Characterization, slab-pair modeling and phase analysis of circular fishnet metamaterials
Yusuf O ¨ ztu¨rk
a,b,* , Asım Egemen Yılmaz
a, Evrim C ¸ olak
c, Ekmel O ¨ zbay
caAnkaraUniversity,DepartmentofElectricalandElectronicsEngineering,Tandog˘an,06100Ankara,Turkey
bTU¨ BI˙TAK-ULAKBI˙M,Bilkent,06539Ankara,Turkey
cNanotechnologyResearchCenter,BilkentUniversity,Bilkent,06800Ankara,Turkey Received9March2012;receivedinrevisedform29May2012;accepted29May2012
Availableonline9June2012
Abstract
Planarmetamaterials,whichhaveincidenttonormalplaneexcitationunlikeSRR-typestructuresandthatareeasilyfabricatedin multilayerform,havereceivedgreatinterestinrecentyears.Inthispaper,one-dimensionalandpolarizationindependentcircular fishnetmetamaterialsandtheirequivalentdiscontinuousslab-pairmodelingfortuningresonancefrequenciesareintroduced.After the numerical and experimental demonstration of the inclusions, the standard retrieval characterization methods and the correspondent/relatedbackward-wavepropagationobservationarerealizedinordertocheckthephysicalexplanationmentioned inthepaper.Inaddition,adetailedphaseanalysisisperformedinordertodemonstratetheapplicationofthesuggestedstructureasa phasecompensator.
#2012ElsevierB.V.Allrightsreserved.
Keywords:Circularfishnetmetamaterials;Doublenegative(DNG)metamaterials;Slab-pairmodeling;Phasecompensation
1. Introduction
The phenomenon of artificial engineered metama- terialsthatcannotbeobtainedwithnaturallyoccurring materialswas initiated withthe theoreticalconsidera- tionofthenegativerefractionconceptbyVeselago[1].
Anexperimentaldemonstrationofthemedium,which was called as electromagnetic metamaterial, was realized by using split ring resonators (SRRs) and continuouswires[2] followingthe ideasdescribedby Pendry et al.In these studies, the periodical arrange- ment of thin wires provides a negative effective
permittivity at frequencies lower than the plasma frequency of the system [3]. The SRRs, as micro- structures built from nonmagnetic conducting sheets, provide a strong magnetic resonance, and exhibit an effectivemagneticpermeability[4].Duetodifficulties withfabricationofSRRswiththeresonancefrequency atthevisiblerangeandthealignmentoftheproduced layers for multilayerapplications, the introduction of planarmetamaterials were suggestedtoovercome the restrictions involving conventional metamaterials [5–
9].Moreover,splitringresonatorsare notsuitablefor the planar utilization of metamaterials, since the incident wave has to be parallel to the SRR, which means thatthe magnetic fieldis perpendicular to the SRR. To satisfy optical magnetism, those alternative structures of metal-dielectriccomposites are madeup withadielectricsubstratebetweenparallelmetalslabs
www.elsevier.com/locate/photonics PhotonicsandNanostructures–FundamentalsandApplications10(2012)624–631
*Correspondingauthorat:TU¨ BI˙TAK-ULAKBI˙M,Bilkent,06539 Ankara,Turkey.Tel.:+905324782678.
E-mailaddress:yusuf.ozturk@tubitak.gov.tr(Y.O¨ ztu¨rk).
1569-4410/$–seefrontmatter#2012ElsevierB.V.Allrightsreserved.
http://dx.doi.org/10.1016/j.photonics.2012.05.013
effectivepermittivityandpermeability[17,18].Onthe other hand, broadband phase shifters/compensators [19,20]andleft-handed medium (LHM)–right-handed medium(RHM)resonators[21]aresomeexamplesof potentialapplicationsofthemetamaterials.
2. Structuredefinition
Inthisstudy,circularfishnetmetamaterial(CF-MM), which is a structure having incident polarization independence,isinvestigated.Forthispurpose,afterits design and fabrication, the structure is measured for completebehavioralcharacterization.Polarizationinde- pendence of the structure is due to its symmetric configuration. A schematic view of the unit cell, multilayer,and equivalentslabpair formsof CF-MMs aredepictedinFig.1.Thestructureconsistsofthelow- lossTeflonsubstrate(wither=2.16andlosstangentof d=0.0004)withatransparentview,andthehighlighted metal parts(copper)as aPEClayer. Lowloss tangent value is vital for achieving left-handed resonance behavior, and therefore, FR-4 like substrates are not suitableforcreatingCF-MMwith thesameor comparable dimensions.TheTeflonlayerasasubstrateandthecopper layerhavethicknessesoft=1mmand20mm,respec- tively.TheunitcellshowninFig.1(a)hascomplementary parameters wherein choosing the dimensions as
structureinordertodevelopasimplemethodsatisfying thedesiredoperationconditions.Taking Fig.1(c)into account, the equivalent model of CF-MMs could be handledasadiscontinuousslab-pairoracut-wirepair form.Negativedielectricpermittivityiseasilyobtained withasystemofsuchparallelwiresandexhibitsDrude- like plasmonic behavior for the frequencies below plasma-frequency(vp),whilenegativepermeabilityin allthesestructurescreatesastrongmagneticresonance at a frequency v=vm by exciting resonant circular currents; this basic process can be simulated by an effective LC-circuit exhibiting a resonance at vm¼ ffiffiffiffiffiffi
pLC
. Similar to what is identified in[16], the inductancevalueLandthecapacitancevalueCcanbe computed by using L¼m0ðleff:tÞ=weff and C¼ere0ðleff:weffÞ=4t, where leff and weff are the effectivelengthandwidthasdepictedinFig.1(c),tis the thickness of the substrate, m0 is permeability in vacuum, e0 is permittivity in vacuum and er is the relative dielectric constant of the Teflon substrate.
Theseequationsresultinthe DNGor LHMmagnetic resonancefrequency(fm)as:
fm¼ 1 2p ffiffiffiffiffiffi
pLC¼ c0
pleff ffiffiffiffier
p (1)
wherec0isthespeedoflightinvacuum.Accordingto Eq. (1), the magnetic-resonance frequency does not
Fig.1.SchematicrepresentationofCF-MMsas(a)unit-cell,(b)multi-layerformoftheunit-cells,(c)equivalentslab-pairform,and(d)the photographyofthefabricated1010cellCF-MMstructure.
depend on the parameters t and weff. In fact, due to symmetry, it could be easily stated that the effective length of the unit-cell must be equal to the effective widthof the unit-cell,namely leff=weff.In thissitua- tion,thethickness(t)istheuniqueparameterindepen- dent of fm and only contributes the RHM resonance frequency.Additionally,thethicknessaffectstheLHM transmissionpeaklevelbasedonthelosstangentvalue.
Infact,theresonancevaluescouldbecalculatedby usingafull-wavesimulatortool,alternatively.Fig.2(a) drawsawireframemeshusing theunit celllengthr/a andtheratiooftheradiustotheunitcelllengthaandthe heightcorrespondstotheLHMresonancefrequencies manuallyselectedduringsimulations.Inthisstudy,the scalabilityofCF-MMsisverifiedforwide-rangeunit- celldimensionsfrom5mmupto20mmandtheratio from 0.25 to 0.30. On the other hand, the substrate thicknessiskeptconstantat1mmduringthescale-up/
downprocess.Asanexample,thecorrespondentLHM resonance frequencies are between 9.7GHz and 38.74GHz for r=0.25a. After the simulation process,the effective length values are calculated by usingtheselectedfrequenciesbasedonEq.(1).Inthis study,weintroducearelationshipbetweentheeffective lengthandthe unitcelllengthwithlinearapproxima- tion.As showninFig.2(b), weanalytically identified theeffectivelengthoftheunitcellasleff0.334awith a very-good agreement with the simulations for r=0.25a and realized the discontinuous slab-pair modelingof CF-MMs. The effective lengths of other unitcells(whicharedesignedfordifferentr/avalues) canbe computedvia Eq. (1) inserting newresonance frequenciesfm.Bymeansofsuchamodelasadesign guideline,forafixedr/aratio,itisnowpossibletotune the resonance frequency to the desired region in the electromagnetic spectrum analytically. Additionally,
availability of thistechniqueistested andverifiedfor the squared-type fishnet metamaterials introduced in [14].
The metamaterialisdesigned andcharacterizedby using the commercial software package, CST Micro- wave Studio.Fig. 3 shows the qualitative analysis of CF-MM structures in the backward and forward propagation cases. In Fig. 3(a), from the top view of theunitcell(yz-plane),itiscleartoobservetheomitted fringing electric field intensities; whereas Fig. 3(b) holds thosevaluesalong the circularsidesof the unit cell. As a physical explanation, we focused on the relationship between the electrical permittivity er and the electric polarization P with the basic formula of D=e0E+Pe=(1+xe)e0E. For xe<1 case, er
becomes negative, satisfying the homogenization subwavelength conditions. This causes the electric polarization P to overcome the electric flux density term,whichise0E.Thesameapproachcanbeusedin ordertoanalyzetherelationshipbetweentheeffective magnetic susceptibility xm and the magnetic flux density B with the second complementary formula B=m0(H+Pm)=(1+xm)m0H.Thecancellationofthe horizontal electric field components produced by circular slots and the corresponding anti-parallelism inthe surfacecurrents areshowninFig.3(a)and(c), respectively. On the other hand, the fringing electric fields and the relevant parallel surface currents are depicted in Fig. 3(b) and (d). In this study, the longitudinal (z-directed) TE or TM electromagnetic field is excited such that azl (the operating wavelength)takesplaceduringthewholecharacteriza- tion process. The CF-MMtype structurehas uniaxial properties (one-dimensional) and this limitation is satisfied with az=l/11.5l/7.5. To sum up, the magneticfieldperpendiculartotheelectricfieldatevery
Fig.2. MeshviewoftheLHMresonancefrequencieswithrespecttor/aanda(a).Theresultsbelongingtothediscontinuousslab-pairmodelingof CF-MMstructureforr=0.25a(b).
pointinspacehasthe impactofcreation ofacircular field surrounding the necks of the structure for RHM investigation.Inthissituation,themagneticfieldinthe apertures ofthe structure consistingof onlydielectric layer has negligible importance. On the other hand, cancellation of the fringing electric field yields in comparable magnetic fieldaround the apertures.This vanishesthecircularityofthemagneticfieldsurround- ingthenecksofthestructure.Underthesehomogenized mediumconditions,surfacecurrentsshowacontinuous movement along the unit cell sheets for the LHM region, and a reversal discrete behavior in the RHM region.
The standard retrieval procedure [17] was imple- mented before the CF-MM structures were manufac- tured and measured. For this purpose, a unit-cell is employed along the z-direction; the effective permit- tivity andpermeabilityvalueswerethenderivedfrom the magnitudes and phases of the transmission/
reflection coefficients (S21 and S11) of a single-layer CF-MMseen inFig.4(a). As showninFig.4(b), the doublenegative(DNG)regioniscreatedbythenegative permeability boundariesof 13.75–14.1GHz, whichis duetotheavailabilityofthe negativepermeabilityfor theentirefrequencyrangebelowtheplasmafrequency (vp) originating from Drude like plasmonic behavior eðvÞ¼1v2p=v2.Thedoublepositive(DPS)medium islocatedinarelativelywiderbandwidthaccordingto
theDNGmediumabove19GHz.Undertheconditions Re(e)<0andRe(m)<0,whichholdforthefrequency intervalof13.75–14.1GHz,LHMbehaviorisexpected.
However,thereisanotherfactoraffectingelectromag- netic wave propagationinthe +zor z direction;the imaginary parts of the refractive index. It is clear to identifythat the imaginaryparts attainzero-value for the resonance frequencies of the LHM and RHM regions,centeredat13.8and19.5GHz.Bycombining alltheinformation,weexpectabandspectrumnarrower than a 13.5–14.1GHz interval. For different designs needing a wider DPS interval, one should either increasetheunitcellradius,orusethemultilayerform ofthe CF-MMinclusions.
3. Experimentalresults
Theexperimentsareperformedinfreespaceandat room temperature by using two standard-gain horn antennas.Thedistancebetweentheantennaswaskept fixedat30cm,andthespecimen(unitcell)waslocated at the center. First, aTRL calibration procedurewas implemented on the network analyzer in order to eliminatetheenvironmentalnoises.Afterthefree-space calibration,thetransmissionspectra andphasespectra havebeenmeasuredatthesameposition.
The measured and calculated transmission and reflection characteristics of the CF-MM medium are
Fig.3. Topviewofthecalculatedelectricfieldintensityvalues(E)inV/mforLHM(in(a))andRHM(in(b)).Atthebottom(in(c)and(d)),the correspondingsurfacecurrentsinA/marepresented.ThePECpartsofthestructuresarepresentedwithfulltransparencyforbettervisualization.
displayedinFig.5.The datashowcompatibility with the outputs of the standard retrieval procedure as depictedinFig.4;wherethefirstresonancefrequency fortheLHM isobservedat13.8GHz,andthesecond resonance frequency for the RHM takes place at 19.2GHz. For this type of metamaterial, there are basically three mechanisms resulting in undesired losses.Theloss-tangentvalueofthedielectricsubstrate hasastrongeffectonthepeakvalueofLHMresonance
frequency. A small amount of degradation from the idealvaluecausesattenuationforthepeakvaluesofthe verynarrowLHMband.Thebestmeasurementforthe LHMresonanceinourexperimentequalsto4.8dB.
The second loss mechanism related to the RHM resonance frequency is the thickness of imperfect conductors, which are modeled as PEC during the simulations.Increasedmetalthicknessresultsinaloss intheRHMresonancepeakvalue;andametalthickness
Fig.4. (a)Thecomputedmagnitudesandphasesofthescatteringparameters(jS11j,jS21j,ArgS11,ArgS21)usedfortheretrievalanalysis.(b)The retrievedeffectiveparametersfortheCF-MMs.Thesolidblueanddashedredlinesshowtherealpartsoftherefractiveindex(n),therelative permittivity(er),andthepermeability(mr).(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversion ofthearticle.)
lessthan20mmshiftsthe RHMresonancelocationto lowerfrequencyvalues.Asaresult,itishighlyprobable that the fabricated specimen has aloss tangent value greater than 0.0004, and a metal thickness less than 20mm due to various uncontrollable effects such as corrosion. On the other hand, the measured phase spectraarecompatiblewiththecalculatedphasespectra inthecharacteristicfeaturesexceptforanoffsetvalue.
We observed phase advance behavior in the LHM region and linear phase lag in the RHM region. In comparisontotheRHMphaselag, thephaseadvance occurs in a more steeperand narrow shape based on whatisdepictedintheretrievalvaluesofn.
4. Theoreticalmultilayerphaseanalysis of CF-MMs
We finally analyzed the transmitted phase of CF- MMs inorder to investigate the change inthe phase velocitiesforthemulti-layerformofthestructure. As expected, the medium with e<0 andm<0 showsa phaseadvanceratherthanaphaselagfortheordinary materials.Thus,themorelayersofthenegative index material, the more phase advance exists in the LHM regionaswellasthemorephaselagintheRHMregion.
Theindexofrefraction(intermsofwavelength,phase shift, and the length-change of the material in the propagationdirection) isgivenby[22]:
n¼Df DL
l
2p (2)
BeforetheimplementationofEq.(2),weperformed apre-processingstudytoobtaintheabsolutephaseshift thatisdefinedasthephasedifferenceinthecalculated phasevalue for port-to-portandthe air-layerbetween
theports.ThisrelationshipisdefinedinEqs.(3a)and (3b):
Dftotal ¼jn1jk0d1n2k0d2 (3a)
Dftotal ¼DfCF-MMDfair (3b)
where n1 and d1 denote the refractive index and the material thickness of CF-MMs, respectively. On the otherhand,n2andd2representtherefractiveindexand the thickness of the air between the ports used for transmitter and receiver devices, where n2=1mm and d2=30mm. It should be noted that, for specific applications,inordertodecreasethethickness(namely thed2value),anothermaterialhavingrefractiveindex valuemorethanunitycouldbeused.
At first glance, Fig. 6(a) seems to be a little bit confusing if one makes a connection between these phase spectra andthe results of the standardretrieval procedureorthetransmissionspectradepictedinFig.4.
Firstofall,thebackwardwavepropagationstartsfrom 13.5GHz,adippointinthetransmissionspectra,and continuesuptotheresonancefrequency.Similartothe LHM region, the forward propagation mechanism is produced by passing the second dip value near to 14.2GHz with maximum attenuation behavior. As a result,thephaseanalysisstudiesgiveusanopportunity toidentifytheboundariesoftheLHMandRHMregions clearly.
Phase compensators are designed to perform the partial or complete removalof phase shift of electro- magneticwavepropagatingthroughastructurecontain- ingbothpositiveandnegativerefractiveindexmaterial.
Oneofthesimpleststructurestoachievethiskindofa device is the combination of two-sequential slabs containing LHM and RHM media in each slab
Fig.5. Calculated(redsolidcurve)andmeasured(bluedashedcurve)transmissionandunwrappedphasespectravaluesforsingle-layerCF-MMin aandb,respectively.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthearticle.)
simultaneously.FocusingonEq.(3a),thethicknessesof eachslabdepend on the refractive indexvalue of the other slab expressed as |n1|/n2=d2/d1. However, by taking the previous works into account, we introduce some difficulties during the implementation of this relationship.InFig.6(a),anearlyconstantphaseshift/
differencecouldbehandledforeveryadditionallayerat a fixed frequency above 19GHz; whereas, it is not possible for the LHM slab in the 13.75–14.1GHz regime. The main reason for this problem is the decreaseofthenegativerefractiveindexvalueobtained from the thicker LHM slab. In previous studies, this changeofthe negativerefractiveindex wasexplained with a Figure of Merit (FOM) expressed as FOM=
|Re(n)|/Im(n). The equilibrium state between the slab thickness and the negative refractive index causes a relativelysmallphasedifferenceincomparisonwiththe RHMslab.
On the other hand, we deployed a different configuration of CF-MMs as depicted in Fig. 6(b).
Thechangeinther/avaluenotonlyshiftstheresonance frequency (fm) up to 14.6GHz, but also affects the dispersioncharacteristics ofthe structure.The config- uration with r/a=0.25 (having a band-stop behavior between the LHM and RHM regions) results in an unmatched case for transmission line modeling, whereastheotherconfigurationwithr/a=0.33shows amatchedbehavior or adirecttransition betweenthe LHM and RHM regions at 14.8GHz. By taking this detail into account, the systematic characterization processoutlinedinthispapercanbeappliedtodifferent versionsof CF-MMs.
5. Conclusion
Insummary,we designed andfabricatedacircular fishnet-typenegativerefractivematerialandperformed
experiments toobservethe exactandrealbehavior of our structure. The simulation withfull-wave analysis andexperimental results for thescattering parameters (S21 and S11) show good agreement with acceptable frequency shifts. In this paper, a direct relationship betweenanti-parallelsurfacecurrentsandthecancella- tionofthefringingelectricfieldstrengthisexplainedin order to clarify the physical mechanism behind the negative refraction phenomenon. In addition, an equivalent discontinuous slab-pair modeling for this typeofmetamaterialisproposedinordertodescribea guidelinefortuningtheresonancefrequencywhilethe sub-wavelength criterion is being considered. More- over, we realized a detailed phase analysis for the complete-regime of the implementation by making a cross-examination ofour resultsandprevious studies.
The backward and forward propagation behavior has been observed as a successfulimplementation of the stackedmultilayerformof CF-MMs.
References
[1] V.G. Veselago, Electrodynamics of substances with simulta- neouslynegativeelectricalandmagneticpermeabilities,Soviet PhysicsUspekhi10(1968)509.
[2] D.R. Smith,W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser,S.
Schultz,Compositemediumwithsimultaneouslynegativeper- meabilityandpermittivity,PhysicalReviewLetters84(2000) 4184–4187.
[3] J.B.Pendry,A.J.Holden,W.J.Stewart,I.Youngs,Extremelylow frequencyplasmonsinmetallicmesostructures,PhysicalReview Letters76(1996)4773–4776.
[4] J.B.Pendry,A.J.Holden,D.J.Robbins,W.J.Stewart,Magnetism from conductors and enhanced nonlinear phenomena, IEEE TransactionsonMicrowaveTheoryandTechniques47(1999) 2075–2084.
[5] C.Enkrich,M.Wegener,S.Linden,S.Burger,L.Zschiedrich,F.
Schmidt, J.F. Zhou, T. Koschny, C.M. Soukoulis, Magnetic metamaterials attelecommunication and visible frequencies, PhysicalReviewLetters95(2005)203901.
Fig.6. Unwrappedtransmittedphasespectrabelongingtothemulti-layerCF-MMswithr/a=0.25(ina)andr/a=0.33(inb).Theinlinepicture representsacloserlookatthetransitionbetweentheLHMandRHMregions.
3198–3200.
[10] K.B.Alici,E.Ozbay,Characterizationandtiltedresponseofa fishnetmetamaterialoperatingat100GHz,JournalofPhysicsD:
AppliedPhysics41(2008)135011.
[11] M.Kafesaki,I.Tsiapa,N.Katsarakis,T.Koschny,C.M.Sou- koulis,E.N.Economou,Left-handedmetamaterials:thefishnet structure and its variations, Physical Review B 75 (2007) 235114.
[12] V.D.Lam,J.B.Kim,S.J.Lee,Y.P.Lee,Left-handedbehaviorof combinedandfishnetstructures,JournalofAppliedPhysics103 (2008)033107.
[13] J.Zhou,T.Koschny,M.Kafesaki,C.M.Soukoulis,Sizedepen- denceandconvergenceoftheretrievalparametersofmetama- terials, Photonics and Nanostructures: Fundamentals and Applications6(2008)96.
fromreflectionandtransmissioncoefficients,PhysicalReviewB 65(2002)195104.
[19] Z.Jaksˇic´, N.Dalarsson,M.Maksimovic´,Negativerefractive index metamaterials: principles and applications, Microwave Review12(2006)36.
[20] I.S. Nefedov, S.A. Tretyakov, On potential applications of metamaterialsforthedesignofbroadbandphaseshifters,Mi- crowaveandOpticalTechnologyLetters45(2005)98.
[21] Y.Li,L.Ran,H.Chen,J.Huangfu,X.Zhang,K.Chen,T.M.
Grzegorczyk, Experimentalrealization of a one-dimensional LHM–RHMresonator,IEEETransactionsonMicrowaveTheo- ryandTechniques53(2005)1522–1526.
[22] K.Aydin,K.Guven,C.M.Soukoulis,E.Ozbay,Observationof negativerefractionandnegativephasevelocityinleft-handed metamaterials,AppliedPhysicsLetters86(2005)124102.
