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1、M.LuoandQ.H.LiuVol.28,No.12/December2011/J.Opt.Soc.Am.B2879Enhancementofsecond-harmonicgenerationinanair-bridgephotoniccrystalslab:simulationbyspectralelementmethodMaLuoandQingHuoLiu*DepartmentofElectricalandComputerEngineering,DukeUniversity,Durham,NorthCarolina27
2、708,USA*Correspondingauthor:qhliu@duke.eduReceivedMay9,2011;revisedSeptember29,2011;acceptedSeptember30,2011;postedOctober6,2011(Doc.ID147180);publishedNovember11,2011Theenhancementofsecond-harmonicgeneration(SHG)acrossa2Dphotoniccrystal(PC)slabconsistingofGaPisinv
3、estigatedinthisstudywiththethree-dimensionalspectralelementmethod(SEM).Thein-planebandstructureiscalculated,anditiscomparedwiththepeaksoftheSHGtorevealthemechanismsbehindtheenhancement.ThenumericalresultfromtheSEMshowsthat,undernormalincidence,thescatteredpowerofth
4、eSHGisen-hancedfortheeigenstateswithlargedecayrates,whilethestoredenergyoftheSHGisenhancedfortheeigen-stateswithazerodecayrate.TheSHGisenhancedundertwoconditions:(i)phasematchingbetweenthefundamentalandsecond-harmonic(SH)fieldsand(ii)symmetrymatchingbetweenthefield
5、patternofthereso-nanteigenstateandthegeneratedSHpolarizationfield.Comparedwithahomogeneousdielectricslab,theair-bridgePCslabcanenhancetheSHGby4ordersofmagnitude.?2011OpticalSocietyofAmericaOCIScodes:000.4430,160.5298.1.INTRODUCTIONRecently,theenhancementofSHGinone-
6、[11–13]andSincethediscoveryofnonlinearopticaleffects[1],therehastwo-dimensional[14,15]PCswasinvestigatedtheoreticallybeenmuchinterestininvestigatingtheirfundamentalphysicsandexperimentally.TheenhancementofSHGwascalculatedandengineeringapplications.Oneofthemostwidel
7、yinvesti-bythemodecouplingmethod[9,12,14],whichrevealsthefun-gatedtopicsissecond-harmonicgeneration(SHG).BecausedamentalphysicalmechanismoftheSHGphenomenon.How-thenonlinearopticalcoefficientsareusuallysmall,theSHGever,theperformanceofthismethodstronglydependsonthee
8、ffectisweak.Furthermore,asopticalmaterialsareusuallychoiceofmodes.Forengineeringdesign,afullynumericalsi-dispersive,theyintroduceaphasemismatchbe