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Current Applied Physics 12 (2012) 443e450

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Current Applied Physics

journal homepage: www.elsevier .com/locate/cap

Dual-band polarization-independent sub-terahertz fishnet metamaterial

Cumali Sabah*, Hartmut G. RoskosJohann Wolfgang Goethe-Universität, Physikalisches Institut, Max-von-Laue-Strasse 1, D-60438 Frankfurt am Main, Germany

a r t i c l e i n f o

Article history:Received 19 April 2011Received in revised form15 June 2011Accepted 29 July 2011Available online 4 August 2011

Keywords:MetamaterialResonancesFishnetDual-bandPolarization-independency

* Corresponding author.E-mail address: sabah@physik.uni-frankfurt.de (C.

1567-1739/$ e see front matter � 2011 Elsevier B.V.doi:10.1016/j.cap.2011.07.047

a b s t r a c t

A dual-band and polarization-independent fishnet metamaterial for the sub-THz frequency range isproposed and investigated. Dual-band modes have two resonances in which the first one is fixed asa left-handed mode and the second one can be arranged as a left-handed or single-negative mode. Weselect the character of second resonance by the choice of substrate properties. The metamaterial featuresof the structure are analyzed using the scattering data and confirmed by applying KramerseKronigrelations. The characteristic features are also verified by the current distribution at the inner metallicsurfaces of the structure. The influence of substrate modifications is studied and the effect of this changeon resonances is discussed. The design of a dual-band and polarization-independent sub-THz meta-material presented here can serve as a model and guide to realize tunable fishnet metamaterials for otherfrequency regimes.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

Single-negative (SNG) or double-negative (DNG) metamaterials(MTMs) are artificially constructed materials engineered to havephysical properties which are not found in conventional materials.MTMs have gained remarkable attention because of their unusualelectric and magnetic features and due to their potential applica-tions [1] in different regimes of the electromagnetic spectrum. Oneof them is the rapidly developing terahertz (THz) range whereMTMs play a role in the development of the THz photonic tech-nology [2e4]. Most THz MTM investigations have been performedbased on structures consisting of split-ring resonators (SRRs) ora combination of SRRs with wire arrays. However, such structureshave severe limitations because the magnetic field should beperpendicular to the SRR surface to achieve a negative permeability,and the electric field should be parallel to the wire arrays to achievea negative permittivity under normal incidence. In addition, thedimension of the structure should be small enough compared to thewavelength which creates challenges in the fabrication of high-frequency devices. As an alternative, cut-wire pairs or plate pairswere proposed for the telecommunications wavelengths in thenear-infrared and shown to have negative magnetic permeability[5]. In the meantime, several studies have been reported in theliterature regarding novel MTM designs of which a very promisingone seems to be the so-called fishnet structure, including the

Sabah).

All rights reserved.

fishnet-type dual-band structures for visible and near-infraredspectra, because of their simplicity in the fabrication process andtheir capability to provide left-handed (LH) characteristics undernormal incidence in the desired frequency range [6e21]. The mainfocus of the present work lies on dual-band operation in the THzfrequency regime with a lower-frequency LH-band and a higher-frequency band which is either LH or SNG, selected by the choiceof the dielectric properties of the substrate. We validate these MTMfeatures of our structural design with the help of the Kra-merseKronig (KK) relation and a consistency check based on ananalysis of the current distribution.

Similar investigations canbe found in literature [6e21]. Regardingthe operation frequency, there are but a few studies dealingwith THzfishnetMTMs in the literature, a lackwhich provides amotivation forthe present study [16,20]. Of the few existing studies, Ref. [16]considers a structure which is not simple as in our case, and thedielectric substrate between the metals is perforated which costsadditional effort in the fabrication process. In addition, the proposedstructure does not provide a dual-band feature. In Ref. [20], thestructure is also not simple and the dual-band feature is obtained bycombining two differently sized plate pairs and equally sized wires.Each combination provides a single resonance (in total two) atdifferent spectral positions. In our case, we do not require the seconddifferently sized unit cell and our structure itself creates the high-order modes. With regard to the dual-band character and thepolarization-independency, there are several investigations in theliterature which explore dual-band or polarization-independentMTMs [6e20]. However, most of them are designed for the

Fig. 1. Schematic representation of the dual-band and polarization-independentfishnet MTM.

C. Sabah, H.G. Roskos / Current Applied Physics 12 (2012) 443e450444

microwave, infrared, and visible regions, not for the THz band. Forexample, adual-bandandpolarization-independentMTMcomprisedof several layers of stacked hole arrays separated by dielectrics wasproposed for the visible spectrum in Refs. [14] and [15]. In thosestudies, the analysis was based on the internal and external SPPmodes, and the resonance peaks were studied in terms of thediffraction order. However, causality was not validated and consis-tency not checked by an analysis of the current distribution. Ingeneral, internal (or gap, or channel) surface-plasmon-polaritons areexcited to achieve the second-order mode [14,15]. In our contribu-tions, we are dealing with a related phenomenon to obtain the dual-band feature for sub-THz frequencies with a single-layer MTM. Inaddition, in some cases, the dual-band negative-index featureappears as a result of the high losses of the structure [8,10], which,however, is not the case in our study. The number of examples can beincreased. Concerning tunability by the substrate, it was alreadystudied in the cases of a SRR structure which operates in the micro-wave region [22] and a fishnet MTMs in the optical range [23,24]. Inthose studies, the structures do not provide the dual-band characterand theyare not polarization-independent. Furthermore, the effect ofthe dielectric properties of the substrate is not studied well for theTHz fishnet MTM, especially for the THz dual-band and polarization-independent fishnet MTMs, in which we present a systematic studywith the verification to control the high-order resonance by thechosen substrate properties. Finally, we point out that the designproposed here with its simple geometry can simplify themanufacturing process.

In this paper, a fishnet MTM for sub-THz frequencies is pre-sented which allows dual-band operation at the fundamentalresonance frequency (low-order mode) and a higher-order mode(second order in our case), with DNG (LH) characteristics for thefirst and selectively DNG or SNG characteristics for the latter. TheLH- or SNG-mode can be selected by the substrate properties suchas the permittivity or the loss tangent. Furthermore, the structuralproperties of the fishnet MTM provide polarization-independencywhich adds an extra advantage to the suggested MTM. In thefollowing, the dual-band feature is analyzed by means of simula-tions of the S-parameters, and validation is obtained by testing viaKramerseKronig (KK) relations [25] that causality is fulfilled. Theeffective constitutive parameters are extracted using standardretrieval methods [26,27]. They reveal the dispersion character ofthe artificially structured MTMs and the occurrence of negativepermittivity and negative permeability. Our results show that onecan have a negative effective refractive index in two different sub-THz frequency regions. Our data suggest that the higher mode canbe agilely switched between negative and positive values bychanging the substrate properties via external control parameters.

2. Simulation and analysis

The polarization-independent fishnet MTM is designed to havean identical configuration in the two lateral dimensions of thesample. Hence, the sample will operate for all polarizations due tothe symmetry of the structure, and the effective refractive indexwill be functionally independent of the polarization of the incidentsub-THz wave. A schematic representation of the single-layerfishnet unit cell, with the relevant geometrical parameters, isshown in Fig. 1. The propagation of the sub-THz wave is in the z-direction, the electric field is oriented in the y-direction, and themagnetic field in the negative x-direction. The metallic part ishighlighted in yellow in the figure (for interpretation of the refer-ences to colour in this figure, the reader is referred to the webversion of this article); gold films with a thickness of 0.5 mm areused for congruent metallization of the front- and back-side of the50-mm-thick substrate. The unit cell has a periodicity of a¼ 250 mm

and is repeated along the x and y-directions. The metallic parts ofthe sample have the same width (w¼ 150 mm) which is carefullyselected to obtain a strong high-order mode (LH or SNG, dependingon the properties of the substrate) of the fishnet MTM. The struc-ture can be considered as a combination of parallel metal platesalong the magnetic-field direction, which provide the magneticresonance (negative permeability), and of pairs of continuous wireswith modulated width along the electric-field direction, whichprovide the electric resonance (negative permittivity) [9].

Thenumerical simulationof thefishnetMTMsample isperformedby a full-wave EM solver based on the method of moments. Periodicboundary conditions are employed along the lateral directions.Waveguide ports are assumed for the excitations and detection of thesub-THz wave. The Drude model approximation is used to describethe effective metallic dielectric properties of the gold metallizationwhichcanbegivenas εðf Þ ¼ 1� f 2p =ðifgþ f 2Þ,where fp is theplasmafrequency and g is the damping rate of the material [28,29]. Thefollowingvalues are used for theplasma frequencyanddamping rate:fp¼ 2175 THz and g ¼ 6:5 THz [28,29]. For the substrates, weassume the parameters of Rogers high-frequency laminates (TMM4or RT/Duroid 5880). TMM4 has a dielectric constant of 4.5 and a losstangent of 0.002 which (together with the metallic parts) providestwo separate LH regions in the frequency spectrum. RT/Duroid 5880has a dielectric constant of 2.2 and a loss tangent of 0.0009 which(together with the metallic parts) provides one LH region and oneSNG-region at two different frequency positions.

The complex S-parameters for a single-substrate-layer sample(front- and back-side metalized) with TMM4 substrate are shown inFig. 2. There are three transmission peaks with the correspondingreflection minima and phase changes at around 0.46 THz, 0.65 THz,and 0.72 THz, with transmission values of approximately �9 dB,�3 dB, and �0.28 dB, which indicate the presence of threeresonances.

To be able to identify the character of these resonances, theretrieval method of Refs. [26,27] is employed for the extraction ofthe complex-valued spectra of the impedance, refractive index,permittivity, and permeability. The results are given in Fig. 3. A firstquality check of the extracted parameters of the material based onthe retrieval process is a survey of the real part of the impedanceand the imaginary part of the refractive index. Both are greater thanzero over the whole frequency range of the plot (0.1e1 THz) asexpected for a lossy (non-amplifying) medium.

0.1 0.5 1.0

-30

-20

-10

0

Frequency [THz]

]Bd[srete

marap-S

S 11

S 21

0.1 0.5 1.0

-3

-2

-1

0

1

2

3

Frequency [THz]

]dar[Sfo

esahP

S 11

S 21

Fig. 2. Frequency response of the reflection and transmission for the fishnet MTM with TMM4 substrate.

C. Sabah, H.G. Roskos / Current Applied Physics 12 (2012) 443e450 445

In the impedance plot, the first and the second transmissionpeaks correspond to LH resonances while the third and strongestone does not. This peak occurs at the electric plasma frequency andresults from the field resonance of the wire array (effective plasmaresonance). In the present case, the effective plasma frequency is0.72 THz and the real part of the permittivity is negative below thisfrequency. The second magnetic resonance occurs at 0.65 THz,hence below the plasma frequency, with the consequence that boththe permittivity and the permeability are negative simultaneouslyat this resonance, and a second LH-mode exists in the spectrum.Such an occurrence of twomagnetic resonances below the effectiveplasma frequency has not been reported in the earlier fishnet orfishnet-like studies of Refs. [5e9,11,12,16e19,21]. Either a second

0.1 0.5 1.0 -1

-0.5

0

0.5

1

Frequency [THz]

] z [ e c n a d e p

m

I

Re(z) Im(z)

0.1 0.5 1.0 -80

-60

-40

-20

0

Frequency [THz]

[ε

y t i v i t t i m

r e P

]

Re( ) Im( )

0.6 0.65 0.7 -1.5

-1

-0.5

0

εε

Fig. 3. Extracted effective parameters retrieved from the reflection an

resonance below the effective plasma frequency did not exist, orthe designs may have allowed only for a very weak transmissionpeak which does not support a second resonance in the higher-mode region. Note that the existence of a second-order magneticresonance for the multilayer metal-dielectric stacked hole arrays asperforatedmetal-dielectric sheets is presented in Refs. [14] and [15]for achieving simultaneous negative permittivity and permeabilityin the visible spectrum. In our case, the structure is not patternedwith hole arrays and it is designed for the sub-THz frequency rangewith the confirmation of causality by the KK relations and thecurrent distributions. Furthermore, the abrupt changes in thetransmission response of our fishnet MTM, responsible for themagnetic resonances, occurs due to the surface-plasmon-

0.1 0.5 1.0

-10

-5

0

5

10

15

Frequency [THz]

] n [ x e d n i

e v i t c a r f e R

Re(n) Im(n)

0.1 0.5 1.0-3

-2

-1

0

1

2

3

4

Frequency [THz]

[μ

y t i l i b a e m

r e P

]

Re(μ ) Im(μ )

d transmission data for the fishnet MTM with TMM4 substrate.

0.1 0.5 1.0

-10

-5

0

5

10

15

Frequency [THz]

] n [ x e d n i

e v i t c a r f e R

Re(n eff )

Im(n eff )

Re(n KK )

Fig. 4. Effective refractive index and KK approximation for the fishnet MTM withTMM4 substrate.

C. Sabah, H.G. Roskos / Current Applied Physics 12 (2012) 443e450446

polaritons excitation and the first resonance corresponds to the(�1, 0) or (0, �1) diffraction order and the second one to the (�1,�1) order. Consequently, we have two modes and each one is beingthe dominant one in different frequency region [18,30]. Thecoupling of the THz wave to the inner mode running betweenmetals is based on the existence of a periodic lattice providing theadditional required parallel component of the wave-vector. Thiswould also explain the different dependency of two resonances onthe substrate too which will be shown in the second example.

Moreover, the refractive index has two DNG regions at thefrequency positions of the magnetic resonances at 0.46 and0.65 THz. The effective permittivity has two small anti-resonancesat the locations of the first and second transmission peak inwhich the second, and weak, anti-resonance is shown in the figureinset of the permittivity plot [31]. Note that the effective permit-tivity has a Drude-like electric response; the interconnection ofmetal plates and wires of our structure hence exhibits an analogousbehavior to what one finds for continuous wires. The effectivepermittivity shows anti-resonant behavior with a negative imagi-nary part at the magnetic resonance frequency positions [31]. Inparticular, the dual-band characteristic of the permittivity is alsoexcited by a plasmonic behavior of the wires. The effectivepermeability has also two negative bands with a Lorentz-likemagnetic response. In contrast to the permittivity, the secondpermeability band is remarkably pronounced.

In order to verify the existence and validity of the negative indexof refraction, a unique retrieval of effective parameters from thereflection and transmission data is obtained by enforcing thecausality. The applied extraction method is based on the KK rela-tions which have been used to calculate the index of refractionusing calculated or measured data sets [25]. Since the imaginarypart of the refractive index is not affected by the branch problem ofthe standard retrieval method, it can be calculated without ambi-guity and hence it can be determined uniquely. By knowing theunique imaginary part of the refractive index, the real part can bedetermined using KK relations and the guidance of the imaginarypart for the correct choice of the branch. The KK relation for the realpart of the refractive index can written as follows:

RennKKeff ðf Þ

o¼ 1þ 2

pPZN

0

f 0Imnneff

�f 0�o

f 02 � f 2df 0 (1)

where P designates the principal value of the integral. Note that tocompute the given integral accurately, the imaginary part of therefractive index must be known for the entire spectrum. For prac-tical reasons, the given integral has to be truncated, which yieldssome error. Nevertheless, the evaluation of the KK equation evenfor the finite bandwidth can provide approximate data for theverification of the actual data. Fig. 4 shows the real part of therefractive index calculated with the two different methods. Theunique imaginary part is also shown in the figure. As it is seen fromthe figure, there is a reasonable agreement between the two resultsfor the real part of the effective refractive indexes which validatesthe existence of the dual-band modes and their DNG character.

Furthermore, the LH character of the corresponding resonancescan also be validatedby the current distribution of the innermetallicplanes of the structure at the resonance frequencies. Figs. 5 and 6show the current distributions at the metallic parts of the struc-ture at the two lower resonance frequencies. The surface currentdistributions show the anti-symmetric responsewhich correspondsto amagnetic resonance. The directions of current floware oppositeto each other at the opposing areas of the metallic crosses. The out-of-phase currents form a virtual current loop, a part of which is thedisplacement current in the dielectric also excited by the

electromagneticwave. The displacement currentflows between theplates and closes the current loop (see Figs. 5c and 6c).The resultingeddycurrent generates an inducedmagneticfieldwhichneutralizes,at least partly, the effect of themagnetic radiation field. The inducedresponse has a pronounced frequency-dependencywhich producesstrong resonances showing negative permeability. In addition, thefirst resonance is stronger than the second one as can be clearly seenfrom those figures and Fig. 3. This is another way to check thecharacter of the resonances and the observation here is consistentwith those of Refs. [9,12e15,18,20,32]. Note that the thickness of theproposed fishnetMTM sample ismuch smaller than thewavelengthof the radiation (approximately l/10 for the first mode and l/13 forthe second mode, where l is the operation wavelength at the reso-nance frequency) which allows to treat the structure as an effectivehomogeneousmedium in the presence of the external THzwave. Asdiscussed already, the external electromagnetic wave excites elec-tric currents which flow in opposite directions in adjacent metallicplates. As each plate represents a front- and a back-side of a currentloop, the current partly cancel; however, the strength of the currentis not the same in the front- and back-side of themetallic parts of thestructure, as the electromagnetic wave is attenuated on its passagethrough the MTM. Therefore, the net current in the system is notzero and a virtual current loop is formed with the help of thedisplacement current [13e15,32]. Finally, a magnetic response isproduced by the anti-parallel current arising from an anti-symmetric SPP mode in metallic part of the MTM and the negativepermeability can be achieved. This is the other way to explain theorigin of the magnetic resonances and the effective negativepermeability.

As a second example, a single-substrate-layer fishnet MTMwithRT/Duroid 5880 substrate is considered. All design parameters arethe same as those of the previous one except for the substrate. Fig. 7displays the complex scattering parameters for the investigatedsample. As it is seen, there are also three resonances as in theprevious example. The transmission peaks are located at around0.65 THz (�4 dB), 0.86 THz (�0.2 dB), and 0.9 THz (�1.4 dB). If onecompares the results of Fig. 2 and Fig. 7, it appears that all trans-mission peaks are higher than the corresponding peaks of theprevious onewhich indicates stronger resonant behavior. However,the high-order mode (the second magnetic resonance with DNG orSNG character) is situated at a frequency above the highest peakwhile it is below the highest peak in Fig. 2. This aspect is discussed

Fig. 5. Current distribution of the inner planes of the MTM sample at the first resonance frequency of 0.46 THz, (a) front-side, (b) back-side, (c) displacement current inside thesubstrate. Coordinate system as in Fig. 1.

C. Sabah, H.G. Roskos / Current Applied Physics 12 (2012) 443e450 447

further below. It is expected that the highest peak is formed by theelectric plasma resonance. The other spectral features occur due tothe electric and magnetic resonances of the designed structure. Thepeak values and frequency positions depend on the substrateproperties, such that the positions are generally shifted towardshigher frequencies when the substrate is changed from TMM4 toRT/Duroid 5880. This result is readily explained on the basis of theLC circuit model for the fishnetMTM. If the real part of the dielectricconstant of the substrate and the loss tangent are decreased, theresonance frequencies increase as a result of the decreasing LCvalues [33]. Simulations show that this effect and the crossing ofthe high-order mode over the electric plasma frequency can beachieved by variation of either the dielectric constant or the losstangent, or by variation of both.

The retrieved effective parameters for the fishnet MTM withRT/Duroid 5880 substrate is shown in Fig. 8. The electric plasmafrequency is at around 0.86 THz which is the result of thecoupling between the electric radiation field and the wires. Thefirst and second resonances are located at around 0.65 THz and

0.9 THz, i.e., below and above the plasma frequency, as can beseen from the frequency responses of the permittivity andpermeability. The negative-permittivity region hence does notoverlap with the second magnetic resonance (second negativepermeability) with the consequence that the material has oneLH- and one SNG-region at two different frequency positions. Theplot of the refractive index correspondingly exhibits only onefrequency region (located around 0.65 THz) where the real partof the refractive index becomes negative. The correctness of theretrieval of the negative-index feature is again tested by KKanalysis. The data shown in the refractive-index graph of Fig. 8corroborate the LH-mode.

3. Discussion

Based on the results of the numerical analysis, one can concludethat the change of the substrate has a strong influence on the MTMproperties, notably on the dual-band resonance of the structure.Changing the substrate from TMM4 to RT/Duroid 5880 decreases

Fig. 6. Current distribution of the inner planes of the MTM sample at the second resonance frequency of 0.65 THz, (a) front part, (b) back part, (c) displacement current inside thesubstrate. Coordinate system as in Fig. 1.

C. Sabah, H.G. Roskos / Current Applied Physics 12 (2012) 443e450448

both the dielectric constant (from 4.5 to 2.2) and the loss tangent(from 0.002 to 0.0009), which leads to a frequency shift of theresonances towards higher frequencies. This means that thenegative region of the permeability also shifts. In addition, the

0.1 0.5 1.0

-30

-20

-10

0

Frequency [THz]

] B d [ s r e t e

m

a r a p - S

S 11

S 21

Fig. 7. Complex scattering parameters for the fis

transmission magnitude of the corresponding resonances ismodified, while there is almost no change in the magnitude of themain (strongest) transmission peak related with the hole (effectiveplasma resonance) mode. We now address the crossover of one of

0.1 0.5 1.0

-3

-2

-1

0

1

2

3

Frequency [THz]

] d a r [ S f o

e s a h P

S 11

S 21

hnet MTM with RT/Duroid 5880 substrate.

0.1 0.5 1.0-2

-1

0

1

2

Frequency [THz]

Impe

danc

e [z

]

Re(z)Im(z)

0.1 0.5 1.0-10

-5

0

5

10

15

Frequency [THz]

Ref

ract

ive

inde

x [n

]

Re(neff )

Im(neff )

Re(nKK )

0.1 0.5 1.0-80

-60

-40

-20

0

Frequency [THz]

Perm

ittiv

ity [

]

Re( )Im( )

0.85 0.95-0.5

0

0.5

1

0.1 0.5 1.0

-2

0

2

4

Frequency [THz]

Perm

eabi

lity

[]

Re( )Im( )

με

εε

μμ

Fig. 8. Retrieved effective parameters for the fishnet MTM with RT/Duroid 5880 substrate.

C. Sabah, H.G. Roskos / Current Applied Physics 12 (2012) 443e450 449

the magnetic resonances over the effective plasma resonancein more detail. When the substrate is changed from TMM4 toRT/Duroid 5880, the magnetic resonances shift from 0.46 THz and0.65 THz to 0.65 THz and 0.9 THz, respectively, their spectral posi-tions scaling inversely with the square root of the substrate’spermittivity. The amount of shift is less pronounced for the effec-tive plasma resonance. Its position moves from 0.72 THz (forTMM4), which places it above themagnetic resonances, to 0.86 THz(for RT/Duroid 5880) where it now lies between the magneticresonances. As the effective permittivity changes from negativevalues to positive ones at the effective plasma resonance, bothmagnetic resonances are of LH character for TMM4 (both magneticresonances overlap with the region of negative effective permit-tivity). In the case of RT/Duroid 5880, only the lower-frequencymagnetic resonance retains its LH nature, while the higher-frequency resonance has turned into an SNG mode because theeffective permittivity is positive at its frequency position. Asa result, the first mode is fixed as LH-mode and the second one canbe arranged as LH- or SNG-mode by suitable selection of thesubstrate.

4. Conclusion

In conclusion, a dual-band and polarization-independent sub-THz fishnet MTM is proposed and analyzed. Dual-band operationwith a lower-frequency LH-band and a higher-frequency bandwhich can be selected to be either LH or SNG in character is shown.The selection is achieved by the dielectric properties of thesubstrate. They allow to tune the electric plasma frequency toa position either below or above the second band, which results in

an LH character in the first case and a SNG character in the second.Confirmation of the assignments is obtained by a KramerseKroniganalysis and by inspection of the current distribution at the innerplanes of the metallic parts of the MTM sample. Our results showthat the choice of the substrate properties significantly influencesthe frequency positions of the resonances and the character of themodes. The real part of the refractive index of the higher-ordermode can be switched between positive and negative values. Thissuggests that one should be able to develop actively controlledfishnet MTMs whose substrate properties e and with them theiroptical properties e can be changed by applying temperature,voltage, electric current, magnetic field, and so on.

References

[1] N. Engheta, R.W. Ziolkowski, Metamaterials e Physics and EngineeringExplorations. Wiley e IEEE Press, Piscataway, NJ, 2006.

[2] T.J. Yen, W.J. Padilla, N. Fang, D.N. Basov, D. Vier, D.R. Smith, J.B. Pendry,X. Zhang, THz magnetic response from artificial materials, Science 303 (2004)1494e1496.

[3] H.O. Moser, B.D.F. Casse, O. Wilhelmi, B.T. Saw, Terahertz response ofa microfabricated rod-splitring-resonator electromagnetic metamaterial,Phys. Rev. Lett. 94 (2005) 063901.

[4] H.-T. Chen, W.J. Padilla, R.D. Averitt, A.C. Gossard, C. Highstrete, M. Lee,J.F. O’Hara, A.J. Taylor, Electromagnetic metamaterials for terahertz applica-tions, Terahertz Sci. Technol. 1 (2008) 42e50.

[5] G. Dolling, C. Enkrich, M. Wegener, J.F. Zhou, C.M. Soukoulis, S. Linden, Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials, Opt.Lett. 30 (2005) 3198e3200.

[6] S. Zhang, W. Fan, K.J. Malloy, S.R.J. Brueck, Near-infrared double negativemetamaterials, Opt. Express 13 (2005) 4922.

[7] S. Zhang, W. Fan, N.C. Panoiu, K.J. Malloy, R.M. Osgood, S.R.J. Brueck, Experi-mental demonstration of near-infrared negative-index metamaterials, Phys.Rev. Lett. 95 (2005) 137404.

C. Sabah, H.G. Roskos / Current Applied Physics 12 (2012) 443e450450

[8] U.K. Chettiar, A.V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V.P. Drachev,V.M. Shalaev, Dual-band negative index metamaterial: double negative at813 nm and single negative at 772 nm, Opt. Lett. 32 (2007) 1671e1673.

[9] M. Kafesaki, I. Tsiapa, N. Katsarakis, Th. Koschny, C.M. Soukoulis,E.N. Economou, Left-handed metamaterials: the fishnet structure and itsvariations,", Phys. Rev. B 75 (2007) 235114.

[10] D. Kwon, D.H. Werner, A.V. Kildishev, V.M. Shalaev, Near-infrared meta-materials with dual-band negative-index characteristics, Opt. Express 15(2007) 1647.

[11] K.B. Alici, E. Ozbay, Characterization and tilted response of a fishnet meta-material operating at 100 GHz, J. Phys. D: Appl. Phys. 41 (2008) 135011.

[12] K.B. Alici, E. Ozbay, A planar metamaterial: Polarization independent fishnetstructure, Phot. Nano. Fund. Appl. 6 (2008) 102e107.

[13] A. Mary, S.G. Rodrigo, F.J. Garcia-Vidal, L. Martin-Moreno, Theory of negative-refractive-index response of double-fishnet structures, Phys. Rev. Lett. 101(2008) 103902.

[14] C. Garcia-Meca, R. Ortuno, F.J. Rodriguez-Fortuno, J. Marti, A. Martinez,Double-negative polarization-independent fishnet metamaterial in the visiblespectrum, Opt. Lett. 34 (2009) 1603e1605.

[15] R. Ortuno, C. Garcia-Meca, F.J. Rodriguez-Fortuno, J. Marti, A. Martinez, Role ofsurface plasmon polaritons on optical transmission through double layermetallic hole arrays, Phys. Rev. B 79 (2009) 075425.1e075425.10.

[16] P. Ding, E.J. Liang, W.Q. Hu, L. Zhang, Q. Zhou, Q.Z. Xue, Numerical simulationsof terahertz double-negative metamaterial with isotropic-like fishnet struc-ture, Photon. Nanostruct. Fundam. Appl. 7 (2009) 92.

[17] C. Helgert, C. Menzel, C. Rockstuhl, E. Pshenay-Severin, E.-B. Kley,A. Chipouline, A. Tuennermann, F. Lederer, T. Pertsch, Polarization-indepen-dent negative-index metamaterial in the near infrared, Opt. Lett. 34 (2009)704.

[18] J. Zhou, T. Koschny, M. Kafesaki, C.M. Soukoulis, Negative refractive indexresponse of weakly and strongly coupled optical metamaterials, Phys. Rev. B80 (2009) 035109.

[19] K.M. Dani, Z. Ku, P.C. Upadhya, R.P. Prasankumar, A.J. Taylor, S.R.J. Brueck,Ultrafast nonlinear optical spectroscopy of a dual-band negative index met-amaterial all-optical switching device, Opt. Express 19 (2011) 3973.

[20] Q.-J. Du, J.-S. Liu, K.-J. Wang, X.-N. Yi, H.-W. Yang, Dual-band terahertz left-handed metamaterial with fishnet structure, Chin. Phys. Lett. 28 (2011)014201.

[21] K. Aydin, Z. Li, L. Sahin, E. Ozbay, Negative phase advance in polarizationindependent, multi-layer negative-index metamaterials, Opt. Express 16(2008) 8835e8844.

[22] Z. Sheng, V.V. Varadan, Tuning the effective properties of metamaterials bychanging the substrate properties, J. Appl. Phys. 101 (2007) 014909.

[23] A. Minovich, D.N. Nesheva, D.A. Powella, Y.S. Kivshara, Influence of thesubstrate on negative index fishnet metamaterials, Opt. Commun. 283 (2010)4770e4774.

[24] D.A. Powell, Y.S. Kivshar, Substrate-induced bianisotropy in metamaterials,Appl. Phys. Lett. 97 (2010) 091106.

[25] V.V. Varadan, R. Ro, Unique retrieval of complex permittivity and permeabilityof dispersive materials from reflection and transmitted fields by enforcingcausality, IEEE Trans. Microw. Theory Technol. 55 (2007) 2224e2230.

[26] A.M. Nicolson, G. Ross, Measurement of the intrinsic properties of materials bytime domain techniques, IEEE Trans. Instr. Measurm. IM-19 (1970) 377e382.

[27] W.B. Weir, Automatic measurement of complex dielectric constant andpermeability at microwave frequencies, Proc. IEEE 62 (1974) 33e36.

[28] P.B. Johnson, R.W. Christy, Optical constants of the noble metals, Phys. Rev. B 6(1972) 4370e4379.

[29] M.A. Ordal, L.L. Long, R.J. Bell, S.E. Bell, R.R. Bell, R.W. Alexander Jr., C.A. Ward,Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and Win the infrared and far infrared, Appl. Optics 22 (1983) 1099e1119.

[30] R.J. Pollard, A. Murphy, W.R. Hendren, P.R. Evans, R. Atkinson, G.A. Wurtz,A.V. Zayats, V.A. Podolskiy, Optical nonlocalities and additional waves inepsilon- near-zero metamaterials, Phys. Rev. Lett. 102 (2009) 127405.

[31] C. Sabah, H.G. Roskos, Numerical and experimental investigation of fishnet-based metamaterial in a X-band waveguide, J. Phys. D: Appl. Phys. 44 (2011)255101.

[32] Z. Huang, J. Xue, Y. Hou, J. Chu, D.H. Zhang, Optical magnetic response fromparallel plate metamaterials, Phys. Rev. B 74 (2006) 193105.

[33] P. Markos, C.M. Soukoulis, Wave Propagation: From Electrons to PhotonicCrystals and Left-Handed Materials. Princeton University Press, NJ, 2008.