超短脉冲的产生课件

TheMetricSystemPrefixes:Milli(m) 10-3Micro(µ) 10-6Nano(n) 10-9Pico(p) 10-12Femto(f) 10-15Atto(a) 10-18Kilo(k) 10+3Mega(M) 10+6Giga(G) 10+9Tera(T) 10+12Peta(P) 10+15SmallBigWe’llneedtoreallyknowthemetricsystembecausethepulsesareincrediblyshortandthepowersandintensitiescanbeincrediblyhigh.TheMetricSystemPrefixes:MillThe"TrottingHorse”ControversyPaloAlto,CA1872TheBirthofUltrafastTechnologyLelandStanford（马场老板）EadweardMuybridge(英国摄影师)TimeResolution:1/60thofasecondBet:Doallfourhoovesofatrottinghorseeversimultaneouslyleavetheground?The"TrottingHorse”TheBirthTrottingHorseTrottingHorseHaroldEdgertonMIT,1942“HowtoMakeApplesauceatMIT”1964“SplashonaGlass”CurtisHurleyJuniorHighSchoolstudent1996TimeResolution:afewmicroseconds'Doc'Edgerton-StrobePhotographyHarold“HowtoMake“Splashon时间尺度电子运动时间尺度：阿秒（1as=10-18s)，电子绕氢原子核一周大约是150阿秒；原子转动时间尺度：皮秒（1ps=10-12s）原子振动时间尺度：飞秒（1fs=10-15s)如监测化学反应过程，需飞秒尺度时间尺度电子运动时间尺度：阿秒（1as=10-18s)TheGenerationofUltrashortLaserPulsesTheimportanceofbandwidthMorethanjustalightbulbLasermodesandmode-lockingMakingshorterandshorterpulses Pulse-pumping Q-switchinganddistributed-feedbacklasers Passivemode-lockingandthesaturableabsorber Kerr-lensingandTi:Sapphire Activemode-locking Othermode-lockingtechniquesLimitingfactorsCommerciallasers

TheGenerationofUltrashortLButfirst:theprogresshasbeenamazing!YEARNd:glassS-PDyeDyeCWDyeNd:YAGDiodeNd:YLFCr:YAGCr:LiS(C)AFEr:fiberCr:forsteriteTi:sapphireCPMw/CompressionColorCenter1965197019751980198519901995Dye2000SHORTESTPULSEDURATION10ps1ps100fs10fs2005Nd:fiberTheshortestpulsevs.year(fordifferentmedia)Butfirst:theprogresshasbeContinuousvs.ultrashortpulsesoflightAconstantandadelta-functionareaFourier-Transformpair.Continuousbeam:Ultrashortpulse:Irradiancevs.timeSpectrumtimetimefrequencyfrequencyContinuousvs.ultrashortpulsLongvs.shortpulsesoflightTheuncertaintyprinciplesaysthattheproductofthetemporalandspectralpulsewidthsisgreaterthan~1.LongpulseShortpulseIrradiancevs.timeSpectrumtimetimefrequencyfrequencyLongvs.shortpulsesoflightFormanyyears,dyeshavebeenthebroadbandmediathathavegeneratedultrashortlaserpulses.Formanyyears,dyeshavebeenUltrafastsolid-statelasermediahaverecentlyreplaceddyesinmostlabs.Solid-statelasermediahavebroadbandwidthsandareconvenient.LaserpowerUltrafastsolid-statelasermeButalightbulbisalsobroadband.

Whatexactlyisrequiredtomakeanultrashortpulse?

Answer:AMode-lockedLaser

Okay,what’salaser,whataremodes,andwhatdoesitmeantolockthem?Lightbulbs,lasers,andultrashortpulsesButalightbulbisalsobroadWhat’stherealmeaningofmodelockingFrequencydomain:alllongitudinalmodesareinphase(phasemoded)Timedomain:FormultrashortpulsesFreerunningModelockingWhat’stherealmeaningofmoModelockedprincipleModelockedprincipleLasersmodes:TheShahfunctionTheShahfunction,III(t),isaninfinitelylongtrainofequallyspaceddelta-functions.tLasersmodes:TheShahfunctiTheFouriertransformoftheShahfunctionIfw

=2np,So: tIII(t)F

{III(t)}TheFouriertransformoftheSMenloSystemsWhataboutthesaturationintensity?Laserslasewhenthegainexceedstheloss.what’stherealmeaningofmodelocking?Activemode-lockingTheFouriertransformofaninfinitetrainofpulsesIfapulseexperiencesadditionalfocusingduetohighintensityandthenonlinearrefractiveindex,andwealignthelaserforthisextrafocusing,thenahigh-intensitybeamwillhavebetteroverlapwiththegainmedium.Additionalfocusingopticscanarrangeforperfectoverlapofthehigh-intensitybeambackintheTi:Sapphirecrystal.Alensisalensbecausethephasedelayseenbyabeamvarieswithx:Theuniverseconspirestolengthenpulses.TitaniumSapphirePassivemode-locking:

thesaturableabsorberKerr-lensingandTi:SapphireF{III(t)}ItcanbeusedtostartaTi:Sapphirelasermode-locking.Noticethattheweakpulsesaresuppressed,andthestrongpulseshortensandisamplified.Bistheabsorptioncross-section,s,dividedbytheenergyperphoton,ħw:s/ħwKilo(k) 10+3Othermode-lockingtechniquesSHORTESTPULSEDURATIONTheShahfunctionandapulsetrainwheref(t)istheshapeofeachpulseandTisthetimebetweenpulses.Aninfinitetrainofidenticalpulses(fromalaser!)canbewritten:ConvolutionMenloSystemsTheShahfunctionTheFouriertransformofaninfinitetrainofpulsesAninfinitetrainofidenticalpulsescanbewritten:E(t)=III(t/T)*f(t)wheref(t)representsasinglepulseandTisthetimebetweenpulses.TheConvolutionTheoremstatesthattheFourierTransformofaconvolutionistheproductoftheFourierTransforms.So:Atrainofpulsesresultsfromasinglepulsebouncingbackandforthinsidealasercavityofround-triptimeT.Thespacingbetweenfrequencies—calledlasermodes—isthendw=2p/Tordn=1/T.TheFouriertransformofaninGeneratingshortpulses=mode-lockingLockingthephasesofthelasermodesyieldsanultrashortpulse.Generatingshortpulses=modeLockedmodesIntensitiesLockedmodesIntensitiesNumericalsimulationofmode-lockingUltrafastlasersoftenhavethousandsofmodes.Numericalsimulationofmode-lAgenericultrashort-pulselaserAgenericultrafastlaserhasabroadbandgainmedium,apulse-shorteningdevice,andtwoormoremirrors:Manypulse-shorteningdeviceshavebeenproposedandused.Mode-lockerAgenericultrashort-pulselasPulsedPumpingLongandpotentiallycomplexpulsePumpingalasermediumwithashort-pulseflashlampyieldsashortpulse.Flashlamppulsesasshortas~1µsexist.Unfortunately,thisyieldsapulseaslongastheexcited-statelifetimeofthelasermedium,whichcanbeconsiderablylongerthanthepumppulse.Sincesolid-statelasermediahavelifetimesinthemicrosecondrange,ityieldspulsesmicrosecondstomillisecondslong.PulsedPumpingLongandpotentiQ-switchingQ-switchinginvolves: Preventingthelaserfromlasinguntiltheflashlampisfinishedflashing,and Abruptlyallowingthelasertolase.Thepulselengthislimitedbyhowfastwecanswitchandtheround-triptimeofthelaserandyieldspulses10-100nslong.100%0%TimeCavityLossCavityGainOutputintensityQ-switchingQ-switchinginvolveQ-SwitchingHowdoweQ-switchalaser?Q-switchinginvolvespreventinglasinguntilwe’reready.APockels’cellswitches(inafewnanoseconds)fromaquarter-waveplatetonothing.BeforeswitchingAfterswitchingPockels’cellaswaveplatew/axesat±45°0°PolarizerMirrorPockels’cellasanisotropicmedium0°PolarizerMirrorLightbecomescircularonthefirstpassandthenhorizontalonthenextandisthenrejectedbythepolarizer.LightisunaffectedbythePockels’cellandhenceispassedbythepolarizer.

Q-SwitchingHowdoweQ-switchPassivemode-locking:

thesaturableabsorberLikeasponge,anabsorbingmediumcanonlyabsorbsomuch.High-intensityspikesburnthrough;low-intensitylightisabsorbed.Passivemode-locking:

thesa0°PolarizerActivemode-lockingTheConvolutionTheoremstatesthattheFourierTransformofaconvolutionistheproductoftheFourierTransforms.Asshortas8fs!Cr:LiS(C)AFTheMetricSystemTheintensespikeusesupthelasergain-mediumenergy,reducingthegainavailableforthetrailingedgeofthepulse(andforlaterpulses).Peta(P) 10+15f(x)=n(x)kLLasermodesandmode-lockingTheeffectofasaturableabsorberAddingtwoprismscompensatesfordispersionintheTi:Sapphirecrystalandmirrors.GainmediumLossesaretoohighforalow-intensitycwmodetolase,butnotforhigh-intensityfspulse.TheGenerationofUltrashortLaserPulsesHigh-intensityspikesburnthrough;low-intensitylightisabsorbed.electronicstateTheyalsoofferotherattractiveproperties,suchasaveryhighthermalefficiencyandhighaveragepower.Continuousvs.t-Pulse100Whataboutthesaturationintensity?Aistheexcited-staterelaxationrate:1/tLaserTransitionPumpTransitionFastdecayFastdecay1230Bistheabsorptioncross-section,s,dividedbytheenergyperphoton,ħw:s/ħwThesaturationintensityplaysakeyroleinlasertheory.Bothsandtdependonthemolecule,thefrequency,andthevariousstatesinvolved.ħw~10-19Jforvisible/nearIRlightt~10-12to10-8sformoleculess~10-20to10-16cm2formolecules(onresonance)105to1013W/cm20°PolarizerWhataboutthesatTheeffectofasaturableabsorberFirst,imagineraster-scanningthepulsevs.timelikethis:Aftermanyroundtrips,evenaslightlysaturableabsorbercanyieldaveryshortpulse.Shorttime(fs)IntensityRoundtrips(k)k=1k=7Noticethattheweakpulsesaresuppressed,andthestrongpulseshortensandisamplified.k=2k=3TheeffectofasaturableabsoModelockedpulseformationModelockedpulseformationPassivemode-locking:the

saturableabsorberHigh-intensityspikes(i.e.,shortpulses)seelesslossandhencecanlasewhilelow-intensitybackgrounds(i.e.,longpulses)won’t.Passivemode-locking:the

saPassivemode-lockingwithaslowsaturableabsorberWhatiftheabsorberrespondsslowly(moreslowlythanthepulse)?Thenonlytheleadingedgewillexperiencepulseshortening.Thisisthemostcommonsituation,unlessthepulseismanypslong.Passivemode-lockingwithaslGainsaturationshortensthepulsetrailingedge.Theintensespikeusesupthelasergain-mediumenergy,reducingthegainavailableforthetrailingedgeofthepulse(andforlaterpulses).GainsaturationshortensthepSaturablegainandlossThecombinationofsaturableabsorptionandsaturablegainyieldsshortpulsesevenwhentheabsorberisslowerthanthepulse.Laserslasewhenthegainexceedstheloss.SaturablegainandlossThecomAdye’senergylevelsDyesarebigmolecules,andtheyhavecomplexenergylevelstructure.S0:GroundelectronicstateS1:1stexcitedelectronicstateS2:2ndexcitedelectronicstateEnergyLaserTransitionLowestvibrationalandrotationallevelofthiselectronic“manifold”ExcitedvibrationalandrotationallevelDyescanlaseintoany(orall!)ofthevibrational/

rotationallevelsoftheS0state,andsocanlaseverybroadband.PumpTransitionAdye’senergylevelsDyesareThePassivelyMode-lockedDyeLaserPassivelymode-lockeddyelasersyieldpulsesasshortasafewhundredfs.They’relimitedbyourabilitytosaturatetheabsorber.PumpbeamGainmediumSaturableabsorberThePassivelyMode-lockedDyeSomecommondyesandtheircorrespondingsaturableabsorbersSomecommondyesandtheircorPumpingthegainmediumwithatrainofalreadyshortpulsesyieldsatrainofevenshorterpulses.what’stherealmeaningofmodelocking?Passivemode-lockingwithaslowsaturableabsorberAnyamplitudemodulatorcanpreferentiallyinducelossesfortimesotherthanthatoftheintendedpulsepeak.Continuousvs.Etaloneffects:LightisunaffectedbythePockels’cellandhenceispassedbythepolarizer.Adye’senergylevelsIfapulseexperiencesadditionalfocusingduetohighintensityandthenonlinearrefractiveindex,andwealignthelaserforthisextrafocusing,thenahigh-intensitybeamwillhavebetteroverlapwiththegainmedium.GainmediumItcanbeusedtostartaTi:Sapphirelasermode-locking.1/60thofasecondMaiTai(Hands-free,~100fspulselength)Agenericultrashort-pulselaserExcitedvibrationalandrotationallevelPrismdispersioncompensatorNano(n) 10-9Passivelymode-lockeddyelasersyieldpulsesasshortasafewhundredfs.High-intensityspikesburnthrough;low-intensitylightisabsorbed.Repetitionrate(MHz)AlensandalensxAlensisalensbecausethephasedelayseenbyabeamvarieswithx:

f(x)=nkL(x)L(x)NowwhatifLisconstant,butnvarieswithx:

f(x)=n(x)kLn(x)xInbothcases,aquadraticvariationofthephasewithxyieldsalens.PumpingthegainmediumwithaKerr-lensmode-lockingAmedium’srefractiveindexdependsontheintensity.

n(I)=n0+n2IIfthepulseismoreintenseinthecenter,itinducesalens.Placinganapertureatthefocusfavorsashortpulse.Kerr-lensingisthemode-lockingmechanismoftheTi:Sapphirelaser.Lossesaretoohighforalow-intensitycwmodetolase,butnotforhigh-intensityfspulse.Kerr-lensmode-lockingAmediumKerr-lensingisatypeofsaturableabsorber.Ifapulseexperiencesadditionalfocusingduetohighintensityandthenonlinearrefractiveindex,andwealignthelaserforthisextrafocusing,thenahigh-intensitybeamwillhavebetteroverlapwiththegainmedium.High-intensitypulseLow-intensitypulseTi:SapphMirrorAdditionalfocusingopticscanarrangeforperfectoverlapofthehigh-intensitybeambackintheTi:Sapphirecrystal.Butnotthelow-intensitybeam!Thisissoftaperturesaturableabsorber.Kerr-lensingisatypeofsatuModelingKerr-lensmode-lockingModelingKerr-lensmode-lockinTitaniumSapphire(Ti:Sapphire)oxygenaluminumAl2O3latticeTi:Sapphireiscurrentlytheworkhorselaseroftheultrafastcommunity,emittingpulsesasshortasafewfsandaveragepowerinexcessofaWatt.TitaniumSapphire(Ti:SapphireTitaniumSapphireItcanbepumpedwitha(continuous)Argonlaser(~450-515nm)oradoubled-Ndlaser(~532nm).Upperlevellifetime:3.2msecTi:Sapphirelasesfrom~700nmto~1000nm.AbsorptionandemissionspectraofTi:Sapphire(nm)TitaniumSapphireItcanbepumMechanismsthatlimitpulseshorteningGainnarrowing: G(w)=exp(-aw2),thenafterNpasses,thespectrumwillnarrowbyGN(w)=exp(-Naw2),whichisnarrowerbyN1/2Group-velocitydispersion: GVDspreadsthepulseintime.AndeverythinghasGVD… Allfslasersincorporatedispersion-compensatingcomponents. We’llspendseverallecturesdiscussingGVD!!Etaloneffects: Thisyieldsmultiplepulses,spreadingtheenergyovertime,weakeningthepulses.Theuniverseconspirestolengthenpulses.MechanismsthatlimitpulseshTheTi:SapphirelaserincludingdispersioncompensationAddingtwoprismscompensatesfordispersionintheTi:Sapphirecrystalandmirrors.Thisiscurrentlytheworkhorselaseroftheultrafastopticscommunity.cwpumpbeamTi:SapphiregainmediumPrismdispersioncompensatorSlitfortuningTheTi:SapphirelaserincludinCommercialfslasersTi:SapphireCoherent: Mira(<35fspulselength,1Wavepower), Chameleon(Hands-free,~100fspulselength),Spectra-Physics: Tsunami(<35fspulselength,1Wavepower) MaiTai(Hands-free,~100fspulselength)CommercialfslasersTi:SapphirVery-short-pulsecommercialfslasersTi:SapphireKMLabs<20fsand<$20KFemtolasersAsshortas8fs!Very-short-pulsecommercialfsThespacingbetweenfrequencies—calledlasermodes—isthendw=2p/Tordn=1/T.Ifapulseexperiencesadditionalfocusingduetohighintensityandthenonlinearrefractiveindex,andwealignthelaserforthisextrafocusing,thenahigh-intensitybeamwillhavebetteroverlapwiththegainmedium.Milli(m) 10-3TheeffectofasaturableabsorberLaserTransitionLightisunaffectedbythePockels’cellandhenceispassedbythepolarizer.Q-switchinganddistributed-feedbacklasersPrismdispersioncompensatorThePassivelyMode-lockedDyeLaserSaturableabsorberWe’llspendseverallecturesdiscussingGVD!!Femto(f) 10-15t-Pulse200GainmediumHigh-intensityspikesburnthrough;low-intensitylightisabsorbed.Passivemode-locking:the

saturableabsorber原子振动时间尺度：飞秒（1fs=10-15s)Q-switchinginvolves:AlensandalensPassivemode-locking:

thesaturableabsorberCommercialfslasers(cont’d)ThespacingbetweenfrequencieSESAMmodelockingTimeSESAMAdvantages:ultrashortpulsegenerationsimplemethodcompactlasersAconventionalsemiconductorsaturableabsorbermirror

(SESAM)SESAMmodelockingTimeSESAMAdvSESAMparametersSESAMparametersCWmodelockingthresholdCWmodelockingthresholdYtterbiumTungstate(Yb:KGW)Modelt-Pulse20t-Pulse100t-Pulse200Pulseenergy(nJ)20100200

Averagepower(W)112Repetitionrate(MHz)501010Ytterbiumdopedlasermaterialscanbedirectlydiode-pumped,eliminatingtheneedforanintermediate(green)pumplaserusedinTi:Sapphirelasers.Theyalsoofferotherattractiveproperties,suchasaveryhighthermalefficiencyandhighaveragepower.AmplitudeSystemesYtterbiumTungstate(Yb:KGW)MActivemode-lockingAnyamplitudemodulatorcanpreferentiallyinducelossesfortimesotherthanthatoftheintendedpulsepeak.Thisproducesshortpulses.ItcanbeusedtostartaTi:Sapphirelasermode-locking.Activemode-lockingAnyamplituGainswitchingModulatingthegainrapidlyisessentiallythesameasactivemode-locking.Thismethodisacommononeformode-lockingsemiconductorlasers.GainswitchingModulatingthegSynchronouspumpingPumpingthegainmediumwithatrainofalreadyshortpulsesyieldsatrainofevenshorterpulses.Trainsof60pspulsesfromaNd:YAGlasercanyield<1pspulsesfromasync-pumpeddyelaser.PumpbeamGainmediumSaturableabsorberShortpulses(ps)Thelaserround-triptimemustpreciselymatchthatofthetrainofpumppulses!SynchronouspumpingPumpingtheHybridmode-lockingHybridmode-lockingisanytypeofmode-lockingincorporatingtwoormoretechniquessimultaneously. Sync-pumpingandpassivemode-locking Activeandpassivemode-locking

Hybridmode-lockingHybridmodeCommercialfsfiberlasersErbiumMenloSystems150fs;150mWIMRAAmericaFrequency-doubledCommercialfsfiberlasersErbiPockels’cellasanisotropicmediumOthermode-lockingtechniquesChameleon(Hands-free,~100fspulselength),Etaloneffects:Commercialfslasers“SplashonaGlass”Asshortas8fs!SHORTESTPULSEDURATIONAndeverythinghasGVD…what’stherealmeaningofmodelocking?ThePassivelyMode-lockedDyeLaserButfirst:theprogresshasbeenamazing!Atto(a) 10-18year(fordifferentmedia)Kerr-lensmode-lockingKilo(k) 10+3Gainnarrowing:SomecommondyesandtheircorrespondingsaturableabsorbersShorttime(fs)f(x)=nkL(x)Questionswhat’stherealmeaningofmodelocking?What’stheprincipleofKerrLensmodelocking?PleasebrieflyinterprettheprincipleofSESAMmodelocking.Pockels’cellasanisotropicTheMetricSystemPrefixes:Milli(m) 10-3Micro(µ) 10-6Nano(n) 10-9Pico(p) 10-12Femto(f) 10-15Atto(a) 10-18Kilo(k) 10+3Mega(M) 10+6Giga(G) 10+9Tera(T) 10+12Peta(P) 10+15SmallBigWe’llneedtoreallyknowthemetricsystembecausethepulsesareincrediblyshortandthepowersandintensitiescanbeincrediblyhigh.TheMetricSystemPrefixes:Mill时间尺度电子运动时间尺度：阿秒（1as=10-18s)，电子绕氢原子核一周大约是150阿秒；原子转动时间尺度：皮秒（1ps=10-12s）原子振动时间尺度：飞秒（1fs=10-15s)如监测化学反应过程，需飞秒尺度时间尺度电子运动时间尺度：阿秒（1as=10-18s)Butfirst:theprogresshasbeenamazing!YEARNd:glassS-PDyeDyeCWDyeNd:YAGDiodeNd:YLFCr:YAGCr:LiS(C)AFEr:fiberCr:forsteriteTi:sapphireCPMw/CompressionColorCenter1965197019751980198519901995Dye2000SHORTESTPULSEDURATION10ps1ps100fs10fs2005Nd:fiberTheshortestpulsevs.year(fordifferentmedia)Butfirst:theprogresshasbeGeneratingshortpulses=mode-lockingLockingthephasesofthelasermodesyieldsanultrashortpulse.Generatingshortpulses=modePassivemode-locking:

thesaturableabsorberLikeasponge,anabsorbingmediumcanonlyabsorbsomuch.High-intensityspikesburnthrough;low-intensitylightisabsorbed.Passivemode-locking:

thesaPassivemode-locking:

thesaturableabsorberLikeasponge,anabsorbingmediumcanonlyabsorbsomuch.High-intensityspikesburnthrough;low-intensitylightisabsorbed.Passivemode-locking:

thesaThePassivelyMode-lockedDyeLaserPassivelymode-lockeddyelasersyieldpulsesasshortasafewhundredfs.They’relimitedbyourabilitytosaturatetheabsorber.PumpbeamGainmediumSaturableabsorberThePassivelyMode-lockedDyeRepetitionrate(MHz)Lockingthephasesofthelasermodesyieldsanultrashortpulse.Aftermanyroundtrips,evenaslightlysaturableabsorbercanyieldaveryshortpulse.TheShahfunctionandapulsetrainS2:2ndexcitedKMLabsThePassivelyMode-lockedDyeLaserControversyFormanyyears,dyeshavebeenthebroadbandmediathathavegeneratedultrashortlaserpulses.,shortpulses)seelesslossandhencecanlasewhilelow-intensitybackgrounds(i.t-Pulse100Atto(a) 10-18SaturableabsorberGainmediumTheshortestpulsevs.Continuousvs.Aftermanyroundtrips,evenaslightlysaturableabsorbercanyieldaveryshortpulse.Q-switchingCommercialfslasersSESAMmodelockingYtterbiumTungstate(Yb:KGW)Modelt-Pulse20t-Pulse100t-Pulse200Pulseenergy(nJ)20100200

Averagepower(W)112Repetitionrate(MHz)501010Ytterbiumdopedlasermaterialscanbedirectlydiode-pumped,eliminatingtheneedforanintermediate(green)pumplaserusedinTi:Sapphirelasers.Theyalsoofferotherattractiveproperties,suchasaveryhighthermalefficiencyandhighaveragepower.AmplitudeSystemesRepetitionrate(MHz)YtterbiumTheMetricSystemPrefixes:Milli(m) 10-3Micro(µ) 10-6Nano(n) 10-9Pico(p) 10-12Femto(f) 10-15Atto(a) 10-18Kilo(k) 10+3Mega(M) 10+6Giga(G) 10+9Tera(T) 10+12Peta(P) 10+15SmallBigWe’llneedtoreallyknowthemetricsystembecausethepulsesareincrediblyshortandthepowersandintensitiescanbeincrediblyhigh.TheMetricSystemPrefixes:MillThe"TrottingHorse”ControversyPaloAlto,CA1872TheBirthofUltrafastTechnologyLelandStanford（马场老板）EadweardMuybridge(英国摄影师)TimeResolution:1/60thofasecondBet:Doallfourhoovesofatrottinghorseeversimultaneouslyleavetheground?The"TrottingHorse”TheBirthTrottingHorseTrottingHorseHaroldEdgertonMIT,1942“HowtoMakeApplesauceatMIT”1964“SplashonaGlass”CurtisHurleyJuniorHighSchoolstudent1996TimeResolution:afewmicroseconds'Doc'Edgerton-StrobePhotographyHarold“HowtoMake“Splashon时间尺度电子运动时间尺度：阿秒（1as=10-18s)，电子绕氢原子核一周大约是150阿秒；原子转动时间尺度：皮秒（1ps=10-12s）原子振动时间尺度：飞秒（1fs=10-15s)如监测化学反应过程，需飞秒尺度时间尺度电子运动时间尺度：阿秒（1as=10-18s)TheGenerationofUltrashortLaserPulsesTheimportanceofbandwidthMorethanjustalightbulbLasermodesandmode-lockingMakingshorterandshorterpulses Pulse-pumping Q-switchinganddistributed-feedbacklasers Passivemode-lockingandthesaturableabsorber Kerr-lensingandTi:Sapphire Activemode-locking Othermode-lockingtechniquesLimitingfactorsCommerciallasers

TheGenerationofUltrashortLButfirst:theprogresshasbeenamazing!YEARNd:glassS-PDyeDyeCWDyeNd:YAGDiodeNd:YLFCr:YAGCr:LiS(C)AFEr:fiberCr:forsteriteTi:sapphireCPMw/CompressionColorCenter1965197019751980198519901995Dye2000SHORTESTPULSEDURATION10ps1ps100fs10fs2005Nd:fiberTheshortestpulsevs.year(fordifferentmedia)Butfirst:theprogresshasbeContinuousvs.ultrashortpulsesoflightAconstantandadelta-functionareaFourier-Transformpair.Continuousbeam:Ultrashortpulse:Irradiancevs.timeSpectrumtimetimefrequencyfrequencyContinuousvs.ultrashortpulsLongvs.shortpulsesoflightTheuncertaintyprinciplesaysthattheproductofthetemporalandspectralpulsewidthsisgreaterthan~1.LongpulseShortpulseIrradiancevs.timeSpectrumtimetimefrequencyfrequencyLongvs.shortpulsesoflightFormanyyears,dyeshavebeenthebroadbandmediathathavegeneratedultrashortlaserpulses.Formanyyears,dyeshavebeenUltrafastsolid-statelasermediahaverecentlyreplaceddyesinmostlabs.Solid-statelasermediahavebroadbandwidthsandareconvenient.LaserpowerUltrafastsolid-statelasermeButalightbulbisalsobroadband.

Whatexactlyisrequiredtomakeanultrashortpulse?

Answer:AMode-lockedLaser

Okay,what’salaser,whataremodes,andwhatdoesitmeantolockthem?Lightbulbs,lasers,andultrashortpulsesButalightbulbisalsobroadWhat’stherealmeaningofmodelockingFrequencydomain:alllongitudinalmodesareinphase(phasemoded)Timedomain:FormultrashortpulsesFreerunningModelockingWhat’stherealmeaningofmoModelockedprincipleModelockedprincipleLasersmodes:TheShahfunctionTheShahfunction,III(t),isaninfinitelylongtrainofequallyspaceddelta-functions.tLasersmodes:TheShahfunctiTheFouriertransformoftheShahfunctionIfw

=2np,So: tIII(t)F

{III(t)}TheFouriertransformoftheSMenloSystemsWhataboutthesaturationintensity?Laserslasewhenthegainexceedstheloss.what’stherealmeaningofmodelocking?Activemode-lockingTheFouriertransformofaninfinitetrainofpulsesIfapulseexperiencesadditionalfocusingduetohighintensityandthenonlinearrefractiveindex,andwealignthelaserforthisextrafocusing,thenahigh-intensitybeamwillhavebetteroverlapwiththegainmedium.Additionalfocusingopticscanarrangeforperfectoverlapofthehigh-intensitybeambackintheTi:Sapphirecrystal.Alensisalensbecausethephasedelayseenbyabeamvarieswithx:Theuniverseconspirestolengthenpulses.TitaniumSapphirePassivemode-locking:

thesaturableabsorberKerr-lensingandTi:SapphireF{III(t)}ItcanbeusedtostartaTi:Sapphirelasermode-locking.Noticethattheweakpulsesaresuppressed,andthestrongpulseshortensandisamplified.Bistheabsorptioncross-section,s,dividedbytheenergyperphoton,ħw:s/ħwKilo(k) 10+3Othermode-lockingtechniquesSHORTESTPULSEDURATIONTheShahfunctionandapulsetrainwheref(t)istheshapeofeachpulseandTisthetimebetweenpulses.Aninfinitetrainofidenticalpulses(fromalaser!)canbewritten:ConvolutionMenloSystemsTheShahfunctionTheFouriertransformofaninfinitetrainofpulsesAninfinitetra