超快光学-第10章-自相关

IntensityAutocorrelation1DPhaseRetrievalagainSingle-shotautocorrelationTheAutocorrelationandSpectrumAmbiguitiesThird-orderAutocorrelationInterferometricAutocorrelationMeasuringUltrashortLaserPulsesI:AutocorrelationWhy?ThedilemmaThegoal:measuringtheintensityandphasevs.time(orfrequency)TheSpectrometerandMichelsonInterferometer1DPhaseRetrieval()It()()ItIt()ItTime(t)Intensity(I)Todeterminethetemporalresolutionofanexperimentusingit.Todeterminewhetheritcanbemadeevenshorter.Tobetterunderstandthelasersthatemitthemandtoverifymodelsofultrashortpulsegeneration.Tobetterstudymedia:thebetterweknowthelightinandlightout,thebetterweknowthemediumwestudywiththem.Tousepulsesofspecificintensityandphasevs.timetocontrolchemicalreactions.Tounderstandpulse-shapingeffortsfortelecommunications,etc.Becauseit’sthere.Whymeasureanultrashortlaserpulse?Asamoleculedissociates,itsemissionchangescolor(i.e.,thephasechanges),revealingmuchaboutthemoleculardynamics,notavail-ablefromthemerespectrum,oreventheintensityvs.time.ExcitationtoexcitedstateEmissionGroundstateExcitedstateImportantpointaboutclaimsofthegenerationofinterestingscientificobjects“Ifyouhaven’tmeasuredit,youhaven’tmadeit!”WayneKnox(1957-)Director,InstituteofOptics,UniversityofRochester,Rochester,NYUSAWayneKnoxInordertomeasureaneventintime,youneedashorterone.Tostudythisevent,youneedastrobelightpulsethat’sshorter.Butthen,tomeasurethestrobelightpulse,youneedadetectorwhoseresponsetimeisevenshorter.Andsoon…So,now,howdoyoumeasuretheshortestevent?PhotographtakenbyHaroldEdgerton,MITTheDilemmaUltrashortlaserpulsesaretheshortesttechnologicaleventsevercreatedbyhumans.Usinganultrashortpulse,youcanmeasurealmostanyevent—providedthatyourpulseisshorter.Sohowdoyoumeasurethepulseitself?Youmustusethepulsetomeasureitself.Butthatisn’tgoodenough.It’sonlyasshortasthepulse.It’snotshorter.Techniquesbasedonusingthepulsetomeasureitselfhavenotsufficed.Blurrypicturemeasuredusinganinsufficientlyshortevent.Theelectricfieldcanbewritten:IntensityPhasee())(p(x)EIttitAlternatively,versusfrequency:SpectralPhaseSpectrum()exp))((SEiWeneedtomeasureboththetemporal(orspectral)intensityandphase.Wemustmeasuretheintensityandphasevs.timeorfrequency.Spectralphase,()FrequencySpectrum,S()Phase,(t)TimeIntensity,I(t)Theinstantaneousfrequency:Example:LinearchirpPhase,(t)timetimeFrequency,(t)timeWe’dliketobeabletomeasure,notonlylinearlychirpedpulses,butalsopulseswitharbitrarilycomplexphasesandfrequenciesvs.time.Thephasedeterminesthepulse’sfrequency(i.e.,color)vs.time.0()/tddtTimeLightelectricfieldThespectrometermeasuresthespectrum,ofcourse.Wavelengthvariesacrossthecamera,andthespectrumcanbemeasuredforasinglepulse.PulseMeasurementintheFrequencyDomain:TheSpectrometerCollimatingMirror“Czerny-Turner”arrangementEntranceSlitCameraorLinearDetectorArrayFocusingMirrorGratingImagingspectrometersallowmanyspectratobemeasuredsimultaneously,oneforeachrowofa2Dcamera.Broad-bandpulseOne-dimensionalphaseretrievalTherearestillinfinitelymanysolutionsforthespectralphase.The1DPhaseRetrievalProblemisunsolvable.E.J.Akutowicz,Trans.Am.Math.Soc.83,179(1956)E.J.Akutowicz,Trans.Am.Math.Soc.84,234(1957)Thisgeneralproblemiscalledthe1Dphaseretrievalproblem.It’smoreinterestingthanitappearstoaskwhatinformationwelackwhenweknowonlythepulsespectrum.Clearly,whatwelackisthespectralphase.Butcanwesomehowretrieveit?Obviouslynot.Butwhatifwehavesomeadditionalinformation?Forexample,whatifweknowwehaveapulse—finiteinduration?2())(SE[())](phaseEandSpectrumSpectralphaseRecall:()()exp()EEtitdtPulseMeasurementintheTimeDomain:DetectorsExamples:Photo-diodes,Photo-multipliersDetectorsaredevicesthatemitelectronsinresponsetophotons.Detectorshaveveryslowriseandfalltimes:~1nanosecond.Asfaraswe’reconcerned,detectorshaveinfinitelyslowresponses.Theymeasurethetimeintegralofthepulseintensityfrom–to+:Thedetectoroutputvoltageisproportionaltothepulseenergy.Bythemselves,detectorstelluslittleaboutapulse.2()detectorVEtdtAnothersymbolforadetector:DetectorDetectorPulseMeasurementintheTimeDomain:VaryingthepulsedelaySincedetectorsareessentiallyinfinitelyslow,howdowemaketime-domainmeasurementsonorusingultrashortlaserpulses?We’lldelayapulseintime.Andhowwillwedothat?Bysimplymovingamirror!Sincelighttravels300µmperps,300µmofmirrordisplacementyieldsadelayof2ps.Thisisveryconvenient.MovingamirrorbackwardbyadistanceLyieldsadelayof:2L/cDonotforgetthefactorof2!Lightmusttraveltheextradistancetothemirror—andback!TranslationstageInputpulseE(t)E(t–)MirrorOutputpulseWecanalsovarythedelayusingamirrorpairorcornercube.Mirrorpairsinvolvetworeflectionsanddisplacethereturnbeaminspace:Butout-of-planetiltyieldsanonparallelreturnbeam.Cornercubesinvolvethreereflectionsandalsodisplacethereturnbeaminspace.Evenbetter,theyalwaysyieldaparallelreturnbeam:Hollowcornercubesavoidpropagationthroughglass.TranslationstageInputpulseE(t)E(t–)MirrorsOutputpulseApollo1122*()()2Re[()()]EtEtEtEtdt2()()()MIVEtEtdt2*()2()2Re()()MIVEtdtEtEtdtPulseenergyThefield