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1、October15,1998/Vol.23,No.20/OPTICSLETTERS1573Omnidirectionalreflectionfromaone-dimensionalphotoniccrystalJoshuaN.Winn,YoelFink,ShanhuiFan,andJ.D.JoannopoulosMassachusettsInstituteofTechnology,77MassachusettsAvenue,Cambridge,Massachusetts02139ReceivedJuly7,1998Wedemonstratethatone-dim
2、ensionalphotoniccrystalstructures(suchasmultilayerfilms)canexhibitcompletereflectionofradiationinagivenfrequencyrangeforallincidentanglesandpolarizations.Wederiveageneralcriterionforthisbehaviorthatdoesnotrequirematerialswithverylargeindices.Weperformnumericalstudiesthatillustratethi
3、seffect.ã1998OpticalSocietyofAmericaOCIScodes:230.4170,230.1480.Low-lossperiodicdielectrics,orphotoniccrystals,allowthewhiteregionstherearenoelectromagneticmodes,thepropagationoflighttobecontrolledinotherwiseregardlessofky.1±4difficultorimpossibleways.Inparticular,apho-Oneobviousfeat
4、ureofFig.1isthatthereisnotoniccrystalcanbeaperfectmirrorforlightfromanycompletebandgap.Foranyfrequencythereexistsdirection,withanypolarization,withinaspecifiedfre-someelectromagneticmodewiththatfrequencyÐthequencyrange.Itisnaturaltoassumethatanecessarynormal-incidencebandgapiscrossed
5、bymodeswithconditionforsuchomnidirectionalreflectionisthatthekx.0.Thisisageneralfeatureofone-dimensionalcrystalexhibitacompletethree-dimensionalphotonicphotoniccrystals.bandgap,thatis,afrequencyrangewithinwhichthereHowever,theabsenceofacompletebandgapdoesarenopropagatingsolutionsofMa
6、xwell'sequations.notprecludeomnidirectionalreflection.ThecriterionHerewereportthatthisassumptionisfalseÐinfactaisnotthattherebenopropagatingstateswithinone-dimensionalphotoniccrystalwillsuffice.Wein-thecrystal;rather,thecriterionisthattherebetroduceageneralcriterionforomnidirectional
7、reflec-nopropagatingstatesthatcancoupletoanincidenttionforallpolarizationsandapplyittothecaseofapropagatingwave.Aswearguebelow,thelatterdielectricmultilayerfilm.Previousattemptstoattaincriterionisequivalenttotheexistenceofafrequencyhighreflectanceforawiderangeofincidentanglesin-range
8、inwhichthepr
