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NANOPHOTONICS

Broadband electro-optic polarization conversion withatomically thin black phosphorusSouvik Biswas1†, Meir Y. Grajower1†, Kenji Watanabe2, Takashi Taniguchi3, Harry A. Atwater1*

Active polarization control is highly desirable in photonic systems but has been limited mostlyto discrete structures in bulky dielectric media and liquid crystal–based variable retarders.Here, we report electrically reconfigurable polarization conversion across telecommunicationwavelengths (1410 to 1575 nanometers) in van der Waals layered materials using tri-layer blackphosphorus (TLBP) integrated in a Fabry-Pérot cavity. The large electrical tunability of birefringencein TLBP enables spectrally broadband polarization control. We found that polarization statescould be generated over a large fraction of the Poincaré sphere through spectral tuning, and thatelectrical tuning enables the state of polarization conversion to span nearly half the Poincarésphere. We observed both linear to circular and cross-polarization conversion with voltage,demonstrating versatility with a high dynamic range.

Polarization is a fundamental property oflight that plays a crucial role in classicaland quantum optics. In tabletop opticalexperiments, it is usually tailored usingpolarizers, wave plates, and phase re-

tarders. Generating arbitrary polarization stateson demand is a requirement for a wide rangeof photonic processes such as circular dichro-ism sensing of chiral molecules and proteins,polarization-sensitive digital holography, im-aging, polarization encoding for photonicqubits, and detecting material quasiparticleexcitations such as phonons, spins, or excitonsand their associated anisotropy (1–6). Activecontrol of polarization demands a platformwith two key ingredients: a material with com-plex refractive indices that can be dynamicallytuned (7, 8) and in-plane symmetry breakingto generate birefringence either from an in-herent material property (9) or through nano-structured metasurface elements (10, 11). Theformer can be achieved using different effects,such as the Pockels effect (magneto-optical),the Kerr effect, Pauli blocking, the quantum-confined Stark effect, free carrier absorption,and optical pumping (8, 12–16). Despite im-portant advances in the exploration of thesephenomena, electrically reconfigurable con-trol of polarization remains largely elusive andsuffers from limited dynamic range of polar-ization conversion. Furthermore, commercialpolarization control devices such as variablephase retarders that use liquid crystal or lith-ium niobate as active media are bulky and

difficult to integrate into integrated photonicplatforms, restricting the miniaturization ofphotonic systems.Two-dimensional (2D) van der Waals semi-

conductors are known to exhibit strongly boundexcitons and are extremely polarizable in thepresence of external electric fields, enablingunprecedented electric field–induced dopingand refractive index modulation (17–19). Theatomic-scale thickness of van der Waals mate-rials and the lack of a lattice-matching require-ment make them attractive candidates forfuture-generation optoelectronics operating inthe visible and telecommunications frequencybands for applications such as coherent con-trol of quantum light, free-space and fiber-based communications, and light detectionand ranging. (20, 21) However, most reportson electro-optic modulation in 2D materialsthus far have largely been limited to grapheneand transition metal dichalcogenides, whichare optically isotropic in the layer plane andthus are not suitable for inherent active po-larization control. Black phosphorus (BP), a2Dquantumwell–like semiconductor, exhibitsnatural birefringence because of its in-planeanisotropic crystal structure (22–24). Itsunique electrically tunable optical dichro-ism demonstrated at the few-layer limit com-bined with its thickness tunable bandgap(~750 nm to ~4 mm) opens possibilities forpolarization-sensitive electro-optic modulationat infrared wavelengths in the telecommuni-cation band with a well-chosen thickness ofBP (23–28).In the conceptual visualization of polariza-

tion conversion (Fig. 1A), an incoming linearlypolarized light illuminates a Fabry-Pérot cav-ity incorporating tri-layer BP (TLBP). The po-larization state of the reflected light can beelectrically tuned to alter its ellipticity (circular

to linear polarization) or its azimuthal angle(s- to p-polarization). Here, the two cavity mir-rors are composed of a highly reflecting, thickback gold (Au) mirror and a partially trans-mitting, thin top Au mirror. The cavity med-ium is formed by hexagonal boron nitride(hBN)–encapsulated TLBP and polymethylmethacrylate (PMMA), which act to adjustthe cavity resonance frequency to a criticallycoupled condition for maximal polarizationconversion.To characterize the electrically tunable com-

plex refractive index of TLBP, gate-dependentpolarized absorption measurements were per-formed on a sample with the following con-figuration: hBN/TLBP (with few-layer graphenecontacts)/hBN/Au (Fig. 1B). The charge neu-tral response (0 V) is dominated by a strongexcitonic feature at 1398 nm, arising from theoptical transition between the lowest (highest)lying conduction (valence) bands, in the quan-tum well–like band structure of TLBP. Forboth positive and negative voltages (electronand hole doping, respectively), the peak ab-sorption reduces along with an increase in thelinewidth of the excitonic transition. A stron-ger change is observed in the hole-doping re-sponse with applied voltage compared withelectron doping. A detailed discussion of themechanism for the strong electro-optic re-sponse is provided in sections S8 and S9 ofthe materials and methods (29). Through aKramers-Kronig consistent transfer matrixanalysis of the gate-dependent absorption,the complex refractive indices (ñ = n + ik)of TLBP for different doping densities wereestimated (Fig. 1, C and D). Near-unity tuningof the complex refractive indices (for both nand k) is observed near the excitonic resonancealong the armchair (AC) direction. No notice-able feature was seen along the orthogonaldirection, zigzag (ZZ), for any voltages, render-ing that polarization passive.We then next designed a heterostructure

for polarization conversion by integrating theTLBP in an optically resonant cavity geometrythat enhances the degree of polarization con-version. A transfer matrix calculation of atypical Fabry-Pérot cavity design (side view inFig. 2A) yields the complex reflection phasor,amplitude, and phase spectra (Fig. 2, B to D,respectively). From the phasor diagram in Fig.2B, a prominently different complex reflectiv-ity feature is seen along the two polarizations.A clear resonance from the cavity is seen at1479 (1470) nm for the AC (ZZ) direction in thereflection amplitude in Fig. 2C, along with aweaker excitonic absorption feature at 1398 nmseen only along the AC direction. The reflectedphase along the AC and ZZ in Fig. 2D showsstrong differences near the cavity resonance.Taken together, these results indicate the po-tential for appreciable polarization conversionof the reflected light. The cavity parameters

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1Thomas J. Watson Laboratory of Applied Physics, CaliforniaInstitute of Technology, Pasadena, CA 91125, USA. 2ResearchCenter for Functional Materials, National Institute forMaterials Science, Tsukuba 305-0044, Japan. 3InternationalCenter for Materials, Nanoarchitectonics, National Institutefor Materials Science, Tsukuba 305-0044, Japan.*Corresponding author. Email: haa@caltech.edu†These authors contributed equally to this work.

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used in Fig. 2, B to D, are not a uniquechoice. In fact, the optical anisotropy in TLBPis broadband, enabling operation over the en-tire wavelength range of the telecommunica-tion E, S, and C bandswith appropriate changesin the cavity parameters, primarily throughadjustment of the thicknesses of the dielec-tric medium (hBN or PMMA) and the top Aumirror. Both parameters are important in de-termining the resonance wavelength and thereflection extinction ratio [see sections S14and S15 in the materials and methods (29)].To experimentally demonstrate the broad-band nature of the TLBP anisotropy, reflectionintensities were measured from five represen-tative heterostructures (Fig. 2E). The PMMAthickness was sequentially tuned to redshiftthe cavity resonance, spanning ~100 nm acrossthe E, S, and C telecommunication bands. Foreach heterostructure device (D1 to D5), a cor-responding spectral trajectory on the Poincarésphere is shown in Fig. 2, F to J, respectively.The blue (red) arrows mark the beginning(end) of the measured spectral trajectory, cor-responding to 1410 (1520) nm for D1 to D4 and1500 (1575) nm for D5. Efficient polarizationconversion can be seen for all the devices,confirming the broadband nature of the ani-sotropy in TLBP coupledwith the cavitymode.The differences in the trajectories arise wherethe cavity resonance wavelength is with re-spect to the beginning and ending point ofthe spectral scans. In addition, the arc lengthsubtended by the trajectories on the Poincaré

sphere is intimately related to how well thecavity critically couples to the incoming free-space electromagnetic field and is dominatedstrongly by the top mirror reflectivity.Planar heterostructure–based optical cav-

ities can act as sensitive probes to any spatiallyvarying features such as dielectric disorder orthickness of BP, which are key to understand-ing polarization conversion dynamics. Spatialfalse-color maps of ellipticity (Fig. 3A) andazimuthal angles (Fig. 3B), measured for hete-rostructure device D4, are shown for four dif-ferent wavelengths near the cavity resonance,showing that the polarization conversion hasstrong spatial variation. An optical image ofthe sample with appropriately outlined barecavity (0), three-layer, and six-layer BP regionsis shown in the inset of Fig. 3E. To gain furtherinsight, spectral scans are shown in Fig. 3, Cand D, for a select few points (appropriatelylabeled) chosen from the aforementioned re-gions. Strong polarization conversion is seenon the trilayer region. For example, a linearlypolarized input (azimuth ~45° to the AC/ZZaxes) is converted to nearly circular (42° ellip-ticity) at the resonance. An associated featureis seen in the azimuth spectrum aswell (with aderivate-like line shape), peaking at –37° and+42° around the ellipticity resonance. As ex-pected, veryweak (no) polarization conversioneffects are seen spectrally in the six-layer (barecavity) region. The weak effect for the six-layerregion presumably originates from the higherquantum–well subband transitions leading

to reduced birefringence. To aid the visualiza-tion of covariation in azimuthal and elliptic-ity spatially, a false-color map of ellipticitysuperimposed withmeasured reflection polar-ization ellipses is shown in Fig. 3E. The white(black) color corresponds to right (left) hand-edness. Finally, in Fig. 3, F and G, spatial mapsof the maximum achieved ellipticity over abandwidth of 70 nm (1450 to 1520 nm) andthe corresponding resonance wavelength areplotted, respectively. The overall achieved max-imum ellipticity is relatively homogeneous, al-though the spectral distribution is quite broad.The histogram in Fig. 3H (filtered for absoluteellipticity values >10°) confirms a strong center-ing of the ellipticity response around the reso-nance wavelength (~1490 nm). Figure 3I showsthe distribution ofmaximum ellipticity achievedfor all pixels across the entire map presentedin Fig. 3F. Two strong peaks are seen near+10° and –35°, corresponding to the peak el-lipticity values observed in most of the trilayerregion. Our observation of spatially varyingcomplex refractive indices is consistent withdielectric disorder seen in typical 2D hetero-structures (30). We speculate the origin ofsuch behavior to be twofold: fabrication-induced trapped hydrocarbons and strainbetween constituent layers in the hetero-structure and different stacking orders inTLBP (ABA, AAB, and ACA) (31–33).The key result of this work, the electrical

tunability of the different polarization param-eters, is summarized for device D1 in Fig. 4.

Biswas et al., Science 374, 448–453 (2021) 22 October 2021 2 of 6

V

Input Tunable

polarization

output V

AC ZZ

θ

ACZZ

Au

hBN

3L-BP

PMMA

A C

D

Zigzag

B

Fig. 1. Schematic of electrically tunable polarization conversionand TLBP birefringence. (A) Schematic of cavity design and polarizationconversion. TLBP is incorporated in a dielectric environment betweentwo mirrors [one partially reflective (top) and one highly reflective(bottom)]. The incoming beam is linearly polarized, and the output beamcan be azimuthally rotated or converted between circular and linearpolarization with applied voltage (between the TLBP and the back

electrode or mirror) for a fixed wavelength. (B) Experimentallymeasured polarized absorption from a TLBP device (non-cavity-integrated) for different doping densities along the ACdirection. The ZZ direction remains featureless for all conditions.(C and D) Extracted complex refractive index (real and imaginarypart, respectively) for TLBP as a function of doping density forthe AC and ZZ directions.

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The Stokes intensity (S0) and the three nor-malized Stokes parameters (s1, s2, s3), whichcompletely characterize the polarization con-version induced by the device, are shown as afunction of wavelength and gate voltage inthe form of false-color maps in Fig. 4, A to D,for hole-doping regime. It can be seen that allthree s parameters tune efficiently around theresonance (~1440 nm) with increased holedoping because of the strong cavity and TLBPinteraction. Our observations of the electri-cally driven changes in the s parameters areconsistent with the measured complex re-fractive indices of TLBP, including a strongerhole-doped response compared with electrondoping [see section S21 of the materials andmethods (29)]. Spectral variation of S0 (Fig.

4A) with doping indicates that the strongestcoupling with the cavity was achieved at ~–18V.Furthermore, in all three s parameters (Fig. 4,B to D), a suppression of the overall magni-tude of the resonance, which is caused by thereduction in excitonic anisotropy, can be seen.In addition, the linewidth of the aforemen-tioned features decreases with increasingvoltage because of the suppression of the lossesalong the AC direction. The polarization rota-tion at the resonance wavelength is primarilyenabled by the higher absorption along theAC axis compared with the ZZ axis (Fig. 1B),and this is further enhanced by the cavity.To better visualize the changes in the re-

flected polarization states, traces on thePoincaré sphere for different wavelengths

around the resonance are plotted as functionsof gate voltage. Figure 4E shows such traces onthe Poincaré sphere for nine different wave-lengths. The dynamic range corresponds tonearly half the Poincaré sphere in terms ofsolid angle subtended by the voltage-drivenarcs. Two interesting traces can be identified.The first one is at 1442 nm,where the ellipticitychanges from 0.3° to 43.7° to 16.8° at 0, –18,and –40V, respectively, showing tunable quarter-wave plate operation. By contrast, at 1444 nm,the azimuthal angle is tuned from 24.6° to89.4° between 0 and –40 V with suppressedellipticity changes, demonstrating tunable half-wave plate operation. At other wave- lengths,it is possible to demonstrate a wide varietyof elliptically polarized states. A 2D map of

Biswas et al., Science 374, 448–453 (2021) 22 October 2021 3 of 6

E-band S-band C-band

Au

PMMA

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hBN

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Ein Eout

A B

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D1-4 D1-4D5 D5

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Measurement window

Fig. 2. Example cavity design for polarization conversion and largeanisotropy bandwidth experimental demonstration. (A) Side view of atypical cavity structure adopted in this work. The top and bottom mirrors areformed by thin and thick Au films, respectively. The cavity is composed ofhBN-encapsulated TLBP and PMMA, which act as the tunable part indetermining the resonance wavelength. (B to D) Theoretically calculatedcomplex reflection phasor, reflection amplitude, and phase spectrum,respectively, for such a typical cavity structure having resonance ~1480 nm,showing differences in both parameters along AC and ZZ and thusestablishing polarization conversion. (E) Summary of reflection amplitudespectra from five representative devices fabricated as part of this studyshowing tunable cavity resonance. The PMMA thickness was tuned

systematically to change the resonance over 90 nm across the tele-communication band (E, S, and C). (F to J) Experimentally measured spectraltrajectories on the normalized Poincaré sphere corresponding to the fivedevice resonances plotted in (E). All trajectories show strong spectralpolarization conversion (either in the azimuthal orientation or the ellipticityor both). The differences in the trajectories are intimately related to thecritical coupling between the cavity and the incoming polarization. For allpresented trajectories, the azimuthal orientation was aligned nearly 45degrees to the AC and ZZ direction of the TLBP flake. For each normalizedPoincaré sphere, the blue arrows mark the beginning of the spectral scan(1410 nm for D1 to D4, 1500 for D5) and the red arrows mark the end(1520 nm for D1 to D4, 1575 for D5), also shown as stars in x-axis of (E).

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different polarization ellipses measured as afunction of nine different wavelengths (samewavelengths and color code as Fig. 4E) isshown in Fig. 4F for voltages between 0 and–40V (hole doping), where the strongestchanges are noted. This map better illustratesthe quarter-wave and half-wave plate–like op-eration, as well as other intermediate polar-ization conversion configurations. A similarlyhigh dynamic range for polarization conver-sion is also seen for electron doping (fig. S24).A general trend observed in these voltage-dependent polarization conversion measure-ments is that upon doping the TLBP, thespectral trajectory on the Poincaré sphere can

be collapsed to a point, a manifestation ofelectrically tunable anisotropy suppression.Thus, the larger the trajectory at nearly charge-neutral doping conditions, the higher the cap-ability to access a wide range of polarizationstates by applying a voltage.Our results demonstrate the versatility of BP

as an active medium for electronically recon-figurable broadband polarization conversion.The G-point nature of the direct-band minimaenables BP to have pronounced band-edge op-tical anisotropy spanning from visible (750 nm)to the mid-infrared (4 mm) (23, 24), whereasfree-carriermodulation provides access tomidto far-infrared wavelengths (>5 mm) (26). TLBP

is of particular interest for polarization conver-sion at telecommunications wavelengths be-cause of its near unity birefringence close tothe excitonic resonance. These findings repre-sent a route for active control of optical polar-ization at the nanoscale. The high dynamicrange of polarization conversion may open anavenue for the realization of densely integratedarrays of nanoscale BP electro-optic polariza-tion converters as a fundamental step beyonddiscrete dielectric polarization converters inlithium niobate or arrays based on micron-scale liquid crystal spatial light modulators.Previous reports on high-speed BP electro-photoresponse (34) and recent advances in

Biswas et al., Science 374, 448–453 (2021) 22 October 2021 4 of 6

1485 nm 1490 nmA

1495 nm 1500 nm

1485 nm 1490 nm

1495 nm 1500 nm

B

C

D

E

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F G

H

I

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1 pixel = 1 sq. μm

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Ellipticity resonance(filtered - >10o)

λ (nm)

Fig. 3. Spatial mapping of optical anisotropy probed by polarizationconversion. (A) Spatial maps of ellipticity angle (in degrees) of deviceD4 for four different wavelengths near the resonance (~1490 nm) of thecavity. Black lines indicate the extent of the tri-layer region [optical imageof D4 is shown in the inset of (E)]. White scale bar, 10 mm. (B) Sameas (A) but for azimuthal angle. (C and D) Ellipticity and azimuthalangle spectral scans for a few points [marked with appropriately coloredstars in (A) and (B)], showing spatial variation of the resonance in thetri-layer region, as well as flat background response from the bare cavityand weak polarization conversion from the six-layer region. (E) Zoom-inspatial color map of ellipticity at 1495 nm, along with superimposed

reflected polarization ellipses at each point, for better visualization ofcovariation of azimuthal and ellipticity angles. White lines correspondto right handedness and black lines correspond to left handedness.Black scale bar, 5 mm. Inset, Optical image of device D4 outlining thethree-layer (“3”) region. Also shown is the six-layer region (“6”) and thebare cavity (“0”). (F) Spatial map of maximum ellipticity for each pointwithin a spectral window between 1450 and 1520 nm. (G) Spatial mapof ellipticity resonance wavelength (filtered for |c| > 10° to only highlightthe three-layer region). (H and I) Histograms of ellipticity resonancewavelength (filtered for |c| > 10°) and maximum ellipticity (in degrees), whereone pixel on the map corresponds to 1 mm2.

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centimeter-scale, layer-controlled growth of BPthin films (35) suggest that possibilities mayemerge for large-area, broadband polarization-selective sensing, photodetection, and activeelectro-optic modulation.

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Fig. 4. Electrically tunable polarization dynamics.(A to D) False-color maps of the evolution of theintensity (S0) and the three normalized Stokes parameters(s1, s2, s3) determining the polarization state of thereflected light as a function of wavelength and negativevoltages (for hole doping). The results are fromdevice D1. Continuous tuning of all four parameterscan be seen around the cavity resonance (~1440 nm) forthe entire range of doping, illustrating efficient tuning ofthe polarization state with voltage. (E) Voltage-dependenttrajectories on the normalized Poincaré sphere fornine different wavelengths showing large dynamicrange in tunability of the reflected polarization state.Each color corresponds to a wavelength [same colorcode in (F)]. The dark arrows mark the beginning of thevoltage scan (0 V), and the correspondingly coloredarrows indicate the end of the voltage scan (–40 V), holedoping. (F) Visualization of the measured reflectedpolarization ellipse for selected voltages and the same ninewavelengths as in (E). At 1442 nm, a strong change inellipticity is seen where the state becomes almost circularat –18 V and the ellipticity decreases for highervoltages, with the device acting as a quarter-wave plate.The change in ellipticity is associated with a changein the azimuthal orientation of the beam. At 1444 nm,however, minimal change in ellipticity is seen witha strong change in the azimuthal orientation, withthe device effectively behaving like a half-waveplate. The solid (dashed) lines correspond to right(left) handedness.

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ACKNOWLEDGMENTS

We thank W. S. Whitney, M. Z. Alam, J. Wong, and P. C. Wufor fruitful discussions; G. R. Rossman for access to Ramanand Fourier transform infrared spectroscopy, and A. Duttfor valuable feedback on the work. Funding: The authorsgratefully acknowledge support from the Department ofEnergy Office of Science under grant DE-FG02-07ER46405.K.W. and T.T. acknowledge support from the ElementalStrategy Initiative conducted by Ministry of Education,Culture, Sports, Science and Technology (MEXT grantJPMXP0112101001), Japan Society for the Promotion ofScience (JSPS KAKENHI grant JP20H00354), and Centersof Research Excellence in Science and Technology (CREST grantJPMJCR15F3), Japan Science and Technology Agency (JST).Author contributions: S.B., M.Y.G., and H.A.A conceivedthe project. S.B. fabricated and characterized the devices.S.B. and M.Y.G. performed numerical calculations andelectrical and optical measurements and discussed the

results. H.A.A. supervised the project. K.W. and T.T. providedhBN and BP crystals. S.B. wrote the manuscript with inputfrom M.Y.G and H.A.A. Competing interests: The authorsdeclare no competing financial interests. Data andmaterials availability: All data required to evaluate theconclusions in the manuscript are available in the main textor the supplementary materials.

SUPPLEMENTARY MATERIALS

science.org/doi/10.1126/science.abj7053Materials and MethodsSupplementary TextFigs. S1 to S36ReferencesMovies S1 to S4

27 May 2021; accepted 13 September 202110.1126/science.abj7053

Biswas et al., Science 374, 448–453 (2021) 22 October 2021 6 of 6

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Science (ISSN ) is published by the American Association for the Advancement of Science. 1200 New York Avenue NW, Washington, DC20005. The title Science is a registered trademark of AAAS.Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claimto original U.S. Government Works

Broadband electro-optic polarization conversion with atomically thin blackphosphorusSouvik BiswasMeir Y. GrajowerKenji WatanabeTakashi TaniguchiHarry A. Atwater

Science, 374 (6566), • DOI: 10.1126/science.abj7053

Metasurfaces tune polarizationIn photonic systems, the polarization state of light is typically manipulated with bulky components based on dielectricsand liquid crystals. Active metasurfaces now provide the possibility of shrinking the size of these components to thenanoscale. Biswas et al. demonstrate an active nanophotonic structure capable of versatile electro-optic polarizationconversion. Using trilayer black phosphorus sandwiched between electrical gates forming a cavity, they show thatthe polarization state of light across telecommunication wavelengths can be electrically switched. Such control canbe useful for a number of applications in communications, imaging, and beam steering where the wavefront of thepropagating light can be actively manipulated. —ISO

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