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Trond I. Andersen, Ryan J. Gelly, Giovanni Scuri, Bo L. Dwyer, Dominik S. Wild, Rivka Bekenstein, Andrey Sushko, Jiho Sung, You Zhou, Alexander A. Zibrov, Xiaoling Liu, Andrew Y. Joe, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Susanne F. Yelin, Philip Kim, Hongkun Park, Mikhail D. Lukin

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[Beam steering at the nanosecond time scale with an atomically thin reflector](https://mdr.nims.go.jp/datasets/730ff662-0992-4a1a-9431-383e97531d50)

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Beam steering at the nanosecond time scale with an atomically thin reflectorARTICLEBeam steering at the nanosecond time scalewith an atomically thin reflectorTrond I. Andersen1, Ryan J. Gelly1, Giovanni Scuri 1, Bo L. Dwyer1, Dominik S. Wild 1,2, Rivka Bekenstein1,3,Andrey Sushko1, Jiho Sung 1,4, You Zhou1,4,5, Alexander A. Zibrov1, Xiaoling Liu1, Andrew Y. Joe1,Kenji Watanabe 6, Takashi Taniguchi 7, Susanne F. Yelin1, Philip Kim 1,8, Hongkun Park1,4✉ &Mikhail D. Lukin 1✉Techniques to mold the flow of light on subwavelength scales enable fundamentally newoptical systems and device applications. The realization of programmable, active opticalsystems with fast, tunable components is among the outstanding challenges in the field.Here, we experimentally demonstrate a few-pixel beam steering device based on electrostaticgate control of excitons in an atomically thin semiconductor with strong light-matter inter-actions. By combining the high reflectivity of a MoSe2 monolayer with a graphene split-gategeometry, we shape the wavefront phase profile to achieve continuously tunable beamdeflection with a range of 10°, two-dimensional beam steering, and switching times down to1.6 nanoseconds. Our approach opens the door for a new class of atomically thin opticalsystems, such as rapidly switchable beam arrays and quantum metasurfaces operating attheir fundamental thickness limit.https://doi.org/10.1038/s41467-022-29976-0 OPEN1 Department of Physics, Harvard University, Cambridge, MA 02138, USA. 2Max Planck Institute of Quantum Optics, Hans-Kopfermann-Straße 1, D-85748Garching, Germany. 3 ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA. 4 Department of Chemistry and Chemical Biology,Harvard University, Cambridge, MA 02138, USA. 5 Department of Materials Science and Engineering, University of Maryland, College Park, MD 20742, USA.6 Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 7 International Center forMaterials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 8 John A. Paulson School of Engineering andApplied Sciences, Harvard University, Cambridge, MA 02138, USA. ✉email: hongkun_park@harvard.edu; lukin@physics.harvard.eduNATURE COMMUNICATIONS |         (2022) 13:3431 | https://doi.org/10.1038/s41467-022-29976-0 | www.nature.com/naturecommunications 11234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-29976-0&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-29976-0&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-29976-0&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-29976-0&domain=pdfhttp://orcid.org/0000-0003-1050-3114http://orcid.org/0000-0003-1050-3114http://orcid.org/0000-0003-1050-3114http://orcid.org/0000-0003-1050-3114http://orcid.org/0000-0003-1050-3114http://orcid.org/0000-0001-7994-7077http://orcid.org/0000-0001-7994-7077http://orcid.org/0000-0001-7994-7077http://orcid.org/0000-0001-7994-7077http://orcid.org/0000-0001-7994-7077http://orcid.org/0000-0002-7390-4567http://orcid.org/0000-0002-7390-4567http://orcid.org/0000-0002-7390-4567http://orcid.org/0000-0002-7390-4567http://orcid.org/0000-0002-7390-4567http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-8255-0086http://orcid.org/0000-0002-8255-0086http://orcid.org/0000-0002-8255-0086http://orcid.org/0000-0002-8255-0086http://orcid.org/0000-0002-8255-0086http://orcid.org/0000-0002-8658-1007http://orcid.org/0000-0002-8658-1007http://orcid.org/0000-0002-8658-1007http://orcid.org/0000-0002-8658-1007http://orcid.org/0000-0002-8658-1007mailto:hongkun_park@harvard.edumailto:lukin@physics.harvard.eduwww.nature.com/naturecommunicationswww.nature.com/naturecommunicationsConventional optical devices, typically made from materialswith relatively weak light-matter interactions and asmooth optical response on the wavelength scale, arebulky to accumulate the desired effect on the optical wavefront.Recent advances in flat optics demonstrate that steep gradientsin the phase, amplitude, or polarization can be used to controllight fields on sub-wavelength scales1–3, enabling novel opticalphenomena and applications, including ultrathin lenses4,5,metasurfaces6, non-reciprocity7, and negative refraction8.While most demonstrations of flat optical elements so far haveinvolved passive devices, their active counterparts have recentlyattracted great interest9–12. Tuning mechanisms includingoptically13 and thermally14 induced phase transitions, as well asmagnetically tuned transparency in magneto-plasmonic crystals15,have been demonstrated. Micro-electrical mechanical systems(MEMS) technology has also been employed to spatially modulatethe optical response16, but the operation speed of such devices istypically limited to the kHz or fewMHz range. A promising avenueto overcome this limitation involves full electrical control, via forinstance ionic17 or electrostatic18–20 gating. In order to achievefully programmable devices, a key challenge is to achieve fast,continuous tunability of multiple independent channels.To address this challenge, we realize a continuously tunable,atomically thin optical device based on phase profile modulationin field-effect transistors composed entirely of two-dimensionalvan der Waals materials. The optically active element of oursystem is exfoliated monolayer MoSe2—an atomically thinsemiconductor that hosts tightly bound excitons in the optical(visible) domain. Excitons in TMDs have been widely proposedas an appealing system for quantum optical devices21, dueto their quantum coherence properties22 and potential forquantum nonlinear effects mediated by confinement-enhancedexciton–exciton interactions23. In high-quality exfoliated flakesencapsulated in boron nitride (hBN), these excitons can exhibitvery strong light-matter interaction, enabling almost perfectreflection from an atomically thin reflector24–26. By employingnear-transparent graphene gates, the exciton resonance in TMDscan be electrostatically tuned27,28. Due to the two-dimensionalnature of TMDs, the exciton resonance is tuned throughout thewhole material, circumventing the effects of screening commonlyencountered in bulk semiconductors29. These features allow forspatially dependent control of the phase and amplitude of thereflected light, which modifies the beam in the far-field due tointerference, enabling wide-ranging possibilities for optical beamcontrol (Fig. 1a).ResultsPhase modulation through electrostatic gating of excitons. Wedemonstrate this approach by realizing fast, continuously tunablebeam steering with a split-gate geometry (Fig. 1b). Using the dry-transfer technique, we assemble our device (Fig. 1b, inset) fromexfoliated flakes of monolayer MoSe2, graphene (top and bottomgates), and hBN (gate dielectric) into a split-gate field-effecttransistor (SG-FET) structure, in which the bottom gate (BG)only covers part of the device. The gate geometry enables inde-pendent electrostatic doping of the two parts of the device, and—because the exciton resonance shifts with doping—a very steepphase gradient near the gate edge. The non-zero width of this stepis due to stray electric fields and is comparable to the thickness ofthe gate dielectric (~50 nm). By focusing light on the gate-edge,the two halves of the reflected wavefront gain a differentphase (Δϕ) and thus constructively interfere in the far-field at anangle to the optical axis (Fig. 1b).Figure 1c shows the absolute reflectance spectrum, collectedaway from the gate edge in the intrinsic regime (T ~ 6 K). TheMoSe2 features a sharp excitonic resonance at λintrinsic ~ 757 nm,with a linewidth of 1.2 nm. The asymmetric line-shape isattributed to the interference between the Lorentzian excitonreflection and light reflected from other interfaces in the device26(Supplementary Notes I and II). By fitting the asymmetricresonance profile (black; Supplementary Note I), we extract thephase of the reflected light (red). The phase of the excitonreflection itself changes by 180° (π) across the resonance, but theinterference with the background reflections reduces the overallphase range (we note that this is not an inherent limitation; seeSupplementary Note II and Supplementary Figs. S1–S3).In order to tune the phase at a given wavelength, we shiftthe exciton resonance by electrostatically doping the MoSe2 withthe top and bottom gates (VTG and VBG, respectively). Figure 1d,e shows the gate dependence of the resonance wavelengths, λleftand λright, on the left and right sides of the gate edge, respectively.The exciton resonance blue-shifts by several linewidths in the p-and n-doped regimes, resulting from bandgap renormalizationand repulsive polaron formation26,28,30. In the left (dual-gated)side of the device (Fig. 1d), the resonance depends on both VTGand VBG; more specifically the weighted sum, 8VTG+ VBG, due tounequal top and bottom hBN thicknesses. In contrast, the excitonresonance on the right (single-gated) side of the device onlydepends on VTG, except for a slight VBG-dependence of the onsetof the p-doped regime due to contact activation (Fig. 1e). Thesedistinct dependencies of λleft and λright on the gate voltages allowfor tuning their relative positioning (Fig. 1f) and are key tocreating the abrupt phase discontinuity.Fitting the spectra at all gate voltage combinations in Fig. 1d, e,we find the gate dependence of the phase difference (Δϕ) betweenthe two sides of the device at λ0= 755.6 nm (Fig. 1g), indicating acontinuously tunable range of 42°. The wavelength is chosen to beblue-detuned relative to the intrinsic exciton resonance, such thatthe exciton resonance is swept through λ0 upon electrostaticgating. Inspecting Fig. 1g, we identify four regimes that are centralto the operation of our system, distinguished by the relativepositioning of λleft and λright: a large positive phase difference isachieved when the resonance on the left side is blue-shifted pastλ0, while λright is kept red-shifted (Fig. 1f, blue box). Conversely, alarge negative phase difference is realized when λright < λ0 < λleft(Fig. 1f, green box). Finally, the magnitude of the phase differenceis much smaller when the two sides are either both doped (Fig. 1f,yellow box) or both intrinsic (Fig. 1f, red box). As can be seen inFig. 1f, the doping induced blue-shift is accompanied by adecrease in amplitude, reducing the maximum phase of thecombined reflection in the doped regimes.One-dimensional beam steering. Having demonstrated inde-pendent phase tunability in the two sides of the device, we nextmeasure the beam steering capabilities by focusing the laser beam(λ0= 755.6 nm; numerical aperture, NA= 0.75) onto the gateedge (see Supplementary Note III for alignment procedure) andimaging the reflected beam in the Fourier plane (see Supple-mentary Video S1). The Fourier plane polar coordinates rF and ϕFare converted to angular deflection via θ= sin−1 (rF/f), where f isthe focal length of the objective, and decomposed into θx= θ ·cos(ϕF) and θy= θ · sin(ϕF). The undeflected beam is approxi-mately Gaussian with an angular width (standard deviation) of17°. Figure 2a shows representative Fourier images in the fourregimes identified in Fig. 1f, g, after subtracting the reflectedintensity without exciton effects (I0), obtained by heavily dopingthe device (VBG= 10 V, VTG= 1.4 V). Defining the center-of-mass deflection of the full (not background-subtracted) reflectionas �θi ¼ ΣIθiΣI , we present scatter plots of�θx and �θy for the full rangeof gate voltages in Fig. 2b, including highlighted deflections in theARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-29976-02 NATURE COMMUNICATIONS |         (2022) 13:3431 | https://doi.org/10.1038/s41467-022-29976-0 | www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsfour regimes (colored circles) and Fourier images without back-ground subtraction (insets).We find that the reflection is deflected in the expecteddirection, perpendicular to the gate edge. The tunable deflectionrange is 9.8°, in very good agreement with theoretical predictionsbased on the phase difference range observed in Fig. 1g.Specifically, for a diffraction-limited beam spot, the deflection ispredicted to be �θ? ¼ NA0:42�ffiffiffiffiffi2π3p � Δϕ ¼ 0:23 � Δϕ, which gives arange of 9.7° (Supplementary Note IV). Moreover, the gatedependence of the deflection (Fig. 2c) closely resembles that ofthe extracted phase difference (Fig. 1g), consistent with thedeflection arising due to the sharp phase discontinuity impartedon the wavefront. We identify distinct steering behavior in thefour regimes: when only one side of the device is kept red-shiftedrelative to λ0 (blue and green boxes in Fig. 2a), the beam isdeflected towards that side. Intuitively, the light from the twosides interferes constructively when the path length is shorter forthe side with the greater phase. In the two other regimes, on theother hand, where the two sides are either both blue-shifted pastλ0 (yellow) or both red-shifted (red), we observe near-zerodeflection, consistent with a much smaller phase difference. Wenote that very similar behavior, although with a smaller deflectionrange, was observed for λ0 down to 752 nm.dipnVBG (V)0-5510λleft (nm)0.70 1.4nipλright (nm)ExcitonExcitoE onaReflection (%)2050403020504030750 755 760750 755 760Wavelength (nm)7500.2fRightLeft gθgrhBNhBNTMDgrVBGVTGbφ ΔφReflection (%)205040307401.2 nm780760Wavelength (nm)c-1020010Phase ( o)VBG = 0 VVTG = 0.5 V0.70 1.4VTG (V)n,pn,in,ni,pi,ii,np,iVTG (V)0.7 4.100-5510VBG (V)VTG (V)e748 7575 μm748 757Δφ (o)-19 23φFig. 1 Continuously tunable phase patterning in a van der Waals heterostructure. a Schematic of our approach: patterned electrostatic doping ofatomically thin transition metal dichalcogenides (TMDs) allows for spatial control of the exciton resonance (inset). Thus, a continuously tunable phaseprofile is imparted on the reflected wavefront, enabling wide-ranging possibilities for beam control. b Schematic of SG-FET structure. Since the bottom gateonly covers part of the device, the phase can be tuned independently in the two sides. The phase discontinuity in the reflected wavefront causes the twohalves to constructively interfere at an angle in the far field. Inset: zoomed-in optical microscope image of the device, with gate edge indicated by whitedashed line. c Representative reflection spectrum (orange) from left side of gate edge in intrinsic regime (VBG= 0 V and VTG= 0.5 V), with asymmetricresonance fit (black), which allows for extracting the phase (red). d, e Gate dependence of λleft and λright, respectively (locations indicated by circles in insetof b). The exciton resonance blue-shifts upon electrostatic doping. While λleft depends on 8VTG+ VBG, λright is largely independent of VBG. The intrinsicregime appears at an offset of VTG= 0.5 V, likely due to charge collection at the top gate. The small voltage range of the intrinsic regime suggests somedoping via in-gap states. f Reflection spectra from left (orange) and right (blue) side of gate edge at different gate voltage combinations shown ascorrespondingly colored crosses in g. Dashed gray line indicates λ0= 755.6 nm. g Gate dependence of phase difference Δϕ between the right and left sideat λ0= 755.6 nm, computed from fits as in (c). A tunable Δϕ-range of 42° is achieved. Large positive Δϕ is achieved when λleft < λ0 < λright (blue cross),while large negative Δϕ is achieved when λright < λ0 < λleft (green). Δϕ is closer to zero when either both sides are doped (λleft, λright < λ0; yellow) or both areintrinsic (λ0 < λleft, λright; red).NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-29976-0 ARTICLENATURE COMMUNICATIONS |         (2022) 13:3431 | https://doi.org/10.1038/s41467-022-29976-0 | www.nature.com/naturecommunications 3www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsFigure 2d shows the gate dependence of the integratedreflection. The different regimes are separated by regions ofstrong reflection, since these indicate that one of the resonancescrosses through λ0. While the four different regimes are easilyidentified, we emphasize that the phase difference, and thusthe beam deflection, is tuned continuously, as shown in Fig. 2b.The continuous tunability is highlighted in Fig. 2e, showinglinecuts from Fig. 2c. Although the reflection amplitude is gatedependent (Fig. 2d, f), the reflection variations can be reducedsubstantially while still keeping a similar deflection range byavoiding the combined resonance (gray linecut), or evendesigning a near-iso-reflection path in voltage space (teal).Two-dimensional beam steering. In order to achieve moreadvanced control of the wavefront profile, we utilize the deviceregion where the edge of the bottom gate intersects a borderbetween monolayer and bilayer MoSe2 (Fig. 3a). Since the excitonresonance in bilayers is red-shifted to ~767 nm due to interlayerhybridization effects31 (Fig. 3b), the bilayer acts as a non-resonantdielectric reflector, thus enabling control of the relative phasebetween the three regions. Figure 3c shows representative FourierFig. 2 Continuously tunable beam steering. a Fourier images of reflectedbeam (λ0= 755.6 nm) in the four regimes after subtracting the reflection inthe highly doped regime (VBG= 10 V and VTG= 1.4 V). When the excitonresonance is blue-shifted past λ0 in only one side of the device (blue,green), the beam is deflected away from that side. If neither or both areblue-shifted past λ0, the phase difference is small and little deflection isobserved (red, yellow). b Scatter plot of the beam deflection (�θx; �θy) for thefull range of gate voltages, showing that the deflection is perpendicular tothe gate edge (dashed line) and continuously tunable. Inset: Fourier imageswithout background subtraction. c The gate dependence of the deflectionperpendicular to the gate edge (�θ?) is in very good agreement with that ofthe phase difference shown in Fig. 1g. d Gate dependence of reflectionamplitude. Regions with high reflection indicate that one of the resonancescrosses through λ0. e, f Linecuts indicated by dashed black, teal, and graylines in (c) and (d), respectively, highlighting the continuous steeringcapability and that the reflection can be kept relatively constant whiledeflecting the beam. Connecting lines in e and f are guides to the eye.Fig. 3 Two-dimensional beam steering. a Zoomed-in optical image ofdevice, indicating regions of monolayer and bilayer MoSe2, as well as gatecoverage. By tuning the relative phase and amplitude of the reflection fromthe three regions, more intricate wavefront phase profiles can be achieved.b Reflection spectra from the dual-gated monolayer (black), single-gatedmonolayer (gray) and the bilayer (purple) in the intrinsic regime (VBG= 0 Vand VTG= 0.5 V). Since the resonance is red-shifted in the bilayer, it acts asa dielectric (non-resonant) reflector at the wavelengths used here. c Fourierimages of reflected beam (λ0= 754.1 nm) in the four regimes aftersubtracting reflection in the highly doped regime (VBG= 10 V andVTG= 1.4 V). The beam is now steered in two dimensions. Red: when bothmonolayer resonances are red-shifted relative to λ0, their phase is higherthan in the bilayer region, causing the beam to deflect upwards. Blue andgreen: when one of the monolayer resonances is kept red-shifted relative toλ0, the beam is deflected towards that monolayer region. d Scatter plot ofthe center-of-mass deflection ð�θx; �θyÞ, with the points from (c) highlighted.The set of beam deflections now span a two-dimensional area. e, f Gatedependence of �θx (e) and �θy (f). While the gate dependence resembles thatof the phase in Fig. 1g, �θx and �θy are now less coupled. g Center-of-massdeflection tracing out “PHYSICS” (rotated 148° counter-clockwise) byapplying a sequence of gate voltage combinations.ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-29976-04 NATURE COMMUNICATIONS |         (2022) 13:3431 | https://doi.org/10.1038/s41467-022-29976-0 | www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsimages of the reflected light in the four different regimes atλ0= 754.1 nm. When both the monolayer resonances are red-shifted relative to λ0, the beam is deflected upwards (red), asopposed to the near-zero deflection observed in Fig. 2. Keepingonly one of the resonances red-shifted causes the beam to deflectupwards at an angle towards the red-shifted side (green and blue).This is further shown by plotting the full set of center-of-massdeflections, �θx and �θy (Fig. 3d); while these were clustered arounda line perpendicular to the gate edge in Fig. 2b, we now observethat they span a broader, two-dimensional area. Consequently,the gate dependence of �θx and �θy (Fig. 3e, f)—while still resem-bling that of the phase in Fig. 1g—is now more intricate. Insteadof simply being (negatively) proportional to each other, �θx takeson both positive and negative values when �θy is intermediate, and�θy can be either large or near-zero when �θx is near zero. Todemonstrate the two-dimensional steering capability, we write adesired two-dimensional pattern with the center-of-mass of thereflected beam (Fig. 3g), by successively applying gate voltagecombinations corresponding to the appropriate beam deflections.The two-dimensional deflection behavior is well understood byconsidering the third reflection source from the bilayer region.When both the monolayer resonances are kept red-detunedrelative to λ0, the phase is higher than in the bilayer region, thusimparting an upwards phase gradient on the reflected wavefront.Similarly, if only one of the monolayer regions is kept red-shifted,the phase gradient points towards that region. Hence, the threereflection sources enable two-dimensional beam control.Switching on the nanosecond scale. We investigate the temporalresponse of our system by applying a small oscillating bottomgate voltage, VBG tð Þ ¼ V0 þ ΔV � sin 2πtτ� � ¼ 0:7Vþ 0:45V �sin 2πtτ� �and a constant top gate voltage VTG= 0.64 V, where τ isthe period (corresponding to twice the switching time). Focusingthe beam at the gate edge, as in Fig. 2, we first measure the beamdeflection using a long period (τ= 2 s) compatible with ourcamera (Fig. 4a). Figure 4b, c shows the change in reflection fromVBG=V0 to VBG=V0+ ΔV and VBG= V0− ΔV, respectively.Next, we measure the optical response at much higher frequenciesby collecting the reflected light in the Fourier plane with anavalanche photon detector (APD; Fig. 4d). In order to ensure thatwe probe beam steering, as opposed to simply changes inreflection amplitude, we separately collect photons from the left(θx < 0) and right parts (θx > 0) of the Fourier plane (inset in toppanel of Fig. 4d). These signals are found to oscillate with a near-180° phase difference, unambiguously indicating high-frequencybeam deflection. Notably, we observe clear oscillations all the waydown to a period of τ= 3.2 ns (ω= 2π ⋅ 0.32 GHz). Normalizingthe oscillations in APD counts to those at τ= 10 μs, we find thatthe amplitude is approximately unaffected at τ= 100 ns, andreduced by ~60% (~80%) at τ= 5.6 ns (3.2 ns). Measurements ofthe high-frequency transmission of electrical connectors leadingup to the device indicate that more than half of this reduction isin fact not due to the device itself, but rather external losses andreflections (Supplementary Note V and Supplementary Fig. S7).Reduction of pixel size and further improvement of contactquality can likely enable switching times down to a few tens ofpicoseconds32,33, ultimately limited by the MoSe2 mobility.DiscussionWhile the above results were obtained at a device temperature ofT= 6 K, almost identical data were obtained at liquid nitrogentemperatures (80 K; Supplementary Note VI and SupplementaryFig. S8). Moreover, deflection was still clearly observed, althoughwith a smaller amplitude, at a temperature easily attainable with aPeltier cooler (T= 230 K), and some deflection effects were evenobserved at room temperature. The deflection range could befurther increased at all temperatures through improvements inmaterial quality or further optimization of the hBN thicknessesand substrate permittivity. In fact, while background reflectionsoften reduce the phase range, optimization of their phase andamplitude can increase the phase range to 2π (SupplementaryNote II and Supplementary Figs. S1–S3). Combined with theintroduction of more pixels in next-generation devices, this isexpected to enable a larger ratio between the steering and beamdivergence angles.These observations demonstrate that our system can be anattractive platform for applications involving high-speed activeoptics, with on-chip integrability and potential for flexibletransparent optics as very appealing features. In addition tothe two-dimensional beam steering demonstrated here, oursystem can be scaled up into more advanced pixel arrays withfeature sizes well below 100 nm through standard etch techni-ques, to enable a broad variety of other atomically thin opticalelements, including atomically flat holograms with many con-trollable outputs and flat lenses with tunable focal length. Inparticular, our approach of using gates in two planes makes itpossible to generate a 2D grid of n × n pixels (2n independentinput channels) by etching the top and bottom gates into thinperpendicular strips (see Supplementary Note VII andFig. 4 High-frequency beam steering. a Oscillations of center-of-massdeflection (λ0= 754.5 nm) induced by oscillating back gate voltage (offset,V0= 0.7 V; amplitude, ΔV= 0.45 V; period, τ=2 s) and VTG= 0.64 V.b, c Fourier plane images collected at VBG=V0+ΔV (b) andVBG= V0−ΔV (c), as indicated by circles in a, after subtracting reflectionat VBG= V0. An inverted telescope was used to shrink the beam to simplifythe subsequent APD measurements. d Photon count oscillations measuredwith APD at τ= 10 μs, 100 ns, 5.6 ns, and 3.2 ns (top to bottom). Darker(lighter) shade curves show photon counts from left (right) side of Fourierplane, as indicated by the inset in the top panel. All curves are normalizedto the corresponding contrast at τ= 10 μs.NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-29976-0 ARTICLENATURE COMMUNICATIONS |         (2022) 13:3431 | https://doi.org/10.1038/s41467-022-29976-0 | www.nature.com/naturecommunications 5www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsSupplementary Fig. S9 for further details). The use of nanoelec-trode arrays is another promising upscaling route. While exfo-liated flakes with areas typically exceeding 100 μm2 can fit a highnumber of pixels, recent progress in chemical vapor deposition(CVD) growth34 can enable scaling up to even larger devices.Importantly, our approach also offers unique features which couldunlock quantum applications that are inherently impossible withconventional spatial light modulator (SLM) technologies. In parti-cular, quantum analogs of metasurfaces that could generate andmanipulate entangled states of light have recently been proposed35,36.The realization of such devices relies on creating metasurfaces fromlocally tunable materials that can exist in a superposition of stateswith different reflectivity and that facilitate quantum nonlineareffects, thus calling for the exploration of new material systems forflat optics. In contrast to materials commonly used in conventionalSLMs, the K/K’ valley exciton species employed here has been widelyshown to exhibit promising, gate-tunable quantum coherenceproperties and can be readily excited to a quantum superposition ofstates that interact only with left- and right-handed circularlypolarized light. Moreover, the use of excitons confined in an atom-ically thin material renders it a promising approach for achievingquantum nonlinear effects mediated by exciton–exciton interactions.Recent works suggest that strong exciton–exciton interactions couldbe achieved in our system through reflective substrate engineering23or by using Rydberg exciton states37, making active flat optics basedon TMDs a very appealing platform for the investigation of quantumoptical metasurfaces35.MethodsDevice fabrication. In order to minimize contact resistance, crucial to high-frequencyoperation, we fabricated bottom contacts to the MoSe238. This was done by firstassembling mechanically exfoliated flakes of graphene and hBN with the dry-transfermethod, and placing them on a quartz substrate. After thermal annealing of the two-flake stack, platinum contacts were defined with e-beam lithography and deposited ontop of the hBN flake through thermal evaporation (1 nm Cr+ 19 nm Pt). The partiallycomplete device was then thermally annealed again, before assembling mechanicallyexfoliated MoSe2, hBN and graphene flakes and placing them on top of the contacts.Finally, extended electrical contacts to the Pt contacts and the graphite gates weredeposited through thermal evaporation (10 nm Cr+ 90 nm Au).Experimental method. All measurements were conducted in a Montana Instru-ments cryostat, using a custom-built 4 f confocal setup with a Zeiss (100x, NA=0.75, WD= 4 mm) objective. Reflection spectra were measured using a halogensource and a spectrometer, and all spectra were normalized to that collected from agold contact. Electrostatic gating was performed with Keithley 2400 multimetersfor DC measurements and with an arbitrary waveform generator (TektronixAWG710) for AC measurements. We used a Ti:Sapphire laser (M Squared) with apower of 5 μW at the sample for Fourier imaging, and imaged the reflected beamwith a CMOS camera in the Fourier plane. At high frequencies, an avalanchephotodetector (APD) was used to collect photons from two different parts ofthe Fourier plane. The time dependence was measured using a Time CorrelatedSingle-Photon Counting system (PicoHarp 300).Data availabilityAll data needed to evaluate the findings in the paper are present in the paper and thesupplementary materials.Received: 26 January 2022; Accepted: 11 March 2022;References1. Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nat. Mater. 13,139–150 (2014).2. Kildishev, A. V., Boltasseva, A. & Shalaev, V. M. Planar photonics withmetasurfaces. Science 339, 1232009 (2013).3. 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Lett. 116, 086601 (2016).ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-29976-06 NATURE COMMUNICATIONS |         (2022) 13:3431 | https://doi.org/10.1038/s41467-022-29976-0 | www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsAcknowledgementsWe acknowledge support from the DoD Vannevar Bush Faculty Fellowship (N00014-16-1-2825 for H.P., N00014-18-1-2877 for P.K.), NSF (PHY-1506284 for H.P. and M.D.L.),NSF CUA (PHY-1125846 for S.F.Y., H.P., and M.D.L.), AFOSR MURI (FA9550-17-1-0002), ARL (W911NF1520067 for H.P. and M.D.L.), the Gordon and Betty MooreFoundation (GBMF4543 for P.K.), ONR MURI (N00014-15-1-2761 for P.K.), DOE (DE-SC0020115 for S.F.Y.), and Samsung Electronics (for P.K. and H.P.). All fabrication wasperformed at the Center for Nanoscale Systems (CNS), a member of the NationalNanotechnology Coordinated Infrastructure Network (NNCI), which is supported by theNational Science Foundation under NSF award 1541959. K.W. and T.T. acknowledgesupport from the Elemental Strategy Initiative conducted by the MEXT, Japan and theCREST (JPMJCR15F3), JST. A.S. acknowledges support from the Fannie and John HertzFoundation and the Paul & Daisy Soros Fellowships for New Americans. This project hasreceived funding from the European Union’s Horizon 2020 research and innovationprogram under the Marie Skłodowska-Curie grant agreement No. 101023276.Author contributionsT.I.A., R.J.G., G.S., D.S.W., R.B., S.F.Y, P.K., H.P., and M.D.L. conceived the project.T.I.A. designed and performed the experiments with assistance from R.J.G., G.S., B.L.D.,A.S., Y.Z., A.A.Z, and A.Y.J. Device fabrication was done by T.I.A., R.J.G., G.S., J.S., andX.L., and the theoretical model was developed by T.I.A., D.S.W., and R.B. T.I.A. wrote themanuscript with extensive input from the other authors. T.T. and K.W. grew the hBNcrystals. S.F.Y., P.K., H.P., and M.D.L. supervised the project.Competing interestsHarvard University has filed a provisional patent application (No. 63/153,726) for a fastspatial light modulator based on an atomically thin reflector, with the following inven-tors: T.I.A., R.J.G., G.S., B.L.D., D.S.W., R.B., A.S., S.F.Y., P.K., H.P., and M.D.L.Additional informationSupplementary information The online version contains supplementary materialavailable at https://doi.org/10.1038/s41467-022-29976-0.Correspondence and requests for materials should be addressed to Hongkun Park orMikhail D. Lukin.Peer review information Nature Communications thanks XYZ and the otheranonymous reviewer(s) for their contribution to the peer review of this work.Reprints and permission information is available at http://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. 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To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2022NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-29976-0 ARTICLENATURE COMMUNICATIONS |         (2022) 13:3431 | https://doi.org/10.1038/s41467-022-29976-0 | www.nature.com/naturecommunications 7https://doi.org/10.1038/s41467-022-29976-0http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.nature.com/naturecommunicationswww.nature.com/naturecommunications Beam steering at the nanosecond time scale with�an atomically thin reflector Results Phase modulation through electrostatic gating of excitons One-dimensional beam steering Two-dimensional beam steering Switching on the nanosecond scale Discussion Methods Device fabrication Experimental method Data availability References References Acknowledgements Author contributions Competing interests Additional information