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1、Second-ordernonlinear-opticaleffectsSymmetryissuesPhase-matchinginSHGPhase-matchingbandwidthGroup-velocitymismatchNonlinear-opticalcrystalsPracticalnumbersforSHGElectro-opticsDifference-frequencygenerationandopticalparametricgenerationFirstdemonstrationofsecon
2、d-harmonicgenerationP.A.Franken,etal,PhysicalReviewLetters7,p.118(1961)Thesecond-harmonicbeamwasveryweakbecausetheprocesswasnotphase-matched.FirstdemonstrationofSHG:thedataTheactualpublishedresults…InputbeamThesecondharmonicNotethattheveryweakspotduetothesecon
3、dharmonicismissing.ItwasremovedbyanoverzealousPhysicalReviewLetterseditor,whothoughtitwasaspeckofdirtanddidn’tasktheauthorsfirst.Symmetryinsecond-harmonicgenerationForthistohold,c(2)mustbezeroformediawithinversionsymmetry.Mostmaterialshaveinversionsymmetry,soy
4、oujustdon’tseeSHG—oranyothereven-ordernonlinear-opticaleffect—everyday.E(t)E2(t)Esig(x,t)?c(2)E2(x,t)Ifweimagineinvertingspace:Esig(x,t)→-Esig(x,t)E(x,t)→-E(x,t)Now,ifthemediumissymmetrical,c(2)remainsunchanged.So:-Esig(x,t)?c(2)[-E(x,t)]2=c(2)E(x,t)2?Esig(x,t
5、)Phase-matchinginsecond-harmonicgenerationHowdoesphase-matchingaffectSHG?It’samajoreffect,anotherimportantreasonyoujustdon’tseeSHG—oranyothernonlinear-opticaleffects—everyday.SinusoidaldependenceofSHGintensityonlengthLargeDkSmallDkTheSHGintensityissharplymaxim
6、izedifDk=0.whichwillonlybesatisfiedwhen:Unfortunately,dispersionpreventsthisfromeverhappening!Phase-matchingsecond-harmonicgenerationSowe’recreatinglightatwsig=2w.FrequencyRefractiveindexAndthek-vectorofthepolarizationis:Thephase-matchingconditionis:Thek-vecto
7、rofthesecond-harmonicis:Wecannowsatisfythephase-matchingcondition.Usetheextraordinarypolarizationforwandtheordinaryfor2w.Phase-matchingsecond-harmonicgenerationusingbirefringenceBirefringentmaterialshavedifferentrefractiveindicesfordifferentpolarizations.Ordin
8、aryandextraordinaryrefractiveindicescanbedifferentbyupto~0.1forSHGcrystals.FrequencyRefractiveindexnedependsonthepropagationangle,sowecantuneforagivenw.Somecrystalshavene
