超快光学--第02章-概述

TheGenerationofUltrashortLaserPulsesTheimportanceofbandwidthMorethanjustalightbulbLasers,lasermodes,andmode-lockingMakingshorterandshorterpulsesPulse-pumpingQ-switchinganddistributed-feedbacklasersPassivemode-lockingandthesaturableabsorberKerr-lensingandTi:SapphireActivemode-lockingOthermode-lockingtechniquesLimitingfactorsCommerciallasersProf.RickTrebinoGeorgiaTech!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,andultrashortpulsesStimulatedemissionleadstoachainreactionandlaseremission.ExcitedmediumIfmanymoleculesinamediumareexcited,onephotoncanbecomemany.Thisistheessenceofthelaser.ThefactorbywhichaninputbeamisamplifiedbyamediumiscalledthegainandisrepresentedbyG.Usually,additionallossesinintensityoccur,suchasabsorption,scat-tering,andreflections.Ingeneral,thelaserwilllaseif,inaroundtrip:TotalGainTotalLossThiscalledachievingThreshold.TheLaserAlaserisamediumthatstoresenergy,surroundedbytwomirrors.Theoutputmirrorispartiallyreflectingandsoletssomelightout.Alaserwilllaseifthebeamincreasesinintensityduringaroundtrip:thatis,if.30IIR=100%R100%I0I1I2I3OutputmirrorBackmirrorLasermediumwithgain,GintheformofexcitedstatesCalculatingtheGain:EinsteinAandBCoefficientsIn1916,Einsteinconsideredthevarioustransitionratesbetweenmolecularstates(say,1and2)involvinglightofirradiance,I:Absorptionrate=BN1ISpontaneousemissionrate=AN2Stimulatedemissionrate=BN2I21whereNiisthenumberdensityofmoleculesintheithstate,andIistheirradiance.LaserGainNeglectingspontaneousemission:2121dIdIcBNIBNIdtdzBNNI21()(0)expIzINNz21expexp()GNNLgLStimulatedemissionminusabsorptionProportionalityconstantistheabsorption/gaincross-section,21gNN12NNIfN2N1:IfN2N1:Therecanbeexponentialgainorlossinirradiance.Normally,N2N1,andthereisloss(absorption).ButifN2N1,there’sgain,andwedefinethegain,G:Thesolutionis:LasermediumI(0)zL0I(L)gandarethegainandabsorptioncoefficients.I=I(z-ct)DNN1N20InversionInordertoachieveG1,stimulatedemissionmustexceedabsorption:EnergyInversion“Negativetemperature”Molecules321BN2IBN1IHere,thereisinversionfromlevel4tolevels3and2.4Inordertoachieveinversion,wemusthitthelasermediumveryhardinsomewayandchooseourmediumcorrectly.Thisconditioniscalledinversion.Itdoesnotoccurnaturally(it’sforbiddenbytheBoltzmanndistribution).It’sinherentlyanon-equilibriumstate.CancelingtheBIfactors,N2N1,or:AchievingInversion:PumpingtheLaserMediumNowletIpbetheintensityof(flashlamp)lightusedtopumpenergyintothelasermedium:IpWillthisintensitybesufficienttoachieveinversion,N2N1?It’lldependonthelasermedium’senergylevelsystem.OutputmirrorBackmirrorLasermediumRateEquationsforaTwo-LevelSystemRateequationsforthedensitiesofthetwostates:2122()pdNBINNANdt1212()pdNBINNANdt222pdNBINANdtDDAbsorptionStimulatedemissionSpontaneousemission12NNND12NNNIfthetotalnumberofmoleculesisN:212122()()NNNNNNND2pdNBINANANdtDDD21N2N1LaserPumpPumpintensityWhyInversionisImpossibleinaTwo-LevelSystem02pBINANANDD12/psatNNIID/satIABInsteady-state:(2)pABINANDwhere:DNisalwayspositive,nomatterhowhighIpis!It’simpossibletoachieveaninversioninatwo-levelsystem!2pdNBINANANdtDDD/(2)pNANABID/(12/)pNNBIADIsatisthesaturationintensity.21N2N1LaserRateEquationsforaThree-LevelSystemAssumewepumptoastate3thatrapidlydecaystolevel2—eliminatingpumpstimulatedemission!212pdNBINANdt112pdNBINANdt1222pdNBINANdtDAbsorptionSpontaneousemission12NNND12NNNThetotalnumberofmoleculesisN:22NNNDppdNBINBINANANdtDDDFastdecayLaserTransitionPumpTransition123Level3decaysfastandsoiszero.12NNNDWhyInversionisPossibleinaThree-LevelSystem1/1/psatpsatIINNIIDInsteady-state:()()ppABINABINDNowifIpIsat,DNisnegative!()/()ppNNABIABIDppdNBINBINANANdtDDD0ppBINBINANANDDFastdecayLaserTransitionPumpTransition123RateEquationsforaFour-LevelSystemNowassumethelowerlaserlevel1alsorapidlydecaystoagroundlevel0.Soalso!And202pdNBINANdt222()pdNBINNANdt2NNDLaserTransitionPumpTransitionFastdecayFastdecay1230Asbefore:Because02NNNThetotalnumberofmoleculesisN:02