超快光学-第13章-脉冲整形

PulseShaping,Whatdowemeanbypulseshapingandwhydowecareaboutit?,MethodsofpulseshapingFouriersynthesisSpatial-lightmodulatorsAcousto-opticmodulatorsDeformablemirrorsAcousto-opticshapingPhase-onlypulseshapingGeneticalgorithmsSimulatedannealingAdaptivepulse-shaping,Whypulse-shape?,TocompresspulseswithcomplexphaseTogeneratepulsesthatcontrolchemicalreactionsorotherphenomenaTogeneratetrainsofpulsesfortelecommunicationsToprecompensatefordistortionsthatoccurindispersivemedia,Pulseshaping:aloosedefinition,Looselydefined:Pulseshapingincludesanythingthatchangesthepulseshape.,Alteringanyofpulsesparameterschangesthepulse.,Recallthatapulseisdefinedbyitsintensityandphaseineitherthetimeorfrequencydomain.,Whatdowereallymeanbypulseshaping?,Tailoringapulseshapeinaspecificcontrolledmanner.,PulseShaper,Experiment,Bychangingthepulseshapewecanaltertheresultsofanexperiment.,Howdowemodulateanultrashortpulse?,Wecouldtrytomodulatethepulsedirectlyintime.Unfortunately,modulatorsaretooslow.,Alternatively,wecanmodulatethespectrum.,Soallwehavetodoistofrequency-dispersethepulseinspaceandmodulatethespectrumandspectralphasebycreatingaspatiallyvaryingtransmissionandphasedelay.,Anall-opticalFouriertransform:thezero-dispersionstretcher,Howitworks:Thegratingdispersesthelight,mappingcolorontoangle.Thefirstlensmapsangle(hencewavelength)toposition.Thesecondlensandgratingundothespatio-temporaldistortions.,ThetrickistoplaceamaskintheFouriertransformplane.,x,FourierTransformPlane,f,f,f,f,f,f,grating,grating,JohnHeritage,UCDavisAndrewWeiner,Purdue,Aphasemaskselectivelydelayscolors.,Anamplitudemaskshapesthespectrum.,TheFourier-synthesispulse-shaper,Wecancontrolboththeamplitudeandphaseofthepulse.Thetwomasksor“spatiallightmodulators”togethercanyieldanydesiredpulse.,AmplitudemaskTransmission=t(x)=t(l),PhasemaskPhasedelay=j(x)=j(l),FourierTransformPlane,Somecommonspatiallightmodulators.,Earlypulseshapersusedmaskscreatedusinglithographictechniquesandthatcouldntbemodifiedoncecreated.Morerecentshapersuse“spatiallightmodulators,”whichcanbeprogrammedonthefly.,TypesofspatiallightmodulatorsLiquidcrystalarraysAcousto-opticmodulatorsDeformablemirrors,LiquidcrystalsorientalongaanapplieddcE-field.Theyyieldaphasedelay(orbirefringence)thatdependsonanappliedvoltage.Theycanyieldbothphaseandamplitudemasks.,Liquid-crystalspatiallightmodulators,Liquidcrystalarrays,Liquidcrystalmodulators(LCMs)consistoftwoliquidcrystalarraysat90toeachotherandat45totheincominglight.Thefirstarrayrotatesthepolarizationofthelightinonedirectionandthesecondintheoppositedirection.Rotatingeachthesameamount(inoppositedirections)yieldsaphaseonlymodulation.Rotatingonemorethantheotheryieldsanamplitudeandphasemodulationofthelight.,Pixel,DeadSpace,ThepixelsinLCMslimittheresolutionofthemodulation.Thefinitewidthcoversarangeofwavelengths,reducingthefidelityoftheshaping.Thedeadspaces(gapsbetweenelectrodes)alsoaddartifactstothepulsetrain(effectivelyanunshapedpulse).,1A.M.Weineret.al.,IEEEJ.QuantumElectron.,28(1992)908.2K.Takasagoet.al.,IEEEJ.Select.TopicsinQuantumElectron.,4(1998)346.,SLM:128pixels(pixelwidth:97mm,pixelgap3mm)Grooveintervalofthegratingd-1=651lines/mm,Inputangle:6.5deg(100nmbandwidth)Focallengthoftheachromaticlensf=145mm,Parameters,Spatial-light-modulatorpulseshaper:details,TakasumiTanabe,KimihisaOhno,TatsuyoshiOkamoto,FumihikoKannari,Spatiallightmodulatorexample,FROGtrace,Asinusoidalspectralphase,Spectrumandspectralphase,Omenettoandcoworkers,LANL,PulseilluminationofSLM,Acousto-opticspatiallightmodulators,Acousto-opticmodulators(AOM)offeramethodofmodulatingthelight.,AOMsofferbothphaseandamplitudemodulation.Thestrengthofthesoundwaveisdirectlyrelatedtotheintensityofthediffractedlight.Thephaseofthesoundwaveisalsowrittendirectlyontothediffractedlight.,AOMshaveaveryhighnumberofeffective“pixels,”thenumberofsoundwavesthatfitacrosstheapertureofthecrystal.AOMefficiencyislessthanothermethodssinceitreliesonthediffractedlight.,WarrenWarrenandcoworkers,Princeton,Deformable-mirrorpulse-shaper,A.Efimov,andD.H.Reitze,Proc.SPIE2701,190(1996)K.F.Wong,D.Yankelevich,K.C.Chu,J.P.Heritage,andA.Dienes,Opt.Lett.18,558(1993),x,Dz,Thismodulatesthephasebutnottheamplitude.,Deformablemirrorpulse-shaper,600nmSiliconNitrideMembraneGoldorSilverCoated1msResponseTime280VDriveVoltageComputerControlled3x13or1x19ActuatorLayout,G.V.VdovinandP.M.Sarro,Flexiblemirrormicromachinedinsilicon,AppliedOptics34,2968-2972(1995)E.Zeek,et.Al.,“Pulsecompressionusingdeformablemirrors”,Opt.Lett.24,493-495(1999),Adisadvantageofalltypesofspatiallightmodulators,Allspatial-light-modulatorpulse-shapersinducespatio-temporaldistortionsinthepulse,whichareproportionaltothemagnitudeoftheshaping.,Advantagesanddisadvantagesofthevarioustypesofspatiallightmodulators,Liquid-CrystalArraysPhaseandamplitudemodulationPixellatedwithdeadspacesEfficient,Acousto-OpticModulatorsPhaseandamplitudemodulationNodeadspacesSmallpixelsInefficient,DeformableMirrorsPhase-onlymodulationNodeadspacesLargepixelsEfficient,Acousto-opticpulse-shaping,Thismethodworkswithoutthezerodispersionstretcherandhencewithoutspatio-temporalpulsedistortions.,Itlaunchesanacousticwavealongthebeaminabirefringentcrystal.Theinputpolarizationisdiffractedtotheotherbythesoundwave.Thefrequencythathasitspolarizationrotateddependsontheacoustic-wavefrequency.Itsrelativedelayatthecrystalexitdependsontherelativephasevelocitiesofthetwopolarizations.,differentfromtheacousto-opticSLM!,Acousto-opticpulseshaping:theory,Theextraphasedelayseenbyeachwavelengthdependsonhowfarintothecrystaltheacousticwavetakesonthatwavelengthandtheordinaryandextraordinaryrefractiveindices.,Thestrengthoftheacousticwaveateachwavelengthdeterminestheamplitudeoftheoutputwaveatthatwavelength.,1F.Verluiseet.al.,Opt.Lett.8(2000)575.2K.Ohnoet.al.,J.Opt.Soc.Am.B,19(2002)inpress,Parameters,Acousto-opticpulse-shaping:details,TakasumiTanabe,KimihisaOhno,TatsuyoshiOkamoto,FumihikoKannari,Commercialdevice:the“Dazzler”,Acousto-opticpulseshapingyieldsintensity-and-phaseshaping,itinducesnospatio-temporalpulsedistortions,anditisavailablecommercially.,ResultsusingtheDazzler,Compensatingthephaseofanultrashortpulse,Theresultingpulselengthisreducedfrom30fsto17fs.,Phase-onlypulseshapingismoreefficient.Butcanitachievethedesiredpulseshape?,RecallthatthespectralphaseismoreimportantthantheamplitudefordeterminingE(t).Socanwegenerateagivenpulsewithonlyaphasemask?Mostly.Butcalculatingaphase-onlymaskisdifficult.,Generallyweregivenatargetwave-form.DirectcalculationofH(w)requiresaphaseandamplitudemask.Wemustcalculatethebestpossiblephase-onlymask.,Therenowexistawholeclassofoptimizationalgorithmsthatspecializeinsuchdifficult(orimpossible)problems.,ThemostcommonareEvolutionary(alsocalled“Genetic”)Algorithms,Evolutionaryalgorithms,Evolutionaryalgorithmsbasetheiroptimizationonasimpleaxiom:Survivalofthefittest.,Evolutionaryalgorithmsdontrequireacarefullychoseninitialguessandhenceprovideasimpleandveryrobustoptimizationmethod.,Usualderivative-basedoptimizationmethod,Evolutionaryalgorithm,Evolutionaryalgorithmsperformapseudorandomsearch.,Startwithasetofparents(initiallyrandom).Makeasetofchildren.Usingcrossovertocombinepartsofparents.Addrandommutations.Evaluatethefitnessoftheindividuals.Ifwekeeptheparentsfromthelastgeneration,itscalledelitism.Selecttheparentsforthenextgeneration.,SecondGeneration,FirstGeneration,Evolutionaryalgorithmexample,Parameter1,Parameter2,Thefirstgenerationevenlysamplestheparameterspace.Fromthis,weselecttheparentsforthenextgenerationThesecondgenerationisconcentratedaroundthefirstsetofparents,and,fromthis,weselectthenextsetofparents.,Evolutionaryalgorithmsareveryreliable,buttheyareslow.,Okay,sowecanpulse-shape.Butwhatifwewanttoamplify,too?,Amplificationwilldistortthepulseshape.Soamplifyfirstandshapesecond.Butshapingisinefficient(rememberthegratings).Soshapefirstandamplifysecond.HmmWorse,wemaynotactuallyknowtheinputpulseshape.ThesolutionisAdaptivePulseShaping.,Adaptivep