pancharatnam-Berry phase of m2α,where m is ‘−’ for right-handed and ‘+’ for left-handed circularly polarized incident light. The secondcomponent can be selected in experiments by usinga quarter-wave plate and a polarizer. Its phasecan cover the entire 2π range if the anisotropicscatterer is rotated from 0 to 180◦. Based onthis principle, a phase-gradient metasurface has beendemonstrated to steer light into different directionsdepending on the handedness of the incident circularpolarization (see figure 4(a)) [45]. The unit cellof the metasurface consists of U-shaped apertureantennas with an incremental angle of rotationbetween adjacent elements, with the total rotationangle being 180◦ within the unit cell. Similar U-shaped aperture antennas have been used to createa planar lens, which either functions as a focusingor diverging lens depending on the handedness ofthe incident circular polarization [45], as shown in

figure 4(b). A broadband phase plate generatingoptical vortex beams has been demonstrated by usingan array of rod antennas with different orientations(figure 4(c) and (d)) [46]. A bi-layer metallic aperturemetasurface was also demonstrated to accomplish thesimultaneous manipulation of polarization and phaseof the transmitted light [47].

The metasurfaces based on the Pancharatnam-Berry phase work for circularly polarized incidentlight and control the component of the circularlypolarized transmission with the opposite handedness.A major advantage of the approach based onthe Pancharatnam-Berry phase is ultra-broadbandperformance: given a certain antenna geometry, themagnitude of the phase jump is only a function ofthe orientation angle of the antenna and the signof the phase jump is determined by the handednessof the incident circularly polarized light; there is nowavefront distortion resulting from antenna dispersion.The operating bandwidth is limited on the long-wavelength side by reduced scattering efficiency and


on the short-wavelength side by the requirement thatthe wavelength has to be at least several times largerthan the spacing between scatterers (i.e., metasurfaceregime). In early demonstrations of broadbandmetasurfaces based on Pancharatnam-Berry phase,the presence of scattered waves that do not carryPancharatnam-Berry phase inevitably decreases theirefficiency. In a new generation of metasurfaces, Luo etal. were able to suppress these scattered componentsand created metasurfaces based on Pancharatnam-Berry phase with efficiency approaching unity [48].They demonstrated two different metasurfaces thatseparate a linearly polarized incident microwave intoa left-handed circularly polarized beam and a right-handed circularly polarized beam over a frequencyrange of 11–14 GHz, within which the linearlypolarized background is very weak. The metasurfacedesign is based on rigorous Jones matrix analyses thatprovide a set of criteria for achieving 100% efficiency[48].

A completely different perspective to under-stand the operation of metasurfaces based on thePancharatnam-Berry phase results from tracing theevolution of polarization in the Poincare sphere [40,49–51]. The phase difference between the scattered wavesfrom any two points on the metasurface is equal to thesolid angle enclosed by their corresponding traces inthe Poincare sphere divided by two [49]. For exam-ple, the solid red trace in figure 4(e) corresponds tolight passing through point A in figure 4(c): The tracestarts at north pole of the Poincare sphere represent-ing right-handed circularly polarized incident light; thetrace passes a point on the equator that represents lin-ear polarization in the vertical direction because theantenna at point A on the metasurface preferentiallyscatters vertically polarized waves; the trace ends atthe south pole because left-handed circularly polar-ized transmission is selectively monitored. Similarly,the dashed red trace in figure 4(e) corresponds to lightpassing through point B on the metasurface shown infigure 4(c). The solid angle enclosed by the two tracesis π; therefore the phase difference between left-handedcircularly polarized light scattering from points A andB on the metasurface is π/2. Similar analyses showthat the phase difference between points A and C is πand between A and D is 3π/2. Therefore, the metasur-face in figure 4(c) introduces a constant phase gradientin the azimuthal direction and the phase variation is2π during one circle around the central point of themetasurface. The metasurface thus imprints a spiralphase distribution to the transmitted wavefront, creat-ing a vortex beam with orbital angular momentum ofL = 1.

3.2. Huygens’ surfaces

To boost the efficiency of a metasurface in controllingthe transmitted light, one has to match its impedancewith that of free space. Complete elimination ofreflection can be realized by controlling the surfaceelectric and magnetic polarizabilities, αe and αm, ofthe metasurfaces so that [52]√αm/αe = η0, (6)

where η0 is the impedance of the surrounding media.The effective electric and magnetic surface currents,which are proportional to αe and αm, respectively,change the boundary conditions at the metasurface andlead to the new scattered wavefronts. The complextransmission coefficient of the metasurface is [52]

T =2− jωαeη0

2 + jωαeη0. (7)

If αe is predominantly real, one can vary αe andαm simultaneously at each point on the metasurfaceto ensure that the waves transmitted through themetasurface acquire a phase jump anywhere from −πto +π according to (7) and that the transmissionefficiency is close to unity by satisfying (6) everywhereon the metasurface. The above design concept has beenimplemented in the microwave spectral region by usingspatially varying copper traces supporting both electricand magnetic polarization currents (figure 5(a)) [52].A transmission efficiency of 86% was experimentallydemonstrated in a beam deflector shown in figure 5(b).Although the demonstrations are in the microwaveregime, the concepts can be adapted to the opticalregime and one example is shown in figure 5(c) and(d) [53]. Another metasurface that is impedancematched to free space and able to fully control thephase of the transmitted light was proposed in a recentpaper [54]. It is designed based on optical nano-circuit concepts and is comprised of three planarizedarrays stacked together, as shown in figure 5(e), wherethe building blocks of the array are subwavelengthcomponents made of metallic and dielectric materialswith different filling ratios and function as LC nano-circuit elements. A beam deflector and a flat lenswith high transmission efficiency were demonstratedin simulations, as shown in figure 5(f) and (g), byengineering the effective surface impedance of themetasurface via tuning of the filling ratios.

3.3. Wavefront shaping and beam forming

Metasurfaces provide us with an unprecedentedopportunity to design the wavefronts of light at will,as we have seen from the descriptions of anomalousreflection/refraction and beam focusing in the previoussections. Figure 6 further shows a few planar devices


Figure 5. (a) Upper panel: photograph of a fabricated microwave metasurface that can redirect an incident beam with nearly100% efficiency into a refracted beam. It is made of a stack of identical circuit board stripes, the top and bottom sides of whichare printed with copper traces. Bottom panel: one unit cell of the metasurface consists of capacitively and inductively loadedtraces to realize desired electric sheet reactance (on the top side of each stripe) and capacitively loaded loops to realize desiredmagnetic sheet reactance (on the bottom side of each stripe). (b) Measured magnetic field distribution of the beam-deflectingmetasurface in (a). (c) Schematic of an optically thin, isotropic Huygens’ metasurface that efficiently refracts a normally incidentbeam at telecommunication wavelengths. Inset: schematic of a unit cell. (d) Simulated electric field distribution of a beam deflectorbased on the metasurface in (c).(e) Left panel: basic building block of a metasurface made of plasmonic (AZO: aluminum-dopedzinc oxide) and dielectric (silicon) materials, with l = 250 nm and h = 250 nm. Right panel: metatransmit-array made of threestacked metasurfaces with center-center distance of d = λ0/8 = 375 nm. (f) and (g) Simulated electric field distributions of a beamdeflector and a flat lens based on the metatransmit-array shown in (e). (a) and (b) reproduced with permission from [52], (c) and(d) reproduced with permission from [53], (e)–(g) used with permission from [54].

based on metasurfaces. To realize flat lenses, ametasurface should impose a phase profile

ϕL(x, y) =2π

λ

(√x2 + y2 + f2 − f

)(8)

to convert incident planar wavefronts into sphericalones, which converge at a distance f from the lenses.The optical wavefronts in transmission or reflection re-main spherical as long as the incident plane wave im-pinges normal to the flat lenses. It is therefore straight-forward to achieve high numerical-aperture (NA) fo-cusing without spherical aberration. Flat lenses attelecom wavelengths have been experimentally demon-strated using V-shaped antennas (see figure 6(a) and(b)) [55]. The efficiency of these flat lenses is, however,rather small (i.e., 1% of the incident optical poweris focused) because of the use of only a single scat-terer layer, the small surface filling factor, and focusingonly the component of the scattered light that is cross-polarized with respect to the incident polarization. AtTHz and microwave frequencies, high-performance pla-nar components can benefit from few-layer metasur-faces, which have enabled highly efficient and ultra-broadband polarization conversion and anomalous re-fraction [56], and highly efficient reflect-array metasur-face lenses [57]. V-shaped apertures allow similar con-trol of scattering polarization, amplitude and phase as

in their complementary V-antennas according to Babi-net’s principle; they have been used to demonstrate flatlenses to focus visible light (figure 6(c) and (d)) [58]and THz waves [59], with one of the advantages beingsignificant suppression of the background light.

Based on the Pancharatnam-Berry phase, U-shaped and other nano aperture antennas have beenused to create a planar lens, which either functionsas a focusing or diverging lens depending on thehandedness of the incident circular polarization (seefigure 4(b)) [45, 61]. A flat lens design at telecomwavelengths with potentially high efficiency has beendemonstrated in simulations (figure 6(e) and (f)) [60].The design uses concentric loop antennas placedon both sides of a substrate to enhance scatteringefficiency and to increase the range of phase coverage.Flat lenses working in the near-infrared with highefficiency have been demonstrated experimentally byusing reflect-arrays of patch antennas [62]. Notethat except for spherical aberration, monochromaticaberrations are still present in the above demonstratedflat lenses. For example, when incident light isnot perpendicular to the lenses, the transmitted orreflected wavefront is no longer spherical becauseits phase distribution is that of (8) plus a linearphase distribution introduced by the non-normal


Figure 6. (a) Left panel: SEM image of a fabricatedmetasurface lens with 3 cm focal length, consisting of an arrayof V-antennas. Right panel: phase profile of the lens discretizedaccording to the phase responses of eight constituent antennas.Insets: zoom-in view of fabricated antennas. (b) 3D plots of thesimulated (top panel) and measured (middle panel) and 1D plots(cross-sectional planes along the lines) of intensity distributionof the lens in (a) on the focal plane. (c) SEM image of a planarplasmonic metalens consisting of V-shaped apertures and with afocal length f = 2.5 µm at an operational wavelength of 676 nm.(d) Intensity distributions for two cross-sectional planes (toppanel) cutting through the center of the metalens in (c), and onthe focal plane of the metalens (bottom panel). (e) Schematicof a metasurface lens consisting of an array of 21× 21 scattererseach made of two silver concentric loops (gray). The scatterersare placed on both sides of the substrate (yellow). (f) Simulatedintensity distribution on the focal plane of the metasurface lens in(e). (a) and (b) used with permission from [55], (c) and (d) usedwith permission from [58], and (e) and (f) used with permissionfrom [60].

incidence angle. Flat lenses also have chromaticaberration, although one can design antennas withmultiple resonances to eliminate it by engineering theirdispersion [63] (see discussions in section 5).

It is of particular interest to focus Gaussianbeams to non-diffracting and long focal depth Besselbeams that are traditionally generated using axiconsand have been widely used in microscopy imaging.A metasurface approach to generate a Bessel beam(axicons) [55, 64] has been demonstrated by creatinga linear phase gradient along the radial direction ofthe metasurface. An arbitrary spatially varying phaseprofile can be created in the azimuthal direction. AV-shaped antenna based metasurface has been used tocreate a vortex beam (i.e., Laguerre-Gaussian modes)from a Gaussian beam [12, 65], resulting in opticalsingularity at the beam center and a helicoidal equal-phase wavefront carrying orbital angular momentum.Using a phase profile based on the Pancharatnam-Berry phase, a broadband phase plate generatingoptical vortex beams has been demonstrated using anarray of rod antennas with different orientations (seefigure 4(c) and (d)) [46].

The most complex and general wavefront shapingis to create a holographic image in the far-field. Meta-surfaces provide the degrees of freedom to engineer thelocal amplitude, phase, and polarization response onan interface, and thus are a good platform to real-ize all types of computer-generated holograms (CGHs)(e.g., binary holograms, phase-only holograms, ampli-tude and phase modulation holograms). Figure 7(a)shows a metasurface consisting of arrays of nanoaper-ture antennas that produce a spatially varying trans-mission coefficient [22]. By utilizing the dispersion ofaperture antennas, the metasurface was designed tooperate as two distinctive binary transmission holo-grams at two different wavelengths, λ1 = 905 nm andλ2 = 1385 nm. It creates a word “META” shown infigure 7 (b) at λ1 = 905 nm and a word “CGH” shownin figure 7 (c) at λ2 = 1385 nm in the far-field. Inanother metasurface hologram, V-shaped aperture an-tennas shown in figure 7(d) were used to introduce aneight-level phase distribution and a two-level ampli-tude distribution [66]. The amplitude and phase dis-tributions approximated the required near-field ampli-tude and phase distributions on the metasurface plane,so that a certain holographic image was obtained inthe far-field, as shown in figure 7(f). Additionally,a reflect-array metasurface that introduced a 16-levelPancharatnam-Berry phase has been demonstrated tocreate complex holographic images in the far-field (fig-ure 7(g), (h) and (i)) [67]. The antenna-orientation-controlled Pancharatnam-Berry phase combined withthe reflect-array design led to broadband performanceand high efficiency of the hologram. Experimentally


Figure 7. Metasurface holograms. (a) SEM image of part of a metasurface hologram consisting of nanoaperture antennas. Differentcolors represent pixels with distinctive transmission coefficients. (b) and (c) Transmitted light intensity of the metasurface in (a)recorded in the far-field at λ1 = 905 nm and λ2 = 1385 nm, respectively. (d) SEM image of a fabricated metasurface for generatinga holographic image of the letter “P”. Inset: zoomed-in view of the hologram. (e) Simulated and (f) measured holographic imagecreated by the metasurface holograms similar to (d) with an eight-level phase modulation and a two-level amplitude modulation.(g) One-pixel cell structure of a nanorod-based hologram. The nanorod can rotate in the x-y plane with an orientation angle φ tocreate different Pancharatnam?Berry phase delays. (h) 16-level phase distribution of the nanorod-based hologram (100× 100 pixelsshown). (i) Experimentally obtained image in the far field created by the nanorod-based hologram at 632.8 nm wavelength. (a)-(c)used with permission from [22], (d)-(f) used with permission from [66], and (g)-(i) used with permission from [67].

demonstrated efficiency reaches 80% at λ = 825 nmand the hologram operates between 630 nm and 1,050nm.

4. Polarization conversion

Polarization state is an intrinsic property of electro-magnetic waves, and the conversion between polariza-tion states is very often highly desirable (or even neces-sary) for many modern electromagnetic and photonicapplications. For instance, in advanced communica-tion and sensing, converting linear polarization to cir-cular polarization makes a beam resistant to environ-

mental variation, scattering and diffraction. Duringrecent years, conversion among polarization states us-ing metasurfaces has attracted increasing interest dueto their design flexibility and compactness. The ac-companied capability of tuning a phase delay spanningthe entire 2π range over a broad bandwidth and witha deep subwavelength resolution could potentially ad-dress some critical issues in the development of flatoptics.

Highly symmetric simple meta-atoms can be ad-vantageous in maintaining polarization states. Break-ing the symmetry can, however, provide additional de-grees of freedom to achieve customized functionality


that enables the manipulation of polarization states.Through tailoring the two eigenmodes correspondingto orthogonal linear polarizations, it is possible to haveequal transmission magnitude but a relative phase de-lay ∆φ at a specific frequency. Narrowband polariza-tion conversions between linear and circular polariza-tion states (∆φ = π/2, quarter wave plates), or linearpolarization rotation (∆φ = π, half wave plates) havebeen realized using single-layer metasurfaces [68–73]or multi-layer cascading metasurfaces [74–76] operat-ing from microwave to optical frequencies. However,the efficiency is limited, in general, up to 50% with abandwidth comparable to a meanderline quarter waveplate [68, 77]. The low level of polarization conversionefficiency can be addressed by the implementation offew-layer metasurfaces.

Following the Jones matrix description [43, 44]the transmission of linearly polarized incident fields(Ex, Ey) through a metasurface can be described as(

Etx

Ety

)=

(Txx Txy

Tyx Tyy

)(Ei

x

Eiy

)= Tlin

(Ei

x

Eiy

), (9)

For circularly polarized incident fields, it becomes(Et

+

Et−

)=

(T++ T+−T−+ T−−

)(Ei

+

Ei−

)= Tcirc

(Ei

+

Ei−

), (10)

where T±± = 12 (Txx + Tyy)± i

2 (Txy − Tyx) and T±∓ =12 (Txx − Tyy)∓ i

2 (Txy + Tyx). Under normal incidenceand in general, x and y directions do not necessarilycoincide with the structure’s principal axes. There area few properties of Jones matrices that are related tometasurface structural symmetries:

(i) All components in the Jones matrices could bedifferent if the metasurface lacks reflection orrotational symmetries;

(ii) If the metasurface structure has a mirror symme-try, Txy = Tyx and T++ = T−−, and if the incidentlinear polarization is further parallel or perpendic-ular to the symmetry plane, Txy = Tyx = 0;

(iii) For metasurface structures with a C4 or C3

rotational symmetry with respect to the z-axis,we have Txx = Tyy, Tyx = −Txy, and T+− = T−+.

When designing metasurfaces for polarization conver-sion between the same kinds (x and y linear polariza-tions or left- and right-handed circular polarizations),we need to maximize the off-diagonal components ofthe Jones matrices. For the conversion between lin-ear and circular polarizations, the metasurfaces needto enable π/2 phase difference between the orthogonalcomponents.

4.1. Linear-to-circular polarization conversion

An antenna array backed with a ground plane has beenwidely exploited at microwave frequencies to enhancethe radiation efficiency and beam directionality. Thisconfiguration also enhances the polarization conversionin reflection for anisotropic subwavelength metallic res-onator arrays. Early work at microwave frequenciesdemonstrated that narrowband conversion to variouspolarization states, including linear-to-circular polar-ization and linear polarization perpendicular to theincident one, is possible depending on the structuralparameters, incident angle, and frequency [78]. It hasalso been shown that a pair of perpendicularly orientedand detuned electric dipoles (e.g., rectangular, ellipti-cal, squeezed cross resonators, etc.) can be used tomanipulate polarization states including the construc-tion of quarter-wave plates operating in reflection atoptical wavelengths [79, 80]. This type of structure issimilar to those widely used in metamaterial perfectabsorbers [81], where the Fabry-Perot-like interferenceplays an important role [82].

New device functionalities could be realized bycontrolling spatial distribution of polarization responseusing metasurfaces. Figure 8 show a metasurface-based quarter-wave plate [33] that generates high-quality circularly polarized light (degree of circularpolarization or ellipticity > 0.97) over a broadwavelength range (λ = 5 to 12 µm) (figure 8(c)). Theunit cell of the metasurface comprises two subunits(colored pink and green in figure 8(a) and (b)). Uponexcitation by linearly polarized incident light, thesubunits generate two co-propagating waves with equalamplitudes, orthogonal linear polarizations, and a π/2phase difference (when offset d = Γ/4), which producea circularly polarized anomalously refracted beam thatbends away from the surface normal.

By increasing the number of layers to two orthree, the near field or Fabry-Perot-like couplingcan significantly enhance the efficiency of linear-to-circular polarization conversion as well as theoperation bandwidth. This property is realized inthe few-layer metasurface structures illustrated infigure 9 and figure 10. An ABA-type, anisotropictri-layer metasurface, shown in figure 9(a), hasenabled narrowband, highly efficient linear-to-circularpolarization conversion in transmission at microwavefrequencies [83]. Here layer A is an electric metasurfacewith periodically arranged resonant microstructures,while layer B is a metallic mesh. There are twomechanisms that are responsible for transparency. Thefirst one is the electromagnetic wave tunneling [84](a mechanism that is essentially equivalent to Fabry-Perot-like resonance [85]), and the second one isthe extraordinary optical transmission (EOT) of layerB that is mediated by the periodic structure of


(a)

(b)

(c)

4 μm

Figure 8. (a) Schematic of a metasurface quarter-waveplate, with the unit cell of the metasurface consisting of twosubunits (pink and green). Each subunit contains eight V-antennas. Upon excitation by linearly polarized incident light,the subunits generate two copropagating waves with equalamplitudes, orthogonal linear polarizations, and a π/2 phasedifference (when offset d = Γ/4), which produce a circularlypolarized anomalous refraction that is separated from thenormal beam. (b) SEM image of a portion of the fabricatedmetasurface quarter-wave plate with a footprint of 230×230 µm2

to accommodate the plane-wave like incident light. Antennaorientation angles are indicated by β1 and β2, and dashed linesrepresent the antenna symmetry axes. (c) Calculated degree ofcircular polarization and intensity of the anomalously refractedbeam as a function of wavelength, showing the broadband andhigh efficiency properties of the quarter-wave plate. Used withpermission from [33].

layer A [83]. Through structural tailoring, thesetwo transparency bands, corresponding to the twoorthogonal linear polarization directions (x and y), canoverlap and, at the same time, have a phase differenceof π/2, as shown in figure 9(b) at the frequencyindicated by the dashed vertical line. This means thatan incident electromagnetic wave linearly polarized at45◦ has been transformed to a circularly polarizedone, with a conversion efficiency greatly exceeding anysingle-layer metasurface.

(a)

(b)

Figure 9. (a) Unit cell of a tri-layer ABA-type narrowbandmicrowave linear-to-circular polarization converter, with thetransmission amplitude and phase shown in (b) at twoorthogonal directions. The operation frequency is indicated bythe dashed vertical line. Used with permission from [83].

Bi-layer metasurfaces have enabled high-efficiencyand broadband conversions from linear to circularpolarizations [86,87]. A bi-layer metasurface comprisedof stacked and twisted metallic wire grids shownin figure 10(a) was developed to operate at THzfrequencies [86]. For normal incidence and linearlypolarized light in the x direction, the first wiregrid is aligned at 45◦ with respect to x direction.The wire grid is designed such that the transmissionamplitude of orthogonal components |txx| and |txy|are approximately constant and equal, while thelinear phase retardance is frequency dependent. Thisfrequency dependent phase retardance is compensatedthrough tailoring the geometric parameters of thesecond wire grid, which also has simultaneously hightransmission coefficients |txx| and |tyy|. The metallicgrids were embedded within a polyimide film sothere are 4 interfaces: front air/polyimide, frontwire grid, back wire grid, and back polyimide/air.Through combining the multiple reflections dueto these interfaces and the dispersion of specially


designed wire grids, the overall output of the twoorthogonal x and y components have approximatelyequal amplitude and a phase delay of about 90◦,resulting in circularly polarized transmission overa relatively broad bandwidth from 0.98 to 1.36THz where the ellipticity is about 0.99, as shownin figure 10(b). Circular-to-circular polarizationconversion was demonstrated employing a tri-layermetasurface designed through the approach developedby Pfeiffer and Grbic [88], with the unit cell illustratedin figure 10(c). The measured and simulated Jonesmatrix of the metasurface [89], shown in figure 10(d),reveals a high transmittance of 50% for right-handedto left-handed circular polarization conversion, whileall other components in the Jones matrix are below2.5%, suggesting an extinction ration of ∼ 20 : 1 at thedesigned wavelength of 1.5 µm. It was also observedthat the circular-to-circular polarization conversionextends over a quite broad wavelength range.

(a) (b)

(c) (d)

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 20

0.1

0.2

0.3

0.4

0.5

0.6

Tra

nsm

itta

nce

T

LLT

LRT

RLT

RR

λ (µm)

Figure 10. (a) Optical images with different levels of zoomingfor a fabricated bi-layer THz metasurface embedded withina polyimide film. (b) Experimentally measured transmissionamplitude, phase retardation, and ellipticity under horizontallypolarized incidence, for the sample shown in (a). (c) Unit cellof a tri-layer metasurface for circular-to-circular polarizationconversion operating at the near infrared, with simulated andmeasured transmittance shown in (d). (a) and (b) used withpermission from [86], (c) and (d) used with permission from [89].

4.2. Linear polarization rotation

Planar chiral response can yield optical activity,rotating the direction of linear polarization. While thepolarization rotation power may significantly exceed

naturally occurring materials per unit thickness,typically it is insufficient to obtain the desirable 90◦

polarization rotation. Increasing the number of layerscan yield half wave rotation; however, in general,this approach cannot sustain the polarization rotationpower through increasing the number of layers bysimple stacking, due to the near-field coupling orinterference of the multireflections. In the past,efficient linear polarization conversion still employedanisotropic properties of metamaterials.

(c)(a)

(b)

Lr

p

px

py

x,E0

k

α θi

H0y

z

wr Ax

Ay

ts

0.4 0.8 1.2 1.6 2.00.0

0.2

0.4

0.6

0.8

1.0

Re

fle

cta

nce

Frequency (THz)

cross-polarization

co-polarization

Re

fle

cte

d f

ield

: im

ag

ina

ry p

art

Reflected field: real part

Reflected field: real part

Re

fle

cte

d f

ield

: im

ag

ina

ry p

art

(d)

1

23

1

2 3

-0.2 0.0 0.2-1.0

-0.8

-0.6

-0.4

-0.2

0.0

-0.4 -0.2 0.0-0.2

-0.1

0.0

0.1

0.2

0.3

Figure 11. Metasurface broadband polarization conversion inreflection. (a) Schematic metasurface structure. The incidenceangle θi = 25◦, and the incident electric field E0 is linearlypolarized in the x direction with an angle α = 45◦ withrespect to the cut-wire orientation. (b) Experimentally measuredco- and cross-polarized reflectance. (c) Cross- and (d) co-polarized multiple reflections theoretically calculated at 0.76THz, revealing the constructive and destructive interferences,respectively. Used with permission from [56].

A simple structure is shown in figure 11(a)where an array of cut-wires was separated from theground plane by a polyimide spacer [56]. Undernormal incidence, the incident x polarized THzwaves were converted to y polarized waves inreflection with a conversion efficiency higher than80% over an ultrabroad bandwidth, as shown infigure 11(b). The co-polarized reflection approacheszero at several individual frequencies where thedestructive interference conditions [56, 82] are largelysatisfied, as illustrated in figure 11(c) and (d), inwhich the superposition seems to be responsible forthe observed broadband performance. Following thisconcept, a variety of metasurface structures, mostlyat microwave frequencies, have been demonstratedto accomplish multi-band and ultra broadband linearpolarization conversion in reflection [90]; even atvisible wavelengths the high efficiency can be still


largely maintained according to the simulation resultsin [91]. The observed linear polarization rotationis consistent with an earlier contribution using asimilar structure to control optical polarization in areflection geometry [92], while the bandwidth wasmuch improved and different theoretical models wereused. In order to avoid the increasing metallic lossin the optical frequency range, dielectric metasurfacesfor linear polarization conversion in reflection were alsodemonstrated, based on the same principle [93] (seediscussions in section 5).

It is more desirable to have linear polarizationconverters operating in the transmission mode. Therehave been a few bi-layer or tri-layer metasurfacesdemonstrated to realize cross polarization conversionoperating at a narrow single band or multiplebands [96–98], where the polarization rotation isinsensitive to the azimuthal angle of the incidentpolarization due to the use of structures with four-fold rotational symmetry. Figure 12(a) shows theanisotropic unit cell of a bi-layer metasurface for 90◦

rotation of the THz linear polarization, consisting of afront array of asymmetric split-ring resonators (ASRR)for polarization conversion and a rear array of S-shaped resonators (SR) for polarization selection [94].For the ASRR metasurface, the incident x -polarizedTHz waves induces currents and forms a net electricdipole in the y-direction, providing both x - and y-polarized components in reflection and transmission.The SR metasurface, however, exhibits negligiblepolarization conversion; it was tailored to havea resonance frequency coinciding with the ASRRsfor x -polarized waves, allowing only y-polarizedwaves to pass through and blocking the x -polarizedwaves. Due to the dispersion of the metasurfacesand through carefully optimizing the PET spacerthickness, a Fabry-Perot resonance occurs within theultrathin polarization rotator, which can enhance thepolarization conversion efficiency exceeding that ofthe ASRR metasurface alone. Although numericalsimulations predict a conversion efficiency of 50%(cross-polarized transmission magnitude 0.71) and apolarization-conversion ratio (PCR) up to 99.9% usinglossless PET spacer, the experimental values realizedare 23% (magnitude 0.48) and 97.7%, respectively,at 1.04 THz as shown in figure 12(b), due to thesignificant loss within the PET spacer [94].

Increasing the conversion efficiency and/or band-width becomes particularly interesting when metasur-faces are used to realize a new class of flat optical com-ponents where the transmission phase can be simul-taneously controlled. An intriguing example for lin-ear polarization rotation is a tri-layer THz metasurfacedemonstrated by Chen and co-workers [56]. It consistsof a pair of identical gratings that are aligned in or-

thogonal directions, and an array of cut-wires tiltedat an azimuthal angle of 45◦, as shown in figure 12(c).The front grating is transparent when the incident THzfield is linearly polarized along the x direction. As itcontinues to propagate and excite the cut-wires, thescattering results in both x and y polarized compo-nents. For forward scattering, the back grating allowsthe newly generated y polarized component to passthrough while blocking the x polarized component; forback scattering, the front grating reflects the y polar-ized component and allows the x polarized componentto pass. This process continues due to a multireflectionprocess within this multi-layer structure. When thethicknesses of the polyimide spacer layers are carefullytuned, a constructive interference enhances the polar-ization conversion and a destructive interference of theco-polarized reflections largely reduces the reflectionloss (insertion loss) at multiple frequencies, as shownin figure 12(d), a mechanism similar to metamaterialantireflection coatings [85] and perfect absorbers [82].The back grating also guarantees a purely y polarizedoutput – there is practically no co-polarized transmis-sion. The overall result is that the x polarized inci-dent THz waves can be completely converted to itsorthogonal y polarization, over a bandwidth exceed-ing 2 octaves and with a conversion efficiency up to80%. Simply by scaling, a variety of similar struc-tures [99, 100] were employed in the microwave andinfrared frequency ranges to demonstrate broadband,high-efficiency linear polarization rotators. Further-more, in the structure shown in figure 12(c), the trans-mission phase can be finely tuned to span an entire 2πrange and with subwavelength resolution through re-placing the cut-wires with a variety of anisotropic res-onators with varying geometric dimensions [56]. Com-bining this property and the high polarization conver-sion efficiency promises great potential in wavefrontcontrol, resulting in a new class of practical flat op-tical devices.

A similar broadband THz polarization rotator wasdemonstrated by Cong et al. [95], where the middlecut-wire array was replaced by a wire grating, asschematically shown in figure 12(e). The formation ofa Fabry-Perot cavity makes this metasurface structureperform in remarkable contrast to cascading wirepolarizers with consecutive 45◦ rotation. The latterdoes rotate the incident linear polarization by 90◦

but allows only up to 25% power transmission. Thismetasurface showed a conversion efficiency up to 85%,and the output waves exhibit extremely clean crosslinear polarization over a broad bandwidth, as shownin figure 12(f), although the transmission phase cannotbe controlled.


(a)x (E)

y (H)

z (k)

0.4 0.8 1.2 1.6 2.0 2.40.0

0.2

0.4

0.6

0.8

1.0

Reflecta

nce / tra

nsm

itta

nce

Frequency (THz)

cross-polarized transmission

co-polarized reflection

Experimental Numerical Theoretical

(b)

(c)

(d)

(e)

(f)

Figure 12. (a) Unit cell (left panel) and optical images (right panel) of a bi-layer polarization rotator, and (b) measured co- and cross-polarized transmission coinciding with the simulated results, together with the polarization conversion ratio. (c) Schematic of theunit cell of a tri-layer metasurface linear polarization converter and (d) cross-polarized transmittance obtained through experimentalmeasurements, numerical simulations, and theoretical calculations, together with the numerically simulated co-polarized reflectance.(e) Schematic of a tri-layer metasurface polarization rotator consisting of three metallic gratings, and (f) experimental transmittancespectra. (a) and (b) used with permission from [94], (c) and (d) used with permission from [56], (e) and (f) used with permissionfrom [95].

4.3. Asymmetric transmission

By reducing the structural symmetry and convertingbetween polarization states, metasurfaces have yieldeda polarization sensitive and asymmetric transmissionwith respect to the direction of wave propagation [101].Asymmetric polarization conversion and transmissionwere observed in planar chiral metasurfaces forcircularly polarized incident fields with T f

±∓ 6=T f∓± and T f

±∓ 6= T b±∓, where the superscripts

“f” and “b” denote the forward and backwardpropagation directions, respectively, though T f

±± =

T b±± and T f

±∓ = T b∓± as required by Lorentz

Reciprocity Lemma. The planar chiral metasurfacesare more transparent to a circularly polarized wavefrom one side than from the other side, with anexperimentally measured transmission difference up to40% at microwave [101] and 15% at visible [102, 103]frequencies. This effect is caused by the differentefficiencies of polarization conversion in the oppositepropagation directions for lossy metasurfaces, inremarkable contrast to the optical activity and Faradayeffect. It implies that when circularly polarized lightpasses through the metasurface and then retracesits path after reflection from a mirror, the finalpolarization state will be different from that of theinitial state [104].

Bi-layer and multi-layer metasurfaces can increasethe polarization conversion and consequently enhancethe transmission asymmetry. Pfeiffer and Grbicrecently presented systematic methods to analyze

and synthesize bianisotropic metasurfaces realizedby cascading anisotropic, patterned metallic sheets.This design approach starts with the desirable S-parameters and solves for the necessary admittancesof the metallic sheets. Once the required sheetadmittances are known, the theory of frequency-selective surface and full-wave numerical simulationsare used for their physical realization. Onesuch metasurface exhibiting strongly asymmetrictransmission of circularly polarized millimeter wavesis shown in figure 13(a) and (b) [88]. As shown infigure 13(c), the S21 parameter (i.e., transmission)is below −10 dB for ++, +−, and −−, and it isabove −0.8 dB for −+, resulting in an asymmetricresponse of 0.99 over a bandwidth of 20% at thedesigned millimeter wavelengths. Similar behaviorswere observed in tri-layer metasurfaces operating atnear infrared wavelengths [89], as shown in figure 10(c)and (d).

A variety of bi-layer metasurfaces have been alsoreported to exhibit asymmetric transmission for lin-early polarized incident light [105,106]. Further devel-opments showed that bi-layer metasurface structurescan be used to demonstrate increased bandwidth of theasymmetric transmission in the near infrared [107,108].It was shown that the interlayer alignment could havevery little effect on the asymmetric transmission [107],which indicates that the near-field coupling is negligi-ble. This advantageous property is particularly use-ful in the optical regime where the interlayer align-


(a) (b)

(c)

(d)

(e)

Figure 13. (a) Schematic of a tri-layer metasurface unit cell and (b) optical image of its top metallic sheet, which exhibitsasymmetric transmission of circularly polarized millimeter waves with transmission coefficients shown in (c). Solid curves: measureddata; dashed curves: simulated data. (d) The unit cell of a tri-layer metasurface which enables (e) broadband and highly asymmetrictransmission of linearly polarized millimeter waves. Used with permission from [88].

ment is challenging. In order to take full advantageof the asymmetric transmission, it is necessary to sup-press other components and only obtain a high contrastasymmetric component (e.g., tyx) within the Jonestransmission matrix [109–111]. Tri-layer metasurfaceshave demonstrated the best performance in both theefficiency and bandwidth. Excellent examples includethe ultra-broadband THz linear polarization rotatorshown in figure 12(c)-(f), which exhibits a bandwidthover two octaves [56,95]. Another tri-layer metasurfaceis shown in figure 13(d) and (e), which demonstrateshighly efficient, broadband asymmetric transmission oflinearly polarized millimeter waves [88]. The simulatedresults show that a 1-dB transmission bandwidth of2.43:1 for the desired polarization is achieved, and thatthe rejection of the unwanted polarization exceeds 30dB in this band.

5. Dielectric metasurfaces

The majority of metasurface research has focused onusing subwavelength metallic structures, where ohmiclosses pose a severe issue, particularly in the opticalfrequency range, limiting the performance of arguablyany desirable functions. Low-loss, high-refractive-index dielectric materials have received much attentionduring recent years partially due to their ability in

addressing the efficiency issue in metallic metasurfaces.Furthermore, the capability of tuning the magneticand electric resonances through tailoring the geometryand spacing of dielectric resonators enables devicefunctionalities beyond metallic metasurfaces.

5.1. Dielectric resonators

Dielectric resonators can be traced back to thediscussions by Richtmyer [112]. Due to the excitationof the resonant modes as well as their leaky nature,dielectric resonators can serve as radiative antennas,as developed theoretically and experimentally in the1980’s by Long et al. at microwave frequencies [113].Increasing the dielectric constant ε can significantlyreduce the required size d of the resonators, whichis related to the free space resonant wavelengthλ0 by d ∼ λ0/

√ε. However, increasing the

dielectric constant also reduces the radiation efficiencyand narrows the operational bandwidth, which isinversely related to the dielectric constant. Typicalvalues of the dielectric constant used range from8 to 100 in order to balance the compactness,radiation efficiency and bandwidth requirements. Veryoften dielectric resonators are mounted on top of ametal ground plane, which improves the radiationefficiency and acts as an electrical symmetry plane


to improve the compactness. Early work in resonantdielectric antennas at microwave frequencies has beensummarized in review articles [114,115].

In the optical regime, low loss dielectric particlessupport strong electric and magnetic scattering knownas Mie resonances, which can be decomposed intoa multipole series. The modes are determined bythe particle size and structural properties [116–119],in contrast to metallic particles where the resonancescattering is dominated by the electric resonances.In most dielectric resonators of regular shapes suchas spheres, cubes, cylindrical disks and rods, thelowest resonant mode is the magnetic dipole resonanceand the second lowest mode is the electric dipoleresonance [119,120]. Figure 14 shows the fundamentalmagnetic and electrical dipole modes for a cubicdielectric resonator [121]. The magnetic resonancemode originates from the excitation of circulatingdisplacement currents, resulting in the strongestmagnetic polarization at the center, similar to the caseof magnetic resonant response in metallic SRRs. Thecontribution from other higher order modes can beignored as the coefficients of these modes are oftenorders of magnitude lower [122].

H

E

kE

k

H

H

E

kE

k

H

Figure 14. Electric and magnetic modes in a cubic dielectricresonator. (a) and (b) Magnetic dipole resonance mode, showingelectric field (a) and magnetic field (b) distributions. (c) and (d)Electric dipole resonance mode, showing electric field (c) andmagnetic field (d) distributions. The incident fields are indicatedin the insets. Reproduced with permission from [121].

Subwavelength dielectric resonators can be usedas the basic building blocks of metamaterials andmetasurfaces, as first suggested by O’Brien andPendry to obtain magnetic activity in dielectriccomposites [123]. A class of Mie resonance-based dielectric metamaterials have been consequentlydemonstrated, with some early work reviewed in [124],where high dielectric constant materials are used tocreate subwavelength resonators for the realization ofnegative electric and magnetic responses. Ferroelectricbarium strontium titanate (BST or Ba0.5Sr0.5TiO3)

was used to demonstrate dielectric metamaterialsbecause of its high dielectric constant (∼ 600) atmicrowave frequencies. Left-handed behavior wasobserved in prisms formed by an array of periodic orrandom subwavelength BST rods [125], and negativemagnetic response was also observed in a bulkmetamaterial consisting of an array of subwavelengthBST cubes [121]. In the optical frequency range,materials used to form dielectric metamaterials includetellurium (Te) cubes on barium fluoride (BaF2) [126],cubic (β) phase silicon carbide (SiC) whiskers onzinc selenide (ZnSe) [127, 128], in the mid-infrared;silicon cylindrical nano disks embedded within silicondioxide [129] in the near infrared; silicon nano sphereson glass [130] and titanium dioxide cylindrical disks onsilver [21] at visible frequencies.

The loss reduction enabled by dielectric metasur-faces becomes clear when functioning as a linear polar-ization rotator as shown in Figure 15, where an array ofanisotropic (rectangular) silicon resonators is separatedfrom a metal ground plane by a thin layer of PMMA. Inexperiments, linear polarization conversion with morethan 98% conversion efficiency was demonstrated overa 200 nm bandwidth in the near infrared [93], as shownin figure 15(c). This result exemplifies the significantloss reduction enabled by the use of dielectric meta-surfaces instead of metallic resonators shown in fig-ure 11, particularly in the infrared and visible fre-quency ranges.

In general, dielectric resonators offer only upto π phase variation in transmission when theelectric and magnetic resonances are at differentfrequencies. By overlapping the electric and magneticdipole resonances through varying the geometryof dielectric resonators, however, it is possible toachieve a phase variation covering the entire 2πrange [131]. This was experimentally verified evenwithout satisfying the condition of equal electricand magnetic resonance width [132]. In cylindricaldielectric disks, the tuning parameter could be the diskheight, diameter, and period (spacing). The spacingbetween resonators further facilitates the tuning ofresonance coupling [118], which affects the dispersionof the scattering phase resulting from the differenttransverse electric and transverse magnetic modes, andalso enables electromagnetically induced transparencyin dielectric metasurfaces with an ultra high qualityfactor [133].

5.2. Directional scattering

In 1983 Kerker et al. discussed electromagneticscattering by magnetic spheres. It was shownthat back scattering can be reduced to zero byspheres with equal permeability µ and permittivityε [134]. In such a situation the particle exhibits


(a) (b)

(c)

Figure 15. Dielectric metasurface for broadband polarizationconversion in reflection. (a) Schematic and (b) SEM image of thedielectric metasurface structure. (c) Experimentally measured(solid lines) and numerically simulated (dotted lines) co- andcross-polarized reflectance. Used with permission from [93].

equal electric and magnetic multipole coefficients,resulting in destructive interference in the backwardpropagating direction and constructive interference inthe forward propagating direction. The magneticMie resonance overcomes the absence of magneticmaterials at optical frequencies and enables theinvestigation of directional optical scattering usingdielectric metasurfaces. The complete cancellation ofback scattering was also theoretically predicted in [118]at an off-resonance frequency in an array of silicon nanospheres where the electric and magnetic polarizabilitieshave equal values. Such a phenomenon corresponds toa ‘Huygens’ secondary source, and was experimentallydemonstrated using nonmagnetic dielectric sphericaland cylindrical scatters with moderate dielectricconstants at microwave [135] and visible [136, 137]frequencies.

The resonant directional scattering is moreinteresting because of the large field enhancementand concentration. Resonant response usuallyaccompanies large back scattering, which makes itmore feasible for dielectric metasurfaces to operatein a reflection configuration [21, 93]. This enabledthe demonstration of broadband dielectric metasurfacemirrors [138–140] and optical magnetic mirrors [141,

142], without reflection phase reversal in the latter.Using geometric shapes other than spherical or cubicdielectric resonators, one could have more degreesof freedom to tune independently the frequencies ofelectric and magnetic resonances to realize resonantdirectional scattering. This is exemplified by thecloser electric and magnetic dipole resonances whensqueezing the silicon spheres in the z-direction, whichresults in a larger forward-to-backward scatteringratio [136]. An array of silicon cylindrical nanodisks, as shown in figure 16(a) and (b), was usedto demonstrate resonant directional scattering in thevisible wavelength range [129]. By varying thediameter of the silicon disks, it was observed thatthe electric and magnetic resonances overlap, resultingin enhanced forward scattering and cancellation ofbackward scattering, as shown in figure 16(c) and (d).

(a) (b)

(c) (d)

Figure 16. (a) Schematic of silicon nanodisks embedded intoa low-index (SiO2) medium. (b) SEM image of the fabricatedsilicon nanodisks before embedding them into SiO2. Theinsets show the close-up top and oblique views. (c) Opticaltransmittance and (d) reflectance spectra of the fabricatedsample, where the white dashed ellipses indicate the regionswhere the back scattering is significantly reduced. Used withpermission from [129].

An ideal dielectric Huygens’ metasurface requiresoverlapping electric and magnetic dipole resonancesof equal resonance strength and width in order tocompletely cancel the reflection and obtain near unitytransmission [132]. High transmittance of 55% atresonance was experimentally demonstrated in thenear-infrared using a silicon metasurface consisting ofan array of cylindrical resonators embedded within an


SiO2 environment, where the condition of equal widthof the electric and magnetic resonances was not yetsatisfied [132]. By tuning the dielectric constant ofthe environment and the geometric dimensions of theresonators, it is possible to achieve spectral overlapand equal width of the resonances. Post-fabricationactive tuning of the resonances is attractive for thispurpose as well. For instance, a layer of liquid crystalswas added on top of the silicon nano disks, providingtemperature-dependent refractive indices when theliquid crystals were switched between the nematicand isotropic phases [143]. It was shown that theelectric resonance has a larger tuning range because ofextended fringing fields outside the resonators, whilethe magnetic resonance has smaller tuning capabilitybecause of the better confined field distributionwithin the dielectric resonators. Reconfigurabledirectional scattering can be also accomplished usingmetasurfaces consisting of semiconducting resonatorarrays through injection of free charge carriers byoptical excitation [144].

5.3. Beam forming and wavefront control enabled bydielectric metasurfaces

Similar to metasurfaces consisting of plasmonic metal-lic resonators, wavefront control and beam formingcan be accomplished using dielectric metasurfaces. Byvarying the dimensions of the rectangular silicon res-onators shown in figure 15, a phase variation can spanthe entire 2π range. This enables the generation ofa near infrared optical vortex beam in reflection withhigh efficiency when a phase gradient profile was cre-ated in the azimuthal direction using 8 elements of dif-ferent sizes [93], as shown in figure 17(a-c). The use ofa PMMA spacer layer between the silicon resonatorsand a metallic back plane not only provides the de-sirable interference resulting from the Fabry-Perot-likemultiple reflections, but also effectively prevents the in-cident light from coupling to surface waves. This is inremarkable contrast to the situation where the dielec-tric resonators are directly mounted onto the metallicsurface [21]. In the latter work, a linear phase gradi-ent at wavelength of 633 nm was created by using sixTiO2 cylindrical resonators of various diameters sittingon top of a silver plane (figure 17(d)), demonstrating adeflection from the specular reflection by the expected20◦ (figure 17(f)) [21]. It was shown that considerabledissipation occurs within the TiO2 resonators, partiallybecause this configuration can also function as a meta-material absorber [145]. Even more optical power iscoupled to surface waves, which was described in arecent theoretical proposal of directional launching ofsurface waves [146].

A metasurface that converts a Gaussian beam intoa vortex beam was demonstrated; it consists of four

(c)(a)

(b)

(d)

θSilver

TiO2

Siliconx

y

y

z

z

E field H field =y

z

TiO2

Silver

0 y

z

0

(e)

(f)

Figure 17. (a) A phase profile in the azimuthal directionwith an increment of π/4, created using (b) silicon rectangularresonators on top of a metal mirror with a PMMA spacer,and enabling the formation of a near infrared optical vortexbeam. The pattern in (c) is the interference between the vortexbeam and a reference Gaussian beam. (d) Schematic of partof a reflect-array metasurface consisting of dielectric resonatorspatterned on a metallic substrate and operating at λ = 633 nm.(e) Simulated electric and magnetic field distributions in adielectric resonator antenna. (f) Simulation showing that atzero-degree angle of incidence the metasurface in (d) generates areflected wave propagating along 20◦ direction from the surfacenormal. (a)-(c) used with permission from [93], (d)-(f) used withpermission from [21].

quadrants with a phase increment of π/2 and eachquadrant consists of an array of cylindrical silicon nanodisks of the same geometry but different separationsbetween adjacent disks [147]. By varying the diame-ter of silicon nanoposts to control the phase profile, ahigh-efficiency lens was demonstrated with measuredfocusing efficiency in transmission up to 82% [148].Through varying the geometric dimensions and cou-pling strength between dielectric resonators, it is pos-sible to create the required phase profiles to simulta-neously control the wavefront at multiple wavelengths.This approach was exploited in the demonstration ofa multi-wavelength dielectric metasurface lens operat-ing near telecommunication wavelengths [63, 149]. Toachieve equal focal lengths at different wavelengths,the metasurface lens imparts a wavelength dependentphase contribution to compensate for the dispersive ac-


400 nm(a)

(b)

(c) (d)

Figure 18. Multi-wavelength dielectric metasurface cylindricallens. (a) False colored side-view SEM image of the metasurfacelens. Each unit cell is identified by a different color. (b)-(d)Measured intensity distributions in the plane perpendicular tothe silicon ridges at wavelengths (b) 1300 nm, (c) 1550 nm, and(d) 1800 nm. Used with permission from [63]

cumulated propagation phase. This is achieved by de-signing the dispersive phase response of coupled dielec-tric ridge patterned on a fused silica (SiO2) substrate,as shown in figure 18(a). It creates a phase profilethat realizes the same focal length for wavelengths at1300, 1550, and 1800 nm as shown in figure 18(b-d).The focusing efficiency, defined as the ratio of powerat the beam focal waist and the input power, is stillrather low, in part due to the reflection loss. Few-layermetasurfaces introduced in previous sections could po-tentially address this issue of impedance mismatch andimprove the focusing efficiency. For wavelengths otherthan these specific values, the operation of the lens fol-lows the normal dispersion curves, which indicates thata dielectric metasurface lens that eliminates chromaticaberration over a broad range of wavelengths is stillchallenging to accomplish.

An alternative approach to create a spatially-varying phase profile is through the use of Pancharatnam-Berry phase [50]. The key is the conversion betweenleft- and right-handed circular polarization states viadifferent routes on the Poincare sphere. The requiredpolarization control can be achieved by the excitationof electric and magnetic resonances in dielectric res-onators. Using silicon nanobeams with appropriategeometric dimensions, it was shown that the incidentcircularly polarized light is partially converted into cir-cularly polarized light with opposite handedness withan imparted Pancharatnam-Berry phase depending onthe orientation of the silicon nanobeams [150]. Thenanobeam metasurface exhibits anomalous refractionwhen forming a constant phase gradient. Linearly po-larized incident light is split into right- and left-handedcircularly polarized beams that propagate in different

directions. Transmission spatial phase profiles havebeen also experimentally demonstrated, functioning aslenses for focusing and axicons for creating a Besselbeam (see figure 19) [150].

50 1000-50z (μm)

10

-10

0

x (μ

m)

(a)

(b)

Figure 19. (a) SEM image of a fabricated dielectric metasurfaceaxicon consisting of silicon nanobeams. (b) Measured intensityprofile of the nondiffractive Bessel beam generated behind theaxicon in (a) in the xz plane. Used with permission from [150].

It is essential to realize simultaneous and completecontrol of polarization and phase with subwavelengthresolution and high transmission. In the opticalregime plasmonic metasurfaces partially accomplishthis goal with limited efficiency [47]. In a recent paperfrom Faraon’s group, a dielectric metasuface platformwas demonstrated based on elliptical high-contrastdielectric nanoposts that provide complete control oftransmissive polarization and phase with measuredefficiency ranging from 72% to 97%, achieved throughvarying the ellipticity, size, as well as orientation ofthe nanoposts [151]. It was shown that most free spacehigh-performance transmissive optical elements can berealized, such as lenses, wave plates, beamsplitters,holograms and arbitrary vector beam generators. Twoexamples are illustrated in figure 20 for incidentpolarization-dependent focusing.

6. Metasurfaces for wave guidance andradiation

In the previous sections we mainly focus on the physicsand applications of metasurfaces in controlling wavesthat propagate in free space. The present sectionreviews the emerging research on using metasurfacesto control guided waves and to couple between guidedwaves and waves propagating in free space. Becauseof the spatial inhomogeneity of metasurfaces, they donot support any eigen guided modes. That is, waves


(a) Simulation Measurement

0

Inte

nsity

(a.u

.)

1

1 mm

500 nm

100 μm

100 μm

z

x

y

x

y

(b)Simulation

0

Inte

nsity

(a.u

.)

1

Measurement(without polarizer)

Measurement(with polarizer)

200 μm

2 μm 2 μm

100 μm

2 μm

Figure 20. (a) Dielectric metasurface that separates the x - and y-polarized incident light, deflecting and focusing them to twodifferent spots. (b) Dielectric metasurface that focuses the incident circularly polarized light to a diffraction-limited spot or adoughnut-shaped spot depending on its handedness. Left column: schematic illustration of the devices; Mid-column: simulated andexperimental results; Right column: SEM images of the dielectric metasurfaces. Used with permission from [151].

propagating along metasurfaces are at a transientstate and are constantly evolving. Thus, metasurfacesare most suitable for realizing mode conversions.By designing the in-plane effective wavevector usingmetasurface structures, one is able to realize conversionbetween two different guided modes or between aguided mode and a mode propagating in the free space.

There are a couple of major differences betweenmode conversion using metasurfaces and using conven-tional grating-based mode convertors:

(1) Metasurfaces can be designed to providea unidirectional phase gradient, or a unidirectionaleffective wavevector. The latter leads to an asymmetriccoupling between modes: electromagnetic energy istransferred preferentially from one mode to the other,while the inverse process can be highly inefficient. Suchasymmetric electromagnetic energy transfer betweenmodes is maintained even when the conventional phasematching condition is not strictly satisfied (i.e., phasegradient dΦ/dr not equal to the difference in wavenumber between two modes, β1 − β2). This propertyensures that mode conversion can be realized over abroad spectral range and won’t be greatly affectedby small structural changes to the metasurfaces. On

the contrary, conventional grating couplers providepositive and negative reciprocal lattice vectors, ±2π/Λ,where Λ is the grating period. The coupling betweentwo modes is symmetric, and thus the phase matchingcondition, β1−β2 = 2π/Λ, has to be strictly satisfied toensure that electromagnetic energy is transferred fromone mode to the other.

(2) The spacing between adjacent constituentelements in a metasurface is subwavelength. Therefore,metasurfaces are able to modify the wavevectorof a guided wave adiabatically. The absence ofabrupt variation of wavevectors prevents scatteringof electromagnetic energy into free space or intothe substrate. Grating couplers, however, have aperiodicity comparable to the wavelength. Guidedwaves are likely to be scattered, which makes in-planeconfinement of electromagnetic energy a challenge.

6.1. Coupling between free space and surface waves

The pioneering work on using metasurfaces to controlguided waves was conducted by Sievenpiper andcolleagues in the microwave spectral range [152].They used the concept of holography to designimpedance surfaces that convert a given surface


(a)

(b)

(c)

(d)

(e)

(f)

Figure 21. (a) Schematic showing the concept of holographic leaky wave antenna. Surface waves (undulating arrows) are excited ona metasurface impedance surface, and are scattered by variations in the surface impedance to produce the desired radiation (straightarrows). (b) Unit cell of the impedance surface consisting of a patch antenna patterned on a metal grounded layer of insulator.(c) A section of the designed scalar impedance surface that scatters a cylindrical surface wave produced by a point source into aplane wave propagating along 60◦ from the surface normal. (d) A section of the designed tensor impedance surface that scatters acylindrical surface wave produced by a point source into a plane wave propagating along 45◦ from the surface normal. (e) Black andgray curves are, respectively, radiation patterns of a monopolar antenna placed on the scalar holographic impedance surface and on asmooth metal surface. (f) Black and gray curves show, respectively, measured radiation patterns with left-handed and right-handedcircular polarization produced by a monopolar antenna placed on the tensor holographic impedance surface. Used with permissionfrom [152].

wave into a freely propagating wave with desiredfar-field radiation pattern and polarization. Theimpedance surface is essentially a hologram, whichis the interference pattern between a reference beamand an object beam, and carries information of thephase, amplitude and polarization of the desiredobject beam. The object beam is reconstructedwhen the reference beam impinges on the hologram.In Sievenpiper’s implementation, a source antennaproduces the reference beam in the form of a surfacewave, Esurf , and the object beam is the desiredwave, Erad, propagating in the half space abovethe surface (figure 21(a)); microwave holograms arecreated according to the interference pattern producedby the two waves and consist of a square latticeof dissimilar sub-wavelength conductive patches ona metal-grounded dielectric substrate. Both scalarand tensor forms of the impedance surfaces wereexperimentally demonstrated.

Surface impedance provides an appropriate lan-guage to characterize the properties of the metasurface.It is defined as the ratio between the electric and mag-netic fields near the surface. For transverse magnetic(TM) waves (i.e., magnetic field transverse to the prop-

agation direction) that propagate in the x -direction,the surface impedance is Z(x, y) = Ex(x, y)/Hy(x, y).The surface magnetic field is proportional to the sur-face current, which is provided by the electromagneticsource. For example, a monopole antenna producesa cylindrical distribution of surface current. The func-tion of the impedance surface is to translate this surfacecurrent to a distribution of electromagnetic waves onthe surface, which matches the desired radiative wave.

In Sievenpiper and colleagues’ work, squarepatch antennas (figure 21(b)) were used to constructscalar impedance surfaces and square patches withan additional slice were used for tensor impedancesurfaces. The three independent terms in theimpedance tensor, Zxx, Zxy = Zyx and Zyy, arecontrolled by the three degrees of freedom in antennadesign: the slice width, its orientation angle, andthe gap between neighboring square patches. In thecase of scalar impedance surfaces, the value of surfaceimpedance of patch antennas was determined by thefollowing procedure:

(i) Calculating dispersion relation of surface wavespropagating on a 2D periodic array of patchantennas. Specifically, Bloch boundary conditions


are applied to a unit cell of the impedancesurface, and eigen surface wave modes and theireigen wavevectors are determined for a range offrequencies.

(ii) Calculating the surface impedance for a given op-eration frequency ω0, Z(ω0) =

∫unit cell

(Ex/Hy)dxdy.

A library that relates the surface impedances and patchantenna geometries can be created by repeating theabove procedure for patch antennas of different sizes.

The distribution of surface impedance Z(x, y) isdetermined by the following holographic technique. Inthe case of a scalar impedance surface, with a surfacecurrent Jsurf(x, y) produced by the electromagneticsource and the object far-field radiation Erad(x, y, z),the required surface impedance is

Z(x, y) = j

{X +MRe

[(Erad,x,Erad,y)

(Jsurf,x

Jsurf,y

)]}.

(11)

In the case of a tensor impedance surface, we have

Z(x, y) = j

(X 00 X

)+ j

M

2Im

[(Erad,x

Erad,y

)(Jsurf,x, Jsurf,y)

−(Jsurf,x

Jsurf,y

)(Erad,x, Erad,y)

]. (12)

In the above two equations, X represents the aver-age impedance value, and M spans the entire availableimpedance range. Using the holographic technique andthe library of patch antennas, Sievenpiper and cowork-ers demonstrated a scalar impedance surface that scat-ters the current generated by a monopolar antenna intoa linearly polarized plane wave propagating along 60◦

from the surface normal (figure 21(c) and (e)). The sur-face current has a cylindrical distribution and can bedescribed by Jsurf = 1

r2 exp(−jk0nsr)(x, y, 0), where

r = (x2 + y2)1/2, k0 is the free space wavevector,and ns is the effective index of the surface current,which is assumed to be a constant and is a functionof the thickness and materials of the dielectric spac-ing layer between the metal patches and the metallicground. They also experimentally demonstrated a ten-sor impedance surface that converts the current gener-ated by a monopolar antenna to a circularly polarizedfar-field radiation propagating along 45◦ direction (fig-ure 21(d) and (f)).

Maci and colleagues used the same holographicprinciple to demonstrate metasurfaces with modulatedsurface impedance [153, 154]. They used square patchantennas of different sizes to create a spiral distributionof surface impedance that converts a surface currentproduced by a monopolar antenna to a collimatedright-handed circularly polarized far-field radiation(figure 22). Podilchak and collaborators demonstrated

(a)

(b)

Figure 22. (a) Section of an impedance surface near the centralmonopolar antenna. (b) Right-handed circularly polarizedradiation profiles produced by the impedance surface antennanear 17 GHz. Inset is the entire antenna with a radius of 9.7 cm.Used with permission from [153].

experimentally [155] that width-modulated microstriplines patterned on a grounded dielectric slab introducea sinusoidally modulated surface impedance andprovide appropriate conditions for leaky wave radiation(figure 23). Figure 24 show a holographic metasurfacethat detects optical vortex beams with specificorbital angular momentum (OAM) [156]. The nano-structured binary holograms shown in the left panel offigure 24(a) were created by calculating the interferencepattern between a converging surface plasmon waveand an incident optical vortex beam. The simulatedresults in figure 24(a) show that a converging surfaceplasmon wave is generated only when an optical vortexbeam with the correct OAM is scattered by thehologram. Experimental results in figure 24(b) showthat a hologram can distinguish an optical vortex beamwith OAM of −1 from optical vortex beams with othervalues of OAM.

The major challenges in coupling an incident wavefrom free space into a surface wave with high efficiencyare to suppress the reflection of the incident waveon the device surface and to prevent decoupling ofthe surface wave back into free space. In a series


(a)

(b)

Figure 23. (a) Planar 2D leaky-wave antenna consisting ofradially directed and width-modulated microstrip lines and isable to transform a cylindrical surface wave into leaky waves. (b)Broadside beam pattern of the leaky-wave antenna. Solid anddashed curves are, respectively, measured and simulated beampatterns at ∼ 22 GHz. Used with permission from [155].

Li = –1

Lg = 0

1

Lg = 1

Li = 0 Li = +1

0.5

I (Arbitary units)

0

Gaussian

Ei

Li = –1

Li = +1

Li = +2

Li = –2

12090 1

60

30

0

330

300270

240

210

180

150

0.8

0.6

0.4

0.2

ϑ°

ϑ°

(a)

(b)

Figure 24. (a) Left panel: metasurface holograms for detectingoptical vortex beams. Right panel: simulation results of theintensity distribution of surface plasmon waves generated byilluminating the holograms at normal incidence with differentoptical vortex beams. (b) Photocurrent as a function of incidentpolarization measured for a metasurface hologram designed fordetecting optical vortex beams with orbital angular momentumof Li = −1. Used with permission from [156].

of work from the Zhou group [14, 157, 158], a fewstrategies were devised to address these challenges:(1) the entire surface of the metasurface coupler isdesigned to be impedance matched with free spaceto minimize direct reflection; (2) the lateral effectivewavevector provided by the metasurface is designedto be sufficiently large so that a surface wave witha wavevector larger than the free space wavevectoris excited; the surface wave becomes even moreevanescent as it further interacts with the gradientmetasurface, which prevents decoupling of the waveback to the free space; (3) the impedance mismatchbetween the supercells of the metasurface coupler isreduced to prevent scattering of the surface wave.Through these approaches, the authors were ableto demonstrate coupling of an incident wave fromfree space into a surface wave with efficiencies of ∼94% in simulations and ∼ 73% in experiments usingmicrowaves [158].

6.2. Control of surface waves

The examples that have been discussed in this sectionso far are all about coupling surface waves and wavespropagating in free space using metasurfaces. Thesubject of controlling the propagation of surface wavesconfined to a 2D plane is a new frontier of metasurfaceresearch.

Vakil and Engheta proposed using graphene as anultra-thin platform for controlling in-plane propagationof infrared electromagnetic waves [159]. They demon-strated theoretically that by designing and manipulat-ing spatially inhomogeneous conductivity patterns ona sheet of graphene using the electric field effect, onecan realize a number of transformation optical devices.The example of a graphene metasurface Luneberg lensis shown in figure 25(a). The research group of S.Maci used patch antennas of different sizes or metallicpins of different heights to demonstrate two types ofin-plane planar lenses (Luneberg lenses and Maxwell’sfish-eye [153]; the latter is shown in figure 25(b)). Intheir pioneering work, Gok and Grbic used the conceptof transformation electromagnetics to demonstrate in-dependent control of the power flow and phase progres-sion of electromagnetic fields in a 2D space (figure 25(c)and (d)) [160]. The resulting metasurface is a highlyinhomogeneous, anisotropic media where each unit cellis characterized by a 2 × 2 permeability tensor in theplane and a scalar permittivity in the surface normaldirection. These parameters were judicially chosen tocreate stipulated 2D distributions of wavevector andPoynting vector, as well as to ensure impedance match-ing between the adjacent unit cells so that there is noreflection and scattering of the surface wave as it prop-agates on the metasurface.

The concept of metasurfaces has been introduced


0 2π

D

Lw

x

z

y

Simulated (Boundary 1)

Simulated (Boundary 2)

Ideal (Boundary 1)

Ideal (Boundary 2)

1

2

xy

z

-5

20Ez (V/m)

(a)

(b)

(c)

(d)(f)

Figure 25. (a) Luneburg lens based on graphene metasurface. Shown is the simulated phase of Ey of the surface plasmon at 30THz on the graphene. D = 1.5 µm, w = 75 nm, and L = 1.6 µm. (b) Snapshot of the field in a metasurface Maxwell’s fish-eyelens consisting of pins of different heights on a grounded slab and curvilinear trajectory of the real part of the Poynting vector. (c)Snapshot of simulated, vertical electric field (Ez) of a metasurface that transforms a cylindrical surface wave into a surface wavewith trapezoidal power density and linear phase progression. (d) Upper panel: simulated and ideal power densities along boundary1 and boundary 2. Lower panel: phase profiles along boundary 1 and boundary 2. (e) Schematic of a telecom TE00-to-TM10 modeconverter consisting of silicon phased array antennas patterned on a Si3N4 waveguide. The phase response is due to the optical Mieresonance in the silicon nanorod. (f) Simulated field evolution in the mode converter. (g) Purity of the converted TM10 mode as afunction of wavelength, showing that the mode converter works over a broad wavelength range. (a) used with permission from [159],(b) used with permission from [153], (c) and (d) used with permission from [160], (e)-(f) used with permission from [161,162].

into the field of integrated photonics where 1D phasedarray antennas patterned on optical waveguides enablethe control of optical power flow and mode couplingin the waveguides. The 1D antenna array introducesa unidirectional phase gradient dΦ/dx, where dΦ isthe difference in phase response between adjacentantennas that are separated from each other by asubwavelength distance of dx. The phase gradientis equivalent to a unidirectional effective wavevector∆k along the waveguide, which leads to directionalcoupling of waveguide modes. That is, optical powercouples preferentially from one waveguide mode toa second waveguide mode, whereas optical couplingfrom the second mode back to the first one is highlyinefficient. As a result, the phase matching conditionsare greatly relaxed, which enables the demonstrationof extremely broadband and robust waveguide modeconversion (figure 25(e-g)) [161,162].

7. Active metasurfaces

Active devices and components play a critical role inmodern electromagnetic and photonic systems. Ac-

tive control of metamaterials and metasurfaces extendstheir exotic passive properties by allowing fine reso-nance tuning to adapt to the operational conditions,and enabling a switchable resonant response, for in-stance, for signal modulation in communication andimaging. Furthermore, the concentration of opticalpower in metasurface resonators integrated with op-tical nonlinear materials can dramatically enhance thenonlinear response, as predicted in Pendry’s originalwork on SRRs [15]. As compared to bulk metamateri-als, the planar configuration of metasurfaces facilitatesthe integration of active functional materials. A vari-ety of functional materials providing tunable refractiveindices through thermal excitation, voltage bias, mag-netic field, optical pump, or mechanical deformationhave been successfully incorporated into metasurfaces.In particular, semiconductors and graphene becomethe materials of choice for electrically tunable activemetasurfaces.


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Figure 26. Optically tunable THz metal/semiconductor hybrid metasurfaces. (a) SEM image of an electric SRR unit cell of afrequency tunable THz metasurface. (b) Upon photoexcitation of the silicon bars, the gap capacitance increases, which results ina lower resonance frequency. (c) Optical microscopy image of an ultra broadband THz modulator. (d) Without photoexcitation,the transmission is high at the low frequency side of the Lorentzian resonance of the gold grid; upon photoexcitation of the siliconregion, it becomes effectively a wire grating showing low transmission. (e) Schematic (left panel) and optical microscopy image (rightpanel) of a THz metamaterial absorber consisting of silicon pads integrated at the gaps of SRRs. (f) Photoexcitation dramaticallytunes the property from dual-band to a broadband absorption. (a) and (b) used with permission from [163], (c) and (d) used withpermission from [164], (e) and (f) used with permission from [165].

7.1. Actively switchable and frequency tunablemetal/semiconductor hybrid metasurfaces

The conductivity of semiconductors can be increasedby orders of magnitude through doping, and thussemiconductors can be converted into plasmonicmaterials in the infrared and spectral ranges withlonger wavelengths. Active tuning of the conductivitycan be realized by carrier injection and depletionthrough photoexcitation and voltage bias. Sucha unique capability makes semiconductors idealmaterials for integration into metamaterial structuresto accomplish active and dynamic functionalities,particularly in the microwave and THz frequencyrange. Varactor diodes have been widely used torealize frequency tunable and nonlinear response [166,167] in microwave metasurfaces. At THz frequencies,SRR arrays can be directly fabricated on top ofsemiconducting substrates such as intrinsic siliconand gallium arsenide, and the resonant responsecan be tuned through photoexcitation of free chargecarriers at the substrate surface [168], resulting inan ultrafast switching speed [169]. Furthermore,semiconductors can be used as part of the resonantstructure. In this case, photoexcitation dynamicallymodifies the structural geometry of the resonator,enabling switchable or frequency tunable response. Asshown in figure 26(a), a pair of silicon bars form apart of the capacitive gap in an electric SRR unit

cell. Under photoexcitation with near-infrared light,the silicon bars become metallic, which increases theSRR capacitance. Therefore, the frequency of theSRR LC resonance is tuned to a lower frequencywith the tuning range of about 20% [163], as shownin figure 26(b). A variety of similar structures weredemonstrated, resulting in a blue shift of the resonancefrequency [170].

Optically modifying the metasurface geometricstructure enables the transition between different typesof resonances. In figure 26(c) silicon is integratedat the gaps of a metal patch array that exhibits adipolar resonance without photoexcitation and allowshigh transmission below the resonance frequency.Under photoexcitation, the metallic silicon connectsthe metal patches, effectively forming a metal wiregrating that blocks the low frequency THz waves,as shown in figure 26(d), and resulting in ultrabroadband THz modulation [164]. Recently, opticallytunable THz metamaterial perfect absorbers [165] weredemonstrated, as shown in figure 26(e) and (f), wheresilicon islands are located at the gaps of electric SRRs.Using such an approach, a variety of optical responsescan be switched/tuned via photoexcitation, such asthe handedness of chiral metasurfaces [171, 172] andplasmonic electromagnetically induced transparency(EIT) [173].

Semiconducting hybrid metasurfaces feature elec-trical tuning of resonances via the application of a volt-


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Figure 27. Electrical modulation of metal/semiconductor hybrid metasurfaces. (a) Schematic of a unit cell of a high-speedTHz metasurface modulator based on double-channel heterostructures. (b) Modulation performance at different frequencies. (c)Schematic of an active THz metasurface diffraction grating formed by 32 columns controlled by independent voltage biases, wheredifferent colors indicate different voltage biases. (d) Dynamic diffraction is enabled by applying reverse voltage biases to alternatecolumns. An unprecedented modulation depth of 22 dB is accomplished at the designed operation frequency of 0.4 THz. (e) THzspatial modulator with 8 × 8 pixels based on electrically switchable THz metasurface absorbers and used for THz compressiveimaging, and (f) the corresponding device schematic consisting of a linked array of metallic resonators making Schottky contactswith an underlying n-doped semiconductor spacer, a metal ground plane serving as the ohmic contact, as well as the accessorystructure enabling independent voltage biases to the pixels. (a) and (b) used with permission from [179], (c) and (d) used withpermission from [180], (e) and (f) used with permission from [178].


age bias, which is more convenient and practical for ap-plications. The most prominent examples are the inte-gration of varactor diodes for microwaves and Schottkyjunctions for THz frequencies. The first demonstra-tion of an electrically switchable THz metasurface fea-tured an unprecedented 50% modulation depth [174],which was further improved to 80% through structuraloptimization [175]. Together with the causally con-nected phase modulation (up to 0.55 rad), this deviceallows broadband THz modulation [174] that can beused to replace a mechanical optical chopper in a lock-in THz detection scheme with modulation speed in theMHz range [176–178], limited either by the large de-vice area accompanied by high stray capacitance orparasitic capacitance from the bonding electrodes andwires. Very recently, GHz electronic modulation speedhas been demonstrated by using double-channel het-erostructures supporting nanoscale 2DEGs with highcarrier concentration and mobility [179], shown in fig-ure 27(a). Through designing a composite hybridmetasurface structure to reduce the stray capacitance,1 GHz modulation speed, 85% modulation depth (fig-ure 27(b)), and a phase shift of 1.19 rad were experi-mentally realized during real-time dynamic tests. Fur-thermore, a wireless free space modulation THz com-munication system based on this external THz mod-ulator was tested using 0.2 Gbps eye patterns. Thisaccomplishment opens an avenue toward the develop-ment of high performance THz wireless communicationand imaging systems.

In recent work, an electrically driven THz meta-surface active diffraction grating was demonstrated torealize background-free THz modulation with an un-precedented 22 dB of dynamic range [180]. Each “grat-ing finger” consists of an array of electrically connectedand switchable SRRs forming a column that is con-trolled by an independent voltage bias, as shown infigure 27(c). The diffractive metasurface grating is cre-ated by applying a voltage bias to alternate columnswithin the 32-column metasurface structure, result-ing in a frequency dependent diffraction angle for theincident broadband THz radiation. At the metasur-face resonance frequency of 0.4 THz, the diffraction isstrongest because of the largest transmission contrastbetween two neighboring columns. However, when thesame voltage bias is applied to each of the columns,the structure behaves as a uniform metasurface withno observable diffraction. Therefore, application of anAC voltage to alternate columns results in background-free diffractive modulation of the incident THz radia-tion, as shown in figure 27(d).

Spatial light modulators have been realized bypixelating the metasurface for independent control ofreflection, transmission, or their phase. A prototypeTHz metasurface spatial light modulator with 4 ×

4 pixels was realized to demonstrate reconfigurableinterference patterns of double slits [181]. THzmetasurface spatial light modulators with a largernumber of pixels are possible, although the increasingnumber of electrical connecting wires makes themmore complicated. One solution to this problemis a reflection-mode metasurface spatial modulatorbased on an electrically tunable metamaterial absorberstructure [178]. As shown in figure 27(f), a linkedarray of resonators and an underlying semiconductorlayer create Schottky junctions, and a metal groundplane serves as the ohmic contact. Application of areverse voltage bias enables tuning the frequency ofthe resonant absorption, with modulation speeds up to10 MHz. This type of THz spatial modulators basedon metamaterial absorbers, shown in figure 27(e),have been recently successfully employed in THzcompressive imaging [182].

7.2. Graphene hybrid metasurfaces

Except for fabrication of metallic metasurface struc-tures directly on a substrate such as those shown infigure 27(a) and (c), integration of crystalline semi-conductor films or islands into the critical regions ofmore complex metasurfaces (e.g., the structure shownin figure 26 and figure 27(f) as well as other few-layer metasurfaces) poses significant fabrication chal-lenges [186] mainly due to the requirement of nano-lithography or transferring fragile semiconductor thinfilms. In this sense, the excellent mechanical propertiesand the tunable carrier density of graphene make it anexcellent material to enable active metasurfaces [187].Graphene has largely tunable optical conductivity inthe mid-infrared and THz frequency ranges. The dop-ing of graphene can be adjusted through changing thebias voltage by a factor of 10 at room temperature,which leads to a large change in its sheet conductiv-ity σ and therefore the in-plane electric permittivityε‖ = 1 + iσ/(ε0ωt), where t = 0.33 nm is the thicknessof single-layer graphene.

The resonant response of metasurfaces is ofparticular importance to enhance interactions betweenatomically thin graphene sheets and mid-infraredand THz radiation. Metallic plasmonic antennasare able to capture light from free space andconcentrate optical energy into subwavelength spots.The electric field at these spots can be two tothree orders of magnitude larger than the incidentfield. By placing graphene in the hot spots createdby metallic plasmonic antennas and by tuning theoptical conductivity of graphene, one can switchthe resonance or tune the resonance frequency ofthe composite over a wide range. In the THzfrequency range, intraband transitions in graphenesheets have been used to demonstrate broadband


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Figure 28. Electrically tunable graphene-based metasurfaces. (a) Schematic of an ultrathin mid-infrared modulator based on atunable metasurface absorber. (b) SEM image of the metasurface absorber. Inset: a zoomed-in view of a portion of the device. (c)Measured reflection spectra (normalized to the reflection spectrum of an aluminum mirror) of the metasurface absorber in (b) atdifferent gate voltages |VG − VCNP|, where VCNP is the gate voltage when the concentrations of electrons and holes in the graphenesheet are equal, i.e., charge neutral point (CNP). (d) SEM image of a metasurface structure exhibiting dual Fano resonances. (e)Average near-field intensity enhancement η on graphene surface. Insets: spatial distribution of η inside the gap for the two Fanoresonances. (f) Measured reflection spectra of the device in (d) as a function of the Fermi energy. (g) Schematic of a metasurfacemodulator based on a graphene Salisbury screen. The inset illustrates the device with the optical waves at the resonance condition.(h) Change in absorption with respect to the absorption at CNP in 40-nm-wide graphene nanoapertures at various doping levels.The solid black curve corresponds to bare (unpatterned) graphene. The inset: AFM image of graphene nanoapertures with 40 nmwidth. (a)-(c) used with permission from [183], (d)-(f) used with permission from [184], (g) and (h) used with permission from [185].

electrical modulation [188], and patterned graphenestructures have been shown to exhibit resonantplasmonic response [189, 190]. Integrating grapheneinto metallic resonators has enabled the demonstrationof THz metasurface electrical modulators [191–193].

Mid-infrared metasurfaces with electrically tun-able spectral properties have been experimentallydemonstrated by controlling the carrier density ofgraphene [194]. Optimizing optical antenna designshas improved both the frequency tuning range and themodulation depth [195]. In figure 28(a), the uppermetasurface layer is separated from a back aluminummirror by a thin aluminum oxide film. Such a reflect-array structure exhibits nearly perfect absorption [183].That is, at the OFF state the reflection is nearly zero,and the frequency at which near-zero reflection occurscan be tuned by applying a voltage bias that modi-fies the dispersion of the top graphene-antenna array(figure 28(c)). This approach provides a modulationspeed in the tens of MHz range and an optical modu-lation depth close to 100% with the latter defined as1−Rmin(λ)/Rmax(λ) where Rmin(λ) and Rmax(λ) arethe minimum and maximum achievable reflectivity at

a certain wavelength λ [183].A narrow spectral width is essential for realizing a

high modulation depth based on resonance frequencytuning. For this purpose one may integrate grapheneinto metasurfaces that exhibit high Q-factor Fanoresonances, such as the one shown in figure 28(d),which consists of an array of connected dipole andmonopole resonators fabricated on top of a thinsilicon dioxide layer on a silicon substrate [184].This metasurface structure exhibits double plasmonicelectromagnetically induced transparency (EIT) asillustrated by the two near-field intensity enhancementpeaks in figure 28(e) and two reflection minima infigure 28(f). The graphene-SiO2-silicon structurealso enables back-gating to tune the graphene carrierdensity, which consequently tunes the Fano resonances(figure 28(f)). At a specific wavelength, it results inhigh reflection “ON” and low reflection “OFF” stateswith an experimentally measured modulation depthup to 90%, though the insertion loss of 81% is stillrather high and the bandwidth is also rather small(a few percent of the operational wavelength) [184].Phase modulation has been also shown recently in


a similar graphene hybrid metasurface in the mid-infrared, which can be potentially used for motionsensing and tunable waveplates [196].

Electrically tunable metasurfaces can be made ofstructured graphene sheets without utilizing metallicplasmonic antennas. Figure 28(g) shows a reflect-array mid-infrared modulator consisting of graphenenanoapertures (i.e., voids cut into a graphene sheet)separated from a metallic back mirror by a thin film ofSi3N4 [197]. The width of the nanoapertures is chosento be in the range of 20-60 nm, so that incident mid-infrared light can excite plasmonic resonances in thenanoapertures, leading to strongly enhanced opticalabsorption of up to 25%. As the bias voltage changesthe carrier doping of the perforated graphene sheet,the plasmonic resonances shift, giving rise to tunableamplitude and spectral position of the absorptionpeaks (figure 28(h)).

7.3. Other resonance switchable and frequency tunablemetasurfaces

While electrically tunable metasurfaces integratedwith semiconductors and graphene are of utmostimportance in applications, there are a variety ofother functional materials and structures that havebeen successfully used to realize active metasurfaces.When a THz metallic SRR array was fabricateddirectly on top of a strontium titanate (STO)substrate (a phase transition material), the resonancefrequency experiences a red-shift with decreasingtemperature, due to the increasing refractive indexof the STO substrate, although it suffers fromsignificant insertion loss due to the high refractiveindex of the STO substrate [199]. Vanadium dioxide(VO2) exhibits thermally driven insulator-to-metalphase transition and has attracted great interest inrealizing thermally active metasurfaces at THz andinfrared frequencies [200–205]. The hysteresis of itsphase transition has been utilized to demonstratemetasurface memory devices [201]. The resonanceof metasurfaces based on VO2 can be also switchedthrough the application of a voltage bias [198]. In thelatter case, a thin layer of ionic gel was applied on thesurface of the metasurface (figure 29(a)). Applicationof positive (negative) voltage selectively tunes themetasurface resonance into the “OFF” (“ON”) stateby inducing the VO2 film into a more conductive(insulating) state. In particular, a positive voltagedrives the following electrochemical reaction: VO2 +2x e− → VO2−x + x O2−, so that VO2 goes across theboundary between the insulating and metallic statesfollowing the pink solid arrow in figure 29(b). As aresult, application of positive voltages damps the SRRresonance, with 3 volts yielding complete suppressionof the resonance (figure 29(c)).

(a)

(b)

(c)

Figure 29. (a) Schematic showing electrolyte gating of VO2-based metasurfaces. (b) Phase diagram of VO2. (c) Voltagedependent THz transmission spectra of the device in (a) at 315K.Insets: photos of gold SRRs sitting on VO2 before the ionic gelis applied. Used with permission from [198].

Liquid crystals can be also conveniently integratedwith metasurface structures, and help realize electri-cally tunable spectral properties when the refractiveindex of liquid crystals is adjusted [206, 207]. The fre-quency tuning range is, however, quite limited and theoperation speed is slow. THz superconducting meta-surfaces consisting of resonant elements made of su-perconducting films instead of the typically used met-als have shown outstanding switching and frequencytuning behaviors via thermal control [208–211] or pho-toexcitation [212], although this only applies to mi-crowave and THz frequencies, limiting the applica-tions of active superconducting metasurfaces. Last butnot least, integration of micro-electro-mechanical sys-tems (MEMS) into metasurfaces has enabled reconfig-


urable resonances by changing the geometry of the res-onant elements through thermal or electrostatic actu-ation [213–217].

7.4. Nonlinear metasurfaces

ETHz

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Figure 30. (a) Top panel: optical image of an array of goldelectric SRRs fabricated on top of a VO2 film showing THz-field-induced damage illustrated by the black spots at the split gaps.The dashed blue circle approximates the THz beam waist, andthe red curve approximates the THz intensity profile. Bottompanels: SEM images of a single SRR show that VO2 is damagedby the vertically polarized THz field, with an expanded viewof damage at the edge of the THz beam (right top) and nearthe beam centre (right bottom). (b) Experimental data showingincident field-dependent nonlinear transmission spectra of SRRson VO2 at 324 K, for in-gap fields ranging from 0.3 to 3.3MV/cm. Used with permission from [218].

The abilities of metasurfaces to promote light-matter interaction and manipulate local optical po-larizations are ideally suited to enhance nonlinear op-tical effects. This is particularly significant in theTHz frequency range due to the difficulties in gen-erating high-power THz radiation. The concentra-tion of incident THz waves relaxes the requirementof a strong THz source, and further reveals the ul-trafast dynamics of electronic responses initiated bythe intense THz pulses. An excellent example isthe THz-field-induced insulator-to-metal transition inmetal/VO2 hybrid metasurfaces, where an array ofelectric SRRs were fabricated on top of a VO2 film(figure 30(a)) [218]. It was shown that the transmis-sion spectra depend on the incident field strength, asshown in figure 30(b), due to the phase transition ofVO2 that is initiated by Poole-Frenkel electron libera-tion, followed by lattice equilibration on a picosecondtimescale. The incident few hundreds kV/cm THz fieldis resonantly enhanced to the MV/cm level within thesplit gap, which is then sufficient to induce irreversibledamage of the VO2 film, as shown in figure 30(a).Such a methodology has been further applied to in-vestigate nonlinear metasurfaces integrated with semi-conductors such as gallium arsenide and indium ar-senide [219, 220], where the electric field induces in-tervalley scattering or impact ionization, resulting in

a reduced carrier mobility or increased carrier density,thereby either damping or strengthening the metasur-face resonant response. Strong THz nonlinear responsewas also observed in superconducting metasurfaces un-der intense THz radiation [221,222]. Although the en-ergy of a THz photon is well below that required todirectly break a Cooper pair upon absorption and theapplied THz pulses do not significantly raise the sam-ple temperature, the transmission measurements revealsignificant field-strength-dependent transmission spec-tra at various temperatures. It would be expected thatthe intense THz field can accelerate electrons that gainsufficiently high kinetic energy to induce Cooper pairbreaking, which damps the resonance similar to thecases of resonance switching and frequency tuning un-der thermal and optical excitation.

Conventionally, the phase matching condition innonlinear processes, such as second harmonic genera-tion (SHG), has to be satisfied in bulk nonlinear crys-tals to achieve efficient nonlinear optical generation.Under the condition of perfect phase matching, non-linearly generated optical signals constructively buildup, and optical power is continuously transferred fromthe pump(s) to the nonlinear optical signal. Metasur-faces greatly relax the requirement for phase match-ing as nonlinear processes occur within metasurfacesthat have significantly reduced thicknesses. Giantsecond-harmonic (SH) response (figure 31(a-c)) hasbeen experimentally demonstrated in plasmonic meta-surfaces integrated with nonlinear media [223]. Specif-ically, InGaAs/AlInAs multiple quantum wells wereused as the nonlinear media, which exhibit giant andelectrically tunable nonlinear coefficients in the mid-infrared [225–227]. The plasmonic metasurfaces weredesigned to not only enhance the local fields of boththe pump and SH signal, but also to manipulate thenear-field polarization, as the relevant field componentsinvolved in the harmonic generation are the ones nor-mal to the quantum wells (due to the selection rules forintersubband transitions within quantum wells [228]).The nonlinear metasurfaces achieved a nonlinear con-version efficiency of ∼ 2×10−6 using a pump intensityof only 15 kW/cm2 [223], corresponding to an effectivesecond-order nonlinear coefficient of χ(2) ∼ 30 nm/V,about three orders of magnitude larger than that ofLiNbO3. Even larger χ(2) ∼ 250 nm/V has been ex-perimentally demonstrated in a nonlinear metasurfaceconsisting of an array of SRRs and InGaAs/AlInAsmultiple quantum wells (figure 31(d,e)) [224]. Thetwo plasmonic resonances of the SRRs enhance, respec-tively, the pump and SH signal (figure 31(d)).

These demonstrations have followed the originalproposal of using SRRs by Pendry in 1999, where theresonance would localize electromagnetic energy withinthe small split-gaps and dramatically enhance nonlin-


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Figure 31. (a) Unit cell of the SHG metasurface. Dimensions of the gold nanocross are given in nm, and the unit cell has a dimensionof 1000 nm × 1300 nm. (b) Conduction band diagram of one period of an In0.53Ga0.47As/Al0.48In0.52As coupled quantum wellstructure designed as the nonlinear media for highly efficient SHG. The moduli squared of the electron wavefunctions for subbands1, 2 and 3 are shown and labelled accordingly. Transitions between pairs of electron subbands are marked with double-headed redarrows, and the values of the transition energies (E21 and E32) and dipole moments (Z21, Z32 and Z31) are shown next to eacharrow. (c) SHG from metasurfaces based on (a) and (b). Shown are SH peak power (left axis) and intensity (right axis) as a functionof pump peak power squared (bottom axis) or peak intensity squared (top axis) at a pump wavenumber of 1240 cm−1 for differentinput/output polarization combinations. (d) Left panel: Schematic of a metasurface consisting of SRRs on top of a stack of MQWs.Upper right panel: Top view of one SRR. Lower right panel: Schematic showing the two main resonant modes of the SRR at thepump and SH frequency, respectively. (e) Intensity of the SH signal propagating in the forward and backward directions with respectto the nonlinear metasurface in (d) as a function of pump intensity. (a)-(c) used with permission from [223], (d) and (e) used withpermission from [224].

ear response in materials being introduced [15]. Mostexperimental demonstrations of nonlinear metamate-rials have been mainly focused in the microwave fre-quency range using packaged nonlinear electronic ele-ments, such as varactor diodes, to introduce nonlinear-ity into the gaps of the metal resonators, resulting innonlinear functionalities such as bistability [229, 230],resonance tunability [166, 231], and harmonic gener-ation [232, 233]. In the optical frequency regime, inaddition to the difficulty in packaging nonlinear ma-terials, it is challenging to fabricate bulk metamate-rials consisting of complex three-dimensional nanos-tructures, and utilize their thickness to enhance non-linear response. Experimental work has been scarceas compared to its microwave counterpart. One ofthe focuses has been harmonic generation using sin-gle layer metal SRR arrays (tens of nanometer thick-ness) excited at their magnetic resonance [234, 235],where the nonlinearity is associated with the dynamicsof free and bound charges, particularly at the metalsurface [236]. This seems to be also responsible forthe recently observed broadband THz generation underfemtosecond near-infrared laser excitation in an arrayof gold SRRs [237]. It was also shown that the ge-

ometry of resonators, particularly the asymmetry ra-tio, plays a critical role as it governs the spatial over-lap of the resonant modes at the pump and harmonicfrequencies [238]. Although the nonlinear coefficientswere often enhanced by orders of magnitude comparedto common nonlinear crystals, the absolute conversionefficiency is still rather low. Further improvement isnon-trivial and cannot be realized by simply stackingmulti-layers for larger interaction thickness due to theimpedance and propagation phase mismatches.

A step further is the demonstration of nonlinearphased arrays that radiate generated SH signals intodifferent directions depending on their polarizationstates [239]. In the metasurface structure shown infigure 32(a), the top row of six identical resonatorswithin the unit cell generate a single u-polarizedbroadside beam, shown in the right panel offigure 32(b), at the SH frequency. In the bottomrow of four resonators within the unit cell, the lefttwo resonators have a π phase difference as comparedto the right two resonators, as the local effectivesecond-order nonlinear coefficient χ(2) changes signwhen the orientation of a SRR rotates by 180◦.Together they generate two v-polarized beams at ±40◦


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Figure 32. (a) SEM image of a portion of a nonlinear metasurface that radiates SH signal of different polarizations into differentdirections (i.e., polarizing beam splitter for SH signal). A unit cell of the metasurface is denoted by the red rectangle. (b) Measuredfar-field profiles for the metasurface in (a) for two orthogonal polarizations of the SH radiation when the pump beam is polarizedalong the vertical direction. (c) SEM image of a portion of a nonlinear metasurface Fresnel zone plate (FZP) showing mirror inversionof SRRs in adjacent zones that radiate SH waves with opposite phases. Arrows mark the effective χ(2) direction. (d) Recordedimages of SH signal at a distance of Z = 0 and Z = 1 mm from the metasurface in (c). (e) Upper and lower panels are, respectively,simulation and measurement results showing the focusing of SH signal by the FZP (m denotes focusing order). (a) and (b) usedwith permission from [239], (c)-(e) used with permission from [240].

as shown in the left panel of figure 32(b), wherethe radiation angles are determined by the period ofthe metasurface structure. The same effect was usedto demonstrate complex wavefront engineering of theSH signal generated from metasurfaces consisting ofgold SRRs (figure 32(c-e)) [240]. Here the surfacesecond-order nonlinearity of gold leads to SHG. Inexperiments a nonlinear Fresnel zone plate (FZP) wasdemonstrated, which focuses the SH signal to the focalspots of the plate, leading to a large enhancement ofthe SH intensity.

8. Summary and outlook

Metamaterials and metasurfaces have led to the real-ization of novel electromagnetic properties and func-tionalities through tailoring subwavelength structuresand integrating functional materials. In this paperwe have reviewed the recent development of two-dimensional metamaterials – metasurfaces – by intro-ducing the fundamental concepts, physical realization,and their promising applications in the control andmanipulation of electromagnetic waves at frequenciesranging from microwave to visible light. One of our fo-cuses is on the creation of an arbitrary phase profile forwavefront control and beam forming using both metal-lic and dielectric metasurfaces. Another focus is on thefew-layer metasurfaces that address the efficiency issue

encountered during the earlier development of meta-surfaces. Active and nonlinear metasurfaces representan important research direction that will greatly ex-pand metasurface functionalities and applications. Asa rapidly developing research field that has attractedworld wide interest, it would be impossible (and notnecessary) to include every aspect of its past success.For instance, we have not included metasurfaces forantireflection coatings [85, 241], photonic spin Hall ef-fects in metasurfaces [242] and ultrathin invisibilitycloaks [243].

We see a number of promising areas in fundamen-tal research and practical applications where metasur-faces could have an important impact:

(1) Dispersionless flat lenses. Flat lenses that areable to correct chromatic aberration over a broad wave-length range, and reduce spherical aberration, coma,and other monochromatic aberrations, could revolu-tionize optical instrumentation. Substantially shrink-ing the complexity and size of optical instruments (e.g.,replacing the entire set of compound lenses in a cameralens with a few dispersionless and aberration-correctedflat lenses) seems feasible in view of recent develop-ments of metasurface lenses.

(2) Optical modulators and spatial light modu-lators (SLMs) in the mid-infrared and THz spectralrange. The lack of compact and fast modulators andSLMs has been a big challenge that prevents the wide


applications of mid-infrared and THz technology infree-space communications, imaging, LIDAR (light de-tection and ranging), and homeland security (e.g., re-mote sensing, surveillance, and navigation in severe en-vironments, such as foggy and dusty weather). Meta-surfaces provide an ideal platform to create flat mod-ulators in the mid-infrared and THz regimes as theyenable a strong interaction between light and materi-als with tunable optical properties, and allow for in-troducing spatially-varying optical response. Stronglight-material interactions enabled by metasurfaces al-low for reducing the amount of tunable materials usedso that one can increase the modulation speed.

(3) Radiative cooling metasurfaces. Metasurfacesthat possess exceptional thermoregulatory propertieshave been an emerging field of research and have thepotential to make an important technological impact.Fan and colleagues are pioneering the research onradiative cooling metasurfaces [244–246], which havestrong reflectivity in the solar radiation spectrum andenhanced emissivity in the thermal radiation spectrum.Metasurfaces based on multilayered thin films havedemonstrated in experiments passive cooling of objectsto a few degrees below the ambient air temperatureunder direct sunlight [246]. Chen and colleaguesrecently proposed a fabric that blocks sunlight andprovides passive cooling via the transmission ofthermal radiation emitted by the human body [247]. Itis interesting to note that radiative cooling has alwaysbeen essential for the survival of animals living inharsh environmental conditions. Yu and co-workersrecently reported the thermoregulatory strategies thatenable Saharan silver ants to forage in the middaysun on the desert surface where temperatures canreach 70◦C (which is not survivable by their primarypredators). It was found that a monolayer of denselypacked hairs with triangular cross-sections, in somesense a biological “metasurface”, enhances not onlythe ant body’s reflectivity in the visible and near-infrared, where solar radiation culminates, but also itsemissivity in the mid-infrared [248]. The combinedeffect enables the ants to minimize absorption fromsolar radiation, and to efficiently dissipate heat backto the surroundings via blackbody radiation. Animalsand plants living in extreme environments couldprovide us valuable scientific and engineering lessonson optical design and thermal management. In general,by designing the structural hierarchy, compositionalheterogeneity, and local anisotropy of metasurfacestructures, one could create coatings that are opticallythin and have desired spectral properties (reflectivity,absorptivity, transmissivity, and emissivity) over anextremely broad electromagnetic spectral range. Suchultra-thin and ultra-broadband metasurfaces will opendoors to a variety of new applications, including control

of radiative heat transfer, infrared camouflage andstructural coloration.

(4) New material platforms for metasurfaces.Investigations of materials with low losses, tunability,high melting point, and CMOS compatibility formetamaterials and metasurfaces have been very activein recent years. Transition-metal nitrides such asTiN show comparable optical properties as gold inthe visible and infrared but have much higher meltingpoints [249–251], a property that can be exploredfor metasurface applications involving high opticalintensity. Transparent conducting oxides (TCOs)such as indium-tin-oxide enable one to control thespectral location of the epsilon-near-zero point, whichis associated with enhanced optical near-fields; theresulting strong interaction between light and TCOscan be exploited for optical modulation [252, 253]and nonlinear optics. Phase-change materials such aschalcogenide alloys that have been used in rewritableCDs, DVDs, and Blu-ray discs, can be switchedbetween the amorphous and crystalline states by laseror electrical current pulses with controlled durationand intensity [254, 255]. This material system hasrecently been used to demonstrate all-optical, non-volatile, metasurface switch [256], and high-resolutionsolid-state displays [257]. SmNiO3, a prototypicalphase-transition perovskite nickelate, exhibits non-volatile and reversible large refractive index changesover an ultra-broad spectral range, from the visibleto the long-wavelength mid-infrared. The superbroadband performance is due to strong electroncorrelation effects [258], and this new mechanism canbe exploited to create a variety of active photonicdevices.

Acknowledgments

H.T.C acknowledges support in part from the LosAlamos National Laboratory LDRD Program. N.Y. acknowledges support from NSF (grant ECCS-1307948), the AFOSR Multidisciplinary UniversityResearch Initiative program (grant FA9550-14-1-0389), and DARPA Young Faculty Award (grantD15AP00111). This work was performed, inpart, at the Center for Integrated Nanotechnologies,a U.S. Department of Energy, Office of BasicEnergy Sciences Nanoscale Science Research Centeroperated jointly by Los Alamos and Sandia NationalLaboratories. Los Alamos National Laboratory,an affirmative action/equal opportunity employer, isoperated by Los Alamos National Security, LLC, forthe National Nuclear Security Administration of theU.S. Department of Energy under Contract No. DE-AC52-06NA25396.


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