超快光学-第10章-自相关

IntensityAutocorrelation1DPhaseRetrievalagainSingle-shotautocorrelationTheAutocorrelationandSpectrumAmbiguitiesThird-orderAutocorrelationInterferometricAutocorrelation,MeasuringUltrashortLaserPulsesI:Autocorrelation,Why?ThedilemmaThegoal:measuringtheintensityandphasevs.time(orfrequency)TheSpectrometerandMichelsonInterferometer1DPhaseRetrieval,Todeterminethetemporalresolutionofanexperimentusingit.Todeterminewhetheritcanbemadeevenshorter.Tobetterunderstandthelasersthatemitthemandtoverifymodelsofultrashortpulsegeneration.Tobetterstudymedia:thebetterweknowthelightinandlightout,thebetterweknowthemediumwestudywiththem.Tousepulsesofspecificintensityandphasevs.timetocontrolchemicalreactions.Tounderstandpulse-shapingeffortsfortelecommunications,etc.Becauseitsthere.,Whymeasureanultrashortlaserpulse?,Asamoleculedissociates,itsemissionchangescolor(i.e.,thephasechanges),revealingmuchaboutthemoleculardynamics,notavail-ablefromthemerespectrum,oreventheintensityvs.time.,Importantpointaboutclaimsofthegenerationofinterestingscientificobjects,“Ifyouhaventmeasuredit,youhaventmadeit!”,WayneKnox(1957-)Director,InstituteofOptics,UniversityofRochester,Rochester,NYUSA,WayneKnox,Inordertomeasureaneventintime,youneedashorterone.,Tostudythisevent,youneedastrobelightpulsethatsshorter.,Butthen,tomeasurethestrobelightpulse,youneedadetectorwhoseresponsetimeisevenshorter.Andsoon,So,now,howdoyoumeasuretheshortestevent?,PhotographtakenbyHaroldEdgerton,MIT,TheDilemma,Ultrashortlaserpulsesaretheshortesttechnologicaleventsevercreatedbyhumans.,Usinganultrashortpulse,youcanmeasurealmostanyeventprovidedthatyourpulseisshorter.Sohowdoyoumeasurethepulseitself?Youmustusethepulsetomeasureitself.Butthatisntgoodenough.Itsonlyasshortasthepulse.Itsnotshorter.Techniquesbasedonusingthepulsetomeasureitselfhavenotsufficed.,Blurrypicturemeasuredusinganinsufficientlyshortevent.,Theelectricfieldcanbewritten:,Intensity,Phase,Alternatively,versusfrequency:,Spectral,Phase,Spectrum,Weneedtomeasureboththetemporal(orspectral)intensityandphase.,Wemustmeasuretheintensityandphasevs.timeorfrequency.,Theinstantaneousfrequency:,Example:Linearchirp,Phase,(t),time,Wedliketobeabletomeasure,notonlylinearlychirpedpulses,butalsopulseswitharbitrarilycomplexphasesandfrequenciesvs.time.,Thephasedeterminesthepulsesfrequency(i.e.,color)vs.time.,Time,Lightelectricfield,Thespectrometermeasuresthespectrum,ofcourse.Wavelengthvariesacrossthecamera,andthespectrumcanbemeasuredforasinglepulse.,PulseMeasurementintheFrequencyDomain:TheSpectrometer,CollimatingMirror,“Czerny-Turner”arrangement,EntranceSlit,CameraorLinearDetectorArray,FocusingMirror,Grating,Imagingspectrometersallowmanyspectratobemeasuredsimultaneously,oneforeachrowofa2Dcamera.,Broad-bandpulse,One-dimensionalphaseretrieval,Therearestillinfinitelymanysolutionsforthespectralphase.The1DPhaseRetrievalProblemisunsolvable.,E.J.Akutowicz,Trans.Am.Math.Soc.83,179(1956)E.J.Akutowicz,Trans.Am.Math.Soc.84,234(1957),Thisgeneralproblemiscalledthe1Dphaseretrievalproblem.,Itsmoreinterestingthanitappearstoaskwhatinformationwelackwhenweknowonlythepulsespectrum.,Clearly,whatwelackisthespectralphase.,Butcanwesomehowretrieveit?Obviouslynot.,Butwhatifwehavesomeadditionalinformation?Forexample,whatifweknowwehaveapulsefiniteinduration?,and,Spectrum,Spectralphase,Recall:,PulseMeasurementintheTimeDomain:Detectors,Examples:Photo-diodes,Photo-multipliers,Detectorsaredevicesthatemitelectronsinresponsetophotons.,Detectorshaveveryslowriseandfalltimes:1nanosecond.,Asfaraswereconcerned,detectorshaveinfinitelyslowresponses.Theymeasurethetimeintegralofthepulseintensityfromto+:,Thedetectoroutputvoltageisproportionaltothepulseenergy.Bythemselves,detectorstelluslittleaboutapulse.,Anothersymbolforadetector:,Detector,Detector,PulseMeasurementintheTimeDomain:Varyingthepulsedelay,Sincedetectorsareessentiallyinfinitelyslow,howdowemaketime-domainmeasurementsonorusingultrashortlaserpulses?,Welldelayapulseintime.Andhowwillwedothat?,Bysimplymovingamirror!,Sincelighttravels300mperps,300mofmirrordisplacementyieldsadelayof2ps.Thisisveryconvenient.,MovingamirrorbackwardbyadistanceLyieldsadelayof:,Donotforgetthefactorof2!Lightmusttraveltheextradistancetothemirrorandback!,Translationstage,Inputpulse,E(t),E(tt),Mirror,Outputpulse,Wecanalsovarythedelayusingamirrorpairorcornercube.,Mirrorpairsinvolvetworeflectionsanddisplacethereturnbeaminspace:Butout-of-planetiltyieldsanonparallelreturnbeam.,Cornercubesinvolvethreereflectionsandalsodisplacethereturnbeaminspace.Evenbetter,theyalwaysyieldaparallelreturnbeam:,Hollowcornercubesavoidpropagationthroughglass.,Apollo11,Pulseenergy,Thefieldautocorrelation:G(2)(t).Looksinteresting,“Interfer-ogram”,Thedetectedvoltagewillbe:,PulseMeasurementintheTimeDomain:TheMichelsonInterferometer,ButtheFouriertransformofG(2)(t)isjustthespectrum!,TheAutocorrelationTheorem,TheFourierTransformofthefieldautocorrelationisthespectrum!Proof:,t=-t,Canweusethesemethodstomeasureapulse?,V.WongequivalenttothespectrumoftheSH(oscillatesat2windelay),Theinterferometricautocorrelationsimplycombinesseveralmeasuresofthepulseintoone(admittedlycomplex)trace.Conveniently,however,theyoccurwithdifferentoscillationfrequencies:0,w,and2w.,InterferometricAutocorrelation:Examples,7-fssech2800-nmpulse,Doublepulse,Pulsewithcubicspectralphase,Doestheinterferometricautocorrelationyieldthepulseintensityandphase?,No.TheclaimhasbeenmadethattheInterferometricAutocorrelation,combinedwiththepulseinterferogram(i.e.,thespectrum),coulddoso(exceptforthedirectionoftime).Naganuma,IEEEJ.Quant.Electron.25,1225-1233(1989).Buttherequirediterativealgorithmrarelyconverges.Thefactisthattheinterferometricautocorrelationyieldslittlemoreinformationthantheautocorrelationandspectrum.Weshouldntexpectittoyieldthefullpulseintensityandphase.Indeed,verydifferentpulseshaveverysimilarinterferometricautocorrelations.,Pulse#2,Phase,tFWHM=5.3fs,-40-2002040,Intensity,Despiteverydifferentpulselengths,thesepulseshavenearlyidenticalIAs!,ChungandWeiner,IEEEJSTQE,2001.,ExampleofInterferometricAutocorrelationambiguity,InterferometricAutocorrelationsforPulses#1and#2:,Pulse#1,Interferometricautocorrelationofaverycomplexpulse,Forcomplexpulses,thestructurevisibilityapproacheszeroinbothintensity-andinterferometric-autocorrelationtraces.,Intensityautocorrelation,Interferometricautocorrelation,Approachesaconstantplusacoherencespike,Intensity,Delay,Delay,InterferometricAutocorrelation:PracticalDetailsandConclusions,Agoodcheckontheinterferometricautocorrelationisthatitshouldbesymmetrical,andthepeak-to-backgroundratioshouldbe8.Thisdeviceisdifficulttoalign;therearefiveverysensitive