Atomically Thin Noble Metal Dichalcogenides for Phase Regulated Meta-optics - Wang et al. - Unknown - Unknown

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SUPPORTINGINFORMATIONforAtomicallyThinNobleMetalDichalcogenidesforPhaseRegulatedMeta-optics†,‡,∥,#†,#†,#§⊥†YingweiWang,Zi-LanDeng,DejiaoHu,JianYuan,QingdongOu,FeiQin,YinanZhang†,XuOuyang†,YueLi£,BoPeng£,YaoyuCao†,BaiOuGuan†,YupengZhang∥‡¥*,⊥*,†,JunHe,Cheng-WeiQiu,QiaoliangBao,XiangpingLi.†GuangdongProvincialKeyLaboratoryofOpticalFiberSensingandCommunications,InstituteofPhotonicsTechnology,JinanUniversity,Guangzhou510632,People’sRepublicofChina‡HunanKeyLaboratoryforSuper-microstructureandUltrafastProcess,SchoolofPhysicsandElectronics,CentralSouthUniversity,932SouthLushanRoad,Changsha,Hunan410083,People’sRepublicofChina§CollegeofPhysicsandElectronicInformation,HuaibeiNormalUniversity,Huaibei235000,People’sRepublicofChina∥KeyLaboratoryofOptoelectronicDevicesandSystemsofMinistryofEducationandGuangdongProvince,CollegeofElectronicScienceandTechnology,ShenzhenUniversity,Shenzhen518060,People’sRepublicofChina.⊥DepartmentofMaterialsScienceandEngineering,andARCCentreofExcellenceinFutureLow-EnergyElectronicsTechnologies(FLEET),MonashUniversity,Clayton,Victoria3800,Australia£NationalEngineeringResearchCenterofElectromagneticRadiationControlMaterialsandStateKeyLaboratoryofElectronicThinFilmsandIntegratedDevices,SchoolofMicroelectronicsandSolidStateElectronics,UniversityofElectronicScienceandTechnologyofChina,Chengdu610054,People’sRepublicofChina1

1¥DepartmentofElectricalandComputerEngineering,NationalUniversityofSingapore,4EngineeringDrive3,Singapore,117583#Thoseauthorscontributedequallytothiswork2

2ThisPDFfileincludes:SupplementaryTextSupplementaryNote1.Loss-assistednontrivialphaseshiftbytemporalcoupled-modetheory.SupplementaryNote2.Transfermatrixmethodforlayeredfilmsandstructureoptimization.SupplementaryNote3.Thicknessandincidentangledependence.SupplementaryNote4.Correlationcharacterizationofholographicimages.Figure.S1.Comparisonoftypicalbinarymeta-opticsperformance.Figure.S2.Temporalcoupled-modetheorymodeloftheNMDs-SiO2-Siresonator.Figure.S3.FittingsobtainedbyTransfermatrixmethod.Figure.S4.Comparisonofthecriticalthicknessofdifferent2Dmaterialstosupportthecriticalcouplingpointinthe2Dmaterial-SiO2-Siconfiguration.Figure.S5.Topologically-protectedstructurerobustnessagainstthefluctuationofthicknessofSiO2layer.Figure.S6.Anglerobustphasemodulation.Figure.S7.Phasordiagramasafunctionofthefilmthickness.Figure.S8.RamanspectrumandX-rayphotoelectronspectroscopy(XPS)spectrumofas-preparedPtSe2thinfilms.Figure.S9.Characterizationofas-preparedPtSe2films.Figure.S10.TheselectedareaelectrondiffractionpatternofthePtSe2layer.Figure.S11.Experimentalconfigurationfordirectlaserwriting.Figure.S12.Characterizationoflaser-scribedPtSe2gratingsatdifferentpowers.Figure.S13.FalsecolorSEMimageofbinaryPtSe2meta-holograms.Figure.S14.Procedureusedtoobtainthecorrelationcoefficient.Figure.S15.Fidelitycharacterizationofreconstructedholographicimages.3

3Figure.S16.Theoptimizedconfigurationforincreaseddiffractionefficienciesbyusinglow-losssubstrates.Tables.S1.Comparisonoftheperformanceoftypicalbinarymeta-opticsmadeofdifferentschemes.References(1-21)4

4SupplementaryTextSupplementaryNote1.Loss-assistednontrivialphaseshiftbytemporalcoupled-modetheory.Inthissection,weutilizethetemporalcoupled-modetheory(CMT)topresentanintuitivephysicalmodelforachievingloss-assistednontrivialphasebehavior.Westartbyregardingthenoblemetaldichalcogenides(NMDs)-SiO2-Simultilayersystemasaresonatorcoupledtoafreepropagatingwavethrougha"couplingchannel"(SupplementaryFigure.S2).Theresonatorisdefinedbytheresonancefrequency0,parametersQrandQa,whicharerelatedtothedissipationratethroughthecouplingchannel(i.e.,radiationrate,r)andintrinsicabsorption(a)viar=0/(2Qr)anda=0/(2Qa).Thedynamicequationcanbewrittenasda00ia()as0dt2Q2Qra,(s1)ssa,(s2)whereisthecouplingcoefficientbetweentheincomingwaves+andresonanceamplitudea;andisthecouplingcoefficientbetweenaandtheoutgoingwaves-,respectively.Theoutgoingwaveisthesumofthedirectreflectionoftheincomingwaveandtheresonanceradiation.Takingenergyconservationandtimereversibilityintoconsideration,thecouplingcoefficientscanberelatedtothedispassionratevia21.Assumingritthattheincomingwavehastheformse,thetotalreflectioncoefficientcanbederivedassQ1rr1si(1)(1Q1Q)20ra.(s3)TheformulaindicatesthatthecouplingbetweenthefreepropagatingwaveandtheresonatorhastwodistinctstatesdeterminedbyparametersQrandQa.WhenQr/Qa<1,theintrinsicabsorptionisweakandtheresonatorisinanover-couplingstate,indicatedbyacurvecrossingtheimaginaryaxisinthephasordiagram(i.e.,Im(r)toRe(r)curve)andaphasemodulationcoveringthefull2range(SupplementaryFigure.S2candFigure.3ain5

5themaintext).Conversely,whenQr/Qa>1,theresonatorisinanunder-couplingwithastrongintrinsicabsorption.Inthiscase,thecurveinthephasordiagramistotallyontheleftoftheimaginaryaxisandthereflectionphaseonlycoversasmallrangefarlessthan?(SupplementaryFigure.S2candFigure.3ainthemaintext).BytuningtheratioofQr/Qa,themultilayercanexhibitnontrivialphaseshiftwhentransitingbetweenunder-couplingandover-couplingstates.Notethatthissimplifiedmodelpredictsamaximumabsolutephasedifferencereachingattheresonancefrequency(Figure.3ainthemaintext).ConsideringthePtSe2-SiO2-Siresonator,itiseasytomodifytheintrinsicabsorptionbychangingthethicknessofthelossyPtSe2layer.Wecalculatedthereflectionfromthisresonatorusingthetransfermatrixmethod(TMM)oflayeredfilms(seeSupplementaryNote2fordetails)andthenobtainedtheparameters0(equalto2c/0,wherecdenotesthevelocityoflightinvacuum),QrandQabyfittingEq.s3tothecalculationresults.SupplementaryFigure.S3,aandbillustratetwoexemplarycasesofover-couplingandunder-couplingstates,inwhichthethicknessesofPtSe2are1nmand5nmandthefittedparametersare0=589nm,Qr=2.6,Qa=3.4and0=612nm,Qr=3.1,Qa=2.0,respectively.SupplementaryFigure.S3cfurthershowsevolutionoffittedQrandQaasafunctionofPtSe2thickness.TheresultsindicatethattheradiationparameterQrremainsnearlyconstantatapproximately2.9;however,theabsorptionparameterQagraduallydecreasesfrom3.4to1.3asthethicknessincreasesfrom1nmto8nm.Thenontrivialphaseshiftoccursatthecriticalthicknessofapproximately2.2nmcorrespondingtotheappearanceofcriticalcouplingpoint.FortheSiO2-SisubstratewithoutthetopPtSe2layer,thefittedparametersare0=583nm,Qr=2.3,Qa=3.9,withQr/Qa=0.59.Consequently,thebinaryarrangementofultrathinlossyPtSe2layerthickerthan2.2nmcanfacilitateagiantphasedifferenceformeta-optics.Thecriticalthicknessofvarious2DmaterialstosupportthecriticalcouplingpointinthesameconfigurationweredepictedinFigure.S4.ThePtSe2filmexhibitingrelativelylargenandksupportssingularphasebehaviorswiththethinnestthickness,whichisfarsuperiortoother2Dmaterials.SupplementaryNote2.Transfermatrixmethodforlayeredfilmsandstructureoptimization.Inthissection,weintroducethecalculationofreflectioncoefficientsfrommultilayerfilmsbyusingtheTMM2andthendiscusstheoptimizationofthelayerthicknesswiththephasordiagram.Consideringamultilayersystemcontainingm+1layerslabeled0tom,thetransfermatrixfrommediumitojcanbewrittenas6

61ttijjirrijjirjiMijtr1jiij,(s4)wheretandraretransmissionandreflectioncoefficientsunderilluminationfromijijmediumitomediumj,andrij(pipj)/(pipj),tij2pi/(pipj),pniicos()i.nisthecomplexrefractiveindexofmediumiandistheanglebetweenthepropagatingiidirectionofthelightwavewithinthemediumandthenormaldirectionofthelayeredfilms.Thecosineofcanbecalculatedusingtheformulai2Re()Sin()n00cos()1iRe()ni.(s5)Thetransfermatrixdescribingthepropagationwithinlayeriofthicknessdiiseinkdiicos()i0Pi0einkdiicos()i,(s6)wherek=/cisthepropagationconstantinvacuum.Hence,thetransfermatrixforamultilayersystemcontainingm+1layersisABMMP...MPMPMm1,mm123212101CD.(s7)Byconvertingthetransfermatrixtothescatteringmatrixusingthefollowingrelationtr00mm1ADBCBS,(s8)rtDC100mmThereflectionfromthismultilayersystemcanbeobtainedasfollows:Crr.(s9)0mD7

7ByusingEq.s9,thereflectioncoefficientsandthephasedifferenceinducedbytheultrathinPtSe2layercanbeeasilycalculated.SupplementaryFigureS5illustratestherobustnessoftheconfigurationagainstthefluctuationofthethicknessofSiO2layer.WhenthethicknessofSiO2changesfrom270nmto300nm,thetrajectoryofthereflectionminimuminthen-kdiagramisslightlydeviated.However,thedispersioncurveofPtSe2alwaysintersectsthezeroreflection.AccordingtotheJordantheorem3,4,thenontrivialphaseshiftistopologically-protectedandrobustagainstthestructurefabricationimperfection.Simultaneously,thecriticalthicknessofPtSe2filmsforthecriticalcouplingpointasafunctionofthethicknessofSiO2wasinvestigated(FigureS5b).Thecriticalthicknessvariesfrom2.25nmto2.6nmcorrespondingtoathicknessofSiO2intheregionof250to310nm.Thus,thethicknessofPtSe2usedinourmanuscriptislargeenoughtoensurethenontrivialphaseshiftevenwithafabricationdeviationof~±30nmfortheSiO2layer.FortheoptimalthicknessoftheSiO2layer,wecalculatedthephasordiagramofcomplexreflectionsofair-PtSe2-Siandair-PtSe2-SiO2-Simultilayers.Therefractiveindicesaren0=1,ñ1=n1+i1,n2=1.52andñ3=n3+i3forair,PtSe2,SiO2andSirespectively,where,ñ1ismeasuredwithaspectroscopicellipsometer,andñ3wastakenfromreference5.SupplementaryFigure.S7ashowsthereflectioncoefficientsforthethree-layerair-PtSe2-Sisystem.Thebluesymbolsindicatetheevolutionofthereflectioncoefficientfor=590nmasthethicknessofthePtSe2filmincreases.Thereflectioncoefficientoftheair-PtSe2-Silayersevolvesfromthatoftheair-Siinterfacetothatoftheair-PtSe2interfaceasthethicknessofthePtSe2layerincreasesfrom0nmtoinfinity.representsthephasedifferencebetweenthecaseswith-andwithout-theultrathinPtSe2layerandisdefinedbytheintersectionanglebetweenthecomplexreflections(SupplementaryFigure.S7a).ThisfindingrevealsthatthemaximumphasedifferenceachievedbybinarypatterningthePtSe2layerontheSisubstrateisrestrictedtofarbelow(shadowedangleinSupplementaryFigure.S7a).Incontrast,byinsertingaSiO2layer,thephasedifferencecanbegreatlyextendednearbythecriticalcouplingpoint.Thereflectioncoefficientsasafunctionofthethicknessdfortheair-PtSe2-SiO2-Siandair-SiO2-SilayersareplottedinSiO2SupplementaryFigure.S7b,whered4.3nmand=590nm.ThephasordiagramsPtSe28

8formtwoclosedcurves.BytuningtheSiO2thicknessd,thephasedifferencecanSiO2bemanipulatedflexibly.AttheoptimalSiO2thicknessof286nm,thephasedifference(theintersectionangleinthephasediagram)reachesitsmaximumofattheresonancewavelengthof590nm.Thephasordiagramprovidesguidanceforexperimentallyoptimizingthestructureandmaterials.SupplementaryNote3.Thicknessandincidentangledependence.Toclearlyobservethethicknessandincidentangledependenceofthenontrivialphaseshift,wefurtherinvestigatedangle-robustphasemodulationbasedontopologically-protectedconcept3,6usingTMMandCMT,asshowninSupplementaryFigure.S6.Thecriticalcouplingpointalsoreferredtoastopologicaldarkness3stemsfromthealways-intersectionbetweenthetrajectoryofthereflectionminimuminthen-kdiagramandthedispersionofabsorbingmaterials4.AsshowninFigure.S6a,thedispersioncurveofPtSe2crossthereflectionminimumtraces,whichinducesperfectabsorptionatthecrosspoints.Itisclearlyseenthat,alongwiththeincreasingoftheincidentangle,theminimumtracesgraduallyshiftsaway.Theshiftingspeedisconsiderablysmallwhentheincidentangleislessthan30degrees,indicatingthattheabruptHeavisidephaseshiftvariesslowlyagainstthetiltoftheilluminationbeam.Theresonancewithinthestructureisastandingwavemodewhoseresonantwavelengthcanbewrittenas2nkdcos()2N,(s10)SiO2SiO2SiO2whereisthephaseinducedbyreflectionfromtheinterfacesofthecavityandNistheresonanceorder.TheresonanceoftheNthordercanbederivedas2nSiO2NdSiO22cos(SiO).(s11)N2Eq.s11showsthattheresonancewavelengthislinearlydependentonthethicknessofthecavitylayer.AccordingtothemodeloutlinedinSupplementaryNote1,itisexpectedthatthewavelengthofthemaximumphasedifferenceisproportionaltothecavitythickness,inaccordwithSupplementaryFigure.S6d.Inaddition,ifwefixthecavitythicknessandtheresonanceorder,combiningEq.s5,itcanbederivedthat9

922ndSiO22SiO22dncos()=sin().ThederivativeofthisNSiO2SiO2SiO20NN22ddsin(2)isNSiO20expressionwithrespectto0,whichisasmallvalued2Nn22sin()0SiO20near=0,indicatingthattheresonancewavelengthhasaminordependenceonthe0incidentanglenearthenormalillumination.0Theforegoingdiscussionrevealsthattheresonanceshiftisinsensitivetotheincidentanglewithinarangeof±20°.ThecalculationresultsbasedontheCMTmodel(SupplementaryFigure.S6b)agreewellwiththeobtainedresultsbyTMM(SupplementaryFigure.S6c),verifyingananglerobustphasedifferencewithawideangletoleranceof±20°(Figure.4jinthemaintext).SupplementaryNote4.Correlationcharacterizationofholographicimages.Thecorrelationcoefficientbetweenreconstructedandoriginalimagesisdefinedasfollows:uv(AuvAB)(uvB)C,(s12)22(AA)(BB)uvuvuvAuvuvBuvwhereA,B.Here,AuvandBuvrepresenttheintensitiesofuvuvindividualinformationunits(u,v),whileAandBdenotetheaverageintensitiesofalltheinformationunitsinthereconstructedandoriginalpatterns,respectively(SupplementaryFigure.S14).10

10FigureS1.Comparisonoftypicalbinarymeta-opticsperformance.Representativeexamplesofbinarymeta-opticsandtheirperformancesarecharacterizedintermsofthickness,operatingfrequenciesandunit-thicknessdiffractionefficiencies(normalizedtosurfacecorrugations),whereapplicable.Differentcolorsstandfordifferentapproaches,suchasplasmonicmetasurfaces(green)7-9,dielectricmetasurfaces(blue)10-12,lowdimensionalmaterials(LDM)(black)13,14.Aredtrianglemarkstheexperimentaldatafromthepresentstudy.11

11Figure.S2.Temporalcoupled-modetheorymodeloftheNMDs-SiO2-Siresonator.(a)Configurationofthestructure.(b)ThereflectionfromacompoundresonatorformedbyNMDs-SiO2-Silayerscanbedescribedbythecouplingbetweenthefreepropagatingwaveandaresonantsystemthroughasinglecouplingchannel.Theresonantsystemischaracterizedbyresonancefrequency0andparametersQrandQarelatedtotheradiationandabsorptiondissipations.(c)ThephasordiagramofcomplexreflectionsplottedusingEq.s3showstwocurvesrepresentingtheUnder-andOver-couplingstates.12

12Figure.S3.FittingsobtainedbyTMM.(a)and(b)ReflectioncoefficientsfromPtSe2-SiO2-SilayerscalculatedbyTMM(symbols)andfittedbyEq.s3(solidcurves).Themodulesandphaseofthecoefficientsareplottedontheleftandrightaxes,respectively.ThethicknessoftheSiO2layeris286nm,andthethicknessofPtSe2layeris1nm(a)or5nm(b),denotingover-couplingandunder-couplingstates,respectively.(c)TheevolutionofthefittedparametersQrandQaasafunctionofthethicknessofthePtSe2layer.13

13Figure.S4.Comparisonofthecriticalthicknessofdifferent2Dmaterialstosupportthecriticalcouplingpointinthe2Dmaterial-SiO2-Siconfiguration.Thecoloredsurfacerepresentsthecriticalthicknessvariationofthecladdinglayeragainsttherealandimaginarypartofrefractiveindices.Thecriticalthicknessesofthe2Dmaterials(Graphene,MoSe2,WSe2,PtSe2)arewithinthesurface.Here,wealsocalculatedthecriticalthicknessforacladdingmadeoftopologicalmaterial,Sb2Te3.Sincethesurfacerefractiveindexoftopologicalmaterialsisdifferentfromthebulkindex,theSb2Te3layerwasconsideredasthreelayersinthecalculation.Consequently,therelatedcriticalthicknessisoutofthesurfacementionedabove.Thedispersionparameterof2Dmaterialsreferencedtopreviousreports,e.g.graphene15,MoSe1616132,WSe2,Sb2Te3,andPtSe2presentwork.ThePtSe2exhibitingrelativelylargenandksupportsthecriticalcouplingpointwiththethinnestthickness,whichisfarsuperiortoother2Dmaterials.14

14FigureS5.Topologically-protectedstructurerobustnessagainstthefluctuationofthicknessofSiO2layer.(A)Thetrajectoryofthereflectionminimuminthen-kdiagramatvariedthicknessofSiO2layerthataredeviatedthedesignedthicknessof286nm(270nm,275nm,280nm,285nm,290nm,295nm,300nm)andthedispersionofPtSe2(PtSe2).(B)ThecriticalthicknessofPtSe2filmssupportsthecriticalcouplingpointasafunctionofthethicknessofSiO2.15

15Figure.S6.Angle-robustphasemodulation.(a)Thetrajectoryofthereflectionminimuminthen-kdiagramatdifferentincidentangle(0°,5°,10°,15°,20°,25°,30°)andthedispersionofPtSe2films(PtSe2).Thecalculatedangle-dependentphasedifferencebasedon(b)CMTmodeland(c)TMMsweepingtheincidentwavelengthandangle(λ:400-750nm;θ:-40-40°).(d)ThecalculatedphasedifferencebasedonTMMbysweepingthethicknessoftheSiO2layerandtheincidentwavelength(λ:400-750nm;thickness:200-400nm).16

16Figure.S7.Phasordiagramasafunctionofthefilmthickness.(a)PhasordiagramillustratingthephasemodulationcapabilitybythepresenceofPtSe2filmsontheSisubstrate.Thebluesymbolsrepresentthereflectionfromair-PtSe2-SilayersasafunctionofthethicknessofPtSe2films,wheretheorangearrowindicatestheincreaseind.ThePtSe2phasemodulationlabeled,anditsmaximumvalueismarkedbymax.(b)Phasordiagramsofcomplexreflectivitiesfromthecaseswithandwithoutthe4.3nmthickPtSe2filmontheSiO2-Sisubstrate,illustratingtheflexiblephasemodulationcapability.BychangingthethicknessoftheSiO2film,thereflectivitiesfromthecaseswithandwithoutthe4.3nmthickPtSe2layerformtwoclosedcurves.Thephasemodulationlabeled,andthe?phasedifferenceattheoptimalSiO2thicknessof286nmismarked.17

17Figure.S8.RamanspectrumandX-rayphotoelectronspectroscopy(XPS)spectrumofas-preparedPtSe2thinfilms.(a)RamanspectrumshowingthetypicalRamansignaturesofatomiclayersofPtSe2.(b),(c)XPSspectrumofSe3dandPt4f,respectively.18

18Figure.S9.MorphologyCharacterizationofas-preparedPtSe2films.(a)OpticalmicroscopyimagesofthePtSe2filmdepositedonSiO2-Sisubstrate(left)andSisubstratelayer(right),Scalebar:1cm.(b)AFMimagesofthePtSe2film,Scalebar:1μm.(c)and(d),Ramanmappingimagesfordifferentregions,Scalebar:1μm.19

19Figure.S10.TheselectedareaelectrondiffractionpatternofthePtSe2layer.20

20Figure.S11.Experimentalconfigurationfordirectlaserwriting.LLS:laserlightsource,LS:lightswitch,OA:opticalattenuator,BS:beamsplitter,3DTS:three-dimensionaltranslationstages,CCD:chargecoupleddevice.21

21Figure.S12.Characterizationoflaser-scribedPtSe2gratingsatdifferentpowers.OpticalmicroscopyimagesandRamanmappingimagesofthesameregionatdifferentincidentlaserpowers:(a)5μW,(b)10μW,(c)20μW,(d)30μW,(e)40μW,(f)50μW,Scalebar:5μmforallopticalmicroscopyimages,3μmforallRamanmappingimages.(g)ThewidthofthemilledPtSe2lineversusthepowerofincidentlaserpowers.(h)TheheightdifferencebetweenthescribedandunscribedPtSe2regionsatdifferentincidentlaserpowers.22

22Figure.S13.FalsecolorSEMimagesofbinaryPtSe2meta-holograms.(a)AzoomoutviewSEMimage.Scalebar:10μm.(b)Zoom-inviewSEMimageshowingthegeometryofasinglelaser-scribedpixel.Scalebar:2μm23

23Figure.S14.Procedureusedtoobtainthecorrelationcoefficient.(a)Theholographyimagereconstructedattheincidentwavelengthof671nm.(b)Thebinarizedintensitypattern.(c)Theoriginalimage.LogousedwithpermissionfromShenzhenUniversity.(d)ThedistributionofthegrayscalevaluesofinformationunitsintheholographyimageandcalculatedcorrelationcoefficientcalculatedbyEq.s12.24

24Figure.S15.Fidelitycharacterizationofreconstructedholographicimages.(a)Thecorrelationcoefficientsofreconstructedholographicimagesatdifferentincidentwavelengths.(b)Thecorrelationcoefficientsofholographyimagesreconstructedatdifferentincidentanglesat590nm.25

25Figure.S16.Theoptimizedconfigurationforincreaseddiffractionefficienciesbyusinglow-losssubstrates.(a)Thereflectioncoefficientsforthewavelengthof590nmfromPtSe2-SiO2-SiandPtSe2-SiO2-Timultilayersplottedinaphasordiagram.ThethicknessesoftheSiO2layerare290nmand272nm,andthethicknessesofthePtSe2layerare4.3nmand16nmforthesiliconandtitaniumsubstrate,respectively.ThesegeometricparametersarechosensothatthemodulesofcoefficientswithandwithoutPtSe2arealmostthesame,resultinginphase-onlymodulations.ItcanbeseenthatifonlythelineconnectingthepointwithandwithoutPtSe2layerpassestheorigin(criticalcouplingpoint),abruptHeavisideπphaseshifthappensbetweenthetwoconfigurations,andthereflectanceisnotnecessarilynearzero.Actually,thereflectancefromsubstrateswithoutPtSe2layerscanbeincreasedbyusinglowintrinsicabsorptionmaterials,andthatfromregionswithPtSe2layerscanbeincreasedbyusingthickerPtSe2films.(b)Thediffractionefficienciestothefirstordersatthewavelengthof590nmfromPtSe2gratingsonsiliconandtitaniumsubstrates,respectively.ThewidthofthePtSe2stripsare1μmandtheperiodicis2μm.Thethicknessparametersarethesameasdescribedin(a).(c)and(d)Theelectricfielddistributionsfromthegratingswithsilicon(c)andtitanium(d)substrates.26

2627

27Table.S1.Comparisonoftheperformanceoftypicalbinarymeta-opticsmadeofdifferentschemes28

28IncidentThicknessPhasemodulationModulationDiffractionUnity-Referenceswavelengthschemelevelsthickness(nm)Efficiencyefficiencyλ(nm)5904.3PtSe2binary4.14%0.96%Presentwork82530PlasmonicAuantennas.16-level-phase80%2.7%1763330PlasmonicAgantennas.16-level-phase32%1%1853230PlasmonicAunanoslitbinary10%0.33%19632.875PlasmonicCrnanoslitbinary23.7%0.32%204451.6%0.03%532602DSb2Te3binary1.5%0.025%136321.35%0.023%633320DielectricSinanopostsbinary19%0.06%2129

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