《精编制作超快光学 第04章 脉冲(2)PPT课件》由会员分享，可在线阅读，更多相关《精编制作超快光学 第04章 脉冲(2)PPT课件（30页珍藏版）》请在金锄头文库上搜索。
1、UltrashortLaserPulsesII Moresecond orderphaseHigher orderspectralphasedistortionsRelativeimportanceofspectrumandspectralphasePulseandspectralwidthsTime bandwidthproduct Prof RickTrebinoGeorgiaTechwww frog gatech edu Frequency domainphaseexpansion RecalltheTaylorseriesfor Asinthetimedomain onlythefir
2、stfewtermsaretypicallyrequiredtodescribewell behavedpulses Ofcourse we llconsiderbadlybehavedpulses whichhavehigher ordertermsin where isthegroupdelay iscalledthe group delaydispersion TheFouriertransformofachirpedpulse WritingalinearlychirpedGaussianpulseas or Fourier Transformingyields Rationalizi
3、ngthedenominatorandseparatingtherealandimagparts AGaussianwithacomplexwidth AchirpedGaussianpulseFourier Transformstoitself where neglectingthenegative frequencytermduetothec c Butwhenthepulseislong a0 whichistheinverseoftheinstantaneousfrequencyvs time Thegroupdelayvs wforachirpedpulse Thegroupdela
4、yofawaveisthederivativeofthespectralphase So ForalinearlychirpedGaussianpulse thespectralphaseis Andthedelayvs frequencyislinear Thisisnottheinverseoftheinstantaneousfrequency whichis 2nd orderphase positivelinearchirp Numericalexample Gaussian intensitypulsew positivelinearchirp 2 14 5radfs2 Hereth
5、equadraticphasehasstretchedwhatwouldhavebeena3 fspulse giventhespectrum toa13 9 fsone 2nd orderphase negativelinearchirp Numericalexample Gaussian intensitypulsew negativelinearchirp 2 14 5radfs2 Aswithpositivechirp thequadraticphasehasstretchedwhatwouldhavebeena3 fspulse giventhespectrum toa13 9 fs
6、one Thefrequencyofalightwavecanalsovarynonlinearlywithtime ThisistheelectricfieldofaGaussianpulsewhosefre quencyvariesquadraticallywithtime Thislightwavehastheexpression Arbitrarilycomplexfrequency vs timebehaviorispossible Butweusuallydescribephasedistortionsinthefrequencydomain Nonlinearlychirpedp
7、ulses 3rd orderspectralphase quadraticchirp Longerandshorterwavelengthscoincideintimeandinterfere beat Trailingsatellitepulsesintimeindicatepositivespectralcubicphase andleadingonesindicatenegativespectralcubicphase S w tg w j w Spectrumandspectralphase 400500600700 Becausewe replottingvs wavelength
8、 notfrequency there saminussigninthegroupdelay sotheplotiscorrect 3rd orderspectralphase quadraticchirp Numericalexample Gaussianspectrumandpositivecubicspectralphase with 3 750radfs3 Trailingsatellitepulsesintimeindicatepositivespectralcubicphase Negative3rd orderspectralphase Anothernumericalexamp
9、le Gaussianspectrumandnegativecubicspectralphase with 3 750radfs3 Leadingsatellitepulsesintimeindicatenegativespectralcubicphase 4th orderspectralphase Numericalexample Gaussianspectrumandpositivequarticspectralphase 4 5000radfs4 Leadingandtrailingwingsintimeindicatequarticphase Higher frequenciesin
10、thetrailingwingmeanpositivequarticphase Negative4th orderspectralphase Numericalexample Gaussianspectrumandnegativequarticspectralphase 4 5000radfs4 Leadingandtrailingwingsintimeindicatequarticphase Higher frequenciesintheleadingwingmeannegativequarticphase 5th orderspectralphase Numericalexample Ga
11、ussianspectrumandpositivequinticspectralphase 5 4 4 104radfs5 Anoscillatorytrailingwingintimeindicatespositivequinticphase Negative5th orderspectralphase Numericalexample Gaussianspectrumandnegativequinticspectralphase 5 4 4 104radfs5 Anoscillatoryleadingwingintimeindicatesnegativequinticphase There
12、lativeimportanceofintensityandphase PhotographsofmywifeLindaandme CompositephotographmadeusingthespectralintensityofLinda sphotoandthespectralphaseofmine andinverse Fourier transforming CompositephotographmadeusingthespectralintensityofmyphotoandthespectralphaseofLinda s andinverse Fourier transform
13、ing Thespectralphaseismoreimportantfordeterminingtheintensity Pulsepropagation Whathappenstoapulseasitpropagatesthroughamedium Alwaysmodel linear propagationinthefrequencydomain Also youmustknowtheentirefield i e theintensityandphase todoso Inthetimedomain propagationisaconvolution muchharder Pulsep
14、ropagation continued usingk w c Separatingoutthespectrumandspectralphase Rewritingthisexpression Thepulselength Therearemanydefinitionsofthewidthorlengthofawaveorpulse Theeffectivewidthisthewidthofarectanglewhoseheightandareaarethesameasthoseofthepulse Effectivewidth Area height Advantage It seasyto
15、understand Disadvantages TheAbsvalueisinconvenient Wemustintegrateto Absvalueisunnecessaryforintensity Thermspulsewidth Theroot mean squaredwidthorrmswidth Advantages Integralsareofteneasytodoanalytically Disadvantages Itweightswingsevenmoreheavily soit sdifficulttouseforexperiments whichcan tscanto
16、 Thermswidthisthenormalizedsecond ordermoment TheFull Width Half Maximum Full width half maximumisthedistancebetweenthehalf maximumpoints Advantages Experimentallyeasy Disadvantages Itignoressatellitepulseswithheights 49 99 ofthepeak Also wecandefinethesewidthsintermsoff t orofitsintensity f t 2 Definespectralwidths Dw similarlyinthefrequencydomain t w TheUncertaintyPrinciple TheUncertaintyPrinciplesaysthattheproductofafunction swidthsinthetimedomain Dt andthefrequencydomain Dw hasaminimum Combi
