miniaturized tunable terahertz antenna based on graphene

9.L.G.Liu,P.F.Guo,J.J.Huang,W.W.Wu,J.J.Mo,Y.Q.Fu,andN.C.Yuan,Designofaninvisibleradomebymetamaterialabsorbersloadedwithlumpedresistors,ChinPhysLett29(2012).10.Z.Shen,B.Zheng,Z.Mei,J.Yang,andW.Tang,Onthedesignofwide-bandandthinabsorbersusingthemultipleresonancesconcept,In:ProceedingsofIEEEinternationalconferenceonmicrowaveandmillimeterwavetechnology,Nanjing,China,2008,pp.32–35.11.E.A.Parker,A.N.A.ElSheikh,andA.C.deC.Lima,Convolutedfrequency-selectivearrayelementsderivedfromlinearandcrosseddipoles,IEEProcH140(1993),378–380.VC2014WileyPeriodicals,Inc.MINIATURIZEDTUNABLETERAHERTZANTENNABASEDONGRAPHENETaoZhou,1ZhiqunCheng,1HongfangZhang,1MartineLeBerre,2LiviuMilitaru,2andFrancisCalmon21MicroelectronicsCADcenter,Hangzhoudianziuniversity,HangZhou,Zhejiang,China;Correspondingauthor:zhou.tao@hdu.edu.cn2Universit󰀂edeLyon,InstitutdesNanotechnologiesdeLyon,INL-UMR5270,CNRS,INSAdeLyon,FranceReceived10December2013ABSTRACT:Atunableterahertznanoantennabasedongrapheneispresented.Theproposedantennahasacharacteristicofdynamicfre-quencyreconfiguration,highminiaturization,easyintegration,lowreflectioncoefficient,andgoodomnidirectionalradiationpattern.Theattractivepropertiesofthegrapheneantennahasthepotentialtobeusedinnanoscalewirelesscommunicationsandsensingsystems.VC2014WileyPeriodicals,Inc.MicrowaveOptTechnolLett56:1792–1794,2014;Viewthisarticleonlineatwileyonlinelibrary.com.DOI10.1002/mop.28450Keywords:terahertz;grapheme;antenna;tunable;miniaturized1.INTRODUCTIONGrapheneisamonoatomictwo-dimensionalcarboncrystal,whichhasrecentlyattractedgreatinterestoftheresearchcom-munityduetoitsuniquecharacteristics[1–4].However,onlyfewpreviousworksconsideredtheantennaapplicationsofgra-phene[5–10].Graphenewasfirstplacedasmiddlelayerundergolddipoleantennaoperatingat120GHz[8],wheregrapheneitselfdidnotsupportradiation.Actually,itwasonlyappliedtopermitorpreventradiationbyelectricbiasfield,whichcouldalsobeeasilyrealizedbyRFswitchesorphaseshifters.Then,thefirststudyongrapheneusedasarealradiatorwasreviewed[9],thesurfaceconductivityofgraphenewithchemicalpotential(0eV)wasgiven,theoperationfrequenciesandtheradiationpropertiesoftwoantennaswithdifferentsizeswerestudied.Anotherconceptofaterahertz(THz)antennausinggraphenestackwaspresented[5],thereitwasapprovedthatthedipole-likegrapheneantennasupportsurfaceplasmonicresonancesintheTHzrange,andtheresonantfrequencycanbetunedviathechemicalpotentialrelatedtotheelectricfield.ATHzopticalantennabasedongrapheneringstructurewasproposed[11],wheregrapheneplasmonswasusedtoreplacetheconventionalmetallicplasmons,theplasmonresonanceoftheperfectgra-pheneringwasillustratedwiththeedgeplamons.Inthisarticle,thetunableTHzantennabasedongrapheneisstudiedsystematically,thesurfaceconductivityofgrapheneunderdifferentchemicalpotentialsarepresented,thecorre-spondingplasmonresonantfrequency,theSparameters,andtheradiationpatternintheTHzbandaregiven.Weindicatebynumericalsimulationsthat,besidetheminiaturizationcorre-spondingtotheplasmonresonanceofgraphene,theproposedantennahascomparableelectromagneticcharacteristicsasthatoftheconventionalmetalliccounterparts.Theproposedgra-pheneantennahassimilarreflectioncoefficientandradiationpatternofmetallicradiator.Therefore,theproposedTHzgra-phenenanoantennacanbeintegratedinnanosystems,wheretheconventionalmetallicantennaisunfeasibleduetothelowmobilityofelectronsandhugeattenuation.Inconsequence,theproposedgraphenenanoantennahasadimensionofafewmicrometers,hasadynamicreconfigurabilityandresonatesatTHzband;itispredictedtobeappliedinwirelesscommunica-tionsinnanosystems.2.THzPROPERTIESOFGRAPHENEThankstothegraphene’satomicthickness,graphenesheetcanbemodeledbyanequivalentsurfacewithagivenconductivityr[9–12],whichcanbecomputedbyKubo’sformula[12].Theconductivitydependsonthechemicalpotentiallc,temperatureT,frequencyx,andtransportrelaxationtimes.Antennasbasedongrapheneareenvisagedtohaveadimensionofafewmicro-meters,foragraphenesheetwithdimensionlargerthan100nm,theedgeeffectsonthegrapheneconductivitycanbeneglected[9,10];therebyinthissection,thesurfaceconductivitymodelwillbeusedtodevelopthegraphenesheet.WiththeDrude-likeintrabandcontribution,thesurfacecon-ductivitycanberepresentedas[10]rxðÞ52e2phkBThln2coshlc2kBT ! !ix1is21(1)whilethesurfaceconductivityduetointerbandcontribution,canbegivenbyrixðÞ5e24hHx2󰀇󰀈1i4xpð10H󰀂ðÞ2Hx2ÀÁx224󰀂2d󰀂󰀂󰀃(2)Thetotalconductivityisrtotal5r1ri(3)Attheinterface,itiswellknownthatthetangentialcompo-nentoftheelectricfieldandthesurfacecurrentareconnectedbythesurfaceimpedanceZs,E!jz505ZsJ!surf(4)Thesurfacecurrentinducedonthegraphenesurfaceisrelatedtothetangentialcomponentoftheelectricfieldandthesurfaceconductivityr.J!surf5rE!jz50(5)Theboundaryconditionsatthegrapheneinterfacecanbedefinedas[10]n!3H!jz5102H!jz520hi5J!surf51ZsE!jz50(6)whereZs51/risthesurfaceimpedanceofthegraphenesheet,theelectromagneticproblemcanbedeterminedbytheboundaryconditions,andcanbeeasilysolvedwithlowercomputationalcosts.1792MICROWAVEANDOPTICALTECHNOLOGYLETTERS/Vol.56,No.8,August2014DOI10.1002/mop