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1、PHYSICALREVIEWE74,0366212006Full-wavesimulationsofelectromagneticcloakingstructuresStevenA.Cummer,*Bogdan-IoanPopa,DavidSchurig,andDavidR.SmithDepartmentofElectricalandComputerEngineering,DukeUniversity,Durham,NorthCarolina27708,USAJohnPendryDepartmentofPhysics,TheBlackettLaboratory,Impe
2、rialCollegeLondon,LondonSW72AZ,UnitedKingdomReceived25May2006;published27September2006Pendryetal.havereportedelectromagneticallyanisotropicandinhomogeneousshellsthat,intheory,com-pletelyshieldaninteriorstructureofarbitrarysizefromelectromagneticÞeldswithoutperturbingtheexternalÞelds.Neit
3、herthecoordinatetransformation-basedanalyticalformulationnorthesupportingray-tracingsimu-lationindicatehowmaterialperturbationsandfull-waveeffectsmightaffectthesolution.Wereportfullyelectromagneticsimulationsofthecylindricalversionofthiscloakingstructureusingidealandnonidealbutphysicallyr
4、ealizableelectromagneticparametersthatshowthatthelow-reßectionandpower-ßowbendingpropertiesoftheelectromagneticcloakingstructurearenotespeciallysensitivetomodestpermittivityandpermeabilityvariations.Thecloakingperformancedegradessmoothlywithincreasingloss,andeffectivelow-reßectionshieldin
5、gcanbeachievedwithacylindricalshellcomposedofaneightÐhomogeneouslayerapproximationoftheidealcontinuousmedium.Animperfectbutsimplerversionofthecloakingmaterialisderivedandisshowntoreproducetheraybendingoftheidealmaterialinamannerthatmaybeeasiertoexperimentallyrealize.DOI:10.1103/PhysRevE.
6、74.036621PACSnumbers:41.20.Jb,42.25.Fx,42.25.GyPendryetal.1havereportedacoordinatetransforma-alizabilityandlimitationsofthisphenomenon.Forexample,tionapproachfordesigninganelectromagneticmaterialinitialsimulationswereunabletoobservetheeffectatallthroughwhichelectromagneticÞeldscanbeexc
7、ludedfroma10,11,despiteidealconditions.OnlythroughgreatcarepenetrableobjectwithoutperturbingtheexteriorÞelds,werelatersimulationsabletodemonstratetheeffect12,therebyrenderingtheinterioreffectivelyÒinvisibleÓtothewhichhighlightedthedelicateconditionsneededt
