Characterization, slab-pair modeling and phase analysis of circular fishnet metamaterials

Characterization,

slab-pair

modeling

and

phase

analysis

of

circular

fishnet

metamaterials

Yusuf

O

¨ ztu¨rk

*

,

Asım

Egemen

Yılmaz

,

Evrim

C

¸

olak

,

Ekmel

O

¨ zbay

a

AnkaraUniversity,DepartmentofElectricalandElectronicsEngineering,Tandog˘an,06100Ankara,Turkey

b

TU¨ BI˙TAK-ULAKBI˙M,Bilkent,06539Ankara,Turkey

c

NanotechnologyResearchCenter,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 theoretical considera-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.}

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.Polarization inde-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.Thestructureconsistsofthe low-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 withasystemofsuchparallelwiresandexhibits Drude-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 vm¼pffiffiffiffiffiffiLC. 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:

f_m¼ 1 2ppffiffiffiffiffiffiLC¼

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

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 this

situa-tion,thethickness(t)istheuniqueparameter indepen-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-range unit-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 unitcelllengthwithlinear approxima-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)takesplaceduringthewhole characteriza-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

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 vanishesthecircularityofthemagneticfield surround-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

eðvÞ¼1v2

p=v2.Thedoublepositive(DPS)medium islocatedinarelativelywiderbandwidthaccordingto

theDNGmediumabove19GHz.Undertheconditions Re(e)<0andRe(m)<0,whichholdforthefrequency intervalof13.75–14.1GHz,LHMbehaviorisexpected. However,thereisanotherfactoraffecting electromag-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

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

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):

Df_total ¼jn1jk0d1n2k0d2 (3a) Df_total ¼Df_CF-MMDf_air (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-magneticwavepropagatingthroughastructure contain-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

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-parallelsurfacecurrentsandthe cancella-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,Compositemediumwithsimultaneouslynegative

per-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

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,Size

depen-denceandconvergenceoftheretrievalparametersof

metama-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,IEEETransactionsonMicrowave

Theo-ryandTechniques53(2005)1522–1526.

[22] K.Aydin,K.Guven,C.M.Soukoulis,E.Ozbay,Observationof

negativerefractionandnegativephasevelocityinleft-handed