Development of bulk optical negative index fishnet meta materials - PDF document

INVITEDPAPERDevelopmentofBulkOpticalNegativeIndexFishnetMetamaterials:AchievingaLowLossandBroadbandResponseThroughCouplingJasonValentineShuangZhangThomasZentgraf,andXiangZhangInthispaper,wediscussthedevelopmentofabulknegativerefractiveindexmetamaterialmadeofcascadedfishnettstructures,withanegativeindexexistingoverabroadspectralrange.Wedescribeindetailthedesignofbulkmetamaterials,theirfabricationandcharacterization,aswellasthemechanismofhowcouplingoftheunitcellscanreducelossinthematerialthroughanopticaltransmission-lineap-proach.Duetotheloweredloss,themetamaterialisabletoachievethehighestfigureofmerittodateforanopticalnega-tiveindexmetamaterial(NIM)intheabsenceofgainmedia.Theincreasedthicknessofthemetamaterialalsoallowsadirectobservationofnegativerefractionbyilluminatingaprismmadeofthematerial.Suchanobservationresultsinanunam-biguousdemonstrationofnegativephaseevolutionofthewavepropagatinginsidethemetamaterial.Furthermore,themetamaterialcanbereadilyaccessedfromfreespace,makingitfunctionalforopticaldevices.Assuch,bulkopticalmetama-terialsshouldopenupnewprospectsforstudiesoftheuniqueopticaleffectsassociatedwithnegativeandzeroindexmaterialssuchasthesuperlens,reversedDopplereffect,back-wardCerenkovradiation,opticaltunnelingdevices,compactresonators,andhighlydirectionalsources.KEYWORDSMetamaterials;nanoscalematerials;negativeindex;opticsSincetheinceptionofnegativeindexmetamaterials(NIMs)inthemicrowaveregion[1],[2]therehasbeenaconstantdrivetolowertheoperatingwavelengthintotheopticalregime[3]–[5].Anegativerefractiveindexisnotexhibitedinnaturallyoccurringmaterialsduetolackofahigh-frequencymagneticresponse.Theabilitytotuneboththepermeabilityandpermittivityofamaterialallowsscientists,forthefirsttime,tofullyexploretheparameterspaceofelectromagneticproperties.Achievingamaterialwithanegativerefractiveindexatopticalfrequenciesisperhapsthemostchallengingimplementationofthemetamaterialconceptasitrequiresengineeringboth ManuscriptreceivedJuly21,2010;revisedSeptember23,2010;acceptedOctober31,2010.ThisworkwassupportedbytheU.S.ArmyResearchOffice(ARO)MURIprogram50432-PH-MURandinpartbytheNationalScienceFoundation(NSF)Nano-ScaleScienceandEngineeringCenterCMMI-0751621.J.ValentinewaswiththeNationalScienceFoundation(NSF)Nano-ScaleScienceandEngineeringCenter(NSEC),UniversityofCaliforniaBerkeley,Berkeley,CA94720USA.HeisnowwiththeMechanicalEngineeringDepartment,VanderbiltUniversity,Nashville,TN37240USA(e-mail:jason.g.valentine@vanderbilt.edu).S.ZhangwaswiththeNationalScienceFoundation(NSF)Nano-ScaleScienceandEngineeringCenter(NSEC),UniversityofCaliforniaBerkeley,Berkeley,CA94720USA.HeisnowwiththeSchoolofPhysicsandAstronomy,UniversityofBirmingham,Edgbaston,BirminghamB152TT,U.K.(e-mail:s.zhang@bham.ac.uk).T.ZentgrafiswiththeNationalScienceFoundation(NSF)Nano-ScaleScienceandEngineeringCenter(NSEC),UniversityofCaliforniaBerkeley,Berkeley,CA94720USA(e-mail:zentgraf@me.berkeley.edu).X.ZhangiswiththeNationalScienceFoundation(NSF)Nano-ScaleScienceandEngineeringCenter(NSEC),UniversityofCaliforniaBerkeley,Berkeley,CA94720USAandalsowiththeMaterialSciencesDivision,LawrenceBerkeleyNationalLaboratory,Berkeley,CA94720USA(e-mail:xzhang@me.berkeley.edu).DigitalObjectIdentifier:10.1109/JPROC.2010.2094593ProceedingsoftheIEEE0018-9219/$26.002011IEEE negativepermeabilityandpermittivityinthesamespectralregion.However,suchamaterialcouldleadtoanumberofnewopticaldevicessuchassuper-resolutionlenses[6]andhighlydirectionalsources[7].Theopticalregimeisalsoparticularlyinterestingduetothepresenceofseveralat-tractiveareasofapplicationofsuchdevicesincludingtele-communications,biologicalimaging/sensing,andlithography.However,therehavebeenbothfundamentalandengineeringchallengesinscalingsuchmetamaterialstoopticalwavelengths.Onafundamentallevel,thein-creasedlossandpenetrationdepthinmetalsatopticalfre-quenciescausesmetamaterialstoabsorbalargeproportionoftheincidentlight.ThisabsorptionisfurtherincreasedbytheresonantnatureofmostNIMs.Anotherfundamentalchallengearisesfromthefactthatatshortwavelengths,westarttoapproachtheplasmafrequencyofmetals,causingsaturationinthemagneticresponseofthestructure[8],[9].Assuch,thefigureofmerit(FOM)foropticalnegativeindexmetamaterialsisdefinedasdescribesthenumberofoscillationsthatlightundergoesinsidethematerialbeforebeingabsorbed[10].Despitethepreviousdemonstrationsofopticalnegativeindexmetamaterials[3]–[5],amonolayerofunitcellsalongthepropagationdirectiondoesnotallowtheinvestigationoftheinterestingphysicsassociatedwithnegativephasepropagation.Thickmaterialsarehighlydesirablesothattheoverallgeometryofthematerialcanbeusedtomanipulatelightpropagationsuchasinalensorprism[11].Theseeffectsaredirectlyconnectedtotheshapeofthesurfaceandthepropagationlengthfordifferentspatialpathsofthebeam.Foramonolayerorathinfilmitissimplynotpossibletoformathickobjectsuchasalenstomanipulatetheflowoflight.However,ontheengineeringlevel,itbecomesdifficulttofabricatethickmetamaterialswiththeproperdimensionalityatopticalfrequencies.Forinstance,atsuchshortwavelengths,nanoscaleimperfectionsareatthescaleoftheincidentradiation,causingscatteringlossandreducedmaterialperformance.Thischallengingscalelevelalsomakesitdifficulttofabricatethickmetamaterialswhilemaintainingtherequisitenanoscaleunitcellgeometries.AmongthemostpopulardesignsofopticalNIMsisthethestructure.Thefishnetcanbethoughtofasacombinationoftwoseparateconstituents,whichallowthepermeabilityandpermittivityofthestructuretobeengineeredindependently[12].Thefirstcomponentofthefishnetmetamaterialisthickmetallicstripsorientedalongthedirectionofmagneticfieldoftheincominglightwhichareseparatedbyadielectriclayer[Fig.1(a)].Thisstructurefunctionsasaninductorandcapacitorresonatorwhereinantisymmetriccurrentsarecreatedinthemetalstrips,whichgiverisetoaninducedmagneticpolarizationinthestructure[Fig.1(e)].Thisprovidesamagneticresponse,orartificialpermeability,thatcanachievenegativevaluesnearreso-nance.Thesecondconstituentconsistsofthinmetallicwiresorientedinthedirectionoftheelectricfieldoftheincominglight[Fig.1(b)].Thesewiresfunctionasadilutedmetalwithdecreasedplasmafrequency,providinganegativeeffectivepermittivitythatcanbeengineeredseparatelyfromthepermeability.Thesetwoconstituentsarecombinedtoformthefishnetmetamaterialwhereboththenegativeperme-abilityandpermittivitycanbeengineeredataparticularwavelength[Fig.1(c)and(d)].Analternativeexplanationofthenegativerefractionarisingfrommultilayerfishnetmetamaterialsisbasedonthespoofplasmon[13]supportedbyeachperforatedmetallicfilm[14],[15].Whileitdescribestheidenticalresponseastheconstituentmodel,thespoofplasmonmodelcanprovideadditionalinsightintotheunderlyingphysics.Itisfoundthatthecouplingofthespoof Fig.1.Fishnetmetamaterialschematicshowingasinglefunctionallayer(metal/dielectric/metal)(a)and(b)schematicsoftheseparateconstituentsofthemetamaterialwhichprovideboth(a)magneticand(b)electricresponse.Thegraylayersaremadeofmetalandthegreenlayeradielectric.Combined(c),theseconstituentsformthecompletefishnetstructure.(d)Unitcellgeometryofthemetamaterial.(e)Depictsthecircuitandcurrentloopthatformthemagneticresponseinthefishnetmetamaterial.Valentineetal.:DevelopmentofBulkOpticalNegativeIndexFishnetMetamaterialsProceedingsoftheIEEE plasmonleadstoanegativedispersionoveracertainfrequencyrange.Inthissense,multilayerfishnetmetama-terialseffectivelyfunctionasa3-Dplasmoncrystal,whereintheaperturesplayanimportantroleindeterminingthespoofplasmondispersion,couplingtheincidentlightintoplasmonmodes,andmediatingthecouplingamongdifferentperforatedmetallayers.Thisalternativeviewshowsthecrucialrolethatthesurfaceplasmonsplayinachievingnegativerefraction.Itisalsoimportanttonotethatwhiletheelectricfieldoflightismainlyconcentratedintheairvoidsofthefishnetmetamaterial,themagneticfieldisconcentratedwithinthemetal/dielectricstack.Thespatialseparationoffieldconcentrationisduetothestrongmagneticresponseofthestructureanddistinguishesitfromawaveguidearraywhereinboththeelectricandmagneticfieldsareconfinedintheairapertures.Thehighestfigureofmeritforasinglefunctionallayerofthefishnetstructure(onemetal/dielectric/metallayer)thathasbeenexperimentallyobtainedis3.0atawave-lengthof1.5m[16].Thefishnetmetamaterialhasalsobeensuccessfulatscalingtheresponseintothevisiblere-gion,however,suchstructuressufferfromconsiderablelossandalowFOM[17],[18].Theshortestwavelengththatthenegativeindexfishnetmetamaterialhasbeendemon-stratedis580nm,whereaFOMof0.3wasachieved[17].Here,wewilldiscusshowbulkmetamaterials,andinparticularthebulkfishnetmetamaterial,canincreasetheFOMofNIMs[19].Thisispossiblebyintroducingstronginteractionsbetweenthelayersintheformofmagneto-inductivecouplinganddestructiveinterferenceofsurfacecurrents.Wewillalsodemonstratehowaprismofthisthickmetamaterialcanbeusedtovisualizeandmeasuretheindexofrefraction.II.BULKFISHNETMETAMATERIALItisimportanttobeginbydefiningwhatabulkmeta-materialentails.Thedefinitionofbulkpropertieshasbeenwellestablishedinsolidstatephysics.Here,theconver-genceofthematerialpropertiesisrequiredfordefiningbulkkaswellastherequirementthatthesurfaceatomiclayersdonotaffecttheoverallpropertyofthesystem.Awell-knownexampleistheintenselystudiedtopicofgraphene.Bilayergraphenehasdifferentpropertiesfromamonolayerbecauseoftheinteractionbetweenthelayers.Byaddingmorelayers,thepropertiesofthemultilayergraphenegraduallyconvergewhereinafteracertainnumberoflayersitcanbecalledgraphite..Graphite,therefore,hasdifferentpropertiesfromthesingle-layergraphene.Likewise,ametamaterialmustalsobeheldtothisstandardtobedefinedasbulk.Inaddition,itisonlystrictlymeaningfultoassignpropertiesofabulkmaterialwhentheeffectivepropertiesarenotalteredbytheenvi-ronment.Asingleorafewfunctionallayersoffishnetmetamaterialscannotbeconsideredasbulksinceitspropertiesaresignificantlyaffectedbythesubstrate.Instackingfunctionallayersofametamaterial,thelayerscanbeeitherweaklycoupled[Fig.2(a)]orstronglycoupled[Fig.2(b)][20].Intheweaklycoupledcase,thelayersarespacedfarenoughawaythattheyhavelittleinteractionwithoneanother.Inthiscase,thepropertieswillconvergequicklyandthemetamaterialwillessentiallyhavethesamepropertiesasasinglelayer.Thisismorelikeagasphasesystem,wheretheinteractionsamongmoleculessarenegligible.Inthestronglycoupledcase,thefunctionallayersarestackedatclosespacing,introducingstrongcouplingbetweenthelayers.Suchastructuremayrequireseverallayerstoconvergetothebulkpropertiesofthemetamaterial,however,additionalbenefits,suchasloweredlossandincreasedbandwidth,canbeobtained.Thisstronglycoupledcaseissimilartotheconceptofatransmissionlineinthemicrowaveregion[21]–[23].Suchtransmissionlineshavesuccessfullyproventogiveanonresonantbasednegativerefractiveindexwithlowlossforthetransmissionofelectromagneticwaves.Itisalsowellknownthatthetransmissionlinepropertiescannotbethesameasasingleunitcell,whichisaresonantstructure.Thisstronglycoupledstructurewithconvergedpropertiesiswhatisreferredtoasabulkmetamaterialinthisreport.Overthepastseveralyears,researchershavemadeprogressinachievingbulkpropertiesformetamaterialsatopticalwavelengths.Inparticular,fishnetmetamaterialswiththreeandfivefunctionallayers[24],[25]havebeenrealizedaswellassplitringresonatormetamaterialswithuptofourlayers[26].Inallthesereports,ashiftintheopticalpropertieswithanincreasednumberofstackinglayersisevident;however,aconvergedindexisnotdemonstrated.Therehavealsobeenrecentreportsonanisotropicmaterialsthatexhibitnegativerefractionatopticalfrequenciesduetoahyperbolicdispersionrelation[27],[28].Whilethesematerialscanbemadeconsiderablythick,ontheorderoftensofmicrometers,theydonotpossessanegativerefractiveindexduetothelackofnegativephasepropagation.III.METAMATERIALDESIGNToacquireaclearunderstandingofthebulkmetamaterial’sopticalresponse,simulationswereperformedwitharigorouscoupledwaveanalysis(RCWA).RCWAexpands Fig.2.Schematicofweaklyandstronglycoupledmetamaterials,shownherewiththreefunctionallayers.(a)Weaklycoupledmetamaterial.(b)Stronglycoupledmetamaterial.Valentineetal.:DevelopmentofBulkOpticalNegativeIndexFishnetMetamaterialsProceedingsoftheIEEE theelectromagneticfieldintoanumberofdiffractionordersandmatchestheboundaryconditionsateachinterface.Thefishnetwasdesignedtoachieveanegativerefractiveindexaround1.5m.Silver(Ag)andmagnesiumfluoride(MgF)wereusedasthemetalanddielectric(grayandgreeninFig.1,respectively).AgwaschosenduetoitsrelativelylowintrinsiclossesatopticalfrequencieswhileMgFwaschosenduetoitssmoothfilmqualityandeaseofdeposition.Thedimensionsofthestructure,correspondingtoFig.1(d),are:860nm,565nm,265nm,30nm,and50nm.Thefunctionallayersarestackeddirectlyontopofoneanotherandtherefractiveindexwascalculatedfordifferentnum-bersofstackedfunctionallayers(Fig.3).Theindexwasfoundbycalculatingthecomplextransmittanceandreflec-tanceusingRCWAwith1313diffractiveordersandsolvingfortheFresnelequation:cosÞ¼ð.Itcanbeseenthatafterstackingthreefunctionallayers,theindexiswellconvergedtothebulkvalueofthemetamaterial.Thisconvergenceisalsoobservedfortheimaginarypartoftherefractiveindexandrepresentsacol-lapsetothesingularBlochmodeindexofthematerial[29].Tobetterunderstandthemicroscopicresponseofthebulkfishnetstructure,finitedifferencetimedomain(FDTD)simulationswereperformed.Inallsimulations,ameshsizeof10nmwasemployed.First,thecascadingofthelayersleadstoastrongmagneto-inductivecouplingbetweenneighboringfunctionallayers,asdeducedfromthecircuitdiagraminFig.4(b).ThetightcouplingbetweenadjacentL-Cresonatorsthroughmutualinductanceresultsinabroadbandnegativeindexofrefractionwithlowloss,whichissimilartothematerialresponseofleft-handedtransmissionlines.Inaddition,thelossisfurtherreducedduetothedestructiveinterferenceoftheantisymmetriccurrentsacrossthemetalfilm,effectivelycancelingoutthecurrentflowinthecenterofthefilm.InFig.4(c),itcanbeobservedthattheelectricfieldonthetopandbottomsurfaceisantisymmetricleadingtothecancellationofelectricfieldinthemiddleofeachmetallayer.Aswewillsee,thedestructiveinterferenceofthefieldalongwiththemagneto-inductivecouplingwillleadtogreatlyreducedlossandincreasedFOMinthebulkfishnetmetamaterial.IV.Oneofthelargestchallengesinrealizingthebulkfishnetstructureisfabricatingathickstructurewithhighaspectratio.Previoussingle-layermetamaterialshavebeentypicallyfabricatedusingelectronbeamlithography(EBL)andaliftoffprocess.Whilethisprocessisidealforthinfilms,itisdifficulttofabricatehighaspectratiostructures.Tomakehigheraspectstructures,onehastoperformmultipleexposure/deposition/liftoffstepswhereeachsubsequentexposuremustbealignedtothefirst.UsingmultiexposureEBL,researchershavemadeprogressfabricatingthickeropticalNIMswithuptofivefunctionallayershavingbeendemonstrated[25].However,thickermaterialsbecomeincreasinglymoredifficulttofabricateduetotheaccumulationofinaccuraciesinthealignmentofthelayers.Itisalsoextremelytimeconsumingtorepeattheprocessmultipletimes. Fig.3.Refractiveindexversusnumberoffunctionallayers.Whilealargeshiftisseenwhenincreasingfromtwotothreelayers,subsequentthicknessincreaseshavenoeffectontheindex,indicatingthatthebulkvaluehasbeenreached. Fig.4.Consequencesofcoupledlayersinthebulkfishnetmetamaterial.(a)Schematicofathree-functional-layerfishnetshowingthecross-sectiontakenin(b)and(c).(b)Depictionofthecascadedcircuitthatleadstothemagneticresponseofthestructure.Noticethatthecurrentflowonthetopandbottomsurfaceofthemetalisoutofphase.(c)ElectricfieldplotofthefishnetgeneratedwithFDTD.Itcanbeobservedthattheelectricfieldonthetopandbottomofthemetalsurfacesisoutofphase.Thisleadstothecancellationoftheelectricfield,andthuscurrent,insidethemetal,reducingthelossesthatoccurduetoabsorptioninthemetal.Valentineetal.:DevelopmentofBulkOpticalNegativeIndexFishnetMetamaterialsProceedingsoftheIEEE AsanalternativetoEBL,herewehaveemployedfo-cusedionbeam(FIB)milling,whichreliesontheselectiveremovalofmaterialratherthanadeposition/liftoffstep.Assuggestedbythename,themillingofthematerialisdonebyafocusedionsource,whichisusuallyaliquidmetal.Thefirststepistodepositthedevicematerial,whichisdonewithelectronbeamevaporation.ThesampleisthenplacedinsidetheFIBwhereabeamisrasteredintheareasofthefilm,whicharetoberemoved.TheprocessflowisconsiderablylesscomplicatedthanEBL,andfurthermore,iscapableofproducingfeatureswithhighaspectratios,enablingthickmetamaterialdeviceswithnoalignmentsteps.ThedrawbacksofFIBare:1)itisarelativelyslowprocesscomparedtoEBLand2)aportionofthemillingions,inthiscaseGallium,areultimatelyembeddedintothedevicematerial,whichintroducesextramaterialloss.Despitethesedisadvantages,thehighaspectratiosthatarecapablewithFIBmakeittheidealtooltoachieveabulkopticalNIM.Tocreatethebulkfishnetmetamaterial,amultilayermetal-dielectricfilmstackwasfirstdeposited.Themultilayerstackwasdepositedbyelectronbeamevaporationofalternatinglayersof30-nmAgand50-nmMgF.Thefinalstackconsistedof21layerswithatotalthicknessof830nmresultingintenfunctionallayers.Theunitcellofthefishnetstructurewasfabricatedwiththedimensionsoutlineearlier.Thenumberoffunctionallayerswaschoseninordertoestablishaconvergenceofrefractiveindex.Thelargethicknessalsoallowsaprismtobecreatedfromthemetamaterialaswillbediscussedlaterinthissection.Twodifferentconfigurationsofthefishnetsampleswerefabricatedonthemultilayerstack.Samplesofthefirstconfigurationconsistof2222in-planefishnetunitcellsandwereusedforthecharacterizationofthetransmittanceandFOM.Ascanningelectronmicroscope(SEM)imageoftheten-functional-layerstructureisshowninFig.5.Samplesofthesecondconfiguration,whichwereusedtomeasuretherefractiveindex,consistofaprismfabricatedonthemultilayerstack,withthenumberoffunctionallayersrangingfromoneononeside,totenontheotherside.TheprismwasformedbyplacingthesampleverticallyintheFIBchamberandthentiltingthesampleataspecifiedanglewithrespecttothefilmsurface,asseeninFig.6(a).Oncetheprismwasmilledintothesurface,thesamplewasremountedhorizontallyinthechamberanda10unitcellfishnetpatternwasmilledintotheprism.Anatomicforcemicroscope(AFM)andSEMimageofthefabricatedprismareshowninFig.6(b)and(c).TheexactangleoftheprismwasmeasuredwithAFMandwasfoundtobeslightlyvariedfordifferentsamples.OPTICALCHARACTERIZATIONANDNUMERICALSIMULATIONSToexperimentallydeterminetheindexofrefractionofthemetamaterial,measurementswerecarriedoutbyobservingtherefractionangleoflightpassingthroughtheprism,followedbyasimplecalculationusingSnell’sLaw.Law.Thisprovidesadirectandunambiguousdeterminationoftherefractiveindex,astherefractionangledependssolelyonthephasegradientthelightbeamaccumulatesfrompropa-gatingthroughdifferentthicknessesofthematerial.Intheexperimentalsetup,lightfromanopticalparametricoscillator(OPO)wasfocusedontotheprismusinganachromaticlens.Asecondachromaticlenswasplacedbe-hindthesamplewithanindiumgalliumarsenide(InGaAs) Fig.5.SEMimageofthe21-layerfishnetstructurewiththesideetched,showingthecrosssection.Theinsetshowsacrosssectionofthepatterntakenata45angle.Thesidewallangleis4.3andwasfoundtohaveminoreffectonthetransmittancecurveaccordingtosimulation.Insetreprintedfrom[19]. Fig.6.FabricationprocedureandSEMimageofthefishnetprism.(a)Tofabricatetheprism,themultilayerstackwasmountedverticallyintheFIBandaprismwasmilledatananglewithrespecttothesurface.(b)AFMimageoffabricatedfishnetprism.(c)SEMimageofafabricatedprismwitha1010unitcellfishnetstructuremilledintothesurface.Valentineetal.:DevelopmentofBulkOpticalNegativeIndexFishnetMetamaterialsProceedingsoftheIEEE infraredcameraplacedatthefocalpositioninordertoimagetheFourierplane[Fig.7(a)].Thepositionofthebeamatthesecondlens’sfocaldistancewasusedtocalculatetheangleofrefraction.Duetolimitedcameraimagingarea,onlythezero-orderFourierimagewasrecorded.Toobtaintheabsoluteangleofrefraction,awindowwithanareaequaltothatoftheprismwasetchedthroughthemultilayerstacktoserveasareference.Thewindow’sFourierimagewasmeasuredatallwavelengths,givingareferencepositioncorrespondingtoarefractiveindexof1.Thecentersofthebeamspotforboththewindowandprismsamplesweredeterminedbyfittingtherecordedintensitywitha2-DGaussianprofileandthetotalbeamshiftatthepositionofthesecondlenswasobtainedbytakingthedifferenceinthetwomeasuredbeamspotcenters.Snell’slaw,,wasthenusedtocalculatetherealpartoftherefractiveindexofthesample.Fig.7(b)depictsthemeasuredrefractiveindexofthe3-Dfishnetmetamaterialatvariouswavelengths.There-fractiveindexvariesfrom05at1200nmto34at1775nm.Therefractiveindexwasdeterminedfrommultiplemeasurementsoftwofishnetprismswithanglesofandforwavelengthsrangingfrom1200to1800nm.Theexpe-rimentalresultsarefoundtobeingoodagreementwiththetheoreticalpredictions[blacklineinFig.7(b)]basedonRCWA.Themeasurednegativerefractionangleisadirectresultofnegativephaseevolutionforlightpropa-gatinginsidethesamplecausedbyanegativerefractiveindex.ThisisillustratedinFig.8(a)and(b)byanumericalcalculationofthein-planeelectromagneticfielddistribu-tioninthefishnetprismatwavelengthsof1200and1763nmwherethestructureshowsapositiveandnegativeindex,respectively.Duetothenegativephasepropagationinsidethemetamaterial,theelectromagneticwaveemerg-ingfromthethickerpartoftheprismexperiencesphaseadvancecomparedtothatpassingthroughthethinnerparts,causingthelighttobendinthenegativedirectionattheexitinginterface.Thiscanbeseeninthetime-steppedimagesofthephasewithinthestructure.WhilephasepropagationisinthedirectionofthePoyntingvectorwhentheindexispositive,itisoppositeatnegativeindices.Wenotethattherefractiveindexremainsconsistentforthe Fig.7.(a)Geometryschematicoftheanglemeasurement.correspondstothepositiondifferenceofthebeampassingthroughawindowinthemultilayerstructureandprismsample.Bymeasuring,theabsoluteangleofrefractioncanbeobtained.(b)Measurementsandsimulationofthefishnetrefractiveindex.Therounddotsshowtheresultsoftheexperimentalmeasurementwitherrorbars(standarddeviation,measurements).ThemeasurementagreescloselywiththesimulatedrefractiveindexusingtheRCWAmethod(blackline).Reprintedfrom[19]. Fig.8.FDTDsimulationsoflightpassingthroughthefishnetprism.(a)Simulationofthein-planeelectricfieldcomponentfortheprismstructureat1200nmwhentheindexispositive.Positivephasepropagationresultsinapositiverefractionangle.(b)Thein-planeelectricfieldcomponentfortheprismstructureat1763nmshowingthephasefrontofthelight.Negativephasepropagationresultingfromthenegativerefractiveindexleadstoanegativerefractionangleasmeasuredbythebeamshiftintheexperiment.Thebottomfiguresshowacloseupofthetimeevolutionofthefielddistributionintheunitcellforbothapositiveandnegativeindexofrefraction.Valentineetal.:DevelopmentofBulkOpticalNegativeIndexFishnetMetamaterialsProceedingsoftheIEEE fishnetmetamaterialwiththreeormorefunctionallayersalongthepropagationdirection,whichleadstoauniformwavefrontexitingtheprism.Allrefractiveindexmea-surementsofthefishnetareperformedatnormalinci-denceasthemetamaterialisinherentlyanisotropic.Atlargeincidentangles,thenonlocaleffectsbegintodomi-natetheresponseduetothetransverseperiodicityofthematerial[30].Inaddition,transmittanceandreflectancemeasure-mentswereperformedonthebulkfishnetmetamaterialinordertocalculatetheFOM.ThesampleconsistedoftenfunctionallayersandwasmeasuredusingaFouriertrans-forminfraredmicroscope(NicoletNic-PlanIRmicro-scope).Thematerialloss[i.e.,]isconservativelyestimatedfromthemeasuredtransmittanceandreflec-tancedatabyassumingasinglepassoflightthroughthemetamaterial,asÞ¼ð,andarethewavelength,samplethickness,trans-mittance,andreflectance,respectively.SimulationswereperformedwithRCWAtodeterminethetheoreticalFOM.Fig.9(a)showsthesimulatedandmeasuredFOMforthebulkfishnetmetamaterial.TheFOMofthesimulatedstructurereachesavalueof18atawavelengthof1750nm.ThisFOMisnearlytenfoldhigherthansingle-layerNIMsandisduetothecombinationofmagneto-inductivecoupl-inganddestructiveinterferenceofsurfacecurrentsinthebulkmetamaterial.Experimentally,thetransmittanceinthenegativeindexbandisfourtimeslowerthanthenumericallycalculated,yieldinganexperimentalFOMof3.5at1775nm.TheloweredtransmissionandthusFOMismostlikelyduetoGadepositionfromtheFIB.Whilesignificantlylowerthanthetheoreticalvalue,thisFOMremainsamongthehighestyetachievedatopticalfre-quencies.Itshouldalsobenotedthattransmissionmea-surementswereperformedwithaslightlyfocusedbeamresultinginsomeoffnormalincidentlight.Duetothefactthatimaginarypartoftherefractiveindexincreaseswithangleofincidence[30],thesemeasurementsprovidealowerboundfortheFOM.TodeterminetheeffectofGacontaminationonthefabricatedstructure,effortshavebeenmadetominimizethecontamination.Toaccomplishthis,bulkfishnetstruc-tureshasbeendepositedandmilledontopof50-nm-thicksiliconnitridefree-standingmembranes.ByallowingtheGafromtheFIBtopassintofreespaceoncethepatternismilled,contaminationofGainthesubstrateislargelyavoided.Inthiscase,thefishnetunitcelldimensionswereslightlymodifiedtopushthenegativeindexregiontoshorterwavelengths.ThesimulatedandexperimentallymeasuredtransmissioncurvesareshowninFig.9(b)forasix-functional-layerdesignwithdimensionsof810nm,546nm,278nm,30nm,and50nm.Themeasuredtransmittanceexhibitssimilarfea-turesasthecalculation,namely,threepeaksimposedoverthetransmissionband,whichareslightlyblue-shiftedwithrespecttothenumericalresults.ThesepeaksareduetoFabry–Peroteffectsinwhichtheimpedancemismatchleadstoreflectanceatthemetamaterial/airandmetamaterial/nitrideinterfaces.ItcanbeobservedthatthetransmissionpeakisclosetothetheoreticalvalueduetothereducedlevelofGacontaminationinthesample.Workiscurrentlyunderwaytomeasuretherefractiveindexofthefree-standing-membrane-basedfishnetstructuretodeterminetheexperimentalFOM.VI.OUTLOOKInhispioneeringtheoreticalworkonnegativeindexmate-rials,VeselagoproposedanumberofexoticphenomenaincludingreversedDopplereffect,backwardCerenkovra-diation,andnegativeradiationpressure[31].Anobserva-tionoftheseeffectsrequiresabulknegativeindexmedia,andthereforetheyhavenotyetbeendemonstratedatop-ticalfrequencies.Withtherealizationofbulknegative Fig.9.FOMoforiginalbulkfishnetandtransmissionofthefishnetmetamaterialonafree-standingmembrane.Measurementswereperformedon2222unitcellfishnetstructures(totalpatternedarea).(a)FOMversuswavelengthforthesimulation(dashedline)andtheexperiment(blacksquares).ThelowerexperimentalFOMisduetoreducedtransmissionresultingfromfabricationimperfections.TheexperimentalFOMreaches3.5at1775nmwhere.(b)Experimental(redline)andsimulatedtransmittance(blackdottedline)ofthebulkfishnetfabricatedonafree-standingmembrane.Fig.1(a)reprintedfrom[19].Valentineetal.:DevelopmentofBulkOpticalNegativeIndexFishnetMetamaterialsProceedingsoftheIEEE indexmaterials,explorationoftheseinterestingphysicsshouldbewithinreach.Theairaperturesinthebulkfish-netmetamaterialalsoallowtheaccessofhighenergyelectrons,andthereforemaketheobservationofreversedCerenkovradiationpossible.Otherinterestingphenomenathatmaybedemonstratedinabulknegativeindexmediumincludenonlinearprocessesthatinvolvethenonlinearinteractionamongopticalwaveswithdifferentsignsoftherefractiveindicesowingtothedispersivenatureofthemetamaterials[32].Althoughbulkfishnetmetamaterialsexhibitmuchlowerlosscomparedtopreviousworks,theyarefarfromhighlytransparent.Inanefforttodecreasetheintrinsiclossofmetamaterials,severalresearchersarecurrentlypursuingincorporationofgainmaterialintotheunder-lyingstructureofthematerial[33].Furthermore,therecentreportsofplasmoniclasers[34],[35]areanencouragingdevelopmentthatdemonstratesthepro-spectsofcompletelosscompensationinplasmonicREFERENCES[1]D.R.Smith,W.Padilla,D.Vier,S.Nemat-Nasser,andS.Schultz,Compositemediumwithsimultaneouslynegativepermeabilityandpermittivity,ty,Phys.Rev.Lett.,vol.84,pp.4184–4187,May2000.[2]R.A.Shelby,D.R.Smith,andS.Schultz,Experimentalverificationofanegativeindexofrefraction,n,Science,vol.292,pp.77–79,Apr.2001.[3]S.Zhang,W.Fan,N.Panoiu,K.Malloy,R.Osgood,andS.Brueck,Experimentaldemonstrationofnear-infrarednegative-indexmetamaterials,,Phys.Rev.Lett.,vol.95,Sep.2005,137404.[4]V.M.Shalaev,W.Cai,U.K.Chettiar,H.-K.Yuan,A.K.Sarychev,V.P.Drachev,andA.V.Kildishev,Negativeindexofrefractioninopticalmetamaterials,,Opt.Lett.,vol.30,pp.3356–3358,Dec.2005.[5]G.Dolling,C.Enkrich,M.Wegener,C.M.Soukoulis,andS.Linden,Simultaneousnegativephaseandgroupvelocityoflightinametamaterial,ial,Science,vol.312,pp.892–894,May2006.[6]J.B.Pendry,Negativerefractionmakesaperfectlens,,Phys.Rev.Lett.,vol.85,pp.3966–3969,2000.[7]S.Enoch,G.Tayeb,P.Sabouroux,N.Guerin,andP.Vincent,Ametamaterialfordirectiveemission,on,Phys.Rev.Lett.vol.89,Nov.2002,213902.[8]J.Zhou,T.Koschny,M.Kafesaki,E.Economou,J.Pendry,andC.Soukoulis,Saturationofthemagneticresponseofsplit-ringresonatorsatopticalfrequencies,es,Phys.Rev.Lett.,vol.95,Nov.2005,223902.[9]A.Ishikawa,T.Tanaka,andS.Kawata,Negativemagneticpermeabilityinthevisiblelightregion,ion,Phys.Rev.Lett.,vol.95,Dec.2005,237401.[10]S.Zhang,W.Fan,K.J.Malloy,S.R.J.Brueck,N.C.Panoiu,andR.M.Osgood,Near-infrareddoublenegativemetamaterials,ials,Opt.Exp.vol.13,pp.4922–4930,Jun.2005.[11]M.Navarro-Cia,M.Beruete,M.Sorolla,andI.Campillo,Negativerefractioninaprismmadeofstackedsubwavelengthholearrays,s,Opt.Exp.,vol.16,pp.560–566,Jan.2008.[12]S.Zhang,W.Fan,N.C.Panoiu,K.J.Malloy,R.M.Osgood,andS.R.Brueck,Opticalnegative-indexbulkmetamaterialsconsistingof2Dperforatedmetal-dielectricstacks,ks,Opt.Exp.,vol.14,pp.6778–6787,Jul.2006.[13]J.B.Pendry,L.Martn-Moreno,andF.J.Garcia-Vidal,Mimickingsurfaceplasmonswithstructuredsurfaces,es,Science,vol.305,pp.847–848,Aug.2004.[14]A.Mary,S.Rodrigo,F.Garcia-Vidal,andL.Martin-Moreno,Theoryofnegative-refractive-indexresponseofdouble-fishnetstructures,,Phys.Rev.Lett.,vol.101,Sep.2008,103902.[15]M.Beruete,M.Navarro-Ca,F.Falcone,I.Campillo,andM.Sorolla,Singlenegativebirefringenceinstackedspoofplasmonmetasurfacesbyprismexperiment,,Opt.Lett.,vol.35,pp.643–645,Feb.2010.[16]G.Dolling,C.Enkrich,M.Wegener,C.M.Soukoulis,andS.Linden,Low-lossnegative-indexmetamaterialattelecommunicationwavelengths,s,Opt.Lett.,vol.31,pp.1800–1802,Jun.2006.[17]S.Xiao,U.K.Chettiar,A.V.Kildishev,V.P.Drachev,andV.M.Shalaev,Yellow-lightnegative-indexmetamaterials,ials,Opt.Lett.,vol.34,pp.3478–3480,Nov.2009.[18]G.Dolling,M.Wegener,C.M.Soukoulis,andS.Linden,Negative-indexmetamaterialat780nmwavelength,,Opt.Lett.,vol.32,pp.53–55,2007.[19]J.Valentine,S.Zhang,T.Zentgraf,E.Ulin-Avila,D.A.Genov,G.Bartal,andX.Zhang,Three-dimensionalopticalmetamaterialwithanegativerefractiveindex,,Nature,vol.455,pp.376–379,Sep.2008.[20]J.Zhou,T.Koschny,M.Kafesaki,andC.Soukoulis,Negativerefractiveindexresponseofweaklyandstronglycoupledopticalmetamaterials,,Phys.Rev.B,vol.80,Jul.2009,035109.[21]O.F.SiddiquiandG.V.Eleftheriades,Periodicallyloadedtransmissionlinewitheffectivenegativerefractiveindexandnegativegroupvelocity,ty,IEEETrans.AntennasPropag.vol.51,no.10,pp.2619–2625,Oct.2003.[22]A.GrbicandG.Eleftheriades,Overcomingthediffractionlimitwithaplanarleft-handedtransmission-linelens,ns,Phys.Rev.Lett.,vol.92,Mar.2004,117403.[23]A.Lai,C.Carloz,andT.Itoh,Compositeright-/left-handedcompositetransmissionlinemetamaterials,,IEEEMicrow.Mag.,vol.5,no.3,pp.34–50,Sep.2004.[24]G.Dolling,M.Wegener,andS.Linden,Realizationofathree-functional-layernegative-indexphotonicmetamaterial,al,Opt.Lett.,vol.32,pp.551–553,Mar.2007.[25]N.Liu,L.Fu,S.Kaiser,H.Schweizer,andH.Giessen,Plasmonicbuildingblocksformagneticmoleculesinthree-dimensionalopticalmetamaterials,,Adv.Mater.,vol.20,pp.3859–3865,Oct.2008.[26]N.Liu,H.Guo,L.Fu,S.Kaiser,H.Schweizer,andH.Giessen,Three-dimensionalphotonicmetamaterialsatopticalfrequencies,es,NatureMater.,vol.7,pp.31–37,Jan.2008.[27]J.Yao,Z.Liu,Y.Liu,Y.Wang,C.Sun,G.Bartal,A.M.Stacy,andX.Zhang,Opticalnegativerefractioninbulkmetamaterialsofnanowires,res,Sciencevol.321,p.930,Aug.2008.[28]A.J.Hoffman,L.Alekseyev,S.S.Howard,K.J.Franz,D.Wasserman,V.A.Podolskiy,E.E.Narimanov,D.L.Sivco,andC.Gmachl,Negativerefractioninsemiconductormetamaterials,,NatureMater.,vol.6,pp.946–950,Dec.2007.[29]J.Yang,C.Sauvan,T.Paul,C.Rockstuhl,F.Lederer,andP.Lalanne,Retrievingtheeffectiveparametersofmetamaterialsfromthesingleinterfacescatteringproblem,,Appl.Phys.Lett.,vol.97,2010,061102.[30]C.Rockstuhl,C.Menzel,T.Paul,T.Pertsch,andF.Lederer,Lightpropagationinafishnetmetamaterial,al,Phys.Rev.B,vol.78,Oct.2008,155102.[31]V.G.Veselago,Electrodynamicsofsubstanceswithsimultaneouslynegativevaluesofsigmaandmu,,SovietPhys.USPEKHI-USSR,vol.10,pp.509–514,1968.[32]A.K.PopovandV.M.Shalaev,Negative-indexmetamaterials:Second-harmonicgeneration,Manley-Rowerelationsandparametricamplification,n,Appl.Phys.B,vol.84,pp.131–137,Mar.2006.[33]S.Xiao,V.P.Drachev,A.V.Kildishev,X.Ni,U.K.Chettiar,H.-K.Yuan,andV.M.Shalaev,Loss-freeandactiveopticalnegative-indexmetamaterials,,Nature,vol.466,pp.735–738,Aug.2010.[34]R.F.Oulton,V.J.Sorger,T.Zentgraf,R.-M.Ma,C.Gladden,L.Dai,G.Bartal,andX.Zhang,Plasmonlasersatdeepsubwavelengthscale,e,Nature,vol.461,pp.629–632,Oct.2009.[35]M.A.Noginov,G.Zhu,A.M.Belgrave,R.Bakker,V.M.Shalaev,E.E.Narimanov,S.Stout,E.Herz,T.Suteewong,andU.Wiesner,Demonstrationofaspaser-basednanolaser,er,Nature,vol.460,pp.1110–1112,Aug.2009.Valentineetal.:DevelopmentofBulkOpticalNegativeIndexFishnetMetamaterialsProceedingsoftheIEEE ABOUTTHEAUTHORS JasonValentinereceivedtheB.S.degreeinmechanicalengineeringfromPurdueUniversity,WestLafayette,IN,in2004andthePh.D.degreeinmechanicalengineeringfromtheUniversityofCaliforniaBerkeley,Berkeley,in2010.In2010,hejoinedthefacultyoftheMechanicalEngineeringDepartment,VanderbiltUniversity,Nashville,TN.DuringhisgraduateworkinProf.Zhang’slaboratoryattheUniversityofCaliforniaBerkeleyfrom2005to2010heworkedondevelopingopticalmetamaterialsandassociateddevices.Hisworkincludesthedevelopmentofbulkopticalmetamaterialsaswellastherealizationoftransformationopticsinspireddevicessuchastheopticalcloak.Hiscurrentresearchinterestsincludemetamaterials,transforma-tionoptics,plasmonics,scalable3-Dmanufacturing,photovoltaics,andbiologicalimaging.Dr.ValentinereceivedtheMaterialsResearchSociety’sGoldStudentAwardforhisworkonopticalcloakingin2010.HisworkhasbeenselectedbyTimeMagazineasoneoftheTop10ScientificDiscoveriesin2008. ShuangZhangwasborninLiaoningProvince,China,in1975.HereceivedtheB.S.degreeinphysicsfromJilinUniversity,Changchun,China,in1993,theM.S.degreeinphysicsfromNortheasternUniversity,Boston,MA,in1999,andthePh.D.degreeinelectricalengineeringfromtheUniver-sityofNewMexico,Albuquerque,in2005.FromDecember2005toAugust2006,hewasaPostdoctoralResearchFellowattheUniversityofIllinoisatUrbana-Champaign,Urbana,andfromAugust2006toMarch2010,hewasfirstaPostdoctoralResearchFellowandlateranAssistantResearchEngineerattheUniversityofCaliforniaBerkeley,Berkeley.InMarch2010,hejoinedthefacultyoftheUniversityofBirmingham,Edgbaston,Birmingham,U.K.,whereheiscurrentlyaReaderintheSchoolofPhysicsandAstronomy.Dr.ZhangistherecipientoftheInternationalCommissionforOptics’sIUPAPYoungScientistPrizeinOptics,2010forhisresearchonopticalmetamaterials.Dr.Zhang’sworkonmacroscopicinvisibilitycloakingofvisiblelightwasselectedasoneoftop10breakthroughsfor20102010byPhysicsWorld. ThomasZentgrafreceivedthePh.D.degreefromtheFacultyofMathematicsandPhysics,UniversityofStuttgart,Stuttgart,Germany,inJuly2006.From2003to2006,hewasaResearchAssistantattheMaxPlanckInstituteforSolidStateResearch,Stuttgart,Germany,andin2005,hewasaVisitingScholarattheLawrenceBerkeleyNationalLaboratory,Berkeley,CA.In2007,hereceivedapostdoctoralfellowshipbytheLandesstiftungBaden-WurttembergandshortlyafterwardshewasawardedwithaFeodorLynenResearchFellowshipfromtheAlexandervonHumboldtFoundationtospendtwoyearsattheUniversityofCaliforniaBerkeley,Berkeley,workingonmetamaterialsandtransformationoptics.Since2009,hehasbeenaResearchAssociateinProf.Zhang’sgroupattheUniversityofCaliforniaBerkeley.Hisresearchinterestscoverdifferentareasofphotonicsandoptics,suchasnonlinear-opticalspectroscopy,ultrafastspectroscopy,near-fieldopticalspectroscopy,plasmonicsystems,andphotonicmetamaterials.Dr.ZentgrafreceivedtheGeorg-Simon-OhmAwardoftheGermanPhysicalSocietyin2002andtheDr.-Heinrich-DukerAwardoftheHeidehofFoundationin2006. XiangZhangreceivedthePh.D.degreeinmechanicalengineeringfromtheUniversityofCaliforniaBerkeley,Berkeley,in1996.HewasafacultymemberatthePennsylvaniaStateUniversityandtheUniversityofCaliforniaatLosAngelespriortojoiningtheBerkeleyfacultyin2004.Currently,heisanErnestS.KuhChairedProfessorattheUniversityofCaliforniaBerkeleyandtheDirectoroftheNationalScienceFounda-tion(NSF)Nano-ScaleScienceandEngineeringCenter(NSEC).Hehaspublishedmorethan180publicationsincludingthoseinScienceNature.Hehasgivenover200invited,keynoteandplenarytalksatinternationalconferencesandinstitutions.Prof.ZhangisanelectedmemberoftheU.S.NationalAcademyofEngineering(NAE)andFellowoftheAmericanPhysicalSociety(APS),theOpticalSocietyofAmerica(OSA),theAmericanAssociationfortheAdvancementofScience(AAAS),andTheInternationalSocietyforOpticalEngineers(SPIE).Hisgroup’sresearchinopticalmetamaterialswasselectedbyTimeMagazineTop10ScientificDiscoveriesin2008.2008.HeisarecipientofanNSFCAREERAward,SMEDellK.AllenOutstandingYoungManufacturingEngineerAward,andanOfficeofNavalResearch(ONR)YoungInvestigatorAward.Valentineetal.:DevelopmentofBulkOpticalNegativeIndexFishnetMetamaterialsProceedingsoftheIEEE