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1、NonlinearOpticsWhydononlinear-opticaleffectsoccur?Maxwell'sequationsinamediumNonlinear-opticalmediaSecond-harmonicgenerationSum-anddifference-frequencygenerationHigher-ordernonlinearopticsTheSlowlyVaryingEnvelopeApproximationPhase-matchingandConservationlawsforphotonsNonlinearop
2、ticsisn’tsomethingyouseeeveryday.Sendinginfraredlightintoacrystalyieldedthisdisplayofgreenlight(second-harmonicgeneration,SHG):Nonlinearopticsallowsustochangethecolorofalightbeam,tochangeitsshapeinspaceandtime,andtocreateultrashortlaserpulses.Whydon'tweseenonlinearopticaleffects
3、inourdailylife?1.Intensitiesofdailylifearetooweak.2.Normallightsourcesareincoherent.3.Theoccasionalcrystalweseehasthewrongsymmetry(forSHG).4.Phase-matchingisrequired,anditdoesn'tusuallyhappenonitsown.Whydononlinear-opticaleffectsoccur?Recallthat,innormallinearoptics,alightwaveac
4、tsonamolecule,whichvibratesandthenemitsitsownlightwave,whichinterfereswiththeoriginallightwave.Wecanalsoimaginethisprocessintermsofthemolecularenergylevels,usingarrowsforthephotonenergies:Whydononlinear-opticaleffectsoccur?(continued)Now,supposetheirradianceishighenoughthatmanym
5、oleculesareexcitedtothehigher-energystate.Thisstatecanthenactasthelowerlevelforadditionalexcitation.Thisyieldsvibrationsatallfrequenciescorrespondingtoallenergydifferencesbetweenpopulatedstates.Nonlinearopticsisanalogoustononlinearelectronics,whichwecanobserveeasily.Sendingahigh
6、-volumesine-wave(purefrequency)signalintoacheapamplifierorcheapspeakersyieldsatruncatedoutputsignal,moreofasquarewavethanasine.Thissquarewavehashigherfrequencies.Wehearthisasdistortion.SharpedgesrequirehigherfrequenciesintheFourierseries.NonlineareffectsinatomsSoanelectron’smoti
7、onwillalsodepartfromasinewave.Thepotentialgetsveryflatoutatinfinity,sotheelectron’smotioncaneasilygononlinear!PotentialduetonucleusNucleusEnergyPositionAnotherwaytolookatnonlinearopticsisthatthepotentialoftheelectronisanatomisnotasimplequadraticpotential.Nonlinearopticsandanharm
8、onicoscillatorsForweakfields,motionisharmonic,a
