第三讲 超短脉冲的产生

Lecture3GenerationofultrashortpulsesTheMetricSystemPrefixes: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.TheTrottingHorse”ControversyPaloAlto,CA1872TheBirthofUltrafastTechnologyLelandStanford（马场老板）EadweardMuybridge(英国摄影师)TimeResolution:1/60thofasecondBet:Doallfourhoovesofatrottinghorseeversimultaneouslyleavetheground?TrottingHorseHaroldEdgertonMIT,1942“HowtoMakeApplesauceatMIT”1964“SplashonaGlass”CurtisHurleyJuniorHighSchoolstudent1996TimeResolution:afewmicroseconds'Doc'Edgerton-StrobePhotography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TheGenerationofUltrashortLaserPulsesTheimportanceofbandwidthMorethanjustalightbulbLasermodesandmode-lockingMakingshorterandshorterpulsesPulse-pumpingQ-switchinganddistributed-feedbacklasersPassivemode-lockingandthesaturableabsorberKerr-lensingandTi:SapphireActivemode-lockingOthermode-lockingtechniquesLimitingfactorsCommerciallasersButfirst:theprogresshasbeenamazing!YEARNd:glassS-PDyeDyeCWDyeNd:YAGDiodeNd:YLFCr:YAGCr:LiS(C)AFEr:fiberCr:forsteriteTi:sapphireCPMw/CompressionColorCenter1965197019751980198519901995Dye2000SHORTESTPULSEDURATION10ps1ps100fs10fs2005Nd:fiberTheshortestpulsevs.year(fordifferentmedia)Continuousvs.ultrashortpulsesoflightAconstantandadelta-functionareaFourier-Transformpair.Continuousbeam:Ultrashortpulse:Irradiancevs.timeSpectrumtimetimefrequencyfrequencyLongvs.shortpulsesoflightTheuncertaintyprinciplesaysthattheproductofthetemporalandspectralpulsewidthsisgreaterthan~1.LongpulseShortpulseIrradiancevs.timeSpectrumtimetimefrequencyfrequencyFormanyyears,dyeshavebeenthebroadbandmediathathavegeneratedultrashortlaserpulses.Ultrafastsolid-statelasermediahaverecentlyreplaceddyesinmostlabs.Solid-statelasermediahavebroadbandwidthsandareconvenient.LaserpowerButalightbulbisalsobroadband.Whatexactlyisrequiredtomakeanultrashortpulse?Answer:AMode-lockedLaserOkay,what’salaser,whataremodes,andwhatdoesitmeantolockthem?Lightbulbs,lasers,andultrashortpulsesWhat’stherealmeaningofmodelockingFrequencydomain:alllongitudinalmodesareinphase(phasemoded)Timedomain:FormultrashortpulsesFreerunningModelockingModelockedprincipleLasersmodes:TheShahfunctionTheShahfunction,III(t),isaninfinitelylongtrainofequallyspaceddelta-functions.tIII()()mttmTheFouriertransformoftheShahfunctionIfw=2np,So:{III()}III(twpF)exp())exp()exp()mmmtmitdttmitdtimwwwtIII(t)F{III(t)}2wpTheShahfunctionandapulsetrain()mftmT()III(/)()EttTftwheref(t)istheshapeofeachpulseandTisthetimebetweenpulses.Aninfinitetrainofidenticalpulses(fromalaser!)canbewritten:(/)()mtTmfttdtConvolutionTheFouriertransformofaninfinitetrainofpulsesAninfinitetrainofidenticalpulsescanbewritten:E(t)=III(t/T)*f(t)wheref(t)representsasinglepulseandTisthetimebetweenpulses.TheConvolutionTheoremstatesthattheFourierTransformofaconvolutionistheproductoftheFourierTransforms.So:()III(/)(2EFTwwpwAtrainofpulsesresultsfromasinglepulsebouncingbackandforthinsidealasercavityofround-triptimeT.Thespacingbetweenfrequencies—calledlasermodes—isthenw=p/Torn=1/T.Generatingshortpulses=mode-lockingLockingthephasesofthelasermodesyieldsanultrashortpulse.LockedmodesIntensitiesNumericalsimulationofmode-lockingUltrafastlasersoftenhavethousandsofmodes.Agenericultrashort-pulselaserAgenericultrafastlaserhasabroadbandgainmedium,apulse-shorteningdevice,andtwoormoremirrors:Manypulse-shorteningdeviceshavebeenproposedandused.Mode-lockerPulsedPumpingLongandpotentiallycomplexpulsePumpingalasermediumwithashort-pulseflashlampyieldsashortpulse.Flashlamppulsesasshortas~1µsexist.Unfortunately,thisyieldsapulseaslongastheexcited-statelifetimeofthelasermedium,whichcanbeconsiderablylongerthanthepumppulse.Sincesolid-statelasermediahavelifetimesinthemicrosecondrange,ityieldspulsesmicrosecondstomillisecondslong.Q-switchingQ-switchinginvolves:Preventingthelaserfromlasinguntiltheflashlampisfinishedflashing,andAbruptlyallowingthelasertolase.Thepulselengthislimitedbyhowfastwecanswitchandtheround-triptimeofthelaserandyieldspulses10-100nslong.100%0%TimeCavityLossCavityGainOutputintensityQ-SwitchingHowdoweQ-switchalaser?Q-switchinginvolvespreventinglasinguntilwe’reready.APockels’cellswitches(inafewnanoseconds)fromaquarter-waveplatetonothing.BeforeswitchingAfterswitchingPockels’cellaswaveplatew/axesat±45°0°PolarizerMirrorPockels’cellasanisotropicmedium0°PolarizerMirrorLightbecomescircularonthefirstpassandthenhorizontalonthenextandisthenrejectedbythepolarizer.LightisunaffectedbythePockels’cellandhenceispassedbythepolarizer.Passivemode-locking:thesaturableabsorber(I)01IIsatLikeasponge,anabsorbingmediumcanonlyabsorbsomuch.High-intensityspikesburnthrough;low-intensitylightisabsorbed.0NWhataboutthesaturationintensity?Aistheexcited-staterelaxationrate:1/t/satI