Complete Complex Amplitude Modulationwith Electronically Tunable GraphenePlasmonic MetamoleculesSangjun Han,†,# Seyoon Kim,*,‡,# Shinho Kim,† Tony Low,§ Victor Watson Brar,‡

and Min Seok Jang*,†

†School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea‡Department of Physics, University of Wisconsin−Madison, Madison, Wisconsin 53606, United States§Department of Electrical & Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455, United States

*S Supporting Information

ABSTRACT: Dynamic high-resolution wavefront modu-lation of light is a long-standing quest in photonics.Metasurfaces have shown potential for realizing lightmanipulation with subwavelength resolution throughnanoscale optical elements, or metaatoms, to overcomethe limitations of conventional spatial light modulators.State-of-the-art active metasurfaces operate via phasemodulation of the metaatoms, and their inability to alsoindependently control the scattered amplitude leads to aninferior reconstruction of the desired wavefronts. Thisfundamental problem posed severe performance limita-tions particularly for applications relying on subwavelengthspatiotemporal complex field modulation, which includes dynamic holography, high-resolution imaging, optical tweezing,and optical information processing. Here, we present the “metamolecule” strategy, which incorporates two independentsubwavelength scatterers composed of noble metal antennas coupled to gate-tunable graphene plasmonic nanoresonators.The two-parametric control of the metamolecule secures the complete control of both amplitude and phase of light,enabling 2π phase shift as well as large amplitude modulation including perfect absorption. We further develop ageneralized graphical model to examine the underlying requirements for complete complex amplitude modulation,offering intuitive design guidelines to maximize the tunability in metasurfaces. To illustrate the reconfigurable capabilityof our designs, we demonstrate dynamic beam steering and holographic wavefront reconstruction in periodically arrangedmetamolecules.KEYWORDS: graphene, plasmonics, nanoresonator, mid-infrared, complex amplitude modulation

Wavefront engineering is a crucial technology forholography, high-resolution imaging, optical tweez-ing, optical data storage, and communication. In thepast decade, metasurfaces have emerged as an effective meansof engineering optical wavefronts. They have been used toproduce nonintuitive refraction phenomena1 and high-resolution images beyond the diffraction limit,2 all of whichare otherwise unachievable in conventional optical devices.Metasurfaces work by utilizing subwavelength scatterers, i.e.,metaatoms, to locally control the amplitude and phase ofreflected or refracted light. In most cases, those metaatoms arecomposed of a metal or dielectric structure with one or morescattering resonances near the operating frequency. The use ofmetasurfaces to modulate the amplitude and phase of thescattered light has enabled general wavefront manipulationfrom ultrathin and flat surfaces.3−12

Dynamic reconfigurability of a metasurface is highlydesirable, as it would extend the application space toholographic projections, fast optical beam steering or routing,and high-speed aberration correction in microscopes ortelescopes. To impart dynamic tunability in these devices,materials with tunable optical properties are included in thescattering structures, which allows the scattering resonances tobe shifted in frequency and amplitude, which in turn affectstheir scattering behavior. For example, by including grapheneor indium tin oxide (ITO), tunable metasurfaces have beenexperimentally demonstrated that can act as either a perfect

Received: November 22, 2019Accepted: December 10, 2019Published: January 6, 2020

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absorber13 or efficient amplitude modulators.14,15 Similarstructures have been used to realize dynamic beam steering16

and to continuously control the phase of a reflected light beamup to 1.2π and 1.7π for graphene17 and ITO,18 respectively.Likewise, direct-gap semiconductors,19 thermo-optically tunedsilicon,20 and other phase change materials21,22 have also beenutilized to dynamically change the scattering behavior ofsubwavelength structures.Despite the rapid progress in the field, current dynamic

metasurfaces suffer from an inevitable interference between

amplitude modulation and phase modulation, where thechange of scattered phase also unavoidably alters its scatteredamplitude, and vice versa. Furthermore, no device thus far hasbeen demonstrated to dynamically tune a scattered wavefrontover a 2π of phase space. These problems stem from the basictuning mechanism. Current metasurfaces have been designedbased on the regulation of a single resonance in an individualmetaatom, which limits the degrees of freedom to control twocomponents independently, i.e., the amplitude and the phase oflight, and the access to the complex amplitude space. The

Figure 1. (a) Schematic of the metamolecule composed of a pair of independently controlled graphene plasmonic metaatoms. Transversemagnetic (TM)-polarized incoming light is assumed. The graphene Fermi levels applied to the graphene plasmonic ribbons (GPRs) aredenoted by EF1 and EF2. The structural parameters are as follows: p1 = 1295 nm, p2 = 1159 nm, g1 = 90 nm, g2 = 80 nm, w1 = 45 nm, w2 = 50nm, h = 80 nm, and d = 250 nm. These parameters were tuned to maximize the tunabilities at a free space wavelength of 7 μm with agraphene carrier mobility of 1000 cm2 V−1 s−1. (b) Amplitude map and (c) phase map of the reflection as independently adjusting thegraphene Fermi levels (EF1 and EF2) of the metaatoms. Reflected transverse magnetic field components (Hy/H0) displaying (d) phasemodulation with a constant amplitude (|r| = 0.5) along the solid blue line and (e) amplitude modulation including perfect absorption with aconstant phase (ϕ = 0) along the solid red line. In (d) and (e), the scale bars are 4 μm. Representative electric field (|E|/|E0|) distributionsaround the metamolecules (f) with a fixed amplitude and (g) with a fixed phase. In (f) and (g), the scale bars are 500 nm.

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limited tunability results in lowering the resolution of imagesor creating undesirable noise in images. To the best of ourknowledge, no active metasurface has yet been reported thatcan control both phase and amplitude independently, i.e.,complex amplitude modulation, which is necessary for completewavefront reconstruction.In this paper, we present an electronically reconfigurable,

reflecting metasurface structure composed of subwavelengthscattering elements that can locally alter the phase of scatteredlight over a complete 2π phase coverage, in conjunction withindependent control of the amplitude of the scattered light. Theunit cell of our proposed structure, herein denoted asmetamolecule, consists of a pair of noble metal antennas,each in contact with graphene plasmonic ribbons (GPRs).Here, the pair of Fermi levels of the GPR constitute the twocontrol parameters for our metamolecule in modulating theamplitude and the phase of light. Each metamolecule operatesat 7 μm and is subwavelength, such that only their collectiveresponses are observable in the far field. In other words, thismetamolecule configuration composes ensembled opticalresponses from a pair of metaatoms, which displays entirelydifferent optical behaviors from each metaatom and providesmore controllability in complex amplitude modulation. Inaddition, a generalized graphical approach based on effectivesurface admittance elucidates the underlying preconditions forthe complete complex amplitude modulation, providingintuitive design guidelines to maximize the tunability of themetamolecules. To illustrate the reconfigurable capability ofour designs, we demonstrate dynamic beam steering andholographic wavefront reconstruction in a structurally identicalmetasurface by simply tuning the graphene Fermi levels of themetamolecules.

RESULTS AND DISCUSSIONDevice Geometry and Complex Amplitude Modu-

lation. Graphene is an exotic mid-infrared plasmonic material,with extremely confined plasmonic modes that are highlyelectronically tunable due to its atomic thickness.23−30 Inaddition, the small optical-mode volumes of grapheneplasmons are beneficial for miniaturizing the active plasmonicdevices as well as driving strong light−matter interactions in adeep subwavelength scale. These optoelectronic properties ofgraphene allow for the creation of electronically tunable lightmodulation devices controlling the intensity and phase of lightfrom the mid-infrared to THz. In particular, our recentexperimental results show that the key components of ourproposed design are experimentally feasible; namely, the stronglight−matter interactions that occur between noble metalantennas and GPRs have been shown to enable large dielectrictunability.13,14 To be specific, it was demonstrated thatoscillator strength in GPRs can be also significantly enhancedby incorporating multiscale nanophotonic structures consistingof noble metal plasmonic structures.13,14,31−40 These sub-wavelength noble metal plasmonic structures improve theradiative coupling to the GPRs by bridging the largewavelength mismatch between free space photons and deep-subwavelength scale graphene plasmons. In addition, non-resonant field enhancement in the noble metal plasmonicstructures augments the oscillator strengths in the GPRs,enabling a large tunability in the local dielectric environment.It will be shown that the incorporation of multiscalenanophotonic structures allows our metamolecule structureto display large amplitude modulation and 2π phase shift, even

with an assumed graphene carrier mobility of ≤1000 cm2 V−1s−1, which is readily accessible in CVD-grown graphene.41

Figure 1a shows the proposed metasurface consisting ofperiodically arranged graphene plasmonic metamolecules,modulating the complex amplitude of the reflected mid-infrared light. The GPRs are combined with noble metalplasmonic structures to enhance the tunability, and a backreflector is incorporated to gate the graphene electrostaticallyand to further intensify the light−matter interactions in thegraphene.13,38,39 In a single metamolecule, or a unit cell of themetasurface, a pair of graphene plasmonic metaatoms arearranged side by side. The GPR is asymmetrically placed onone side of a metal strip such that each GPR is electronicallyisolated from another metal strip. This configuration allows usto tune the graphene Fermi level in each metaatom individuallythrough a gating voltage between the back gate and the metalstrip connected to the GPR, thus providing two degrees offreedom necessary for independently modulating the ampli-tude and the phase of the reflected light. In this way, ametasurface consisting of periodically arranged grapheneplasmonic metamolecules enables the electronic modulationof the complex amplitude by simply tuning the two grapheneFermi levels of the metamolecule. Here, we point out that thedynamic optical resonances in the proposed metasurfaceoriginate from strong plasmonic resonances in the GPRs,and not the metal strips. In fact, the plasmonic resonances ofthe metal strip are very much detuned from that of graphene.The metal strips are exploited to enhance the oscillatorstrengths of the GPRs by nonresonant focusing effects42 anddo not support additional plasmonic resonances. This impliesthat an optical response of each metaatom is independentlytunable with negligible intercoupling between the adjacentmetaatoms.Figure 1b,c illustrate the amplitude and the phase of

reflection coefficients of the proposed structures as a functionof the graphene Fermi levels (EF1 and EF2, as denoted in Figure1a). The geometries of the structure are carefully tailored toexhibit maximum tunability at a free space wavelength of 7 μmwith a graphene carrier mobility of 1000 cm2 V−1 s−1, andnormal incoming light with transverse magnetic polarization isassumed. The structural parameters are presented in thecaption of Figure 1a. Figure 1d,e illustrate the capabilities ofthe complex amplitude modulation in the proposedmetamolecules. A 2π phase shift with a fixed amplitude (|r| =0.5) of reflection and a large amplitude modulation with a fixedphase (ϕ = 0) metaatom can be achieved through the two-parametric tuning, EF1 and EF2, of the metamolecules.Representative electric field distributions around the meta-molecules are displayed in Figure 1f,g.Figure 1b shows that two perfect absorption conditions exist

at different ranges of graphene Fermi levels, whereas perfectabsorption is not achievable in a single metaatom. Thegraphene Fermi levels in Figure 1d,e are chosen along the solidblue line (constant amplitude, |r| = 0.5) and the solid red line(constant phase, ϕ = 0) in Figure 1b,c, respectively. Thegraphene Fermi levels (EF,1 and EF,2) used in Figure 1d,e aresummarized in the Supporting Information, Table S1. Similarcomplex amplitude modulations can also be realized along thedotted lines in Figure 1b,c, and the calculation results arepresented in the Supporting Information, Figure S1.

Generalized Graphical Approach to Complex Ampli-tude Modulation. Admittance analysis is convenient forinvestigating a stratified structure by a series of admittance for

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each layer. Moreover, our previous results demonstrated thateffective surface admittance accurately describes grapheneplasmonic nanostructures when the thickness and the period ofthe structures are in the subwavelength regime.13 To elucidatethe underlying requirements for the complete complexamplitude modulation, we develop a generalized graphicalmodel based on surface admittance. This approach can beexploited to devise general metasurfaces and to analyze theirdynamic complex amplitude behaviors.The proposed structure can be divided into two parts: a

structured surface and a substrate including a back reflector.Then, the complex reflection coefficient (r) of the structure interms of the admittances with normal incident light is derivedas

rY YY Y

11

s sub

s sub= −

̃ + ̃ −̃ + ̃ + (1)

where Ỹs and Ỹsub are the surface admittance and the substrateadmittance, respectively, normalized by the free spaceadmittance (Y0). The surface admittance, Ỹs, strongly dependson the tunable responses of the metasurface. For a metasurfacecomposed of a single type of metaatom, its plasmonicresonance follows a Lorentzian line shape as a function ofthe graphene Fermi level, which can be represented as acircular trajectory in the complex plane, rotating clockwise withincreasing graphene Fermi level (see Supporting Information,Note S1). The substrate admittance, Ỹsub, is determined by thestructural geometry and the dielectric constant of the

Figure 2. (a) Surface admittances and (b) complex amplitudes in the ideal case exhibiting closed circles. (c) Surface admittances and (d)complex amplitudes in an actual case exhibiting arcs. In (a)−(d), the solid color lines correspond to the metaatoms, and the shaded areasrepresent the reconstructed area by the metamolecule. The dotted lines correspond to the denoted amplitudes (|r|), and the gray lines in (a)and (c) represent the negative imaginary part of the substrate admittance (Ỹsub). In (d), the maximum amplitude covering 100% of the areais 0.566.

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substrate.13 Here, the substrate admittance can be consideredas a purely imaginary value when there is negligible absorptionin the substrate. More details on the surface admittance modelare given in the Supporting Information, Note S1.The advantage of this approach is that we can easily

ascertain the surface admittances necessary for a specificcomplex amplitude modulation range by using eq 1. Forexample, by transforming the origin of the r-plane, we canobtain the required surface admittance condition, Ỹs = 1 − Ỹsub,for perfect absorption (r = 0). We point out that any set ofconcentric circles centered at the origin of the r-plane (i.e., theconditions for phase modulation with constant reflectionamplitudes) can be mapped onto a set of nonconcentric circleswith radii of 2|r|/(1 − |r|2), as displayed by the dotted lines inFigure 2a (see Supporting Information, Note S2). In particular,all centers of the dotted lines are placed on the −Im(Ỹsub) axis.Recognizing that the surface admittance of a grapheneplasmonic metasurface inherently spans a circular trajectoryin the Ỹs-plane,

13 the problem of designing its dynamicresponse can be reduced to locating the desired center andradius of the circle in the Ỹs-plane by judiciously choosing thestructural parameters of the metasurface.The dynamic behavior of the metamolecule can be deduced

from the properties of the constituent metaatoms. The solidred (Ỹs1) and blue (Ỹs2) curves in Figure 2a correspond to the

proposed metaatoms’ surface admittances in the ideal case.Note that the centers of both circles are aligned with the−Im(Ỹsub) axis to maximize the tunability of the complexamplitude. Since the two types of metaatoms are connectedserially, the effective surface admittance Ỹs of the metamoleculeis obtained by the weighted harmonic mean of the two surfaceadmittances as Ỹs

−1 = (p1Ỹs1−1 + p2Ỹs2

−1)/(p1 + p2). In the idealcase where Ỹs1(EF1) and Ỹs2(EF2) form closed circles, theresulting surface admittance of the metamolecule Ỹs(EF1, EF2)spans the disc area displayed as the shaded region in Figure 2a.In other words, by tuning the graphene Fermi levels of the twometaatoms, one can independently control the amplitude andthe phase of the reflection from the metamolecule within theshaded area in Figure 2b. In Figure 2a,b, small voids appearinside the reconstructed areas of the metamolecule. Thesevoids originate from the weighted averaging method, and wecan eliminate the voids by balancing the radii of the Ỹs-circlesand the pitches of the metaatoms (see Supporting Information,Note S3).In realistic devices, the range of graphene Fermi level is

bounded by the breakdown voltage of the insulating layer. Dueto the limited tuning range, the surface admittance curves ofthe metaatoms cannot produce a closed circle but lead to theformation of an arc with a small opening as displayed by solidcolor lines in Figure 2c. Here, we assume that the graphene

Figure 3. (a) Schematic of the circuit model for a metaatom. Surface admittances evaluated by the circuit model (b) as the pitch is variedwith a fixed metal gap and (c) as the metal gap is varied with a fixed pitch. In (b) and (c), the solid color lines are calculated by full-wavesimulations, and the dotted color lines are evaluated by the circuit model.

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Fermi level can be tuned from 0 to 1 eV. This limitation causesadditional unfilled areas in the reconstructed surfaceimpedance area (see Supporting Information, Note S3). Thesurface admittance lines stop extending at the end due to thelimited range of the graphene Fermi levels. In addition, theinterband absorption in graphene inherently produces smalldeviations at low graphene Fermi levels, resulting in smallbending. In spite of these imperfections, Figure 2c shows thatthe metamolecule covers a wide range of surface admittance

values. The dotted color lines indicate the surface admittancescorresponding to the various reflection amplitudes.Figure 2d shows the reconstructed complex amplitudes from

the metamolecule (the shaded area) by independently tuningthe metaatoms (the solid color lines). The proposedmetamolecules produce 100% of the |r| ≤ 0.566 domain and98.1% of the |r| ≤ 0.6 domain. In particular, Figure 2dillustrates the limited modulation range when we rely onregulating a single resonance in metasurfaces. The results givenin Figure 2d are calculated by full-wave simulations. In the

Figure 4. Beam steering with angles (θr) of (a) 20.9°, (b) 45.5°, and (c) 72.0°. In (a)−(c), the target amplitudes are fixed at 0.5, and the scalebars are 5 μm. (d) Magnitude of the scattering parameters (|S|) of the beam steering. (e) Schematic of holographic wavefront calculation andreconstruction with metamolecules. (f) Reflected magnetic intensity (|H|2/|H0|2) distribution of single focusing with a beam spot located at(x, z) = (0 μm, 7 μm), where a free space wavelength (λ0) is 7 μm. Here, the air/metasurface boundary corresponds to z = 0. The maximumintensity at the focal spot is 2.21. (g) Magnetic intensity (|H|2/|H0|2) distribution of triple focusing with beam spots located at (x1, z1) = (−14μm, 56 μm), (x2, z2) = (0 μm, 31 μm), and (x3, z3) = (14 μm, 56 μm). The maximum intensities and the transverse full width half-maximums(FWHMs) at the focal spots are 1.48 and 0.52λ0 for ①, 1.57 and 0.43λ0 for ②, and 1.46 and 0.50λ0 for ③. In (f) and (g), the metasurfaceconsists of 75 metamolecules, and the scale bars are 20 μm.

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Supporting Information, Figure S7 reveals that the evaluationby the weighted averaging method for the metamoleculeadmittance shows excellent agreement with the full-wavesimulation results. This comparison also confirms that theintercoupling between the metaatoms is negligible. Moredetails are presented in the Supporting Information, Note S4.Circuit Analysis. To maximize the tunability in the

complex amplitude plane, the metamolecule should bedesigned such that the surface admittance curves of theconstituent metaatoms have maximum radii, while theircenters are placed on the −Im(Ỹsub) axis. To understand theelectromagnetic behaviors depending on the structuralparameters, we develop an analytic model describing themetasurface as a collection of effective circuit components, asshown in Figure 3a. The normalized surface admittance of ametasurface composed of a single metaatom can be expressedas

Y Ypg

Y

pY

i L Li C C

pg

Y( )1

( )

s metal GPR

0m k

c g

1

GPR

Ä

Ç

ÅÅÅÅÅÅÅÅÅÅÅ

É

Ö

ÑÑÑÑÑÑÑÑÑÑÑω

ω

̃ = ̃ + ̃

= − + +− +

+ ̃−

(2)

where ω, Ỹmetal, and ỸGPR are the operating frequency,normalized surface admittance of the metallic structure, andnormalized surface admittance of the equivalent GPR arraywithout the metallic structure, respectively. The elementalinductance (L) and capacitance (C) are determined by thestructural parameters, and Lm, Lk, Cc, and Cg correspond to themagnetic inductance, kinetic inductance, coplanar capacitance,and gap capacitance of the metallic structure, respectively.More details are provided in the Supporting Information, NoteS5. We note that the analytic circuit model shows goodagreement with full-wave simulation results as shown in Figure3b,c. The advantage of this circuit model is that we caninvestigate the electromagnetic behaviors of the GPRs and themetallic structure separately. The (p/g)ỸGPR in eq 2 describesthe plasmonic resonance of the GPRs depending on thegraphene Fermi level and thus determines the radius of thesurface admittance circle. Here, the p/g ratio is the fieldenhancement factor originating from the nonresonant antennaeffect by the metallic structure.42 A larger p/g ratio enhancesthe oscillator strength of the GPRs, resulting in a larger surfaceadmittance circle, as shown in Figure 3b,c. The radius of thesurface admittance circle depends linearly on p but quadrati-cally on 1/g because both the field enhancement factor and thedensity of the equivalent GPR array are directly proportional to1/g. The widths (w) of the GPRs primarily determine theresonant graphene Fermi level of a metaatom. In our proposeddevice, the GPR widths of the two metaatoms are chosen to be45 and 50 nm. These GPR widths lead to plasmonicresonances at the graphene Fermi levels of 0.506 and 0.603eV, respectively, at a free space wavelength of 7 μm (seeSupporting Information, Figure S3).The imaginary offset of the surface admittance curve is

mainly determined by the Ỹmetal in eq 2. In our design space,the Ỹmetal is dominated by the capacitance of the metallicstructure, whose contribution to the surface impedance is anorder of magnitude higher than that of the inductivecomponents. For a given thickness of the metallic layer (h),which in our case is approximately 2 orders of magnitude

shorter than the free space wavelength to ensure effectivesurface description, the imaginary offset increases in thenegative direction (i.e., the metasurface becomes morecapacitive) with larger pitches (p) and with narrower metallicgaps (g), as shown in Figure 3b,c. Since Cc and Cg areproportional to log(p/g) and 1/g, respectively, Ỹmetal ≈ −iωp(Cc + Cg)/Y0 depends superlinearly on p and sublinearly on1/g. For both metaatoms, the pitches and the gaps are chosento align the Ỹs-circles on the −Im(Ỹsub) axis.

Active Beam Steering and Holographic WavefrontReconstruction. Figure 4 illustrates the capability of theproposed metamolecules in dynamic wavefront reconstruction:active beam steering and beam focusing via holographicwavefront reconstruction. In these demonstrations, themetasurfaces are composed of periodically arranged meta-molecules, and the graphene Fermi levels are tuned to generatetarget complex amplitudes.In active beam steering, the graphene Fermi levels are tuned

to generate a linearly graded phase profile, ϕ(x) = kxx with aconstant amplitude of |r| = 0.5, where kx is the in-planewavevector of the target output beam. Since the width of ametamolecule, p = p1 + p2 = 2454 nm, is much shorter than thefree space wavelength λ0 = 7 μm, the proposed device cansufficiently resolve the wavefront of a beam with a largedeflection angle. Therefore, unlike conventional spatial lightmodulators whose elements are larger than the diffractionlimit, this device can steer a light beam at a wide angle withoutthe aid of external magnifying optics. As shown in Figure 4a−c,the full-wave simulation results demonstrate that the reflectedwavefronts are well aligned with the target refraction angles of20.9°, 45.5°, and 72.0°, which correspond to the phase rampΔϕ = kxp = π/4, π/2, and 2π/3, respectively. The scatteringparameters |S| presented in Figure 4d confirm good beamsteering performance with small side lobes, where nonzero sidelobes would originate from discrete sampling of the phase frontand crosstalk between the neighboring metamolecules.Figure 4e displays a schematic of the holographic wavefront

calculation and reconstruction for beam focusing. By placingsources at desired positions and evaluating the complexamplitude of light propagating from the sources, we cananalytically calculate the amplitude and the phase of light alonga metasurface plane. After tuning the graphene Fermi levels toproduce the necessary complex amplitudes, we can reconstructthe focal points in the free space. Figure 4f,g show lightfocusing with a single spot and triple spots with 75metamolecules via full-wave simulations. The target amplitude|r| and the phase ϕ profiles used for these calculations arepresented in the bottom panels. The subwavelength wavefrontresolution of the metamolecules, combined with their ability toaddress arbitrary complex amplitude response, makes possiblethe generation of a clear and compact focal spot merely a singlewavelength above the metasurface, as shown in Figure 4f. Thetransverse and vertical full width at half-maximums (FWHMs)of the focal spot are approximately 0.36λ0 and 0.77λ0,respectively, indicating high-resolution wavefront reconstruc-tions. As the focal length increases, the size of the focal spotbecomes slightly larger due to the decreased numericalaperture, but the field intensity at the focal point increases,as illustrated in the Supporting Information, Figure S10. Thesame metasurface can also produce multiple focal spots in freespace via the same methodology prescribed earlier. As shownin Figure 4g, the metasurface can construct rapidly varyingphase and amplitude profiles for three focal spots separated by

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a few wavelengths from each other, while maintaining thetransverse FWHM of the foci to be under 0.52λ0. These high-resolution focal spots can only be produced when both theamplitude and phase of light are precisely controlled, a clearadvancement that our metamolecule-based metasurface hasachieved.Dependency on Graphene Carrier Mobility. The

structural parameters of the metamolecule presented in Figure1a are designed to exhibit maximum tunability with a graphenecarrier mobility (μ) of 1000 cm2 V−1 s−1, and the maximumgraphene Fermi level (EF,max) is assumed to be 1 eV. Inexperiments, these conditions might not be accessible. First,inevitable imperfections in the processed graphene samples,such as edge defects in the GPRs and residues, lower the

effective graphene carrier mobility. In our previous research,we obtained μ ≈ 500 cm2 V−1 s−1 in patterned graphene.13,14In addition, EF,max is limited by the breakdown voltage of theinsulating layer, and EF,max ≈ 0.6 eV for a normal dielectriclayer, such as SiO2 or SiNx, using an electrostatic gatingmethod.13,14

In spite of these limitations, complete complex amplitudemodulation is still achievable in the proposed metamoleculesby tuning the structural parameters. Complex amplitudemodulations with different graphene carrier mobilities arepresented in Figure 5. The geometries used in Figure 5 areadjusted to exhibit the maximum modulation range for thecorresponding graphene carrier mobility when we assume thatEF,max is 0.6 eV. The structural parameters are summarized in

Figure 5. Complex amplitudes with graphene carrier mobilities (μ) of (a) 500 cm2 V−1 s−1, (b) 1000 cm2 V−1 s−1, (c) 2000 cm2 V−1 s−1, and(d) 4000 cm2 V−1 s−1. The geometries are optimized to exhibit maximum tunabilities when we assume that the available graphene Fermilevels (EF,max) are limited by 0.6 eV, and the structural parameters are given in the Supporting Information, Table S3. The green and purpleareas correspond to the complex amplitudes when we tune the graphene Fermi levels up to 0.6 and 1 eV, respectively. In (a)−(d), themaximum amplitudes covering 100% of area with EF,max = 0.6 eV are 0.186, 0.362, 0.585, and 0.689, respectively.

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the Supporting Information, Table S3. Of course, a higher μand a larger EF,max enlarge the range of complex amplitudemodulations owing to stronger oscillator strengths in theGPRs, as shown in Figure 5. However, this relationship doesnot indicate that a complete complex modulation is infeasiblewith low graphene carrier mobilities and a limited range ofgraphene Fermi levels. As demonstrated in Figure 5a, acomplete complex amplitude modulation is achievable withinthe range of |r| = 0.186 even with μ = 500 cm2 V−1 s−1 andEF,max = 0.6 eV.

CONCLUSIONSIn summary, graphene plasmonic metamolecules enablecomplete complex amplitude modulation at mid-infraredfrequencies. In the proposed metamolecules, electronicallytunable responses are achieved by graphene plasmonic ribbons,and noble metal plasmonic structures are incorporated toenhance the light−matter interactions. In particular, the twodegrees of freedom required to independently modulate theamplitude and phase of light are obtainable through individualcontrol of the graphene Fermi levels of the two constituentmetaatoms. To investigate the electromagnetic behaviors of themetamolecules, we developed a graphical method based on thesurface admittance and surface impedance. This approachoffers intuitive guidelines for designing metamolecules as wellas general metasurfaces for complex amplitude modulation. Inaddition, the proposed circuit model allows the efficient designof metamolecules without involving brute-force simulations.The capabilities of the proposed metamolecules were provenby demonstrating active beam steering and holographicwavefront reconstruction with high figure-of-merit. Ourproposed metamolecule represents a conceptual advancementto metasurface design, allowing for complete amplitude andphase control of light, and should find its application inthermal engineering, optical phased arrays, and real-timehologram systems beyond the mid-infrared.

METHODSOptical Simulations. The frequency-dependent dielectric func-

tions of SiO2 and Au were obtained from the Palik data.43 Graphene

was modeled by a sheet with zero thickness, and its optical surfaceconductivity σ was calculated by local random phase approxima-tion,44,45 which depends on the frequency ω and the graphene Fermilevel EF as follows:

Ei e k T

iEk T

ie i

Ef E f E

i E

( , )2( )

log 2cosh2

( )

d( ) ( )

( ) (2 )

F

2B

2F

B

2

0

d d2 2

Ä

Ç

ÅÅÅÅÅÅÅÅÅÅÅikjjjjj

y{zzzzz

É

Ö

ÑÑÑÑÑÑÑÑÑÑÑ

∫

σ ωπ ω

ωπ

ω

=ℏ + Γ

+ + Γ ×

− −[ℏ + Γ ] −

∞

where fd(E) = 1/{1 + exp[(E − EF)/kBT]}, Γ = eνF2/μEF is thescattering rate, νF is the Fermi velocity, and μ is the graphene carriermobility. The temperature T was set as 300 K. The optical responsesof the metaatoms and the metamolecules were calculated by full-wavesimulations with the finite-difference time-domain method and thefinite element method, and the results from both simulation methodswere crosschecked for validation.Effective Surface Admittance. A thin metasurface that has a

deep subwavelength thickness can be modeled by a two-dimensionalsheet with an effective surface admittance (Ỹs). The surfaceadmittances of the metasurfaces were evaluated from the givenreflection coefficients (r) by Ỹs = (1 − r)/(1 + r) − Ỹsub, where Ỹsub isthe substrate admittance. The effective surface impedance (Z̃s) of ametasurface can be directly calculated from its surface admittance by

Z̃s = Ỹs−1. Using this model, the optical properties of the full

metasurface stacks can be predicted analytically by solving a set ofsimple equations. In the quasi-static limit, the surface admittance of ametasurface can be approximated by treating the metasurface as aconnected set of lumped circuit elements, as described in theSupporting Information, Note S5. More details on the surfaceadmittance and the surface impedance are presented in theSupporting Information, Notes S1−S3.

ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acsnano.9b09277.

Details on surface admittance; relation among reflectioncoefficient, surface admittance, and surface impedance;analysis of reconstructed surface impedance area; detailson circuit analysis; comparison between full-wavesimulation results and analytic evaluation (PDF)

AUTHOR INFORMATIONCorresponding Authors*E-mail: skim886@wisc.edu.*E-mail: jang.minseok@kaist.ac.kr.ORCIDSeyoon Kim: 0000-0002-8040-9521Tony Low: 0000-0002-5759-5899Min Seok Jang: 0000-0002-5683-1925Author Contributions#S. Han and Se. Kim contributed equally to this work. S.H. andM.S.J. conceived the ideas. S.H. and Se.K. performed thesimulations and theoretical analysis. All authors co-wrote thepaper, and Se.K. and M.S.J. supervised the project.NotesThe authors declare no competing financial interest.

ACKNOWLEDGMENTSThis work was supported by the Samsung Research FundingCenter of Samsung Electronics under Project Number SRFC-IT1702-14.

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