A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

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1、JOURNALOFLIGHTWAVETECHNOLOGY,VOL.27,NO.19,OCTOBER1,20094241AStudyonUnconditionallyStableFDTDMethodsfortheModelingofMetamaterialsValtemirE.doNascimento,Kyung-YoungJung,Member,IEEE,Ben-HurV.Borges,Member,IEEE,andFernandoL.Teixeira,SeniorMember,IEEEAbstract—We

2、assesstheperformanceofthreeunconditionallyThefinite-differencetime-domain(FDTD)method[9],[10]stablefinite-differencetime-domain(FDTD)methodsfortheisapopularnumericaltechniquethatiscapableofmodelingmodelingofdoublydispersivemetamaterials:1)locallyone-di-comple

3、xfrequencyresponsesofsuchmetamaterialsinthemensionalFDTD;2)locallyone-dimensionalFDTDwithStrangsplitting;and(3)alternatingdirectionimplicitFDTD.Weusebothtimedomain.However,highlyrefinedgridsshouldbeem-double-negativemediaandzero-indexmediaasbenchmarks.ployed

4、toaccuratelymodelstrongevanescentwavesthatarepresentinconnectionwithdouble-negativemedia.EvanescentIndexTerms—Alternatingdirectionimplicit(ADI),Crank–Nicolsonscheme,FDTDmethods,locallyone-dimensional(LOD),wavesarecriticalfor(subwavelength)imagingquality[11]

5、.metamaterials,Strangsplitting.Moreover,resonantsurfacepolaritonscanalsobepresentatdouble-negativemediainterfaces,whichrequirelongintegra-tiontimesduetoslowtransientbehavior[12].Unfortunately,I.INTRODUCTIONthetimestepsizeofFDTDisrestrictedbythewell-knownCou

6、rantFriedrichLevystabilitycondition,whichimposesanOUBLE-NEGATIVE(left-handed)mediahaveattractedupperboundtothetimestepsizeaccordingtothespatialcellDgreatinterestduetotheirpotentialtoyieldunusualef-size[10],[13].Thesimultaneousrequirementsofsmalltimefects,su

7、chasnegativerefractionandbackwardwavepropaga-stepsandlongintegrationtimesmakethecomputationalcosttion[1].Onewayofobtainingmaterialswithdouble-negativeofFDTDbecomeprohibitive,especiallyfor3-Dproblems.behaviorisbyconstructingtridimensionalcompositematerialsAp

8、ossiblewaytoovercometheCourantFriedrichLevymadeofconductingwires[2](toyieldnegativepermittivity)limitisthroughtheuseofoperator-splittingtechniques,suchandsplitringresonators[3](toyieldnegativepermeabil