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1、Second-ordernonlinear-opticaleffectsSymmetryissuesPhase-matchinginSHGPhase-matchingbandwidthGroup-velocitymismatchNonlinear-opticalcrystalsPracticalnumbersforSHGElectro-opticsDifference-frequencygenerationandopticalparametricgenerationFirstdemonstrationofsecond-harmonicgeneratio
2、nP.A.Franken,etal,PhysicalReviewLetters7,p.118(1961)Thesecond-harmonicbeamwasveryweakbecausetheprocesswasnotphase-matched.FirstdemonstrationofSHG:thedataTheactualpublishedresults…InputbeamThesecondharmonicNotethattheveryweakspotduetothesecondharmonicismissing.Itwasremovedbyanove
3、rzealousPhysicalReviewLetterseditor,whothoughtitwasaspeckofdirtanddidn’tasktheauthorsfirst.Symmetryinsecond-harmonicgenerationForthistohold,c(2)mustbezeroformediawithinversionsymmetry.Mostmaterialshaveinversionsymmetry,soyoujustdon’tseeSHG—oranyothereven-ordernonlinear-opticalef
4、fect—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)Phase-matchinginsecond-harmonicgenerationHowdoesphase-matchingaffectSHG?It’
5、samajoreffect,anotherimportantreasonyoujustdon’tseeSHG—oranyothernonlinear-opticaleffects—everyday.SinusoidaldependenceofSHGintensityonlengthLargeDkSmallDkTheSHGintensityissharplymaximizedifDk=0.whichwillonlybesatisfiedwhen:Unfortunately,dispersionpreventsthisfromeverhappening!P
6、hase-matchingsecond-harmonicgenerationSowe’recreatinglightatwsig=2w.FrequencyRefractiveindexAndthek-vectorofthepolarizationis:Thephase-matchingconditionis:Thek-vectorofthesecond-harmonicis:Wecannowsatisfythephase-matchingcondition.Usetheextraordinarypolarizationforwandtheordinar
7、yfor2w.Phase-matchingsecond-harmonicgenerationusingbirefringenceBirefringentmaterialshavedifferentrefractiveindicesfordifferentpolarizations.Ordinaryandextraordinaryrefractiveindicescanbedifferentbyupto~0.1forSHGcrystals.FrequencyRefractiveindexnedependsonthepropagationangle,sow
8、ecantuneforagivenw.Somecrystalshavene
