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1、LETTERdoi:10.1038/nature12066PhotonicFloquettopologicalinsulators1211122MikaelC.Rechtsman*,JuliaM.Zeuner*,YonatanPlotnik*,YaakovLumer,DanielPodolsky,FelixDreisow,StefanNolte,12MordechaiSegev&AlexanderSzameit1Topologicalinsulatorsareanewphaseofmatter,withthestrikingofasinglewave
2、guidemodecompleting,20cyclesinphasewhile1–3propertythatconductionofelectronsoccursonlyontheirsurfaces.propagatingfromz50toz510cm.TheincreaseinrefractiveindexIntwodimensions,electronsonthesurfaceofatopologicalinsulator24associatedwiththewaveguidesisDn57310.Thequantummecha-arenot
3、scattereddespitedefectsanddisorder,providingrobustnessnicalanalogueofequation(1)describesthepropagationofaquantumakintothatofsuperconductors.Topologicalinsulatorsarepredictedparticlethatevolvesintime—forexample,anelectroninasolid.Thetohavewide-rangingapplicationsinfault-toleran
4、tquantumcom-waveguidesactlikepotentialwells,similarlytonucleiofatomsinputingandspintronics.Substantialefforthasbeendirectedtowardssolids.Thus,thepropagationoflightinthearrayofhelicalwaveguides4–13realizingtopologicalinsulatorsforelectromagneticwaves.One-asitpropagatesinthezdire
5、ctionisequivalenttothetemporalevolu-dimensionalsystemswithtopologicaledgestateshavebeendemon-tionofanelectronasitmovesthroughatwo-dimensionallatticewithstrated,butthesestatesarezero-dimensionalandthereforeexhibitnoatomsthatarerotatingintime.11,12,14transportproperties.Topologic
6、alprotectionofmicrowavesAmicroscopeimageoftheinputfacetofthephotoniclatticeishasbeenobservedusingamechanismsimilartothequantumHallshowninFig.1a,andadiagramofthehelicalwaveguidesarranged15effect,byplacingagyromagneticphotoniccrystalinanexternalinahoneycomblatticeisshowninFig.1b.
7、Theperiod(orpitch)ofthe5magneticfield.Butbecausemagneticeffectsareveryweakatopticalhelicalwaveguidesissufficientlysmallthataguidedmodeisadiabati-frequencies,realizingphotonictopologicalinsulatorswithscatter-freecallydrawnalongwithawaveguideasitcurves.Wethereforetrans-edgestates
8、requiresafundamentallydifferentmechanism—oneformthecoo
