1 Controlling hybrid nonlinearities in transparent conducting oxides via two-colour excitation M. Clerici, 1 N. Kinsey, 2,* C. DeVault, 3 J. Kim, 2 E. G. Carnemolla, 4 L. Caspani, 4,5 A. Shaltout, 2,** D. Faccio, 4 V. Shalaev, 2 A. Boltasseva, 2,+ and M. Ferrera 4,‡ 1 School of Engineering, University of Glasgow, Glasgow, G12 8LT, UK 2 School of Electrical and Computer Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA 3 Dept. of Physics & Astronomy and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA 4 Institute of Photonics and Quantum Sciences, Heriot-Watt University, SUPA, Edinburgh, Scotland, EH14 4AS, UK 5 Institute of Photonics, Department of Physics, University of Strathclyde, Glasgow G1 1RD, UK * Now with: Dep. of Electrical and Computer Engineering, Virginia Commonwealth University, Richmond, Virginia 23284, USA ** Now with: Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA +,‡ Corresponding authors: [email protected]; [email protected]. ABSTRACT Nanophotonics and metamaterials have revolutionised the way we think about optical space (, ), enabling us to engineer the refractive index almost at will, to confine light to the smallest of the volumes, and to manipulate optical signals with extremely small footprints and energy requirements. Significant efforts are now devoted to finding suitable materials and strategies for the dynamic control of the optical properties. Transparent conductive oxides exhibit large ultrafast nonlinearities under both interband and intraband excitations. Here, we show that combining these two effects in aluminium-doped zinc oxide via a two- colour laser field discloses new material functionalities. Owing to the independence of the two nonlinearities the ultrafast temporal dynamics of the material permittivity can be designed by acting on the amplitude and delay of the two fields. We demonstrate the potential applications of this novel degree of freedom by dynamically addressing the modulation bandwidth and optical spectral tuning of a probe optical pulse. INTRODUCTION The continual success of electronics is largely due to the extreme miniaturization of devices and the ability to achieve exceptional functionality with a limited number of constituent materials. Currently, these areas are major weaknesses of photonics which hinder the primary advantage of increased operational bandwidth 1–3 . Specifically, the diffraction limit sets the minimum size of photonic components to about half their operational wavelength, while a plethora of photonic materials are needed to accomplish all the basic functionalities typically available in electronics. During the last decade, plasmonics and metamaterials have both gained great momentum because they provide a way to overcome the previously mentioned limitations. This is attained by coupling the electromagnetic radiation to the oscillating electronic plasma at the metal/dielectric interface. 4,5 However, the ability to squeeze optical modes well below the diffraction limit, and engineer the effective permittivity at will with structured materials is not free. By tightly confining light to metal layers, the propagation
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Controlling hybrid nonlinearities in transparent conducting oxidesviatwo-colourexcitationM.Clerici,1N.Kinsey,2,*C.DeVault,3J.Kim,2E.G.Carnemolla,4L.Caspani,4,5A.Shaltout,2,**D.Faccio,4V.Shalaev,2A.Boltasseva,2,+andM.Ferrera4,‡1SchoolofEngineering,UniversityofGlasgow,Glasgow,G128LT,UK2SchoolofElectricalandComputerEngineeringandBirckNanotechnologyCenter,PurdueUniversity,WestLafayette,IN,47907,USA3Dept.ofPhysics&AstronomyandBirckNanotechnologyCenter,PurdueUniversity,WestLafayette,IN,47907,USA4InstituteofPhotonicsandQuantumSciences,Heriot-WattUniversity,SUPA,Edinburgh,Scotland,EH144AS,UK5InstituteofPhotonics,DepartmentofPhysics,UniversityofStrathclyde,GlasgowG11RD,UK*Nowwith:Dep.ofElectricalandComputerEngineering,VirginiaCommonwealthUniversity,Richmond,Virginia23284,USA**Nowwith:GeballeLaboratoryforAdvancedMaterials,StanfordUniversity,Stanford,California94305,USA+,‡Correspondingauthors:[email protected];[email protected].
ABSTRACTNanophotonicsandmetamaterialshaverevolutionisedthewaywethinkaboutopticalspace(𝜀, 𝜇), enabling us to engineer the refractive index almost atwill, to confine light to thesmallestofthevolumes,andtomanipulateopticalsignalswithextremelysmall footprintsandenergyrequirements.Significanteffortsarenowdevotedtofindingsuitablematerialsand strategies for the dynamic control of the optical properties. Transparent conductiveoxidesexhibitlargeultrafastnonlinearitiesunderbothinterbandandintrabandexcitations.Here,weshowthatcombiningthesetwoeffectsinaluminium-dopedzincoxideviaatwo-colourlaserfielddisclosesnewmaterialfunctionalities.Owingtotheindependenceofthetwo nonlinearities the ultrafast temporal dynamics of the material permittivity can bedesigned by acting on the amplitude and delay of the two fields. We demonstrate thepotential applications of this novel degree of freedom by dynamically addressing themodulationbandwidthandopticalspectraltuningofaprobeopticalpulse.
INTRODUCTIONThecontinualsuccessofelectronicsislargelyduetotheextrememiniaturizationofdevicesand the ability to achieve exceptional functionality with a limited number of constituentmaterials.Currently,theseareasaremajorweaknessesofphotonicswhichhindertheprimaryadvantageof increasedoperationalbandwidth1–3.Specifically,thediffractionlimitsetstheminimumsizeofphotoniccomponentstoabouthalftheiroperationalwavelength,whileaplethoraofphotonicmaterialsareneededtoaccomplishallthebasicfunctionalitiestypicallyavailable inelectronics. During the lastdecade,plasmonicsandmetamaterialshavebothgainedgreatmomentumbecausetheyprovideawaytoovercomethepreviouslymentionedlimitations. This is attained by coupling the electromagnetic radiation to the oscillatingelectronicplasmaatthemetal/dielectricinterface.4,5However,theabilitytosqueezeopticalmodeswellbelowthediffraction limit,andengineertheeffectivepermittivityatwillwithstructuredmaterials isnot free.By tightlyconfining light tometal layers, thepropagation
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lossesareincreasedwhichcanbeproblematicformanyapplications.6Tosolvetheserelevanttechnologicaldrawbacks,newmaterialplatformshavebeenrecentlyinvestigatedwiththegoal of removing metal constituents from both plasmonic technologies and artificialmaterials.7,8Amongalternativeplasmonicmaterials,transparentconductiveoxides(TCOs)areauniqueclassofwide-bandgapsemiconductors.Theycansupportextremely largedoping levels (≃10)*cm-3)withloweffectiveelectronmasses(≃ 0.3𝑚.;𝑚. =free-electron-mass),enablingametallic response in the near-infrared (NIR) region and high transmission in the visibleregion.8–12 Such materials have been employed as transparent electrodes in variousapplications,13,14butarerecentlyreceivingattentioninnanophotonics,owingtotheirhighlytunablestaticpropertiesandpotentialforbothelectricalandopticalcontroloftherefractiveindex.15–21ThisversatilityisextremelyattractiveasTCOscanservemultipleroles,forexampleas dynamic, plasmonic, and dielectric layers,which enable extreme flexibility to optimisestructures fordifferingconditions,allwitha singlematerial. Furthermore,manyTCOsarenaturallysuitedtoachievetheepsilon-near-zero(ENZ)22conditioninthetelecommunicationsbandwhereby the low refractive index, that is, less than unity, enables the potential forenhancednonlinearities,super-coupling,anddeeplysub-wavelengthfieldconfinement.19,23–28 Aluminium-doped zinc oxide (AZO)12 is one suchmaterialwhich combines all of thesepropertieswithreducedopticallossescomparedtootherTCOs8andalowmanufacturingcostduetoitswidelyavailableelementalcompounds.Consequently,oxygendeprivedAZO(seeMethods)isanattractivematerialfordynamiccontrol.Theopticalinjectionofcarriersintotheconductionband(interbandexcitationintheultraviolet–UV–spectralregion,𝜆34 = 325nm)enabledcontrolofthereflectionandtransmissionupto40%and35%,respectively,withsub-picosecond recovery time.18 Intraband excitationswith below-bandgap pulses (in thenear-infrared –NIR– spectral region, 𝜆789 = 787 nm) resulted in up to 90% and 800%modulationofthereflectionandtransmission,respectively. Here,wedemonstratethattheopticalpropertiesofAZOcanbedynamicallyaddressedon a sub-picosecond time-scale by a clever combination of the interband and intrabandnonlinear effects, driven by two different wavelength pump pulses (𝜆34 = 262 nm and𝜆789 = 787nm).WefirstshowthattheAZOcomplexrefractiveindexatinfraredwavelengths(𝜆= = 1300nm)canbecontrolledbyatwo-colourpumppulse(𝜆34 + 𝜆789).Wethentunethe delay between the two pumps to demonstrate the dynamic control of the probemodulationbandwidth,between0.8and2THz,andopticalspectrumwithawavelengthshiftof±4nm.
RESULTSPumpandprobeexperiments.Thepump-probeexperimentisschematicallyshowninFigure1a. SeeMethods for details on the experimental settings. We measure the probe pulsetransmission(T)andreflection(R)froma900nmthickAZOfilmdepositedona1mmthicksilicasubstrate.Theprobepulsewavelengthissetto𝜆= = 1300nm,closetothezero-epsilonwavelengthofthematerial.BothTandRarerecordedasafunctionofthedelay𝛥𝜏between
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the pump pulses and the probe. In Figure 1b we show the measured delay-dependentreductionoftransmissivityasaresultofinterbandcarrierexcitation,drivenbyanultravioletpulse (𝜆34 = 262nm) of ≃ 65 fs duration and fluence 𝐹34 ≃ 5mJcmG). Therecombination time(≃ 600fs) andmodulationamplitude(≃ 45%) are consistentwithpreviousmeasurementsperformedwithapumppulseat325nm.18InFigure1cweshowthemeasured delay-dependent increase of transmissivity due to intraband carrier excitation,drivenbya100fsnear-infraredpulse(𝜆789 = 787nm)withfluence𝐹789 ≃ 16mJcmG).Thismetal-likenonlinearityistheresultofthermalsmearingoffree-electronscausingdecreasedabsorptionandreflectionattheprobewavelengthandexhibitsanextremelyfastdecayrateof≃ 170fs.AsshownbythedottedcurvesinFigs.1band1c,theinterbandandintrabandmaterialresponsescanbesuccessfullymodelledusingaDrudemodelcoupledtotheexcesscarrierpopulationandthetwo-temperaturemodel,respectively(seeMethods).
Figure1.Two-colourpump-probeexperiment.a,Schematicofthetwo-colourpump–probeexperimentalsetupwherethetwopumpwavelengths,787nm(near-infrared–NIR)and262nm(ultraviolet–UV),areillustrated along with the probe wavelength of 1300 nm. The delay between the two pump pulses isdenoted∆𝑡whilethedelaybetweentheprobeandUVsignalisdenoted𝛥𝜏.Forintrabandexcitationusingonly theNIRpump,∆𝜏 isdefinedas thedelaybetweentheprobeandNIRpumppulsearrivaltime.Theblackarcsindicatethearrivaltimeofthepulses.b,Changeintransmissionat1300nmversusthepump–probedelay∆𝜏under262nmexcitationfittedwithsimulation.Insetillustrates theprocessdiagramforinterbandexcitation:UVlight(𝐸34)generateselectron-holepairs(𝛿O, 𝛿=)abovetheFermilevel(𝐸P) inaddition to the intrinsic concentration (𝑁R) which recombine throughmid-gap trap states (𝑁S, 𝜏T.U). c,Changeintransmissionat1300nmversusthepump–probedelay𝛥𝜏under787nmexcitationfittedwithsimulation. Inset illustrates the process diagram for intraband excitation: NIR light (𝐸789) raises thetemperatureofconductionbandelectrons(𝑇UWWX → 𝑇ZWS)whichrelaxthroughscatteringprocesses(𝜏.G=),heatingthelattice.Thechangeintransmissionfromtheexperimentwasobtainedthrough∆𝑇 = 𝑇 − 𝑇\,whereT0 is thetransmissionoftheprobefar fromthepumppulse.Forcomparisonwiththetheoreticalresults, the amplitude of the induced transmission change was normalized using ∆𝑇OWT]^XR_.` =∆𝑇/|∆𝑇]^c|,where|∆𝑇]^c|isthemagnitudeofthepeakchangeintransmission.Thesameprocedurewascompletedforthesimulationresults.
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Remarkably, AZO shows simultaneously strong ultrafast interband and intrabandnonlinearitieswithreadilyavailablewavelengthsfromasinglelasersource Theobservedcoexistenceofbothintrabandandinterbandnonlinearitiessuggeststhepossibility of achieving new dynamic functionalities through their combined effect and ifthesetwoexcitationregimesareindependent,thecorrespondingeffectscanbealgebraicallycombined.We thereforeperformeda thorough investigationof theAZOoptical responseundercombinedUVandNIRexcitationasafunctionoftherelativedelay∆𝑡betweenthetwopumpsand∆𝜏betweenthepumpsandtheprobe(theUVpumpsignalisusedasthetimereference).Fromthe recordedprobe reflectionand transmissionasa functionof the twodelays,𝑅=(∆𝑡, ∆𝜏)and𝑇e(𝛥𝑡, ∆𝜏),respectively,(seeSupplementaryFigure1),weretrievetherealandimaginaryrefractiveindexofthefilmusingatransfer-matrixapproach,asdescribedelsewhere29.TheextractedvaluesareshowninFigure2,wherethetime-dependentrelative
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Figure2.DynamicchangeintheopticalresponseofAZOthinfilmstriggeredbytwo-colourexcitation.Percentagechangeofthereal(a-e)andimaginary(f-j)partoftherefractiveindexasafunctionofthedelay∆𝜏betweentheultraviolet(UV)pumpandtheinfraredprobepulses.Multipleverticalplotsareshown,fordifferentdelay∆𝑡betweentheUVandthenear-infrared (NIR)pumppulses.Shadedareasindicatewhether theUVpump,whichisusedastimereference,precedes(lightblue)orfollows(lightred)theNIRpump.Overlappingtheresultsobtainedbysimultaneoustwo-colourpumping(redcurves)weplotthecomputedchangeinrefractiveindexcalculatedbythealgebraicsummationoftheresultsobtainedfromexperimentswithseparateUVandNIRpumppulses(blackdashedcurves).Theprobe,theNIR,andtheUVpumpwavelengthsweresetto1300nm,787nmand262nm,respectively.Theprobeintensitywas low: 𝐼= ≃ 200MWcmG), while the pump fluenceswere𝐹34 = 5mJcmG) and𝐹789 =14mJcmG).
Itisworthmentioningthatalltheexperimentsareperformedinaconditionofbalancedexcitation,meaningthattheadoptedfluencesforUVandNIRpumpingwereset insuchawaytoproducesimilaralterations(inamplitudebutnotinsign)onthetransmittedpower.Operatively speaking,we first arbitrarily choosea fluence for theUVbeamwhile theNIRpumpfluenceissetafterwards,toinduceachangeonthetransmittedpowerofthesamemagnitude as that obtained with the UV pump. Such a change saturates for both UV(∆𝑇 𝑇\ ≃ 75% at𝐹34 ≃ 15mJcmG)) andNIR (∆𝑇 𝑇 ≃ 100% at𝐹789 ≃ 60mJcmG))pumping.
Whilecross-couplingbetweeninterbandandintrabandeffectsisnegligibleatthepumpfluences used in these experiments, we observed that it becomes appreciable for higherfluences.Toevaluatetheimpactofcrosstalkwecalculatetherelativedifferencebetweenthemeasured (me) and ideal (id) change in the real and imaginary refractive index 𝐷T,R =𝑛T,R]. − 𝑛T,RR` /𝑛T,RR` for increasing pump fluences. In this case, “measured” refers to therefractiveindexwiththesimultaneouspumpingschemewhile“ideal”referstothealgebraicsum of the refractive indices retrieved with independent UV and NIR excitations. In theexperimentalconditionsofFig.2weestimate𝐷T ≤ 6%and 𝐷R ≤ 3%,whereasathigherpump fluences𝐹34 = 10mJcmG) and𝐹789 = 24mJcmG)weobserve stronger crosstalk:𝐷T ≤ 22%and𝐷R ≤ 7%(seeSupplementaryNote1andSupplementaryFigure2).
Modulation bandwidth andwavelength control. The ability to optically control the AZOpropertieswithnonlinear effectsof similar amplitude yetopposite signpaves theway tointriguingapplications. InFig.3weshowtwoneweffectsenabledby the two-colourAZOmodulation.The first, inFigs.3aand3b, is thedynamiccontrolof theopticalmodulationbandwidthoftheAZOfilm,whilethesecond,inFigs.3cand3d,isthedynamiccontrolofthetransmittedprobewavelength.
All-optical modulation of infrared radiation is relevant to the development of futuretelecommunicationsanddatanetworkstechnologies30–32.Anultrafast,> 1THzmodulationbandwidthofAZOviainterbandpumpinghasbeenrecentlyreported18.Figure3ashowsthe
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changeinToftheAZOfilmpumpedbybothUVandNIRlight,resolvedasafunctionoftheinter-pumpdelay𝛥𝑡andthepump-probedelay𝛥𝜏.TheeffectoftheUVpumpistoreducethetransmission(thehorizontalblueandpurpleband),whiletheeffectoftheNIRpumpistoincrease the transmission (the diagonal, green-to-red band). Performing the Fouriertransformalong theverticaldirectionprovides themodulationbandwidthof theopticallyexcitedfilmasafunctionoftheinter-pumpdelay𝛥𝑡andisshowninFig.3b.Theblueandreddashed lines indicate the bandwidth (rms) obtained by only UV and only NIR pump,respectively.Thefasterdynamicoftheintraband(≃ 1.7THz)comparedtotheinterband(≃1.55 THz) nonlinearity is clear. The proposed two-colour pump configuration remarkablyallowsonetomodifythemodulationbandwidthofthefilmviathedelayofthetwopumpfields,asshownbytheblackcurveinFig.3b.Thisenablestheobservationofafastoscillationbetweenareduction(≃ 0.75THzat𝛥𝑡 ≃ 0)andanincrease(≃ 2THzat𝛥𝑡 ≃ 130fs)ofthe
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Figure3. Two-colourpumpingeffects.a, Change in theprobepulse transmissionas a functionof thepump-probedelay(∆𝜏)andtheinter-pumpdelay(∆𝑡).TheUVpumpdecreasesthetransmission,whereasthe NIR increases it. The combined effect produces a Δt-dependent modulation. The modulationbandwidthisevaluatedbyperformingaFouriertransformalong∆𝜏,andisshownbytheblackcurveinb.Fordelayscloseto∆𝑡 = 0themodulationbandwidthcanbedecreasedorincreasedbythetwo-colourcombinedeffect.TheblueandreddashedlinesshowthebandwidthoftheUV-onlyandNIR-onlydrivenmodulation.c,Measuredcentralwavelengthshiftofthetransmittedprobepulse(≃ 15nmbandwidth)inazoomed∆𝑡 − 𝛥𝜏region(squareboxina).TheUVpumpblue-shiftstheprobewavelength,whereastheNIRpumpdoestheopposite.At∆𝑡 ≃ 0theoppositeeffectsalmostentirelycancelthewavelengthshift.d,Summaryof the findings inc, showingthemaximumpositive(𝛥𝜆m)andnegative(𝛥𝜆G)wavelengthshiftfortheNIR-only(reddashed/dotted),UV-only(bluedashed/dotted)andtwo-colour(solidblack)AZOexcitation.
Further, we show how the probe wavelength can be dynamically modified by acombinationofthetwoUVandNIRpumppulses.InFig.3cweshowthechangeinthecentralwavelengthofthe𝜆= ≃ 1300nmprobepulse,recordedwithanInGaAsspectrometer,asafunction of both 𝛥𝑡 and 𝛥𝜏 and for pump fluences 𝐹34 = 22mJcmG) and 𝐹789 =42mJcmG).WenotethatthewavelengthshiftinducedbytheUVpumpisnegative,whiletheNIRpumpgivesbothapositiveandnegativeshift,dependingonthedelaywiththeprobe.Figure3dshowsthemaximumpositive(𝛥𝜆m)andnegative(𝛥𝜆G)frequencyshiftinducedbytheUVandNIRpumpsalone(blueandredcurves,respectively)andcombined(blackcurves).Interestingly,thewavelengthshiftinducedbythetwoindependentexcitationmechanismscanalsobealgebraicallyadded.Therefore, foraspecificchoiceofthepumpfluences, thewavelengthshiftisalmostcancelledwhenthetwopumppulsesaretemporallyoverlapped.Wenotethat,forhigherpumpfluences,wavelengthshiftsexceedingthepulsebandwidthcanbeachieved.
DISCUSSIONAZOfeaturesbothaninterbandandintrabandtransitionatwavelengthsthataredifferentenough to separate the twoeffects, yet closeenough tobe addressed simultaneouslybyfrequency conversion of standard laser sources. This is in contrastwithmostmetals andsemiconductorswherethenonlinearitiesareeitherspectrallyoverlapped(metals),difficulttoaccess(deep-UV),orspacedtoofaraparttoenabletheircombineduse(semiconductors).However,theobservedpropertiesarenotuniquetoAZO,ratheracommonfeaturetotheclassoftransparentconductiveoxides.Infact,weobservesimilarbehaviours,thatis,theco-existence of interband and intraband nonlinearities with opposite optical effects, incommercially available indium tin oxide (ITO) films (see Supplementary Note 2 andSupplementaryFigure3).AlthoughathoroughcomparativeanalysisofthetwoTCOsgoesbeyondthepurposesofthiswork,oxygen-deprivedAZOshowsstrongerandfastertemporaldynamics.Therefore, it isoneofthebestoptionsforapplicationsrelyingontheproposedhybridnonlinearityattelecomwavelengths.
Toconclude,wehighlightthatthelargeanddynamicallyaddressablemodulationoftheAZOrefractiveindexwithterahertzbandwidthsisanewphotoniccapabilitythatmayleadtointeresting developments in signal processing, ultrafast optics, andopticalmetrology. Forexample, itmay enable complex coding schemes such as code divisionmultiple access33,whichisofhighinterestforopticalcommunication.Similarly,engineeringtherecombinationrate to match the thermal relaxation rate of the intraband excitation may lead to theimplementationof an all-optical XORgate via two-colour excitation. Finally, theobservedultrafastandcontrollablewavelengthshiftmaylaythebasisforanovelclassofultrafastandcompactopticalrouters.
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METHODSPump-probeexperiment. For theexperimentwe reliedonaTi:Sapphire laser (AmplitudeTechnologies),whichdeliveredupto10mJenergypulsesat787nmcentralwavelength,with100fspulseduration.Afractionofthelaserpowerwasroutedtoacommercialwhitelightseededopticalparametricamplifier(Topas,LightConversionLtd),whichproducedtheshort(< 120fs)probepulseatawavelengthtunablebetween1100-2600nm.Fortheexperiments,wecontrolledthewavelengthinthe1250-1350nmrange.Thes-polarisedprobebeamwasspatially filtered, reduced inenergywithneutraldensity filters,andfocusedbya250mmfocallengthlensontotheAZOfilm,atasmallangletothenormalofthefilmsurface(< 10deg).Theprobebeamwaistonthesamplewasmeasuredusingtheknife-edgetechniquetobe65μm.Theprobeintensityinthefocuswasfoundtobe200MWcmG),determinedbymeasuringthepulseenergyandduration.Theprobepulsedelayfromthepumppulseswassetbyacomputercontrolledlineartranslationstage(M-VP-25XA,Newport),equippedwithagold-coatedhollowretroreflector(PLXInc.).TheUVpulse(262nm)wasproducedbypumpinganin-linethird-harmonicgenerationsetup(Femtokit,EksmaOptics)with≃ 1mJ,787nmpulses.Theoutput200μJ,≃ 65fs,262nmpulseswere cleaned from the residual 787 nm and 393 nm radiation using four dichroicmirrors(HR@266nm,HT@400nm&@800nm,LayertecGmbH).Thes-polarisedUVpulsewasfocusedatnormalincidencewitha𝑓 = 250mmfocallengthCaF2lens.Thebeamsizemeasuredwithaknife-edgewas400μm.TheUVenergywascontrolledbyactingonthehalf-waveplateattheinputofthethird-harmonicgenerationtool.TheNIRpumpwasobtainedbysplittingaportionofthelaserbeamanddelayingitfromtheUVpulseusingacomputercontrolled linear translation stage (M-VP-25XA, Newport), equipped with a silver-coatedhollowretroreflector(PLXInc.).Thes-polarisedNIRpumpwasfocusedatnormalincidenceonto the AZO film. A dichroic mirror (HR@266 nm, HT@800 nm, Layertec GmbH) wasemployed for combining the two pump pulses. The beam waist of the NIR pump wasmeasuredtobe210μmusingtheknife-edgetechnique.Thepulseenergywascontrolledwithawaveplateinfrontofathin-filmpolariser(Altechna).TheUV,NIRandprobeenergiesweremeasuredwithathermopiledetector(XPL12,Gentec-EO). The reflected and transmitted signals were recorded with amplified Germaniumphotodetectors(PDA50B-EC,Thorlabs).Samplefabricationandcharacterization.Theoxygendeprivedaluminium-dopedZnO(AZO)filmsweredepositedusingpulsed laserdeposition (PVDProducts Inc.)withaKrFexcimerlaser (Lambda Physik GmbH) operating at a wavelength of 248 nm for source materialablation.A2wt%dopedAZOtargetwaspurchasedfromtheKurtJ.LeskerCorp.withapurityof 99.99 % or higher. The energy density of the laser beam at the target surface wasmaintained at 1.5JcmG) and the deposition temperature was 75°C.Wemaintained theoxygen pressure under 0.01 mTorr to achieve additional free carriers from the oxygen
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vacancies.Theprepared thin filmswerecharacterisedby spectroscopicellipsometry (J.A.WoollamCo.Inc.)inthespectralregionfrom300-2500nm.ThedielectricfunctionoftheAZOwasretrievedbyfittingaDrude(when𝜔W = 0)andLorentzoscillatormodel,Eq.(1),tothe ellipsometry data. The optical properties at 262 nm were estimated from a splineextrapolation of themeasured properties combined with bounds provided by data fromsimilar films.34Toprobetheelectricalpropertiesof thin filmssuchasmobilityandcarrierconcentration, we carried out the Hall measurement (MMR Technologies) at roomtemperature.
𝜀 = 𝜀q +rst
rutGrt Gvrw (1)
Interbanddynamicsandmodelling.Theinterbandmodulation,𝐸Zx > 𝐸y,andrelaxationoftheAZOfilmwerefirstobservedindividuallyusingonlythe262nmUVpumpandprobe.Thesub-picosecond recombination time is indicative of Shockley-Read-Hall recombinationprocesses, which result in a reduced recombination time according to 𝜏T.U ∝ 1 𝑁S𝜎𝑣SZ,where𝑁Sisthetrapdensity,𝜎isthecapturecrosssection,and𝑣SZisthethermalvelocityofcarriers.35 The interband dynamics were modelled using a 2D spatial and temporaldiscretization(seeSupplementaryDiscussionfordetails).
The change in the optical properties was then determined using the transfer matrixmethodforthegradedindexprofilewherebyamatrixwascalculatedforeachlayer𝛿𝑧andmultipliedtodetermineaneffectivetransfermatrixateachtimestepassuminganinfinitesubstrate of fused silica. The amplitude of the change was then normalized and therecombination ratewas fitted to theexperimentaldata. Subsequently, the recombinationtimeofthefilmwasestimatedtobe≃ 600fs.Intrabanddynamicsandmodelling.Theintrabanddynamics,𝐸Zx < 𝐸yoftheAZOfilmwerealsoobservedindividuallyusingonlythe787nmexcitationandprobe.At787nmtheAZOisa lossy dielectric, but the excitation is still far from the band-edge (𝜆 ≃ 320 nm).Subsequently,theabsorptioninthisregimeisdominatedbytheresidualDrudeloss,i.e.,freecarriers in the conduction band. This excitation results in a non-equilibrium hot electronpopulationwhich relaxes through various scatteringprocesses(𝜏.G=), heating the lattice.Consequently, the intraband dynamics of the AZO film were modelled using the two-temperature model, whereby the change in the electron temperature and latticetemperature are captured as a function of time for the material (see SupplementaryDiscussionfordetails).Following,theresultingchangeintheopticalpropertieswasmodelledusing an effective thermally dependent complex index, 𝑛SZ, such that 𝛥𝑛~�� = 𝛥𝑇. +𝛥𝑇X 𝑛SZ. The transfer matrix method was used to determine the change in the opticalpropertiesofthegradedindexmaterial.Thereflectionandtransmissionofthesamplewerenormalized,andtheratewasfittedtoextracttheelectronphonon-couplingcoefficientandfoundtobe𝐺 ≃ 1.410*�WKG*mG�.Afterthenormalisationprocedure,onlythesignofthe complex effective thermal index is relevant, and it was found that the extinction
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coefficient decreases while the index increased, i.e. 𝑛SZ > 0 and 𝑘SZ < 0, matching theexperimental results. However, unlikeothermaterials,wedid not observe a long-lastingthermaloffsetarisingfromheatdissipationandremovalfromthelattice.Thisislikelyduetothe significant disparity between the electron and lattice heat capacities of AZO (seeSupplementaryDiscussion).Thus,forasmallapplicationofenergytheelectrontemperatureincreasessignificantly,givingrisetoalargenonlinearresponseandanobservablechangeinthereflection/transmission,althoughthisenergydoesnotresultinasubstantialincreaseinthelatticetemperature.Data availability. All relevant data present in this publication can be accessed at:http://dx.doi.org/10.17861/8f45636c-0560-427b-992e-87ba6d9090ab.Acknowledgements. This work was supported by the NSF MRSEC Grant DMR-1120923,AFOSR Grant FA9550-14-1-0138, and AFOSR Grant FA9550-14-1-0389. D.F. acknowledgesfinancialsupportfromtheEuropeanResearchCouncilundertheEuropeanUnionʼsSeventhFramework Programme (FP/2007-2013)/ERC GA 306559 and EPSRC (UK, grantEP/M009122/1). M.C. acknowledges support from EPSRC (Grants No. EP/P009697/1 andEP/P51133X/1) and from BLM s.p.a.. L.C. acknowledges the support from the PeopleProgramme(MarieCurieActions)oftheEuropeanUnion’sFP7ProgrammeunderREAGrantAgreementsNo.627478(THREEPLE).M.F.acknowledgessponsorshipfromEPSRC(UK,grantEP/P019994/1).TheauthorsthankProf.ArrigoCalzolari,CNRNanoModenaItaly,forhelpfuldiscussionsduringthedevelopmentofnumericalmodels
