34 September 20041527-3342/04/$20.00©2004 IEEE

Metamaterials are artificial structures that can be designed to exhibitspecific electromagnetic properties not commonly found in nature.Recently, metamaterials with simultaneously negative permittivity(ε) and permeability (µ), more commonly referred to as left-handed(LH) materials, have received substantial attention in the scientific

and engineering communities. Science magazine even named LH materials (LHMs) asone of the top ten scientific breakthroughs of 2003 [1]. The unique properties of LHMshave allowed novel applications, concepts, and devices to be developed. In this arti-cle, the fundamental electromagnetic properties of LHMs and the physical realizationof these materials are reviewed based on a general transmission line (TL) approach.The general TL approach provides insight into the physical phenomena of LHMs andprovides an efficient design tool for LH applications. LHMs are considered to be amore general model of composite right/left hand (CRLH) structures, which also

include right-handed (RH) effects that occur naturally in practical LHMs.Characterization, design, and implementation of one-dimensional (1-

D) and two-dimensional (2-D) CRLH TLs are examined. In addition,novel microwave devices based on CRLH TLs and their applicationsare presented.

LHMsThe concept of LHMs was first theorized by the Russian physicistVeselago in 1967 [2] (Veselago’s paper was translated into English in1968; the translated paper mistakenly notes 1964 as the original year ofpublication). In his paper, Veselago speculated on the possible exis-

tence of LHMs and anticipated their unique electromagnetic propertiessuch as the reversal of Snell’s Law, the Doppler effect, and the Vavilov-

Cerenkov effect (radiation produced by a fast-moving particle as it trav-els through a medium). Veselago showed that the electric field, magnetic

field, and wavevector of an electromagnetic wave in an LHM form an LH

Anthony Lai (antlai@ee.ucla.edu) and Tatsuo Itoh are with the Electrical Engineering Department, University of California, Los Angeles, CA 90095 USA.

Christophe Caloz is with the Département de Génie Electrique,Ecole Polytechnique de Montréal, Montréal, Québec H3T 2B1, Canada.

©DIGITAL VISION

September 2004 35

triad. As a result, LHMs support electromagnetic waves with group and phase veloci-ties that are antiparallel, known as backward waves [3]. Consequently, while energystill travels away from the source, so as to satisfy causality, wavefronts travel backwardtoward the source in an LHM, a phenomenon which is associated with negative indexof refraction.

Although Veselago predicted the existence of LHMs, experimental verification ofLHMs did not occur until three decades later by a group at University of California,San Diego (UCSD). The UCSD’s LHM consisted of copper split-ring resonators (SRRs)and thin copper wires, providing negative permeability and negative permittivity,respectively [4]. By constructing a wedge-shaped structure with their SRR-based LHM,the group at USCD demonstrated the concept of a negative index of refraction. A groupat Massachusetts Institute of Technology (MIT) repeated this experiment, confirmingUCSD’s findings [5]. Following these experimental verifications, severalresearchers have further studied the characteristics and applicationsof SRR-based LHMs [6]–[8]. However, since resonant structures suchas SRRs are lossy and narrow-banded, they are often difficult toimplement for microwave applications. Several researchers soonrealized that a TL approach towards LHMs was possible [9], [10].The TL approach of LHMs, presented in this article, has led to non-resonant structures with lower loss and wider bandwidth. In par-ticular, metamaterials with RH and LH properties known as CRLHmetamaterials have led to the development of several novelmicrowave devices which are discussed in this article.

CRLH TheoryTL theory has long been a powerful analysis and design tool for con-ventional (i.e., RH) materials. By modeling a CRLH metamaterial as anequivalent TL, TL theory can be used to analyze and design 1-, 2-, or even3-D CRLH metamaterials. In the following sections, the TL approach to CRLHmetamaterials will be developed. First, the CRLH metamaterial will be repre-sented by an equivalent homogeneous (continuous and invariant along the direc-tion of propagation) CRLH TL to gain immediate insight into its fundamental charac-teristics. Then, an LC network implementation of the TL will be developed, sincehomogeneous CRLH structures do not appear to exist in nature. The LC network pro-vides a realistic description of the CRLH metamaterial. Finally, physical realizations ofthe LC network will be discussed. For simplicity, only the lossless TL will be examined.

Anthony Lai, Christophe Caloz, and Tatsuo Itoh

36 September 2004

Homogeneous CaseThe homogeneous models of a purely RH (PRH), purely LH (PLH), and CRLH lossless TL are shown inFigure 1(a), (b), and (c), respectively. The PRH TLmodel, shown in Figure 1(a), can be represented as thecombination of a per-unit length series inductance L′

Rand a per-unit length shunt capacitance C′

R. The PLHTL model, shown in Figure 1(b), is the combination of atimes-unit length series capacitance C′

L and a times-unitlength shunt inductance L′

L and is the dual of the PRHTL. In reality, a PLH structure is not possible because ofunavoidable RH parasitic series inductance (L) andshunt capacitance (C) effects (parasitic capacitance isdue to development of voltage gradients, and unavoid-able parasitic inductance is due to current flow alongthe metallization). Therefore, a CRLH structure repre-sents the most general form of a structure with LH

attributes. The general CRLH TL model shown inFigure 1(c) consists of an inductance L′

R in series with acapacitance C′

L and a shunt capacitance C′R in parallel

with an inductance L′L.

The propagation constant of a TL is given byγ = α + jβ = √

Z′Y′ , where Z′ and Y′ are, respectively,the per-unit length impedance and per-unit lengthadmittance. In the particular case of the CRLH TL, Z′and Y′ are defined as

Z′(ω) = j(

ωL′R − 1

ωC′L

),

Y′(ω) = j(

ωC′R − 1

ωL′L

). (1)

Therefore, the dispersion relation for a homogenousCRLH TL is

β(ω) = s(ω)

√ω2L′

RC′R + 1

ω2L′LC′

L−

(L′

RL′

L+ C′

RC′

L

), (2)

where

s(ω) =

−1 if ω < ω1 = min

1√

L′RC′

L

,1√

L′LC′

R

+1 if ω > ω2 = max

1√

L′RC′

L

,1√

L′LC′

R

.

(3)

The phase constant β in (2) can be purely real or pure-ly imaginary depending on whether the radicand ispositive or negative, respectively. In the frequencyrange where β is purely real, a pass-band is presentsince γ = jβ . In contrast, a stop-band occurs in the fre-quency range where β is purely imaginary since γ = α.

This stop-band is a unique character-istic of the CRLH TL, which is notpresent in the PRH or the PLH cases.

Figure 2(a), (b), and (c) shows theω − β or dispersion diagram of aPRH TL, PLH TL, and CRLH TL,respectively. The group velocity(vg = ∂ω/∂β ) and phase velocity(vp = ω/β ) of these TLs can beinferred from the dispersion dia-gram. These diagrams show that vg

and vp for a PRH TL are parallel(vgvp > 0), while vg and vp for a PLHTL are antiparallel (vgvp < 0). Inaddition, the CRLH TL’s dispersiondiagram shows that it has an LH(vgvp < 0) and RH (vgvp > 0) region.Figure 2(c) also illustrates the stop-band that occurs when γ is purelyreal for a CRLH TL.

In general, the series and shunt res-onances of the CRLH TL are different.This is called the unbalanced case.

However, when the series and shunt resonances are equal

L′RC′

L = L′LC′

R, (4)

the LH and RH contribution exactly balance each otherat a given frequency, as it will be shown shortly.Therefore, this condition is called the balanced case, andthe resulting simplified circuit model is shown in Figure3(a). It can be shown that under condition (4), the prop-agation constant in (2) reduces to the simpler expression

β = βR + βL = ω

√L′

RC′R − 1

ω√

L′LC′

L

, (5)

where the phase constant distinctly splits up into the RHphase constant βR and the LH phase constant βL. The

Figure 1. Equivalent circuit model. (a) Homogeneous RH TL. (b) HomogeneousLH TL. (c) Homogeneous CRLH TL.

L'R∆z

C 'R∆z

∆z

C'L/∆z

L'L/∆z

∆z

∆z

L'R∆z

C 'R∆z

C 'L/∆z

L'L/∆z

Z '

Y '

(a) (b)

(c)

September 2004 37

CRLH TL is increasingly dispersive as frequencyincreases, since the phase velocity (vp = ω/β) becomesincreasingly dependent on frequency, as shown in (5),which also illustrates the dual nature of the CRLH TL; atlow frequencies the CRLH TL is dominantly LH, whileat high frequencies the CRLH TL is dominantly RH. Thebalanced CRLH TL’s dispersion diagram of Figure 3(b)indicates that an LH to RH transition occurs at

ω0unbalanced= 1

4√

L′RC′

RL′LC′

L

balanced= 1√L′C′ , (6)

where ω0 is referred to as the transition frequency.Thus, there is a seamless transition from LH to RH forthe balanced case, because γ is always purely imagi-nary, unlike the unbalanced case. As a result, the bal-anced CRLH TL’s dispersion curve does not have astop-band. Although β is zero at ω0, which correspondsto an infinite guided wavelength (λg = 2π/|β|), wavepropagation still occurs since vg is nonzero at ω0. Inaddition, at ω0 the phase shift for a TL of length d iszero (φ = −βd = 0). Phase advance (φ > 0) occurs inthe LH frequency range (ω < ω0), and phase delay(φ < 0) occurs in the RH frequency range (ω > ω0).

The characteristic impedance of a TL is given byZo = √

Z′/Y′ . For the CRLH TL, the characteristicimpedance is

Zounbalanced= ZL

√L′

RC′Lω2 − 1

L′LC′

Rω2 − 1balanced= ZL = ZR, (7a)

ZL =√

L′L

C′L, (7b)

ZR =√

L′R

C′R

, (7c)

where ZL and ZR are the PLH andPRH impedances, respectively. Whereasthe characteristic impedance for theunbalanced case is frequency depen-dent, (7a) indicates that the balancedcase is frequency independent and,therefore, can be matched over a widebandwidth.

The TL relations derived above canbe related to the constitutive parametersof a CRLH material. As stated above, thepropagation constant of a TL is γ =jβ = √

Z′Y′ . Since the propagation con-stant of a material is β = ω

√µε, the fol-

lowing relation can be set up:

−ω2µε = Z′Y′. (8)

Similarly, the TL’s characteristic impedanceZo = √

Z′/Y′ can be related to the material’s intrinsicimpedance η = √

µ/ε by

Zo = η orZ′

Y′ = µ

ε, (9)

which with (8) relates the permeability and permittivi-ty of a material to the impedance and admittance of itsequivalent TL model

µ = Z′

jω= L′

R − 1ω2C′

L, (10a)

ε = Y′

jω= C′

R − 1ω2L′

L. (10b)

The index of refraction (n = cβ/ω) for the balancedand unbalanced CRLH TL is displayed in Figure 4. Thisfigure shows that the CRLH TL has a negative index ofrefraction in its LH range and a positive index of refrac-tion in its RH range.

LC NetworkThe homogeneous CRLH TL does not appear to exist innature. However, CRLH TLs that are effectively

Figure 2. Dispersion diagrams for the TLs of Figure 1. (a) Homogeneous RH TL[11]. (b) Homogeneous LH TL [11]. (c) Homogeneous CRLH TL (unbalanced).

ω

+βc−βc

β

ω

+βc−βc

β(a) (b)

ω

ωΓ2

ωΓ1

ω0

+βc−βc

β(c)

38 September 2004

homogenous—when an elec-tromagnetic wave does not“see” discontinuities of thestructure, because the guidedwavelength is much larger thanthem—in a certain range of fre-quencies can be manufactured.An effectively homogeneousCRLH TL of length d can beconstructed by cascading theband-pass LC unit cell of Figure5(a) in either a nonperiodic orperiodic fashion. Usually peri-odicity is preferred for compu-tational and fabrication conve-nience of the CRLH TL [11].

The unit cell of Figure 5(a) is dimensionless, unlikethe incremental model of Figure 1(c), which has aninfinitesimal physical length of z (in meters). Thephase of the LC unit cell can only be described in termsof its electrical length, θ = φ (rad). However, a phys-ical length p will be eventually associated with a prac-tical implementation of the inductors and capacitorsused [The LC unit cell’s physical dimensions dependon the technology used (e.g., microstrip, coplanarwaveguide, surface mount components, etc.)]. In thelimit p = z → 0, the LC unit cell of Figure 5(a) isequivalent to the incremental model of Figure 1(c).Therefore, a TL equivalent to an ideal homogeneousCRLH TL of length d can be formed by cascading theLC unit cell with the homogeneity condition p → 0, asshown in Figure 5(b) [11]. The homogeneity condition

Figure 3. Balanced form of Figure 1(c). (a) Simplified equivalent circuit model.(b) Dispersion diagram showing seamless LH to RH transition [11].

(a)

L'R∆z C 'L/∆z

C 'R∆z L'L/∆z

∆z

βR βLω

+βc−βc

ω0

β

(b)

Figure 5. LC-based CRLH TL. (a) Unit cell. (b) LC periodic network equivalent to a homogeneous CRLH TL of length d forp = z → 0 [11].

Z

Y

LRCL

LLCR

∆θ

(a) (b)

p p p

N2

d=Np

γ, Zo

d

1

Figure 4. Typical index of refraction plots for the balanced(green) and unbalanced (red) CRLH TL.

ω

ωΓ2ω0ωΓ1n

September 2004 39

ensures that the TL appears homogeneous to the elec-tromagnetic wave. In practice, if the unit cell is small-er than the guided wavelength p < λg/4, then the elec-trical length of the unit cell is smaller than π/2 and theLC-based CRLH TL is seen as effectively homoge-neous by electromagnetic waves [11].

By applying periodic boundary conditions (PBCs)related to the Bloch-Floquet theorem to the LC unit cell[11], the LC dispersion relation

β(ω) = 1p

cos−1(

1 + ZY2

)(11)

is obtained, where the series impedance (Z) and shuntadmittance (Y) of the LC unit cell are given by

Z(ω) = j(

ωLR − 1ωCL

), Y(ω) = j

(ωCR − 1

ωLL

).

(12)

Since the electrical length of the unit cell is small, theTaylor approximation cos(βp) ≈ 1 − (βp)2/2 can beapplied and (11) becomes

β(ω) = s(ω)

p

√ω2LRCR + 1

ω2LLCL−

(LR

LL+ CR

CL

)

(13)

,

which is identical to the homogeneous dispersionrelation of (2) (with L′

R = LR/p, C′R = CR/p, L′

L =LL p, C′

L = CL p). This result shows that the LC-based

CRLH TL is equivalent to the homogeneous CRLH TLfor small electrical lengths. The dispersion diagram for abalanced and unbalanced LC-based CRLH TL is shownin Figure 6. The LH portion of the dispersion curve wasfolded around the ω-axis to generate Figure 6.

This diagram shows that the band-pass LC-basedCRLH TL exhibits a LH high-pass stop-band and a RHlow-pass stop-band, unlike the ideal homogeneousCRLH TL, which does not exhibit any filter behavior.Although the LC-based CRLH TL is essentially a band-pass filter, the design of CRLH metamaterials has little todo with filter design for several reasons [11]. First, CRLHstructures are designed to meet specific phase responseswhile filters are generally designed to meet magnitude

Figure 6. Dispersion diagram for the balanced and unbalancedLC-based CRLH TL. Balanced: LR = LL = 1 nH,CR = CL = 1 pF; unbalanced: CR = 1 pF, CL = 2 pF [21].

BalancedUnbalanced

ωΓ2

ωΓ1

ω0

LH High-Pass Stop Band

RH Low-Pass Stop Band

00 π/(2p)

β (rad/m)

π/p

2

4

6

8

10

12

Freq

uenc

y (G

Hz)

Figure 7. 2D CRLH TL. (a) Unit cell [11]. (b) Dispersion diagram for a balanced (green) and unbalanced (red) 2-D CRLHTL. Balanced: LR = LL = 1 nH, CR = CL = 1 pF; unbalanced: LR = 1 nH, LL = 0.5 nH, CR = 1 pF, CL = 2 pF. The insetshows the Brillouin zone of the 2-D periodic structure.

Z/2 y

x

Z/2

LR/2

2CL

LR/2

LR/2LR/2

Z/2Z/2

2CL

2CL2CL

CR LL

Y

(a) (b)

0

2

4

6

8

10

12

14

16

Freq

uenc

y (G

Hz)

Γ X M Γβ (rad/m)

ωΓ1

ωΓ2

ωX2

ωX1 ωM1

ωM2

ω0

ky

kx

π /p

π /p

−π/p

−π/pΓ

M

x

40 September 2004

specifications. Secondly, as stated previously, the unitcell of CRLH metamaterials has to satisfy the homo-geneity condition, |φ| < π/2, but conventional filtersusually do not need to satisfy this condition. In addi-tion, conventional filters are 1-D, while CRLH metama-terials can be 2- or 3-D and behave as bulk media.

The 1-D CRLH TL can be extended to a 2-D CRLHTL [11], [12] by using the modified unit cell of Figure7(a). Similar to the design of a 1-D CRLH TL, a 2-DCRLH TL can be constructed by repeating the 2-D unitcell of Figure 7(a) along two directions. The 2-D CRLHTL supports wave propagation in any direction withinthe structure. As a result, the phase constant β is a vec-tor quantity for the 2-D CRLH TL,

−→β = xkx + yky

where kx and ky are the propagation constants for the xand y directions. By applying PBCs to the 2-D unit cellalong the x and y directions, the 2-D dispersion relation

(e− jkx p − 1)2

e− jkx p+ (e− jkyp − 1)2

e− jkyp− ZY = 0, (14)

is obtained, where the series impedanceZ and shunt admittance Y of the unit cellare given by (12). This dispersion rela-tion reduces to the 1-D dispersion rela-tion of (11) when either kx or ky is zero.

Figure 7(b) shows the correspondingdispersion diagram and Brillouin zone[13] for the 2-D CRLH TL, where(kxp = kyp = 0), X(kxp = π, kyp = 0),and M(kxp = kyp = π) represent thehigh-symmetry points of the Brillouinzone. The structure is LH from ω1 toωM1 and RH from ω2 to ωM2, as seen inFigure 7(b). For the unbalanced case, a

stop-band occurs between ω1 and ω2. The stop-banddisappears for the balanced case and ω1 = ω2 = ω0.

Physical ImplementationThe previous section presented the LC approach tocreate a 1- or 2-D CRLH TL. However, the LC networkmust be realized with physical components that cangenerate the required capacitances (CR and CL) andinductances (LR and LL). Currently, surface-mounttechnology (SMT) chip components or distributedcomponents have been used to realize the LC net-work. Distributed components can be implementedvia microstrip, stripline, coplanar waveguide, oranother technology.

The choice of SMT chip or distributed componentsdepends on several factors. In terms of analysis anddesign, SMT-based CRLH structures are generally eas-ier and quicker to implement. SMT chip componentsare readily available and do not need to be designedand fabricated, unlike their distributed counterparts.However, SMT components are only available in dis-

Figure 8. A 1-D microstrip CRLH TL consisting of interdigital capacitors andshorted stub inductors [11].

Ground Plane

InterdigitalCapacitor

Stub

Via

z

Figure 9. 24 unit-cell microstrip CRLH TL based on Figure 8. (a) Photograph of prototype. (b) Unit cell used for parameterextraction [11].

WC

WS

p

z

ISIC

(a) (b)

September 2004 41

crete values and are limited to low frequencies (3–6GHz, depending on their values). As a result, specificphase responses and operational frequency ranges arelimited for SMT-based CRLH structures. In addition,the choice between SMT chip and distributed compo-nents depends on the intended application. For exam-ple, SMT chip components are difficult to implementfor radiation-type applications.

An example of a distributed component based 1-DCRLH TL is shown in Figure 8. This structure is imple-mented on microstrip with interdigital capacitors andstub inductors connected to the ground plane. The unitcell of the structure shown in the inset is equivalent tothe circuit model of Figure 5(a). The interdigital capac-itors and stub inductors provide the LH and also theRH contributions. In particular, the RH capacitance CR

is attributed to the capacitance between the trace andground plane, and the RH inductance LR is caused bythe magnetic flux generated by the current flow in thedigits of the interdigital capacitor.

A balanced, 24 unit-cell microstrip CRLH TL basedon Figure 8 is displayed in Figure 9(a). The entire circuitwas implemented on Rogers RT/Duroid 5880 withdielectric constant εr = 2.2 and thickness h = 1.57 mm.Parameter extraction was based on the unit cell of Figure 9(b) with p = 6.1 mm, lc = 5.0 mm, w c = 2.4mm, l s = 8.0 mm, w s = 1.0 mm, and five pairs of dig-its with widths of 0.15 and 0.1 mm spacing. The extract-ed LH and RH parameters were LL = 3.38 nH,CL = 0.68 pF, LR = 2.45 nH, and CR = 0.50 pF. Theexperimental dispersion diagram is compared with thehomogeneous TL relation (2) and LC network relation(11) in Figure 10.

One possible way of creating 2-D CRLH TL struc-tures is by periodic repetition of the capacitivelyenhanced mushroom structure of Figure 11(a) [14]. Themushroom structure was first proposed by Sievenpiper

et al. [15] for the realization of high-impedance sur-faces. Our group at UCLA demonstrated thatSievenpiper’s mushroom structure is, in essence, aCRLH structure, capable of exhibiting a negative indexof refraction [14]. The mushroom structure of Figure11(a) is equivalent to the 2-D circuit model of Figure7(a). The LH capacitance CL is provided by the capaci-tance couplings of the top patch with adjacent patches,and the LH inductance is provided by a via connectedto the ground plane. The caps are used to enhance theweak capacitance couplings between adjacent patches.The magnetic flux caused by the flow of current on thetop patch contributes to the RH inductance LR, whilethe parallel-plate structure between the patch and theground plane contributes to the RH capacitance CR.The 2-D CRLH structure of Figure 11(b) is open to airand can be implemented with microstrip.

Figure 10. Experimental dispersion diagram comparedwith the homogeneous TL relation (2) and LC network rela-tion (11) for the 24-cell CRLH TL of Figure 9(a) [11].

0

1

2

3

4

5

6

7

8

9

10

Freq

uenc

y (G

Hz)

−π +π0

βp (rad)

ExperimentalLC RelationHomogeneous

Figure 11. Open 2-D CRLH mushroom structure. (a) Unit cell [14]. (b) 2-D CRLH structure formed by periodic repetition ofthe unit cell. The caps are floating (not connected to the vias) patches located at a short distance from the connected patch toenhance CL contribution [14].

(b)

Top Patch

CapsVia

Ground Plane

(a)

42 September 2004

The dispersion diagram of the open mushroom struc-ture, shown in Figure 12, was generated by full-wave(FEM) simulation with unit cell parameters indicated inFigure 13. This dispersion diagram shows that the fun-damental mode of the structure is a mixed LH–RH

mode, because the LH mode of the open structurealways couples with the TM air mode [16]. In contrast, a2-D CRLH mushroom structure closed to air, which canbe implemented by stripline, has a dominant mode thatis purely LH [14]. The dispersion diagram also showsthat the structure has two RH modes. However, the firstRH mode is actually a degenerate TE mode and does notcorrespond to the RH mode of the circuit model, unlikethe second RH mode. Figure 12 also shows that the LHmode is shifted towards higher frequencies when thecaps are removed from the mushroom structure. Theremoval of the caps decreases the LH CL contribution.

Microwave ApplicationsThe CRLH TL has lead to several novel microwaveapplications and devices. This section presents guided,radiated, and refracted applications that utilize theunique features of CRLH TLs.

Guided Wave Applications

Dual-Band Branch-Line CouplerConventional branch-line couplers (BLCs) can onlyoperate at their design frequency ( f1) and at their odd

harmonics (3 f1). Since, dual-band wireless commu-nication systems have operational frequencies sepa-rated by various/nonharmonic frequencies, the con-ventional BLC is not a practical solution for thesesystems. To overcome this drawback, the conven-tional BLC can be modified by replacing its RH TLswith CRLH TLs to yield a novel BLC with an arbi-trary second operating frequency [17]. The advan-tage of the CRLH TL over the RH TL for a dual-bandBLC can be seen in the phase-response diagram ofFigure 14. Since the phase-response curve of the RHTL is a straight line from dc to f1, the design fre-quency f1 at −90 determines the next usable fre-quency 3 f1 at −270. By changing the phase slopeof the RH TL, the frequency at −270 can be varied,but −90 is no longer at the design frequency. Sincethe CRLH TL has a dc offset, it has an additionaldegree of freedom compared to the RH TL. Bychanging the dc offset and phase slope, the CRLHTL’s phase-response curve can intercept a desiredpair of phases at any arbitrary pair of frequencies( f1, f2) for dual-band operation.

Figure 15(a) shows a CRLH-based BLC withoperational frequencies at f1 = 930 MHz andf2 = 1, 780 MHz and corresponding phase delaysof 90 and 270, respectively. The CRLH TLs wereimplemented with SMT chip components. Themagnitude response of the CRLH-based BLC is alsoshown in Figure 15(b); |S21| and |S31| of −3 dB areachieved at both operational frequencies.

In general, this CRLH dual-band concept can beapplied to any microwave component (phaseshifters, matching networks, baluns, etc.) [18].

Figure 12. Dispersion diagram (first 2–3 modes) of theCRLH mushroom unit cell of Figure 13 obtained by full-wave simulation (FEM) with PBCs. Dashed lines are for theopen structure without the caps [14].

0

5

10

15

20

25

Freq

uenc

y (G

Hz)

Γ ΓX M

βp (rad)

1

1

2

2

3Air

Mod

e Air M

odeRH Mode

TE Mode (N

o Caps)

TE Mode

LH (No Cap)

LH Mode

Figure 13. Parameters of the mushroom structure to be ana-lyzed. The period of the unit cell is 5.0 × 5.0 mm (square latticepx = py = p). The two substrates used have a relative permittivi-ty of 2.2 and thicknesses of h1 = 0.127 mm and h2 = 1.57 mm,respectively. The diameter of the vias is 0.2 mm (their length ish1 + h2 = 1.697 mm). (a) Dimensions of the patches and caps[14]. (b) Cross-sectional view of the open structure [14].

(a)

4.6

4.0

4.6

4.6 y

x

h2

h1

Top Patches

Cap

Ground PlaneVias

(b)

September 2004 43

Asymmetric Backward-WaveDirectional CouplerConventional microstrip directional couplers are typi-cally capable of operating over a broad bandwidth(>25%) but have loose coupling levels of −10 dB or less.Noncoupled-line couplers, such as branch-line and ringcouplers, offer tight coupling levels (−3 dB) but at theexpense of a lower bandwidth (<10%). The Lange cou-pler is able to achieve both broad bandwidth and tightcoupling. However, it requires the use of cumbersome,expensive wire bonds. The novel coupler of Figure 16offers an alternative to these conventional couplers [19].It is capable of achieving any arbitrary coupling levelover a 50% bandwidth without any wire bonds.

The novel coupler of Figure 16 is a quasi-0dB asym-metric coupler consisting of a CRLH line and a con-ventional microstrip (CµS) line implemented onRogers RT/Duroid 5880 with dielectric constantεr = 2.2 and thickness h = 1.57 mm. This CµS/CRLHcoupler consists of 9 CRLH unit cells of the type usedin the CRLH TL of Figure 9(a). The spacing betweenthe coupled lines is s = 0.3 mm, and the length of thecoupler is d = 62 mm. By operating the CRLH line inits LH region, backward coupling is achieved. Withreference to Figure 16, when an input signal is appliedto Port 1, power (Poynting vector, S) propagatestoward Port 2, but phase (propagation constant, β)travels toward Port 1. Since coupling to the conven-tional microstrip line results from evanescent waves inthe transverse direction, the coupled power travelstoward Port 3.

The CµS/CRLH coupler, like any conventionalasymmetric coupler, is based on the phase differencesbetween the c and π modes [20]. The coherence length(the length required for maximum coupling) of a con-ventional asymmetric coupler is given by

dmax = π

|βc − βπ | , (15)

where βc and βπ are the c and π mode propagationconstants. Under the assumption of weak couplingfor the CµS/CRLH coupler, βc is equal to the propa-gation constant of the CRLH TL (βc = βCRLH), and βπ

is equal to the propagation constant of the conven-tional TL (βπ = βCµS). Since βCRLH is negative (LHregion), the coherence length of the CµS/CRLH cou-pler is given by

dmax = π

|βCRLH| + βCµS. (16)

Therefore, the CµS/CRLH coupler can achieve amuch smaller coherence length than the conventionalasymmetric coupler because of the plus sign in the

Figure 14. General phase response of a RH TL and a CRLHTL [17].

0

−270

−180

−90

90

Pha

se R

espo

nse

(Deg

rees

)

0 f1 f2 3f1

Frequency

RH TL

CRLH TL

Figure 15. Dual-band BLC. (a) Photograph of completed dual-band BLC with CRLH TLs indicated [17]. (b) Measured S-parameters [17].

Isolated Out

OutIn

1 2

34

CRLHTLs

(a)

−25

−20

−15

−10

−5

0

S-P

aram

eter

s (d

B)

0.6 0.8 1 1.2 1.4 1.6 1.8 2

Frequency (GHz)

(b)

S11S21S31S41

f2f1

44 September 2004

denominator, which strongly reduces d max in com-parison to (15).

Figure 17 shows the performance of the CµS/CRLHcoupler described above. Backward coupling of −0.7 dBis achieved over 2.2 GHz to 3.8 GHz, which represents a53% bandwidth. A conventional coupler with an identi-cal line spacing (s = 0.3 mm) can only provide a −10 dBcoupling. By varying the number of CRLH unit cells orthe line spacing, the CµS/CRLH coupler can achieve anarbitrary level of coupling. In [21], a symmetric CRLHcoupler, based on a different principle than the coupler

of Figure 16, but achieving comparable performancewas also demonstrated.

Zeroth Order ResonatorAs mentioned above, a unique feature of CRLH meta-materials is that a β of zero can be achieved at a non-zero frequency. This property can be used to create anovel zeroth order resonator (ZOR) which is depictedin Figure 18(a) [22]. The resonator consists of one unitcell of Figure 8 open-ended by capacitive slits withparameters shown in Figure 18(b). The resonator wasimplemented on Rogers RT/Duroid 5880 substratewith dielectric constant εr = 2.2 and thickness h = 1.57mm. At β = 0 there is no phase shift across the res-onator since phase shift is determined by φ = −βd = 0.In addition, it can be shown that the resonance is inde-pendent of the length of the structure but depends onlyon the reactive loadings.

The unloaded quality factor Qo of the ZOR depictedin Figure 18(a) is given by [22]

Qo =√

CR/LL

G, (17)

where G is the shunt conductance of a lossy CRLH TL.Note that this quality factor is independent of the number of unit cells.

The measured resonance characteristic of the ZOR iscompared with Method of Moments (MoM) simulationresults in Figure 19. An unloaded quality factorQo = 250 was obtained at 1.9 GHz, which is compara-ble to the unloaded quality factor of a conventionalhalf-wavelength resonator on the same substrate andwith the same resonant frequency [22].

Other Guided Wave ApplicationsBesides the above-mentioned applications, CRLHmetamaterials can be applied to a variety of other guid-ed-wave applications. Size reduction and bandwidthenhancement of conventional microwave components

Figure 16. Photograph of the nine-cell quasi-0dB asymmet-ric CµS/CRLH coupler. β and S represent the propagationand Poynting vector respectively in each line [19].

Coupled

In Through

Isolated

β S3

1

4

2

Figure 17. Measured S-parameters of the quasi-0dBCµS/CRLH coupler. The CRLH transition frequency isf0 = 3.9 GHz [19].

Figure 18. One-cell ZOR. (a) Photograph of prototype [22]. (b) Layout with parameters shown [22].

Input Output

w1D wstub

lstub

l1D

g

l1D = 10.2 mm, w1D = 1.0 mm, g = 0.2 mmlstub = 9.9 mm, wstub = 2.0 mm.Via Diameter: 0.4 mm.# of Fingers: 5 Pairs Each Side of Stub.Width of Fingers: 0.3 mm.Gap Between Fingers: 0.2 mm.

(a) (b)

−40

−35

−30

−25

−20

−15

−10

−5

0

S-P

aram

eter

(dB

)

1 1.5 2 2.5 3 3.5 4 4.5 5

Frequency (GHz)

S11S21S31S41

LH RH

September 2004 45

can be achieved with the use of CRLH metamaterials.For example, by replacing the 270 branch of the con-ventional hybrid ring with a −90 CRLH TL branch,the novel hybrid ring of [23] achieved a 50% bandwidthenhancement and a 67% size reduction over a conven-tional hybrid ring. In [24], the properties of nonlinearCRLH TLs, which are formed by incorporating nonlin-ear active devices (varactor diodes) to the CRLH TL,were investigated. The unique voltage response of thenonlinear CRLH TL can be potentially used to generateultra-short pulses for ultra-wideband (UWB) systems.Finally, the guided-wave applications discussed so farutilized the passband region of the CRLH TL, in whichpermittivity and permeability are simultaneously posi-tive or negative. However, the CRLH has either a neg-ative permittivity (−ε) or negative permeability (−µ) inits stop-band. By combining a −ε CRLH TL with a −µ

CRLH TL, a resonator independent of physical lengthsimilar to the ZOR was demonstrated in [25].

Radiated Wave Applications

Zeroth Order Resonator AntennaThe ZOR discussed above can be used to construct aZOR antenna as shown in Figure 20 [26]. Themicrostrip-based unit cell consists of aninterdigital capacitor and a shunt mean-der line connected to a rectangularpatch. The rectangular patch behaves asa virtual ground plane.

Since resonance is independent ofphysical dimensions for the ZOR, thesize of the antenna can be smaller than ahalf-wavelength. Instead, the antenna’ssize is determined by the reactive load-ings in its unit cells. Figure 21 shows thesize reduction that is possible with aZOR antenna with a design frequency of4.88 GHz. The size of the antenna is 10mm, while the length of the λ/2

microstrip patch antenna with the same substrate anddesign frequency is 20.6 mm. The antenna of Figure21(a) was implemented on a substrate with dielectricconstant εr = 2.68 and thickness h = 0.79 mm. The peri-od of the unit cell is 2.5 mm with four pairs of digits forthe interdigital capacitors and three turns for the meander

Figure 19. Measured and simulated |S11| and |S21| for theZOR of Figure 18(a) [22].

Figure 20. Four-cell ZOR antenna layout [26].

−80

−60

−40

−20

0

S21

(d

B)

S21

S11

ExperimentsMoM Simulation

n = 0

−15

−10

−5

0

0 2 4 6 8

Frequency (GHz)

S11

(d

B)

50 ΩInterdigital Capacitor

Unit CellVirtual Ground

Capacitor

Meander-LineInductor

ZT

IT

Figure 21. Antenna comparison. (a) Four-cell ZOR antenna ( f0 = 4.88 GHz) [26]. (b) Microstrip patch antenna on the samesubstrate ( f0 = 4.90 GHz) [26].

(a) (b)

46 September 2004

line. The width of each digit and of the meander line is100 µm. The virtual ground patch size is 2.0 × 4.8 mm2,and the antenna is matched to 50 .

The measured and simulated (MoM) radiation pat-terns of the ZOR antenna are shown in Figure 22. Theexperimental results agree well with the simulatedresults. In addition, a −11 dB return loss was obtained.

Backfire-to-Endfire Leaky-Wave AntennaThe balanced CRLH TL of Figure 9(a) can be used as anefficient, frequency-scanned leaky-wave (LW) antennawhen optimally matched to the air impedance [27]. ACRLH LW antenna has two distinct advantages overconventional LW antennas. First, a CRLH LW antennacan operate at its fundamental mode, because thismode contains a radiation (or fast-wave) region(|β| < k0, where k0 is the free-space propagation con-stant) in addition to a guided (or slow-wave) region(|β| > k0), as shown in Figure 23(a). In contrast, RHstructures have to be operated at higher order modes inorder to radiate and, consequently, require a more com-plex and less-efficient feeding structure, because the

fundamental mode of RH structures arealways guided (β > k0). Second, aCRLH LW antenna is capable of contin-uous scanning from backward (backfire)to forward (endfire) angles, unlike con-ventional LW antennas. This can be seenby examining the LW antenna scanningangle equation

θ = sin−1(

β0 + 2nπ/pk0

), (18)

where β0 is the propagation constant ofthe fundamental mode, n is the spaceharmonic [28], and p is the period. For a

nonperiodic LW antenna, n = 0, and β0 is the propaga-tion constant of the operating mode. For the CRLH LWantenna (n = 0, fundamental mode), θ can take on val-ues from −90 (backfire) to +90 (endfire), since|β| < k0 for a continuous frequency range as seen inFigure 23(a). Figure 23(b) depicts the scanning opera-tion of the CRLH LW antenna. By operating the CRLHLW antenna below or above its transition frequency ω0,forward and backward scanning is achieved. Referringto Figure 23, the antenna radiates backward in Region II(LH), and the antenna radiates forward in Region III(RH). At ω0, the antenna is able to radiate broadsidebecause vg = 0 at β = 0 for the balanced CRLH TL. Incontrast, a conventional nonperiodic LW antenna canonly scan from broadside to endfire, since β is alwayspositive. In addition, a conventional nonperiodic LWantenna cannot radiate at broadside because vg = 0(standing wave) at β = 0 for a RH structure. A conven-tional periodic LW antenna is able to scan from backfireto endfire by operating at negative and positive spaceharmonics (n = ±1, ±2, . . . ) [27], but broadside radia-tion cannot occur.

Figure 22. Radiation patterns of the four-cell ZOR antenna [26].

Experimental (Copolar)

Experimental (Crosspolar)

Simulation (Copolar)

Simulation (Crosspolar)

−40

−30

−20

−10

0[dB]

180

135

90

45

0

Figure 23. CRLH LW Antenna. (a) Typical dispersion diagram showing guided and radiation regions. (b) Scanning operation.

Source

BwdBwd

FwdFwd

BroadsideBroadside

X(b)

Y

Z

θ

ω = −βco ω = +βco

ω

β

ω0

ILH

Guided

IILH

Rad.

(a)

IVRH

Guided

IIIRH

Rad.

September 2004 47

To radiate efficiently, the TL of Figure 9(a) is termi-nated with a matched load to eliminate reflections whichwould otherwise produce spurious beams. Continuousbackfire-to-endfire scanning was achieved from 3.1 to 6.0GHz, as displayed in Figure 24(a). Measured radiationpatterns demonstrating backward, broadside, and for-ward scanning are shown in Figure 24(b).

Electronically Controlled LW AntennaLike in most LW antennas, the scanning angle of theCRLH LW antenna discussed above is determined by itsoperation frequency. However, frequency-dependent LWantennas are not practical for most modern wireless com-munication systems, which generally operate at a fixedfrequency for effective channelizing [29]. There have beenseveral efforts to develop frequency-independent LWantennas [30]–[32]. However, most of the resulting anten-nas were only able to scan at two discrete angles orrequired a dc magnetic field supply, which is generallynot practical for microwave applications. In [29], a fre-quency-independent LW antenna capable of continuousscanning and beamwidth control was realized with a TLcomposed of voltage-controlled CRLH unit cells. By con-trolling the bias voltage of varactor diodes included in theCRLH unit cell, the capacitance of the cell is changed. Asa result, the propagation constant of the CRLH unit cellbecomes a function of voltage as illustrated in Figure 25.

Since the voltage applied to each cell can be differ-ent, the voltage distribution on the antenna can be uni-form or nonuniform. Depending on the type of voltagedistribution, the antenna can be used as a scanning orbeamwidth-controlling LW antenna. In the case of uni-form distribution, the propagation constant of eachunit cell is identical, and each cell radiates toward thesame angle, so that directivity is maximal. Since β is afunction of V, the scanning angle of (18) becomes

θ(V) = sin−1(

β(V)

k0

)(19)

for a fundamental mode (n = 0) LW antenna. Therefore,the antenna functions as a voltage-controlled scanningLW antenna when voltage is uniformly distributed. Incontrast, under nonuniform voltage distribution, thepropagation constant of each unit cell can be individu-ally controlled, and each cell radiates towards a differ-ent angle, which results in a broader radiation beam. Bycontrolling the voltage applied to each cell, the beampattern of the antenna can be varied. Therefore, theantenna functions as a beamwidth-controllable LW

Figure 24. Measured Results. (a) Scanning angle versus frequency [27]. (b) Radiation patterns for 3.4, 3.9, and 4.3 GHz [27].

ILH

Guided

IILH

Rad.

IIIRH

Rad. IVRH

Guided

x y

z

2 3 4 5 6 7Frequency (GHz)

(a)

90

60

30

0

−30

−60

−90

Sca

nnin

g A

ngle

(D

egre

es)

f0

θ

0

0

−10

−20

−30

−20

−10

120

150

180

210

240

270

(b)

300

330

0

30

6090

3.4 GHz

3.9 GHz

4.3 GHz

Figure 25. Principle of voltage controlled CRLH unit cell.Dispersion curves are shifted vertically as the voltage isvaried [29].

ω

ω0

ββRH > 0 βLH < 0β=0

V2

V2

V1

V1

V3

V3

ω = +βCo

48 September 2004

antenna when the cells are nonuniformly biased. Thisbeamwidth control principle is illustrated in Figure 26.

Figure 27 shows the 30-cell, voltage-controlled, 3.33-GHz CRLH LW antenna presented in [29]. As seen in theinset of Figure 27, each unit cell consists of three varactordiodes, two in series and one in shunt configuration. Thisconfiguration was used to maintain constant characteris-tic impedance and attain high design flexibility [29]. Theantenna was implemented on Rogers RT/Duroid 5880with dielectric constant εr = 2.2 and thickness h = 1.57mm. Metalics MSV 34060-E28X Si abrupt varactor diodeswere used in the unit cells. Port 2 of the structure wasterminated with a 50- load to suppress spurious beams.

Figure 28 shows the theoretical and experimentalscanning angle versus the reverse bias voltage relation-ship of the antenna under uniform biasing. By increasingthe voltage, the antenna scans from backward to forwardangles (99 range). A maximum gain of 18 dBi isobserved at broadside. In [29], the half power beamwidth(HPBW) of the antenna under nonuniform biasing wasalso measured. The HPBW was increased by 43% to200% compared to the uniformed biased case.

Other Radiated-Wave ApplicationsAnovel reflectodirective system was demonstrated in [33]by combining a frequency-scanned CRLH LW antennaand heterodyne mixing. This system is able to receive anincident signal at any angle and reflect it at any arbitraryangle by tuning the local oscillator frequency. Fixed-fre-quency scanning can be achieved by using the electroni-cally controlled CRLH LW antenna in place of the fre-quency-scanned CRLH LW antenna. The CRLH LWantennas discussed so far were only able to scan in one-dimension. By using an open mushroom structure similarto Figure 11(a) [34] demonstrated an LW antenna capableof 2-D scanning, which is useful for anticollision systemswhere full-space scanning is required. This 2-D CRLH LWantenna achieved a scanning range of 15–33 in the back-ward region and a 27–63 range in the forward region.

Refracted Wave Applications

Planar NegativeRefractive Index LensIn [14], a negative refractive index (NRI) planar lens

was fabricated with the openmushroom structure of Figure11(a) to demonstrate the reversalof Snell’s Law. The NRI lens, con-sisting of a 20 × 6 CRLH unit cellarray, was sandwiched betweentwo RH parallel plate waveguides(PPWs). The completed NRI lensis shown in Figure 29(a), and across-sectional view is shown inFigure 29(b). The top view of theCRLH structure is shown inFigure 13(a), and the dispersiondiagram of the mushroom unitcell used for the NRI lens isshown in Figure 12. A coaxial linesource is placed 15 mm away

Figure 26. Principle of beamwidth control. (a) Narrow beamwidth with uniform voltage distribution [29]. (b) Widebeamwidth with nonuniform voltage distribution [29].

(a)

Beamwidth

V0 V0 V0 V0 V0 V0

Unit Cell

+− +− +− +− +− +− +− +− +− +− +− +−

(b)

Beamwidth

V1 V2 V3 V4 V5 V6

Unit Cell

Figure 27. A 30-cell electronically scanned LW antenna [29].

Shunt Varactor

Port 1

Pin

38.34 cm

Port 2

ZL

d=1.2 cmdd

GND, Vb(−)

Series Varactors

Via Via

3.02 cm

Inductor (dc Feed)

dc Bias, Vb(+)

September 2004 49

from the CRLH structure to excite one of the PPWs. Afocus will appear in the center of the CRLH structure ifits refractive index (nLH) is the negative of the refrac-tive index (nPPW) of the PPW (nLH = −nPPW).

At an operation frequency of 3.737 GHz, the CRLHstructure possess a refractive index ofnLH = −3.40. In contrast, the PPW has arefractive index of nPPW = 2.77. Thecoaxial source was excited at 3.737 GHz,and the field distribution above the LHstructure was measured with a verticalprobe on an automated stage. The mag-nitude and phase of the measured elec-tric field are respectively shown inFigure 30(a) and (b). Despite the slightmismatch of the refractive indices, afocus can be observed in the LH struc-ture. In [35], an NRI lens composed ofSMT chip components produced similarresults that demonstrated the reversal ofSnell’s Law.

Other Refracted Wave ApplicationsAlthough refractive, 2-D CRLH meta-materials are still at the level of con-ceptual demonstration, they arepromising for imaging and polariza-tion applications not possible withconventional RH materials. For exam-ple, an NRI lens with ε = −1 andµ = −1, can achieve subwav-lengthfocusing, as predicted by Pendry [36].Such a lens will allow focusing of lightin an area smaller than λ2 and was ver-ified by numerical simulations in [37].In addition, anisotropic CRLH meta-materials, which exhibit a positiverefractive index (PRI) in one directionand an NRI in an orthogonal direction,can be used to design polarizationselective antennas/reflectors [38].

ConclusionIn this article, the fundamental proper-ties of LHMs were discussed. In partic-ular, an overview of the more generalCRLH materials was presented basedon an extended TL theory. Both 1- and2-D CRLH TL structures weredescribed, and various physical realiza-tions of these structures were discussed.To demonstrate the practicality ofCRLH TL structures, various guided,radiated, and refracted microwaveapplications were presented. Theseapplications demonstrate that the TLapproach of LHMs offers an efficient

alternative to the original physical realization of LHMsbased on SRRs. This article has shown that low-loss,wide-bandwidth, and highly versatile LHMs are pos-sible and constitute a very promising new paradigmfor microwave and optical engineering.

Figure 28. Measured and theoretical scanning angle versus reverse bias volt-age [29].

Theory from Parameter ExtractionMeasurement

60

40

20

0

−20

−40

−60

Sca

nnin

g A

ngle

(D

egre

es)

0 2 4 6 8 10 12 14 16 18 20 22

Reverse Bias Voltage (V)

Figure 29. NRI lens (20 × 6 cells). (a) Photograph of entire structure [14]. (b)Cross-sectional view.

140

mm

140 mm

(a)

(b)

Source(Coax)

2-D CRLH Structure

PPW

PPW Top Patches

h1 h1 = 0.127 mm

h2,PPWh2,PPW = 1.270 mm

h2,LH

h2,LH = 1.570 mmVia Cap

Via Radius: 0.1 mmPeriod of Unit Cell: 5 mmSubstrate 1 Substrate 2

Ground Plane

εR=2.2 εR=10.2

50 September 2004

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Figure 30. Measured electric field distribution over theNRI lens of Figure 29. (a) Magnitude [14]. (b) Phase [14].

(a)

(b)