A Negative-Refractive-Index Metamaterial for Incident Plane Waves of Arbitrary Polarization

ANegative-Refractive-IndexMetamaterialforIncidentPlaneWavesofArbitraryPolarization

LoïcMarkley,StudentMember,IEEE,andGeorgeV.Eleftheriades,Fellow,IEEE

Abstract—Inthisletter,aleft-handedartificialdielectricisproposed.Usingresonatingbroadsidecoupledpatchestogen-erateanegativepermeabilityandthinstripstogeneratenegativepermittivity,anegativeindexofrefractionthatismatchedtofreespacecanbedesigned.Thestructureisfabricatedfromasingledielectricsheetprintedonbothsidesbymetalpatternsthatcoupletoexternallyincidentplanewavesofanylinearpolarization.Unlikemanypreviouslypublishedstructures,thewavesinteractthroughperpendicularincidencetothesurface.Anexperimentwascarriedoutat10GHztoverifytheleft-handedbehaviorwithanextractedindexofrefractionof1.04matchedtofree-spacewith26.0dBreturnlossand0.77dBinsertionloss.Amultilayerversionwasalsodesignedthatachievedfractionaldispersionbandwidthscomparabletothoseoftransmission-lineimplementations.

IndexTerms—Left-handedmedia(LHM),negativepermeability,negativepermittivity,negativerefractiveindex,polarizationindependence.

Fig.1.Proposedstructure’sunitcell(explodedview).

I.INTRODUCTION

VERsinceVeselagotheorizedthataleft-handedmedium(LHM)wasimpliedfromthepresenceofsimultaneouslynegativepermeabilityandpermittivity[1],scientistsanden-gineershavestrivedtomakeonephysicallyrealizable.Negativestructureshavelongbeenwellunderstoodbutitwasnotuntildevelopmentsweremadeintheareaofartificialmagneticma-terials[2]thatanegative-refractive-index(NRI)structurewassuccessfullyconstructedandtested[3].

TheLHMof[3]usedthinwiresplacedparalleltotheelec-tricfieldandsplit-ringresonators(SRRs)alignedwiththemag-neticfieldtogenerateanNRImedium.DrawinganalogieswithNRItransmission-linetheory[4],thewiresactasshuntinduc-torswhiletheSRRsmutuallycoupletothehostmediumse-riesinductanceinsuchawayastoproduceaneffectiveseriescapacitance.

ThisletterintroducesanalternativeNRI(LHM)structurethatcouplestoincidentplanewavesfromfreespaceatadesignfre-[5].AlthoughitderivesfromtheSRRquencyof

andthin-wiremechanisms,unlikethestructurein[3]thatisdesignedsuchthattheelectromagneticwavestravelalongtheplanesoftheprintedboards,thisletter’sproposedstructurere-quiresonlyasinglethindielectricsheetplacednormaltothe

Fig.2.Transmission-lineequivalentcircuit.

E

directionofpropagation.Fullyprintable,thisstructuredemon-stratesagreatlysimplifiedfabricationprocedureandfurther-more,duetothestructure’shighsymmetry,itisresponsivetoeverytypeoflinearpolarization.Itmustbenotedthatthepro-posedtopologyhasastructuralsimilaritytothe“fishnet”designintroducedin[6]butgiventhatitoperatesatmicrowavefrequen-cies,itcannotutilizethesurfaceplasmawaveeffectsfromtheopticalregimetoobtaintheNRIresponse.In[7],asimilarcon-ceptwasindependentlydevelopedalsoatmicrowavefrequen-ciesbutonlyforasinglepolarizationandcharacterizedonlyfornormalincidence.Moreover,inthisletteramultilayerversionofthisNRImetamaterialisintroducedwhoseunderlyingtransmis-sion-lineeffectallowsthefractionaldispersionbandwidthtobeextendedsignificantlyabovethatofthesingle-layerstructure.

II.PROPOSEDGEOMETRY

Theproposedstructure’sunitcellisillustratedinFig.1withtheequivalentcircuitinFig.2.Thestructureisformedfroma

anddielectricconstantdielectricslabofthickness

printedidenticallyonbothsideswitha17metal

layer.Themetallizationpatternhasaunitcellofdimension

andcanbedeconstructedintoanarrayofsquarepatches

andanarrayofthinstripsofwidthofwidth

.

Thethinstripsalignedwiththeelectricfieldprovideanegativethroughtheadditionofashuntinductancetothetransmission-linemodel(seeFig.2).Analyzedin[8]and[9],the

ManuscriptreceivedNovember3,2006;revisedDecember5,2006.

TheauthorsarewiththeDepartmentofElectricalandComputerScience,UniversityofToronto,Toronto,ONM5S3G4,Canada(e-mail:gelefth@waves.utoronto.ca).

DigitalObjectIdentifier10.1109/LAWP.2007.890758

1536-1225/$25.00©2007IEEE

MARKLEYANDELEFTHERIADES:NEGATIVE-REFRACTIVE-INDEXMETAMATERIAL29

effectivecanbeexpressedby(1),where

isthe“plasmafrequency”oftheeffectivemediumwiththeper-unit-lengthinductanceofasingleisolatedwireandandthewirespacingsalongthetwoaxesorthogonaltothewireaxis.Theadditionofasecondsetofstripsperpendiculartothefirstprovidesanequalresponsetoalllinearelectricfieldpolarizations.

(1)

TheseriescapacitancenecessarytoachievenegativearisesfromthesamemechanismasforSRRswithcapacitivelyloadedconductingloopscouplingtothemagneticfield,asshowninFig.2.Theexpressionfortheeffectiveisgivenby(2),where

istheloopresonantfrequency,is

apositivescalingquantitylessthanunity,isthelooparea,istheloopvolumedensity,istheloopinductance,andistheloopcapacitance.

(2)

Thebroadsidecoupledpatchesarelinkedbyfringingcapac-itanceateachedge,completingaconductingpathforthecur-rentinducedbythemagneticfield.Thisissimilarinnaturetoideaspresentedin[10]forplasmonicnanowiremedia.Lumpedcapacitorscanbeusedtoenhancethefringingcapacitanceandreducetheunitcellsizebutatthecostofincreasedmanufac-turingcomplexity.

III.SIMULATIONRESULTS

IftheLHMstructureistreatedasahomogeneousdielec-tricslab,theeffectiveand

canbeextractedfromthetwo-portscatteringparameters.UsingAnsoft’sHFSSfinite-el-ement-methodsoftwarepackage,oneunitcellofthisstructurewassimulatedinsideanidealparallel-platewaveguideandthecomplexreflectionandtransmissioncoefficientsmeasured.Themethodoutlinedin[11]and[12]detailshowtheeffectiveindexofrefractionandrelativecharacteristicimpedanceofthestructurecanbecalculatedandfromthem,andextracted.Homogeneityisjustifiedbytreatingthemetamaterialslabasa“blackbox”andobservingthatthephase-shiftthroughitforanincidentplanewavewillbeindistinguishablefromthatofahomogeneousslabhavinganequivalentindexofrefraction.Combiningthethin-wirestructurewiththepatchstructurein-troducedmutualcouplingthatshiftedtheresponsesofandfromthepreliminarysimulationswheneachwasexaminedwithouttheother.Thepresenceofthepatchesdecreasedthein-ductanceofthewiresbyreducingthecirculatingmagneticfluxwhilethewiresloweredthepatchresonancebyincreasingthecapacitivecouplingbetweenadjacentunitcellpatches.Further-more,thissamecapacitanceincreasedtheeffectivewithfre-quencywhilearesonance-antiresonancecouplingwasobservedatthepatchresonantfrequencygivingrisetoaregionwheretheimaginarycomponentofwaspositive.Thislasteffectisaphysicallyunrealisticresultthathasbeenobservedbefore[13]andhasbeenattributedtothelongeffectivewavelengthcloseto

Fig.3.Extracted󰀏and󰀖fornormallyincidentwavesofhorizontal(lines)anddiagonal(markers)polarizations.Atthedesignfrequency󰀏=01:03and󰀖=0the1:diagonally00forthehorizontallypolarizeddata.

polarizeddataand󰀏=01:04and󰀖=01:01forFig.4.Extractednandscatteringparametersfornormallyincidentwavesofhorizontal(lines)anddiagonal(markers)polarizations.Atthedesignfrequencynzontally=01polarized:01with43.1datadBandreturnn=0loss1:03andwith0.0042.6dBdBinsertionreturnlosslossforandthe0.00hori-dBinsertionlossforthediagonallypolarizeddata.

theresonancecondition.Byfine-tuningthegeometricalparam-eters,aneffective

wassuccessfullydesignedusingthephysicalthicknessofthestructureastheeffectivethicknessoftheextractionprocedure.TheeffectiveparametersareplottedversusfrequencyinFigs.3and4.

TheunitcellofFig.1wasdesignedwithahighdegreeofsymmetryinordertoprovidecompletepolarizationindepen-denceatnormalincidence.Thispropertywasverifiedwithin1%numericalerrorbyilluminatingthestructurebyaplanewave

asinFig.5(a)andcomparingtheresultsfrom

and.A.LossandOff-NormalAnalyses

Sinceallpreviousresultswerebasedonlosslessmaterials,thestructurewasre-simulatedwitharealisticlossyRT/Duroid

dielectric(losstangent

)withcoppermetallization(conductivity).Thenewextractedeffec-tiveindexofrefractionandscatteringparametersaresuperim-posedonthelosslessparametersinFig.6.Notethatalthoughtherealpartofisbarelychangedat,animaginarycompo-nentisintroducedtoaccountforthe10%totallossinpower.

30Fig.5.(a)Variablepolarizationsetup.(b)Off-normalplanewavesetup.

Fig.6.Extractednandscatteringparametersforthelossless(lines)andlossy(markers)designs.Atthedesignfrequencythelossystructurehasann=00:980j0:10with32.8dBreturnlossand0.47dBinsertionloss.

Fig.7.Extractednandscatteringparametersfortheoff-normaldesignunderTEpolarization.

Thiscanbecomparedtothepatchresonancelossof26%at

wherethecurrentscirculatingthroughthepatch

loopsarehighest.Theoperatingfrequencyisfarenoughawayfromthisresonancepeakthatthemagneticresponselossesaresignificantlyreducedandthepermittivitylossesdominate.Thesubsequentsimulationsexaminedtheeffectoftiltingtheincidentplanewavetooff-normalincidenceasshowninFig.5(b).Thetransverse-electric(TE)modewasexamined

underincidenceanglesrangingbetween

withtheresultsdisplayedinFig.7.Althoughthestructurebecamemismatchedtofreespaceatincreasinglyoff-normalincidence,theeffectiveremainednegativeasitdroppedtoat.Theinversionalgorithmusedtoextracttheeffectivesimplemediumindexofrefractionwasderivedalongthelinesofthederivationin[11].Theanisotropicnatureoftheproposedstructureinwhichonlytheandcomponentsoftheandtensorsarenegativeimpliesthatnegativerefractionatoff-normalanglesonlyoccurswiththepropagationvector,andnotthePoyntingvector.Thismeansthattheeffective

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Fig.8.(a)Unitcellforthemultilayerstructureillustratingthealternatingpatchandwiremetallayers.(b)DispersiondiagramforthemultilayervariationoftheproposedNRIstructure.

indexofrefractionrefersonlytoaphaseadvance.Moreover,atoff-normalangles,polarizationindependenceoftheindexforTEandtransverse-magneticpolarizationscouldbeachievedas

longasthetensorcomponentsandwereequal.B.ExtensiontoaMultilayerStructure

Thestructureexaminedthusfarisasingle-layerimplementa-tionthatdoesnothavetheflexibilitytobeusedinapplications

requiringthickerNRImedia.Althoughthecurrentsingle-layerstructurecanbeformedintoamultilayermediumifthelayersarespacedby2.5-mmairgaps,theNRIregionbandwidthdropsto2%andtheoperatingfrequencyispushedclosertothelossyresonance.

Byincreasingthewirespatialfrequencytoensuretheoverlapbetweenthenegativeandregions,thelayerswerestackedcontiguouslytoproducea47%fractionalNRIbandwidth.Thiswasasignificantimprovementoverthe4%bandwidthofthesingle-layerstructureandwasaconsequenceofthecloselycou-pledpatchresonatorswhichcombinedwiththewirestoformatrueNRItransmission-linemedium[4].

Ontheotherhand,tooptimizethematchingtofreespaceandensureindependenceoftheeffectiveparametersoverthetotalslabthickness,thewireandpatchpatternswereseparatedintoalternatingmetallayersasshownindetailinFig.8(a).Theunitcellwidth,thickness,anddielectricconstantwereunchangedfromtheinitialproposedsingle-layerstructure,butthemetal

geometryparameterswerechangedto

and.

Fig.8(b)presentsthedispersiondiagramfortheresultingmultilayerstructurewithimprovedmatchingtofreespace.Aneigenmodesimulationontheunitcellconvergedat10GHztoabackward-wavemodewithafractionalbandwidthof19%.Theextracteddatafromaone-layerscatteringparameteranal-ysisisplottedonthesamegraphwithabackward-wavemodeoccurringoverroughlythesamefrequencyrangeasfortheeigenmodedata.Thematchingcapabilityofthisstructurewasdemonstratedbytuningtheone-layergeometryuntilareturnlossof30.7dBwasreachedat10GHz.

IV.MEASUREMENTRESULTS

Inordertocarryouttheexperimentalmeasurementsonthesingle-layerstructure,a1515unitcellsamplewasfabricated

MARKLEYANDELEFTHERIADES:NEGATIVE-REFRACTIVE-INDEXMETAMATERIAL31

Fig.9.Free-spacetwo-portS-parametermeasurementapparatus.

Fig.10.Extracted󰀏and󰀖fromtheexperimentaldataforhorizontalpolar-ization(lines)anddiagonalpolarization(markers).Attheoperatingfrequency,󰀏and=󰀏0=1:0011:013j00:28j0:26andand󰀖=󰀖=010:070:9900j0j:007:11forforthethehorizontaldiagonalpolarization.

polarizationusinganLPKFProtoMatH100millingmachine.Thesubstrateusedwasa100-milRogersRT/Duroid6010LMwithhalfouncecoppercladdingoneachside.Thefirstconstructedsampleex-hibitedaneffectivethin-wireplasmafrequencybelowthede-signfrequencyandsoanadditionalsamplewasfabricatedusing

awirethicknessof

andapatchsizeof.Thisiterativeprocesswasnecessarytofine-tunethe

geometrytothedesignobjectives.

TheexperimentalsetupincludedtwoATMX-bandstandardgainhornantennaswith8inchbiconvexRexolitelensestofocusthebeamthroughthesample(seeFig.9).AnAgilentE8364Bnetworkanalyzercalibratedusingafree-spaceTRLmethodmeasuredthetwo-portscatteringparameterswhichwerein-vertedtoextracttheconstitutiveparameters.

ThedatainFigs.10and11confirmexperimentallytheproposedNRIbehaviorattheoperatingfrequencyof

.Thepermeabilityandpermittivityexhibitthe

expectedresonanceandplasmonicresponses,combiningtoprovideanegativeindexofrefractioncloseto1andwellmatchedtofreespace.Theadditionallossesincurredduringtheexperimentcanbelargelyattributedtotheuseofthebulkconductivityofcopperinsimulationswhichdoesnotaccountforsurfaceroughnesseffects[14].Ignoringtheheavyburringalongtheedgesofthecoppertracesandtheroughnessintro-ducedbythemillingprocess,the1.9

roughnessgivenbythesubstratedatasheetraisestheinsertionlossto0.63dB.

V.CONCLUSION

AnNRImediumthatcancoupletoexternallyincidentplane

waveshasbeensuccessfullydemonstrated.Negative

wasFig.11.Extractednandscatteringparametersfromtheexperimentaldataforhorizontalpolarization(lines)anddiagonalpolarization(markers).Attheop-eratingfrequency,n=01:040j0:17with26.0dBreturnlossand0.77dBinsertionlossforthehorizontalpolarizationandn=01:060j0:18with26.9dBreturnlossand0.84dBinsertionlossforthediagonalpolarization.

achievedthroughcapacitivelyloadedconductingloopsimple-mentedasresonatingbroadsidecoupledpatches,whilenegative

arosefromthinstriparrays.Thestructurewasdesignedtoproduceanindexofrefractionofmatchedtofreespacewithareturnlossof43.1dB.Varyingthepolarizationangledidnotaffectorthematchingwhileintroducinglossesonlyraisedtheinsertionlossto0.47dB.Sweepingtheinci-denceanglefromnormalto

off-normalreducedtherefractiveindexto

whileraisingthemismatchto8dBreturnloss.

Amultilayervariationofthisstructurewasalsodesignedandsimulatedwithabackward-wavemodeat10GHzcoveringafractionalbandwidthof19%andexhibitingacharacter-isticimpedanceneartothatoffree-space.Theextendedbandwidthofthemulti-layerstructurecanbeattributedtoatransmission-lineeffectwhichtakesplacebecausethepatchresonatorsarecloselycoupledtogetherintandem.

Asamplesingle-layerstructurewasconstructedandtheNRIpropertiesexperimentallyverifiedwithafree-spacescatteringparametersetup.Themeasurementdatawasanalyzedtoyield

anextracted

matchedwith26.0dBreturnlossand0.77dBinsertionloss.Withafullyprinteddesignusingasingledielectricsheet,thisstructureisverysimpletofabricateandprovidesanalternativeimplementationtotheLHMsfoundintheliteraturetoday.

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