Experimental demonstration of the enhanced transmission through circular and rectangular sub-wavelength apertures using omega-like split-ring resonators

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Experimental

demonstration

of

the

enhanced

transmission

through

circular

and

rectangular

sub-wavelength

apertures

using

omega-like

split-ring

resonators

Damla

Ates

a,b,

*

,

Filiberto

Bilotti

c

,

Alessandro

Toscano

c

,

Ekmel

Ozbay

a,b

a

DepartmentofElectricalandElectronicsEngineering,NanotechnologyResearchCenter,BilkentUniversity,06800Ankara,Turkey

b

DepartmentofPhysics,BilkentUniversity,06800Ankara,Turkey

c‘‘

RomaTre’’University,ViadellaVascaNavale,84,00146Rome,Italy

Received22March2012;receivedinrevisedform5August2012;accepted27August2012

Availableonline20September2012

Abstract

Enhancedtransmissionthroughcircularandrectangularsub-wavelengthaperturesusingomega-shapedsplit-ringresonatoris numericallyandexperimentallydemonstratedatmicrowavefrequencies.Wereportamorethan150,000-foldenhancementthrough adeepsub-wavelengthaperturedrilledinametallicscreen.Totheauthors’bestknowledge,thisisthehighestexperimentally obtainedenhancementfactorreportedintheliterature.Inthepaper,weaddressalsotheoriginsandthephysicalreasonsbehindthe enhancementresults.Moreover,wereportonthedifferencesoccurringwhenusingcircular,rectangularaperturesaswellas double-sidedandsingle-sidedomega-likesplitringresonatorstructures.

#₂₀₁₂_Elsevier_B.V._All_rights_reserved.

Keywords: Electromagneticwavetransmission;Metamaterials;Resonators

1. Introduction

Recently,electromagnetictransmissionthrough sub-wavelengthaperturesisreceivingagrowinginterestin thescientificcommunity,duetoitspotentialapplications indifferentscientificfields.Powertransmissionthrough electricallysmallaperturesdrilledinanopaquescreen (e.g.ametallicscreenatmicrowavefrequencies)canbe controlled inbothintensity andfrequency byproperly designing the geometry of the aperture. Bethe has reported therelationbetweenthetransmissionandthe

linear dimension (r) of the aperture compared to, the wavelength(l)oftheelectromagneticfieldimpingingon thescreenas(r/l)4[1].Thismeansthat,asexpectedfrom intuition,powertransmissionisextremelylowwhenthe apertures are characterized by deeply sub-wavelength dimensions.However,inseveralapplicationsinscience, suchashigh-capacityopticalmemories,high-resolution laserlithography,high-capacityoptical switches, high-efficient and electrically small microwave aperture antennas, high-resolution microwave and optical ima-gingandscreeningsystems,itisneededtoextracteven morepowerfromelectricallysmallapertures.Inorderto get the required transmission enhancement, different physicalphenomenacanbeused.

The experiments have been conducted at optical frequencies,whereresearchers investigatedtheeffects

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PhotonicsandNanostructures–FundamentalsandApplications11(2013)55–64

*Correspondingauthorat:DepartmentofElectricalandElectronics

Engineering,NanotechnologyResearchCenter,Bilkent University,

06800Ankara,Turkey.

E-mailaddress:damla@ee.bilkent.edu.tr(D.Ates).

1569-4410/$–seefrontmatter#₂₀₁₂_Elsevier_B.V._All_rights_reserved.

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on the transmission efficiency of surface plasmon polaritonsexcitedonthemetallicsurfaceofthescreens. Particularly,ithasbeendemonstratedthatthe transmis-sionthroughsub-wavelengthaperturescanbeenhanced by using the surface plasmon polariton phenomenon

[3,4].

Perturbing surface plasmon propagating on a metallic screen by the means of corrugations with proper periodicity surrounding the aperture [5,6], in fact, it is possible to couple the impinging electro-magneticwavewiththesurfaceplasmonpolaritonsand excitetheaperture[7].AfterPendryandhiscolleagues haveshownthatsurfaceplasmonsnotonlyexistinthe opticalregimebutcanalsoexistasspoofplasmonsat microwave frequencies, enhanced transmission by periodic corrugations has been demonstrated also in themicrowaveregime[8,9].

When, metamaterials came into play, it has been demonstratedthatenhancedtransmissionatmicrowave frequenciescanbeobtainedbyreplacingcorrugations around the aperture with proper metamaterial covers made of epsilon-near-zero or mu-near-zero materials

[10,11].Asimilarbutmorecompactsetupintermsof

coverthicknesshas been alsodemonstrated, byusing conjugate-matchedlayersofepsilon-negativeand mu-negativemetamaterials[12].

However,boththe corrugation-basedapproach and the metamaterial approach, rely on the coupling betweentheimpingingwavesandpropagatingsurface mode. This leads to an electrically large transverse extensionofeithercorrugationsorthecoveraroundthe aperture[13,14].

In order to overcome this limitation, another approach to the enhanced transmission has been presented by Aydin et al. and is based on the employmentof asingleringresonatorplacedinfront oftheaperture[15,16].Sincethedimensionsofthesplit ring resonator are comparable to the ones of the aperture, this setup is extremely compact. The experimentally achieved transmission at microwave frequencies demonstrated a 740-fold enhancement factor. Recently, Ates et al. have demonstrated that the transmission enhancement can be increase up to 70,000-fold (with the same dimensions of the screen and the same free-space measurement setup) by inserting connected split-ring resonators across the aperture [17]. The dramaticincrease of the enhance-mentfactorcomparedtotheprevioussetupwasdueto: (a)theemploymentof asymmetricstructure(i.e. one split-ringresonatorateithersideofthescreen)and(b) the physical connection between the two split-ring resonators.

In thispaper,we reportfurther increased enhance-mentfactorsbyusingadifferenttypeofmetamaterial resonator, such as the design of omega-likesplit-ring resonator.Thedesignofomegaparticleshasbeenfirst introducedbySaadoumandEnghetain1992inorderto synthesizebi-anisotropicand‘‘pseudo-chiral’’artificial materials and then deeply investigated also by Tretyakov, Simovski and Sochova [18,19]. Recently, ithasbeendemonstratedthatomega-likeinclusionscan be successfully used to obtain also left-handed metamaterials. In this case,in order to eliminate the intrinsic chirality of the medium, two omega-like resonatorsare deposited inoppositedirections on the twosidesof aprintedcircuit board,leading toalow, moderate bandwidth left-handed material design

[20,21]. Aydin et al. have also reported on the

characteristics of such omega-like structures experi-mentallyandnumerically[22].

The advantages of using omega-like split-ring resonatorsinsteadofconventionalsplit-ringresonators encouragedustousesuchstructuresinthetransmission enhancement experiments, in order to obtain better enhancement factors with respect to other reported results[15–17].

2. Omega-likesplit-ringresonator configurations

We connecttogether twoomega shaped split-ring resonatorsthroughtheirarmsandweobtaintheparticle depicted in Fig. 1(a). The samples are produced by printingtwoidenticalparticlesinoppositedirections on the two sides of a 0.5mm thick FR-4 dielectric boardwith0.035mm copperthicknessasinFig.1(a) and(b).Thedimensionsofthegeometricalparameters of the omega samples and metallic screen (see

Fig. 1(a)) are r=3mm, w=1mm, h=7.5mm and

l=4mm.

3. Experimental environment

In the experiments, two largecopper screens with dimensions 700mm700mm0.5mm were used. The firstmetallicscreen hadacircularapertureinthe center witha radiusof 3.75mm, whereas the second metallic screen had a rectangular aperture with dimensions 3mm7.5mm. The omega samples are insertedacrosstheaperturesasshowninFig.1(c)and (d),respectively.

Transmissionmeasurementshavebeenconductedin free-space illuminating the screen by using the conventional waveguide antennas operating in the

D.Atesetal./PhotonicsandNanostructures–FundamentalsandApplications11(2013)55–64

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range3–6GHz.Themetallicscreenswereplaced,one by one, on a holder at the center between the two antennas as depicted in Fig. 2. The waveguide ports wereconnectedtoanHP8510Cnetworkanalyzerand the S21transmissionparametersweremeasured. 4. Transmissionenhancementresults

Weperformthefirsttransmissionmeasurementwith thecopperscreenhavingthecircularaperture.Then,we

performed the second transmission measurement by insertingtheomega-likesplit-ringresonatorsacrossthe aperture. The measurement results are shown in

Fig.3(a).

Then, we have calculated the enhancement factor fromtheobtainedmeasurementresultsbydividingthe transmission result of the circular aperture with the omega-like split-ring resonators to the transmission results of the circular aperture alone (shown in

Fig. 4(a)). From these results we can see two

Fig.1. (a)Schematicofthedesignedomega-likesplit-ringresonatorsfromthefrontsidewheretheparametersarer=3mm,w=1mm,and

l=4mm.(b)Designedomega-likesplit-ringresonatorfromthebackside.(c)Copperscreenwithomega-likesplit-ringresonatorsinsertedinthe

circularaperturewherethedimensionsareh=7.5mmandL=700mm.(d)Copperscreenwithomega-likesplit-ringresonatorsinsertedinthe

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enhancementpeaks,oneat3.15GHzandanotheroneat 3.95GHz.Weobtained4014-fold enhancementatthe first peak, whereas at the second peak, we obtained 9262-foldenhancement.

Werepeatedthemeasurementsbyusingthemetallic screen withthe rectangularapertureandthe transmis-sionresultsare depictedinFig.3(c).

Wehavecalculatedtheenhancementfactorsfromthe obtained transmission results in a similar way to the enhancementcalculationsofthecircular aperturecase. Theenhancement resultwhen usingthe omegashaped split-resonators across the rectangularaperture is pre-sentedinFig.4(b).Wegetagaintwopeaks.Thefirstone waslocatedat3.15GHz,andthesecondoneat3.95GHz, whicharenearlyatthesamefrequenciesoftransmission peaks of the circular aperture. This means that the transmissionfrequenciesaregovernedbythegeometrical parameters of the omega resonators and are slightly influencedbythesurroundingenvironment.Wereporta 20,780-foldenhancementatthefirstpeakanda 154,500-fold enhancement at the second peak. As already anticipated,theseresultsaremuchhigherthantheones obtainedbyusingdifferenttypesofresonators[15–17]. 5. Physicalanalysisandtheverificationof the experiments bysimulations

Thetwopeaksobtainedinbothexperimentscanbe explained as follows. The connected omegas are

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Fig.2. Schematicdemonstrationofthetransmissionenhancement

experimentsusingopen-endedwaveguideantennasandtheHP8510C

networkanalyzer.

Fig.3. (a)Measuredand(b)simulatedresultsofthetransmissionintensity(dB)throughthecircularaperture.(c)Measuredand(d)simulatedresults

fortherectangularaperture(solidblacklineisforthesingleaperture,solidredlineisfortheomega-likesplit-ringresonatorsinsertedacross

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geometrically symmetric (i.e. made of two identical halves) and, as any symmetric structure, support two fundamental modes of operation. One of them is characterized by an even field symmetry (i.e. the electricfieldisevenlydistributedonthetwohalvesof thestructurewithrespecttotheapertureplane)andthe otherbyanoddfieldsymmetry(i.e.theelectricfieldis oddlydistributedonthetwohalvesofthestructurewith respect to the aperture plane). When our designed omega-likesplit-ringresonatorsareinsertedacrossthe aperture,theloopsoftheomegasbehaveaselectrically short resonant antennas working in the transmitting mode onthe oneside ofthe screenand thereceiving modeontheothersideofthescreen.Atthefrequency forwhichtheelectricfieldexhibitsanevensymmetry, thearmsoftheomegasarenotexcited;however,thetwo antennas are electromagnetically coupledthrough the aperture,as showninFig.5(a).

On the other hand, atthe frequency for which the electric field exhibits an odd symmetry as shown in

Fig.5(b), thearmsofthe omegasare stronglyexcited and, thus, the two antennas are connected by a transmission line leading to astronger coupling and, thus,toahighertransmission.Insummary,thus,thefirst peakobtainedintheexperimentsphysicallyoriginates fromtheevenmode,whereasthesecondpeakfromthe odd mode. For sake of completeness, we show in

Fig.5(c)thesimulatedfielddistributionatafrequency after the two transmission peaks, where the two antennas are not coupled at all and no transmission enhancement isachieved.

To validate the experimental results,we have also performed a numerical analysis of the transmission setupbyusing CSTMicrowaveStudio.First,wehave

modeledthetwoconventionalwaveguideantennasused in the experiments and we have excited them by waveguideports.Westayedloyal totheexperimental environment as much as possible. Open boundary conditionswereemployedtoemulatetheexperimental environment.Inthesimulations,wemodeledtheFR-4 dielectric slab of the PCB with a relative dielectric constant of e=4 and a loss tangent of d=0.01. Simulation results are sketched in Fig. 3(b) for a metallicscreenwithacircularapertureandinFig.3(d) for ametallicscreen witharectangularaperture.The simulation results present a better transmission and higherenhancementfactors.Oneofthemainreasonsof thisdiscrepancyresidesinthediffractionsattheedges of the metallic screen, which are cut-off in the simulation environment. The effects of diffractions areexplainedbyAtesetal.[17].Inaddition,thereare someotherminordifferencesbetweenthesimulations and experiments due to manufacturingprocesses and approximatemodelinginthe simulationenvironment.

Furthermore,we wanted toconsider the effects of circular and rectangular apertures. As previously anticipated,thetworesonantfrequencies are indepen-dentfromthesizeandgeometryofthe apertures.The size andgeometryof the apertures onlyinfluencethe transmission intensity and, thus, the enhancement factors. Clearly, the surface area of the rectangular apertureissmallerthanthesurfaceareaofthecircular one.Hence,whenusingaregularrectangularaperture instead of a regular circular one, the transmission intensity is expected to be lower and, thus, when inserting the omega shaped split-ring resonators, the enhancementfactorisexpectedtobehigher.Measured transmission difference between the circular and the

Fig.4. Enhancementfactorinthecaseoftheomega-likesplit-ringresonatorsinserted(a)acrossthecircularapertureand(b)acrosstherectangular

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rectangularapertureisdepictedinFig.6(a).According tothisgraph,acircularaperturehashighertransmission intensity, due to the size effects. The calculated enhancement factor difference is shown in Fig. 6(b). As explained,by using arectangularaperture we can obtain154,500-foldenhancement.

We have also analyzed the effects of the double-sideddepositedandsingle-sideddepositedomega-like SRRs.Inthefirstcase,weconsideredthesamplesthat areproducedbytwoidenticalomega-likeSRRsamples printedinoppositedirectionsonthetwosidesofthe FR-4 board (PCB), which is named as ‘‘double-sided

60

Fig.5. Surfacecurrentdensity(a)at3.15GHz(evenmodeoperation)wherethefirstenhancementpeakoccurs(MEDIAI),(b)at3.95GHz(oddmode

operation)wheresecondenhancementpeakoccurs(MEDIAII),(c)at5.00GHz(non-resonantfrequency)wherenoenhancementoccurs(MEDIAIII).

Fig.6. (a)Differenceofthetransmissionthroughcircularandrectangularaperturesand(b)differenceoftheenhancementfactorwhenomega-like

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Fig.7.Electricfielddistributionmapsofthe(a)double-sidedomega-likeSRRacrosstherectangularapertureat3.95GHz(above,MEDIAIV),

5.00GHz(below,MEDIA V),(b)single-sidedomega-likeSRRacrosstherectangularapertureat3.95GHz(above,MEDIA VI),5.00GHz(below,

MEDIAVII),(c)rectangularaperturewithoutomega-likeSRRat3.95GHz(above,MEDIAVIII),5.00GHz(below,MEDIAIX).

Fig.8. (a)Transmissioncharacteristicsofdouble-sided(solidred),Single-sidedomega-likeSRRs(solidblue),aperturewithoutomega-likeSRRs

(solidblack),(b),(c)and(d)electricfielddistributionmapscollectedat3.95GHz(resonancefrequency)respectively.Regardingmedia:MEDIAX,

MEDIAXIandMEDIAXIIfor(b),(c),and(d)respectively.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferred

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omega-likeSRRs’’.The sampleswhich arenamed as ‘‘single-sided’’areproducedbysingleomega-likeSRR printedononeofthesidesofthePCB.Here,wepropose thatalthoughthesinglesidedomegastructuresarestill resonators,thereasonofthehighenhancementisdueto thesymmetricdesignoftheomega-likeSRRs.Inorder to demonstrate the effect of the symmetric and non-symmetricdesign, wehave analyzedthe electric field distribution maps for three different cases that are showninFig.7.Thesecasesarethefielddistributionsof the double-sided omega-like SRRs inserted in the rectangular aperture (Fig. 7(a)), single-sided omega-likeSRRinsertedintherectangularaperture(Fig.7(b)) and rectangular aperture without omega-like SRRs (Fig.7(c))atthefrequencies3.95GHz(highlyresonant frequencywheresecondenhancementpeakoccurs)and 5.00GHz(non-resonantfrequencywhereno enhance-mentoccurs).

AccordingtoFig.7(a),itisobservablethattheelectric field distribution isstronger atthe resonant frequency (above) andelectric field is weak at the non-resonant frequency (below). Although the field is simulated at the sameresonant frequency in Fig. 7(b) (above),the field strength is weaker than the double-sided cases.

This weaknessoccursduetonon-symmetricnature of the omega-like SRRs design. In other words, the strongenhancementisachievedwhenthedouble-sided (symmetric) omega-like SRRs is used. However, the resonant frequencyof the single-sidedomegaismuch moresensitivetothesurroundingenvironmentthanthe double-sided one. The resonant frequency, thus, may vary if it is not exactly aligned at the center of the aperture. Nevertheless, the single-sided structure still worksasaresonatorandthefieldstrengthisstrongerthan thecasewithoutaresonator.Finally,thefield distribu-tions,whichrepresentweaktransmissionintheabsence of omega-like SRRs, are observed in Fig. 7(c) at 3.95GHz(above) and5.00GHz (below).In this case, thereislowtransmissionandhencenoenhancementcan beobtainedduetoabsenceoftheresonator.

Adeeperanalysishasbeen donebycomparingthe transmissionspectra ofthe double-sided,single-sided, and in the absence of omega-like SRR across the rectangular aperture in Fig. 8(a). According to the figure,when thesingle-sided omega-likeSRRis used insteadofdouble-sided,itisapparentthatenhancement peaksvanishandtransmissionbehavesasinthecaseof the absence of omega-like SRRs. Furthermore, we

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Fig.9.Fielddistributionmaps(a)0.1laway(b)0.5laway,(c)0.7lawayfromOmega-likeSRR,and(d)normalizedtransmittedintensityversus

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obtainedthefielddistributionmapsforthesethreecases by field monitors at the highly resonant frequency (3.95GHz) as in Fig. 8(b)–(d). The strong coupling between the receiver and transmitter compartments occursduetodouble-sidedomega-likeSRRasshownin

Fig.8(b),whereasinFig.8(c),couplingisdestroyedby using single-sided omega-like SRR. Also, in the absence of omega-like SRRs, there is no coupling; hencenotransmissionenhancementoccursaspresented inFig.8(d).

Asafinalissue,weanalyzedthefieldlocalizationof thetransmittedwaveattheexitsideoftheomega-like SRRs.Inthiscase,wehaveuseddouble-sided omega-like SRRs analyzedatthehighly resonantfrequency (3.95GHz).Theelectricfieldsatthevariousdistances inthedirectionofthepropagationat theexit sideof omegasamplesarecollectedbyelectricfieldprobes. Byusingthesedata,wehavecalculatedthenormalized electric field intensity. The normalized electric field intensityofthetransmittedwaveversusdistanceaway from the omega-like SRR in terms of operational wavelength isdepictedinFig.9(d).Inthefigure,the transmitted wave decays as the electric field probe movesawayfromtheomega-likeSRRattheexitside.

Fig. 9(a) represents the field distribution when the probe is 0.1l away from the omega-like SRR, (b) represents when the probe is 0.5l away from the omega-like SRR and finally (c) represents when the probe is 0.7l away from the omega-like SRR. This explainsthe evanescentfield ishighly localizednear theomega-likeSRRandastheprobemovesawayfrom theresonator,theevanescentfielddecayswhichresult inlowtransmission.

6. Conclusionsandfuturework

To summarize, we expected higher transmission enhancement resultsthantheones alreadyreportedin theliteraturebyusingregularsplit-ringresonators,due tothelow-lossandbi-anisotropicnatureoftheproposed omega-like split-ring resonator. The extremely high results,ontheorderof150,000-fold,demonstratedboth experimentally andnumerically, confirmour expecta-tions.Wealsoobservedthatthegeometricalparameters of the omegas control the frequencies at which enhanced transmission is obtained and that such frequencies do not depend on the environment surrounding the resonators. At the final stage, we analyzed the physicaloriginsofthe enhancementand the effects of using symmetric and non-symmetric omega-like SRR designs. Furthermore, we demon-stratedthehighlylocalizedelectricfieldsinthevicinity

of omega-like SRRs. The proposed structure can be successfully used to design microwave waveguide components,sensors,electricallysmallaperture anten-nas, high-sensitive probes for imaging and screening systems.

Acknowledgements

This work is supported by projects DPT-HAMIT, EU-PHOME, EU-N4E, NATO-SET-181, and TUBI-TAK under project Nos., 107A004, 107A012, and 109E301.Oneoftheauthors(E.O.)alsoacknowledges partialsupportfromtheTurkishAcademyofSciences. AppendixA. Supplementarydata

Supplementarydataassociatedwiththisarticlecan be found, in the online version, at http://dx.doi.org/

10.1016/j.photonics.2012.08.002.

References

[1] H.A. Bethe, Theory of diffraction by small holes, Physical

Review66(1944)163–182.

[3] G.Q.J.A. Porto,F.J. Garcia-Vidal,J.B. Pendry, Transmission

resonancesonmetallicgratingswithverynarrowslits,Physical

ReviewLetters83(1999)2845–2848.

[4] L.Martin-Moreno,F.J.Garcia-Vidal,H.J.Lezec,K.M.Pellerin,

T.Thio,J.B.Pendry,T.W.Ebbesen,Theoryofextraordinary

opticaltransmissionthroughsubwavelengthholearrays,

Physi-calReviewLetters86(2001)1114–1117.

[5] L.Martin-Moreno,F.J.Garcia-Vidal,H.J.Lezec,A.Degiron,

T.W.Ebbesen,PhysicalReviewLetters90(2003)167401.

[6] S.Akarca-Biyikli,I.Bulu,E.Ozbay,Enhancedtransmissionof

microwaveradiationinone-dimensionalmetallicgratingswith

subwavelength aperture, Applied Physics Letters 85 (2004)

1098–1100.

[7] S.Akarca-Biyikli,I.Bulu, E.Ozbay, Resonantexcitation of

surfaceplasmonsinone-dimensionalmetallicgratingstructures

atmicrowavefrequencies,JournalofOpticsA:PureandApplied

Optics7(2005)S159–S164.

[8] J. Pendry, L. Martin-Moreno, F. Garcia-Vidal, Mimicking

surfaceplasmonswithstructuredsurfaces,Science305(2004)

847–848.

[9] E. Ozbay, Plasmonics:merging photonicsand electronics at

nanoscaledimensions,Science311(2006)189.

[10] N.Katsarakis,M.Kafesaki,I.Tsiapa,E.N.Economou,C.M.

Soukoulis,Hightransmittanceleft-handedmaterialsinvolving

symmetricssplit-ringresonators,PhotonicsandNanostructures

–FundamentalsandApplications5(2007)149–155.

[11] A.Alu,F.Bilotti,N.Engheta,L.Vegni,Metamaterialcovers

overasmallaperture,IEEETransactionsonAntennas

Propaga-tion54(2006)1632–1643.

[12] A.Alu`,F.Bilotti,N.Engheta,L.Vegni,Subwavelengthplaner

leaky-wave components with metamaterial bilayers, IEEE

TransactionsonAntennasPropagation55(2007)882–891.

[13] R.Marques,F.Mesa,J.Martes,F.Medina,Comparativeanalysis

(10)

meta-materialdesign-theoryandexperiments,IEEETransactionson

AntennasPropagation51(2003)2572–2581.

[14] F.Bilotti,L.Scorrano,E.Ozbay,L.Vegni,Enhanced

transmis-sionthrougha sub-wavelengthaperture:resonantapproaches

employingmetamaterials,JournalofOpticsA:PureandApplied

Optics11(2009)114029.

[15] K.Aydin,A.O.Cakmak,L.Sahin,Z.Li,F.Bilotti,L.Vegni,E.

Ozbay, Split-ring-resonator-coupled enhanced transmission

throughasinglesubwavelengthaperture,PhysicalReview

Let-ters102(2009)013904.

[16] A.O.Cakmak,K.Aydin,E.Colak,F.Bilotti,L.Vegni,E.Ozbay,

Enhancedtransmissionthroughasubwavelengthapertureusing

metamaterials,AppliedPhysicsLetters95(2009)052103.

[17] D.Ates,A.O.Cakmak,E.Colak,R.Zhao,C.M.Soukoulis,E.

Ozbay,Transmissionenhancementthroughdeepsubwavelength

aperturesusingconnectedsplitringresonators,OpticsExpress

18(2010)3952–3966.

[18] M.M.I.Saadoum,N.Engheta,Areciprocalphaseshifterusing

novelpseudochiralorvmedium,MicrowaveandOptical

Tech-nologyLetters5(1992)184.

[19] C.R.Simovski,S.A.Tretyakov,A.A.Sochava,B.Sauviac,F.

Mariotte,T.G.Kharina,Antennamodelforconductiveomega

particles,JournalofElectromagneticWavesandApplications11

(1997)1509–1530.

[20] C.R.Simovski,S.He,Frequencyrangeandexplicitexpressions

fornegativepermittivityandpermeablityofanisotropicmedium

formedbya lattice ofperfectlyconductingOmega-particles,

PhysicalReviewA311(2003)254.

[21] L.Ran,J.Huangfu,H.Chen,Y.Li,X.Zhang,K.Chen,J.A.

Kong,Microwavesolid-stateleft-handedmaterialwithabroad

bandwidthandanultralowloss,PhysicalReviewB70(2004)

073102.

[22] K.Aydin,Z.Li,S.Bilge,E.Ozbay,Experimentalandnumerical

studyofomegatypebianisotropicmetamaterialcombinedwitha

negativepermittivitymedium,PhotonicsandNanostructures–

FundamentalsandApplications6(2008)116–121.

Furtherreading

[2] T.W.Ebbesen,H.J. Lezec,H.F.Ghaemi, T.Thio,P.A. Wolff,

Extraordinaryopticaltransmissionthroughsub-wavelengthhole

arrays,Nature391(1998)667–669.