超快光学 第07章 非线性光学

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1、NonlinearOpticsWhydononlinear-opticaleffectsoccur?Maxwell'sequationsinamediumNonlinear-opticalmediaSecond-harmonicgenerationSum-anddifference-frequencygenerationHigher-ordernonlinearopticsTheSlowlyVaryingEnvelopeApproximationPhase-matchingandConservationlawsforphotonsNonlinearopticsisn’tsomething

2、youseeeveryday.Sendinginfraredlightintoacrystalyieldedthisdisplayofgreenlight(second-harmonicgeneration,SHG):Nonlinearopticsallowsustochangethecolorofalightbeam,tochangeitsshapeinspaceandtime,andtocreateultrashortlaserpulses.Whydon'tweseenonlinearopticaleffectsinourdailylife?1.Intensitiesofdailyl

3、ifearetooweak.2.Normallightsourcesareincoherent.3.Theoccasionalcrystalweseehasthewrongsymmetry(forSHG).4.Phase-matchingisrequired,anditdoesn'tusuallyhappenonitsown.Whydononlinear-opticaleffectsoccur?Recallthat,innormallinearoptics,alightwaveactsonamolecule,whichvibratesandthenemitsitsownlightwave

4、,whichinterfereswiththeoriginallightwave.Wecanalsoimaginethisprocessintermsofthemolecularenergylevels,usingarrowsforthephotonenergies:Whydononlinear-opticaleffectsoccur?(continued)Now,supposetheirradianceishighenoughthatmanymoleculesareexcitedtothehigher-energystate.Thisstatecanthenactasthelowerl

5、evelforadditionalexcitation.Thisyieldsvibrationsatallfrequenciescorrespondingtoallenergydifferencesbetweenpopulatedstates.Nonlinearopticsisanalogoustononlinearelectronics,whichwecanobserveeasily.Sendingahigh-volumesine-wave(purefrequency)signalintoacheapamplifierorcheapspeakersyieldsatruncatedout

6、putsignal,moreofasquarewavethanasine.Thissquarewavehashigherfrequencies.Wehearthisasdistortion.SharpedgesrequirehigherfrequenciesintheFourierseries.NonlineareffectsinatomsSoanelectron’smotionwillalsodepartfromasinewave.Thepotentialgetsveryflatoutatinfinity,sotheelectron’smotioncaneasilygononlinea

7、r!PotentialduetonucleusNucleusEnergyPositionAnotherwaytolookatnonlinearopticsisthatthepotentialoftheelectronisanatomisnotasimplequadraticpotential.NonlinearopticsandanharmonicoscillatorsForweakfields,motionisharmonic,a