1276IEICE TRANS. ELECTRON., VOL.E89–C, NO.9 SEPTEMBER 2006

PAPER Special Section on Metamaterials for Microwave and Millimeter-Wave Applications

Novel Two-Dimensional Planar Negative Refractive Index Structure

Naoko MATSUNAGA†, Atsushi SANADA††a), and Hiroshi KUBO††, Members

SUMMARY A novel purely distributed two-dimensional (2D) planarstructure with a negative refractive index (NRI) is proposed. The struc-ture consists of a 2D periodic array of unit cells with metal patterns on theboth sides of a substrate. The unit cell with the dimension of 5 × 5 mm2 isdesigned at an operation frequency of about 5 GHz by full-wave finite ele-ment method simulations. Numerical simulations on the dispersion charac-teristics are carried out and NRI property of the structure is confirmed. Aequivalent circuit taking into account the mutual capacitance between theadjacent ports in the unit cell is introduced, and theoretical investigationsbased on the equivalent circuit reveals that the anisotropy can be controlledby the mutual capacitance. A 10 × 20 unit-cell NRI material is fabricatedand the NRI property has been confirmed experimentally in excellent agree-ment with Snell’s law.key words: metamaterials, negative refractive indices, left-handed materi-als, anisotropy

1. Introduction

Materials with simultaneously negative permittivity and per-meability are referred to as the left-handed (LH) materials[1] and possess unusual electromagnetic property; for in-stance, backward wave support, negative refractive index(NRI) property, evanescent wave amplification, and the like.By exploiting the unusual property, totally novel functionsor drastic performance improvements are expected in mi-crowave and millimeter-wave circuit device or antenna ap-plications for wireless communication or radar systems [2]–[7].

Realization of the LHM is classified into two cate-gories; the resonant type [8] and the non-resonant type [2]–[4]. The resonant type LHM is a composite meta-structureof electric and magnetic plasma particles like metallic wiresand split-ring resonators, while the non-resonant type LHMis fundamentally the dual of the conventional transmission-line (TL) circuit model. The non-resonant LHM intrin-sically has low loss and wide bandwidth characteristicscompared with the resonant type LHM, therefore the non-resonant type LHM is preferable from an application pointof view.

Non-resonant LHMs in two-dimensional (2D) configu-ration have already been proposed [9], [10]. A 2D LH circuitnetwork using LC lumped elements has been proposed [9]

Manuscript received January 24, 2006.Manuscript revised April 6, 2006.†The author is with the Information Technology R&D Center,

Mitsubishi Electric Corporation, Kamakura-shi, 247-8501 Japan.††The authors are with the Graduate School of Science and En-

gineering, Yamaguchi University, Ube-shi, 755-8611 Japan.a) E-mail: sanada@ieee.org

DOI: 10.1093/ietele/e89–c.9.1276

and its NRI property has been verified experimentally. Afully distributed planar 2D NRI structure has also been pro-posed [10]. This structure is an array of unit cells with, soto called, ‘mushroom structure’ of a metal patch and a viato the ground plane. It has much higher frequency scalabil-ity than the LC lumped element LH network. However, thisstructure still has a fabrication limitation in terms of upperlimit of via density and accuracy tolerance of via dimen-sions.

In this paper, a novel 2D planar distributed NRI struc-ture is proposed. The structure consists of a 2D periodicarray of unit cells with metal patterns on the both sides ofa substrate and it does not require any vias. Without vias,is the structure scalable to millimeter-wave frequency rangeor above. It is also advantageous that the structure can befabricated by using conventional MMIC processes. In thefollowing sections, dispersion and NRI characteristics of theproposed structure are calculated numerically by full-wavesimulations based on the finite element method (FEM). Inorder to give an insight into anisotropy property of the struc-ture, an equivalent circuit model for a unit cell taking intoaccount the mutual capacitance between the adjacent ports isintroduced and the effect of the capacitance on the isotropyproperty is discussed. In addition, an experimental verifica-tion of the negative refraction at the interface between theproposed structure and a right-handed (RH) parallel-platewaveguide (PPW) is carried out.

2. Proposed Planar 2D NRI Structure

The proposed structure is the planar structure with metalpatterns on both the upper and lower layers of the substrateas shown in Figs. 1(a) and (b), respectively. Let us considera square unit cell with the period a in both the x and y direc-tions for simplicity. The unit cell is depicted with the dottedline in Figs. 1(a) and (b). On the upper layer, are the 45-degree rotated square metal patches with the side s. On thelower layer, four isosceles triangles surrounded by a squareframe are connected at their apex, and from the connectedportion, four narrow metal strips are radially connected tothe outer frame in the unit cell. The upper layer patternlies on the lower layer pattern with the relation shown inFig. 1(c). The upper metal patch overlaps the isosceles tri-angles forming an MIM capacitor, which provides a largeseries capacitance between the adjacent unit cells. The fourradial strips bridge the series capacitor and the outer frame.When the area of the outer frame is large enough and has

Copyright c© 2006 The Institute of Electronics, Information and Communication Engineers

MATSUNAGA et al.: NOVEL TWO-DIMENSIONAL PLANAR NEGATIVE REFRACTIVE INDEX STRUCTURE1277

Fig. 1 Proposed 2D NRI structure. (a) Upper layer. (b) Lower layer. (c)Unit cell. (a = 5.0 mm, s = 2.9 mm, wstub = 0.2 mm, lstub = 2.0 mm,wgp = 0.2 mm, ggp = 0.4 mm)

a quasi-ground voltage, the bridging strips work as shuntinductances. The conceptual equivalent circuit for the struc-ture is superimposed in Fig. 1(c). When the series capaci-tance and the shunt inductance are large enough, the struc-ture is expected to work as a left-handed structure, however,the actual wave propagation in this complex structure hasto be carefully considered, which will be discussed in thefollowing sections.

3. Negative Refractive Index Property

3.1 Dispersion Characteristics

In order to discuss wave propagation in the proposed struc-ture, full-wave FEM simulations are carried out using thecommercially available software Ansoft HFSS. For the unitcell shown in Fig. 1(c), periodic boundary conditions are ap-plied for the symmetrical planes in the x and y directions,and dispersion characteristics are calculated. In the FEMsimulations, the perfectly matched layer (PML) boundaryconditions are applied 6.0 mm (∼ λ0/10) above and belowthe substrate due to the limitation of the computer resources.Figure 2 shows the dispersion characteristics (frequency ver-sus wave number) of the lowest mode in the full kx-ky do-main for the structure with the structural parameters; perioda = 5.0 mm, s = 2.9 mm, wstub = 0.2 mm, lstub = 2.0 mm,wgp = 0.2 mm, ggp = 0.4 mm (see Fig. 1). The permit-tivity and thickness of the substrate are εr = 10.2 andh = 0.780 mm, respectively. Figure 3 also shows the disper-sion characteristics along the paths between the high sym-metry points Γ (kxa = kya = 0), X (kxa = π, kya = 0), andM (kxa = kya = π) in the Brillouin zone. It can be seen from

Fig. 3 that when β =√

k2x + k2

y is close to that in the vacuum

k0(= ω/c0) near the Γ-point, the lowest mode couples to theTM air mode [11] with the dispersion relation f = c0β/(2π)when β is small. When β is large in the Γ-X and Γ-M paths

Fig. 2 Dispersion characteristics of the NRI structure in the full kx-kydomain (full-wave simulation). (a) Contour plot. (b)Frequency plane plot.

Fig. 3 Dispersion diagram (full-wave simulation).

(Γ → X,M), the group velocity (vg = ∂ω/∂β) is negative,while the phase velocity (vp = ω/β) is positive, leadingto the anti-parallel group and phase velocities (vpvg < 0).Therefore, the structure supports the backward (LH) wavesin this region. It is noted that other paths than Γ-X or Γ-M(kx ky, kx 0, ky 0), the gradient of the frequencyplot (∂ω/∂kx, ∂ω/∂ky) and the wavenumber vector (kx, ky)are not anti-parallel anymore as seen in Fig. 2. The phaseand energy flow in the different directions in this case, lead-ing to strong anisotropy of the structure. Anisotropy of thestructure will further be discussed in the following section.

The accompanying RH wave (∂ω/∂kx, ∂ω/∂ky > 0when kx, ky > 0) propagates in the higher frequencies abovethe LH propagation band as see in Fig. 3. In between the LHand RH frequency bands, another propagation band with aquasi-TE mode in which the electric field is almost parallelto the ground plane exists as seen in Fig. 3. The RH wave as

1278IEICE TRANS. ELECTRON., VOL.E89–C, NO.9 SEPTEMBER 2006

Fig. 4 Refractive indices of the structure calculated from the dispersioncharacteristics of Fig. 2.

well as the LH wave can be easily excited by the microstripline or parallel plate waveguide mode (quasi-TEM mode),while the quasi-TE mode can not since they are approxi-mately orthogonal each other.

3.2 Refractive Indices

Figure 4 shows the refractive indices calculated from thefull-wave simulated dispersion relation of Fig. 2. Since thestructure exhibits anisotropy, the refractive index n is calcu-lated by

n =c0

vp(1)

for typical directions of propagation with θ = 0, 10, 25, 45degrees from the kx axis with corresponding vp’s in the Bril-louin zone (see the inset in Fig. 4). The sign of n is to betaken as negative in the LH frequency range. It can be seenfrom the figure that the absolute value of n decreases withincreasing frequencies, which is a consequence of the in-trinsic dispersion of the LH structure. The value |n| alsodecreases with increasing θ at a certain frequency; for in-stance, at 5.37 GHz, the refractive index is in a range of−5.7 < n < −4.2 when 10 < θ < 45 deg. When 0 < θ < 10deg, the wave does not propagate due to the cut-off propertyin the directions. The anisotropy leads to aberration whenthe structure is used in the NRI slab lens [12], which shouldbe taken into account in the design of the structure.

4. Anisotropy

In order to have an insight into the anisotropy of the struc-ture and to control the anisotropy, a simple equivalent circuitmodel extended from the 2D composite right/left-handed(CRLH) TL model [13] is introduced. Figure 5(a) showsthe equivalent circuit of the CRLH TL unit cell. Now, let usconsider an extended equivalent circuit shown in Fig. 5(b).Here, a mutual capacitance Cm is introduced between eachpair of adjacent ports in the unit cell, and a square unit cellis assumed. The mutual capacitance Cm is considered to besignificant when the gap on the upper layer becomes small.However, when the gap becomes small, the other parameters

Fig. 5 Equivalent circuits. (a) Equivalent circuit of the CRLH TL. (b)Extended equivalent circuit. (c) Four-port-pair network model.

in the unit cell will also change to some extent. In order tosimplify the problem and to estimate the pure effect of Cm

as a first step of the anisotropy analysis, we will rely on thecircuit analysis.

The unit cell model can be expressed in a general formof a four-port-pair network as shown in Fig. 5(c) with a 4×4transmission matrix F = Fi j; Denoting the voltage V (n)

x

and current I(n)x at the n-th port in the x direction and the volt-

age V (n)y and current I(n)

y in the y direction, we have

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

V (n)x

I(n)x

V (n)y

I(n)y

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦= F

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

V (n+1)x

I(n+1)x

V (n+1)y

I(n+1)y

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦. (2)

By using Bloch-Floquet theory, the characteristic equationis given by

det(F − Γ) = 0, (3)

where, Γ is a 4×4 diagonal matrix diag[eγxa, eγxa, eγya, eγya].Here, γx = αx + jβx, γy = αy + jβy, and a is the period of theunit cell. The characteristic equation for the structure withthe unit cell of Fig. 5(b) taking Cm into account is calculatedas in (4) in the top of next page, and the effect of Cm onthe anisotropy is studied. It can be shown from (4) that thevalue of Cm affects the X-point (kxa = π, kya = 0) frequencybut does not the M-point (kxa = kya = π) frequency northe Γ-point frequency (kxa = kya = 0). Therefore, it isexpected that the anisotropy can be controlled by choosingan appropriate value of Cm to change the X-point frequency.

This is confirmed by calculating the dispersion char-acteristics from (4). Figure 6 shows dispersion character-istics on the kx-ky domain calculated by solving (4) for thecase when the mutual capacitance is ignored (Cm = 0). Theother parameters are chosen as arbitrary values CL = 0.8 pF,LR=0.7 nH, CR=0.1 pF, and LL=0.07 nH so that the LH fre-quency band can become approximately the same as that ofthe simulation results of Fig. 2. Note that Fig. 6 corresponds

MATSUNAGA et al.: NOVEL TWO-DIMENSIONAL PLANAR NEGATIVE REFRACTIVE INDEX STRUCTURE1279

det

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

2Y

(1 +

ZZm

) (1 − e jβxa

)ZY

(1 + e jβxa

)0 0

2Y

(1 +

ZZm

)2(1 +

ZY2− e jβxa

)−ZY

Zm

(1 + e jβya

)−2

(e jβya − 1

)

0 0 2Y

(1 +

ZZm

) (1 − e jβya

)ZY

(1 + e jβya

)

−ZYZm

(1 + e jβxa

)−2

(e jβxa − 1

)2Y

(1 +

ZZm

)2(1 +

ZY2− e jβya

)

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

= 0. (4)

Fig. 6 Dispersion diagrams (Cm = 0 pF). (a) Contour plot. (b) Frequencyplane plot.

Fig. 7 Dispersion diagrams (Cm = 0.5 pF). (a) Contour plot. (b) Fre-quency plane plot.

Fig. 8 Dispersion diagrams (Cm = 2.0 pF). (a) Contour plot. (b) Fre-quency plane plot.

to the conventional CRLH TL dispersion characteristics.The dispersion characteristics for the case Cm = 0.5 pF and2.0 pF are also shown in Figs. 7 and 8, respectively, as acomparison. It can be seen from Fig. 6 that even when Cm isignored, a certain anisotropy arises which alike what calcu-lated by the full-wave simulation for a real structure shownin Fig. 2 except for the coupling with the air mode when kx

and ky are small. When the mutual capacitances Cm’s ex-ist as in Figs. 7 and 8, the structure becomes more isotropicand the isotropy enhances with increasing Cm. For instance,in order to quantify the isotropy, the isotropy factor IF is

Fig. 9 Isotropy factor.

defined as

IF =kdiag

korth, (5)

where kdiag and korth are the wave numbers in the diago-nal and orthogonal directions at a certain frequency, andIF for the structure with the unit cell of Fig. 5(b) is calcu-lated in the wave number domain as shown in Fig. 9. Theisotropic factor IF is almost unity when korth is small, how-ever, it decreases with increasing korth for any Cm values,leading to the fact that the structure is isotropic near theΓ-point (λg = ∞) and becomes anisotropic as the guidedwavelength becomes small (λg ∼ 2a). When the value ofCm increases, the value of IF increases; i.e. the isotropy isenhanced. The same tendency is obtained with other cir-cuit parameters. Consequently, it can be concluded that theisotropy can be controlled by introducing the mutual capac-itance Cm between the adjacent ports in the unit cell. In apractical implementation, individual control of the value ofCm, might be difficult, however, the foregoing result will behelpful for an intuitive design of the 2D NRI structure.

5. Experiments

In order to demonstrate NRI properties of the proposedstructure, the structure with the unit cell designed inSect. 3.1 is fabricated. Figures 10(a) and (b) show the up-per and lower layers of the prototype fabricated on a sub-strate with the relative permittivity εr = 10.2 and thicknessh = 0.780 mm, respectively. The detailed structural param-eters are shown in the caption of Fig. 1. The structure with

1280IEICE TRANS. ELECTRON., VOL.E89–C, NO.9 SEPTEMBER 2006

10×20 unit cells is interfaced with a parallel plate waveguide(PPW) with the angle of 15 degrees as shown in Fig. 11so that the structure can be excited by a quasi-TEM wavewith the angle. The width of the PPW is W = 78.1 mm (thecharacteristic impedance is 1.3Ω) and the PPW is fed by a

Fig. 10 Photographs of the NRI strucure. (a) Upper layer. (b) Lowerlayer.

50Ω microstrip line at the center through a λ/4 impedancetransformer to reduce a reflection at the microstrip to PPWtransition. According to the equivalent circuit analysis ofFig. 5, the characteristic impedance of the periodic structuredepends much on frequencies and changes from zero to infi-nite in this unbalanced case [10]. However, a certain amountof refracted power can be expected in an LH frequency bandaround a frequency at which the characteristic impedance ofthe structure matches with that of the PPW impedance. Thelength of the PPW is approximately 1.1 λg (λg is the guidedwavelength at the center of the LH band). The other sides ofthe NRI structure are surrounded by absorbers.

The refracted wave is observed by near field measure-

Fig. 11 Prototype for the negative refraction experiment. (a) Upper sidepattern. (b) Back side pattern.

Fig. 12 Measured electric-field distribution on the NRI structure. (a) Magnitude and phase at the LHfrequency 5.23 GHz. (b) Magnitude and phase at the RH frequency 8.10 GHz. Each phase is normalizedby the value at the origin.

MATSUNAGA et al.: NOVEL TWO-DIMENSIONAL PLANAR NEGATIVE REFRACTIVE INDEX STRUCTURE1281

(a)

(b)

Fig. 13 Phase distributions along the x- and y-axes. (a) Phase distributions at the LH frequency5.23 GHz. (b) Phase at the RH frequency 8.10 GHz. The slope of each graph corresponds to the wavenumber.

ments using a coaxial probe. In the measurements, enoughspaces are taken on above and below the substrate so thatguided waves in the structure can not be perturbed. Themagnitude and phase distributions of the x-component ofthe measured electric field 1.0 mm above the structure inthe 35 × 35 mm2 area indicated in Fig. 11(a) are shown inFigs. 12(a) and (b) for f = 5.23 GHz (LH frequency re-gion) and f = 8.10 GHz (RH frequency region), respec-tively. Here, the magnitudes are normalized by each max-imum value, and the phase references are set at the origin(upper right corner) of the measurement area in Fig. 11. Forthe LH frequency region of Fig. 12(a), it can be seen fromthe amplitude distribution that a certain amount of powerflows in the NRI structure. It is noted that the phase de-velops positively as the refracted wave propagates (white toblack in the figure of the phase distribution), which leadsto the conclusion that the structure supports the backwardwaves at the frequency.

In order to obtain the refraction angle from the mea-sured results, the phases of Fig. 12 are plotted on the x- andy-axes as in Fig. 13. The wave numbers kx and ky can becalculated as the slopes of those graphs as

kx =∆φ

∆x, ky =

∆φ

∆y. (6)

The refraction angle θr is obtained from kx and ky by

θr = tan−1

(kykx

). (7)

From Fig. 13(a), the wave numbers kx and ky are obtainedas averages of the slopes of these lines as kx = −274 rad/mand ky = 49 rad/m at the LH frequency 5.23 GHz (the aver-age slope are shown by the thick dotted line in Fig. 13(a)).Therefore, the refraction angle θr is obtained as θr = −10.3deg according to (7). The refractive index n is calculatedfrom Snell’s law as n = nPPW sin θi/ sin θr = −2.69 (nPPW

= (εr,eff,PPW)1/2 = 3.19). On the other hand, the refrac-tive index calculated from (1) is n = c0/vp = c0β/ω =

c0

√k2

x + k2y/ω = −2.54. These agree well with each other.

The wave front and the direction of the wave propagation issuperimposed in the phase of Fig. 12(a).

Incidentally, the simulated frequency band for a wavepropagating in the direction with −10 deg is from 5.37 GHzto 5.51 GHz as seen in Fig. 4, while the frequency at whichthe negative refraction of −10 degrees is observed in the

1282IEICE TRANS. ELECTRON., VOL.E89–C, NO.9 SEPTEMBER 2006

measurement, 5.23 GHz, is slightly lower than the simulatedfrequency band. However, the frequency obtained by themeasurement is considered to be within an error range dueto the fabrication and measurement errors.

Similarly, at 8.10 GHz in the RH frequency region, thewave number kx and ky are obtained as kx = 249 rad/m andky = 35 rad/m. The refraction angle θr is, therefore, obtainedas θr = +7.97 deg according to (7). The refractive index n iscalculated from Snell’s law as n = nPPW sin θi/ sin θr = 2.09,which is in a good agreement with that calculated from therefractive index calculated from (1); n = c0/vp = c0β/ω =

c0

√k2

x + k2y/ω = 1.48.

6. Conclusions

The novel 2D planar structure with an NRI property hasbeen proposed. The structure with 5×5 mm2 unit cells oper-ate at 5 GHz band has been designed and their NRI charac-teristics have been confirmed by calculating dispersion char-acteristics and refractive indices by full-wave FEM simu-lations. From the circuit analysis, it has been shown thatthe anisotropy can be controlled by the mutual capacitancebetween the adjacent ports of the unit cell. In order to vali-date the NRI properties of the proposed structure, the experi-ments on a 10×20 unit-cell prototype interfaced with a PPWhave also been carried out, and the negative refraction in theLH frequency region have been confirmed by the near fieldmeasurements. The positive refraction in the RH frequencyregion has also been confirmed, which can be predicted bythe CRLH theory [10], [13]. Being a purely distributed andplanar structure without using any vertical metallic vias, thestructure is advantageous in easy fabrication and high scal-ability.

References

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[2] C. Caloz and T. Itoh, “Novel microwave devices and structures basedon the transmission line approach of meta-materials,” IEEE MTT-SInt. Microwave Symp. Dig., pp.195–198, June 2003.

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Naoko Matsunaga was born in Fukuoka,Japan, in 1981. She received the B.E. and M.E.degrees in Electrical and Electronic Engineeringfrom Yamaguchi University, Yamaguchi, Japan,in 2004 and 2006, respectively. She is cur-rently with Mitsubishi Electric Corporation. Herresearch interest includes left-handed materialsfor microwave applications. Ms. Matsunagais a recipient of the 2006 Young Researcher’sAward.

Atsushi Sanada received his B.E., M.E. andD.Eng. degrees in electronic engineering fromOkayama University, Okayama, Japan, in 1989,1991 and 1994, respectively. In 1994, he joinedthe Faculty of Computer Science and SystemEngineering, Okayama Prefectural University asa Research Associate. In 1999, he joined theFaculty of Engineering, Yamaguchi Universitywhere he is now an Associate Professor since2004. He is now a Visiting Researcher at theAdvanced Telecommunications Research Insti-

tute International (ATR). He was a Visiting Researcher at the Universityof California, Los Angeles in 1994 and 2002 and at the NHK Science andTechnical Research Laboratories in 2005. His research is concerned withmetamaterials, high-Tc superconducting microwave devices, magnetostaticwave devices, holographic radar systems and microwave power combining.Dr. Sanada is a member of IEEE.

Hiroshi Kubo received the B.E., the M.E.,the D.E. degrees in computer science & com-munication engineering from Kyushu Univer-sity, Fukuoka, Japan, in 1978, 1980, and 1993,respectively. In 1980 he joined Nippon Elec-tric Company, Tokyo, Japan where he was en-gaged in development on mobile communica-tion system. From 1987 to 1991, he was a Re-search Associate at Kyushu University. Since1991 he has been with Yamaguchi University,Ube, Japan where he is now an associate profes-

sor. His main area of research interest is radio communication network andmicrowave communication devices. Dr. Kubo is a member of IEEE andIEEJ.