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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 12, DECEMBER 2010 3645

Coupled Composite Right/Left-HandedLeaky-Wave Transmission Lines Based on

Common/Differential-Mode AnalysisMohammed Reza M. Hashemi, Student Member, IEEE, and Tatsuo Itoh, Life Fellow, IEEE

AbstractA systematic analysis for two types of symmetricalcoupled composite right/left-handed (CRLH) leaky-wave (LW)transmission lines (TL) based on the common/differential-modeexcitations is presented. The first proposed coupled CRLH LW-TLis a 4-port via-free coupled CRLH LW-TL that behaves as a con-ventional CRLH LW-TL under differential-mode excitation. Butwhen common-mode excitation is applied, the structure has theability to suppress the left-handed waves by operating in thecutoff mode, and only supporting right-handed guided as well asradiating waves. The second type of the proposed coupled CRLHLW-TL is a modification of the first type by inserting vias at the

center of the left-handed stub of each unit-cell along the symmetryplane to provide a physical short-circuit to the ground. Thisstructure behaves as a conventional CRLH LW-TL under bothcommon- and differential-mode excitations but with orthogonalpolarizations when operating in the fast-wave region. As a result,a dual polarized CRLH LW-TL is obtained.

Index TermsCommon/differential-mode, composite right/left-handed (CRLH) transmission line, dual polarization, leaky wave(LW).

I. INTRODUCTION

SINCE the first conceptual metamaterial paper by Veselago

[1], a tremendous amount of work has been done towards

understanding and development of the metamaterial concept

and its applications [2][4]. The transmission-line (TL) ap-

proach to metamaterials based on the periodic unit-cells has led

to the concept of composited right/left-handed (CRLH) TLs

[2] resulting in novel multifunctional and compact microwave

devices [2].

The unique characteristic of a CRLH-TL is the ability of

phase advance/delay. In addition, unlike the conventional mi-

crostrip-based TL [5], under fundamental mode of operation a

CRLH-TL can guide energy when operating in the slow-wave

(SW) (also known as guided-wave region) or behave as a leaky-wave radiator (antenna) while operating in the fast-wave (FW)

or leaky-wave (LW) region. The use of a CRLH-TL as a dom-

inant leaky-wave structure has led to a novel radiating device

Manuscript received April 14, 2010; revised August 25, 2010; acceptedSeptember 09, 2010. Date of publication November 09, 2010; date of currentversion December 10, 2010. This work was supported by Honeywell throughthe UC Discovery program.

The authors are with the Department of Electrical Engineering, Universityof California, Los Angeles, Los Angeles, CA 90095 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMTT.2010.2086371

which offers the capability of radiating a backward wave as well

as a forward wave including broadside direction, in a continuous

fashion [6][8], enhancing the operation over conventional LW

antennas. Continuous frequency beam scanning capability, rel-

atively high gain, being low profile and simple feeding mech-

anism make CRLH LW-TL suitable for integration with active

devices, conformal surface applications, and vehicle awareness

systems. These benefits have inspired the development of nu-

merous novel 2-port CRLH LW-TLs [8][11].

Although, the 2-port conventional CRLH LW-TLs are con-sidered revolutionary, they have a common disadvantage which

is their comparable radiating cross- and co-polarized compo-

nent strength levels when operating in the fast-wave mode [12],

[13]. In this paper, the reasoning behind this characteristic is

explained and it is shown by using coupled CRLH LW-TL this

disadvantage can be overcome and the level of cross-polariza-

tion can be suppressed.

The conventional coupled TLs have been one of the key

components in microwave electronics and there are well-known

techniques to analyze such structures [14][16]. Recently, the

concept of coupled CRLH-TL structures has become of interest

and various studies have been done in developing novel cou-pled CRLH-TL structures, such as metamaterial coupled-line

couplers [17], [18], a CRLH-TL based broadband Balun [19],

an integrated antenna front-end based on a balanced mixer with

differential-mode excitation [20], conductor-backed coplanar

strips CRLH-TL [21], and a two layer negative refractive

index TL-based LW antenna [22]. The structures presented in

[20][23] have CRLH characteristics only when a differen-

tial-mode (out-of-phase) excitation is applied.

This main focus of this paper is on two types of symmetrical

coupled CRLH LW-TLs. By taking advantage of the sym-

metrical nature of these two coupled CRLH LW-TL types, a

systematic analysis is performed on each proposed type using

the common/differential-mode (even/odd-mode) excitation.The common/differential-mode excitation introduces an ad-

ditional degree of freedom in each case resulting in unique

characteristics for each of the proposed coupled CRLH LW-TL

types. The first proposed coupled CRLH LW-TL type is a 4-port

via-free coupled CRLH LW-TL. This structure behaves as a

conventional CRLH-TL supporting both forward (right-handed,

RH) as well as the backward (left-handed, LH) waves under

differential-mode excitation. When common-mode excitation

is applied, the LH waves will be cutoff and the via-free cou-

pled CRLH LW-TL will only support RH waves not only as

a guided structure but also as radiating structure performing

a RH frequency beam scanning. The second coupled CRLH

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3646 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 12, DECEMBER 2010

LW-TL type is a modification of the first type by inserting

a ground via at the center of the LH stub of each unit-cell

along the symmetry plane to provide a physical short-circuit

to the ground under both common-mode and differential-mode

excitation. This type of coupled CRLH LW-TL behaves as a

conventional CRLH LW-TL under both common-mode and

differential-mode excitation, supporting both LH and RHguided and radiating waves. The advantage of this type of

coupled CRLH LW-TL is that it can be considered as dual

polarized CRLH LW-TL when it is operating in the LW mode.

The dual polarity of this structure is a result of two orthogonal

polarizations while common-mode and differential-mode are

applied. The preliminary common/differential-mode analysis

of the dual polarized coupled CRLH LW-TL has been reported

by the authors in [24].

The behavior of each of the two coupled CRLH LW-TLs

will be analyzed and explained through unit-cell characteri-

zation, current distribution along the CRLH-TL for different

frequencies, comparison between the simulated and mea-

sured scattering parameters and far-field radiation patterns.Moreover, through the common/differential-mode analysis it

will be shown and confirmed that the radiation caused by the

CRLH-TL operating in the LW mode is associated with the LH

capacitance and LH inductance.

This paper is organized as follows: Section II presents the

theory behind the proposed coupled CRLH LW-TLs, and the

coupled-line approach to analyze them. Section III develops

a common/differential-mode analysis of the via-free coupled

CRLH LW-TL. This is done by using the dispersion diagram,

current distributions, scattering parameters, and radiation pat-

terns. In Section IV, common/differential-mode analysis is per-

formed on the dual polarized coupled CRLH LW-TL in the samemanner as Section III. Finally, Section V presents conclusions.

For the ease of comparison, the correspondent figures to the

via-free and the dual polarized coupled CRLH LW-TL are or-

ganized in a way that one follows the other or have been placed

side-by-side. However, the relevant discussion of each figure is

presented in the designated section as outlined above.

II. THEORY

A. Via-Free Coupled CRLH LW-TL Unit-Cell

The conventional TL can be modeled as a combination of a

per unit length series inductor along with a per unit lengthshunt capacitor . In the case of the CRLH-TL, this model

needs to be modified to realize a single unit-cell by adding a

series capacitor and shunt inductor [2]. This equiv-

alent circuit model can be then realized using microstrip imple-

mentation using interdigital capacitors for and stub inductor

shorted to the ground (GND) through a via as . and

are the results of the parasitic effects [2].

The via-free coupled CRLH unit-cell can be obtained

by connecting two 2-port CRLH unit-cells together trough

their LH stub inductor and eliminating the ground vias as

shown in Fig. 1. This coupled unit-cell is analyzed using

common/differential-mode excitations by exciting the input

port in phase or 180 out-of-phase, respectively. The dis-persion curve, attenuation constant and Bloch impedance

Fig. 1. Via-free coupled CRLH unit-cell. (a) Microstrip implementation and(b) equivalent circuit model.

Fig. 2. Dual polarized coupled CRLH unit-cell. (a) Microstrip implementationand (b) equivalent circuit model.

extraction for the common-mode and the differential-mode

using the coupled-mode analysis is discussed in the next

section. Under differential-mode a virtual short-circuit (SC)

is created along the symmetry plane of the unit-cell. As a

result, will be in parallel to resulting in an equivalent

circuit model of a conventional CRLH unit-cell supporting

both RH and LH guided-wave and leaky-wave modes. But

when the common-mode is applied, a virtual open-circuit (OC)

is created along the symmetry plane, therefore will have

no influence and it can be effectively eliminated. As a result

the via-free coupled CRLH LW-TL only supports RH guided

and leaky-waves and LH waves are cutoff. The RH radiation

is caused by the capacitive coupling between the interdigital

fingers. The via-free coupled CRLH LW-TL is advantageous

when dealing with high frequency operation where fabrication

of the ground via is troublesome. In addition this structure has

the ability to suppress and cutoff LH waves and support both

RH guided-wave and radiating-wave under common-mode

excitation.

B. Dual Polarized Coupled CRLH LW-TL Unit-Cell

A dual polarized CRLH unit-cell, shown in Fig. 2(a) can be

obtained by modifying the via-free coupled CRLH unit-cell,

discussed above, by inserting a ground via along the symmetry

plane of the unit-cell providing a physical short-circuit as shownin Fig. 2(a). The ground via introduces an inductance, , to

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HASHEMI AND ITOH: COUPLED COMPOSITE RIGHT/LEFT-HANDED LEAKY-WAVE TRANSMISSION LINES 3647

the ground, as shown in Fig. 2(b), which can be considered as

two inductors connected in parallel to the ground. When

common-mode excitation is applied, a virtual open-circuit is

created along the symmetry plane, resulting in a CRLH unit-cell

configuration with a left-handed inductance of . On

the other hand, differential-mode excitation creates a virtual

short-circuit along the symmetry plane of the unit-cell, whichwill short out . Therefore, differential-mode excitation

also results in a configuration of a CRLH unit-cell with a

left-handed inductance of . Thus, this unit-cell behaves

as a conventional CRLH unit-cell under both common-mode

and differential-mode excitation with different left-handed

inductance values, supporting both RH and LH guided-wave as

well as leaky-wave modes for each excitation.

A dual polarized coupled CRLH LW-TL can be obtained by

cascading the proposed coupled CRLH unit-cells. When this

CRLH LW-TL operates in the FW (fast-wave) region, under

common-mode the -plane would be along the direction of the

interdigital capacitors as the dominant current distribution will

be in this direction since the currents flowing in the stub in-ductor are in the opposite direction and will cancel each other

out at the symmetry plane. Assuming the structure is laying

in the -plane and oriented along the x-direction as shown in

Fig. 3, common-mode excitation causes dominant polariza-

tion. On the other hand, dominant current distribution occurs at

the center of the LH stub inductor under differential-mode as

the currents add up at the symmetry plane of the TL. This re-

sults in the -plane to be oriented along the LH stub inductor

in the -plane of Fig. 3 which is orthogonal to that of the

common-mode. Therefore, the dominant radiated field polariza-

tionwill be . In turn, a dual polarized coupled CRLHLW-TL

is obtained.

C. Coupled-Line Approach

Analyzing differential type structures and those with more

than two ports can be somewhat difficult and costly. In order

to analyze the proposed coupled CRLH LW-TLs, we take ad-

vantage of the symmetrical nature of each structure to perform

the common/differential-mode analyses. This is done by first

obtaining the single-ended -parameters using the two

port network analyzer. Then, a simple matrix transformation

[16] is used to convert the single-ended -parameters to the

common/differential-mode -parameters as shown in (1)

Fig. 3. Theoretical layout of the dual polarized CRLH LW-TL. (a) Common-mode excitation and (b) differential-mode excitation. Port numbers are writtenin orange.

at the bottom of the page, where subscripts and stand

for common and differential, respectively. The port numbering

is according to Fig. 3.

Using the conventional CRLH propagation and Bloch

impedance relations [2] along with (1), the phase constant(dispersion relation), the attenuation constant and the Bloch

impedance relations for the common-mode and the differen-

tial-mode excitations are derived and shown in (2)(4)

(2a)

(2b)

(3a)

(3b)

(4a)

(4b)

Here, and are the common-mode and differential-

mode phase constants, and are the common-mode

and differential-mode attenuation constants, and . and

are the Bloch impedances for the common-mode and

(1)

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Fig. 4. Prototype of the 25-cell via-free coupled CRLH LW-TL.

Fig. 5. Prototype of the 25-cell dual polarized coupled CRLH LW-TL.

TABLE IVIA-FREE/DUALPOLARIZEDCOUPLEDCRLH UNIT-CELLEQUIVALENT

CIRCUITMODELPARAMETERS

differential-mode, respectively. Also, corresponds to the pe-

riod of the unit-cell and is equal to the reference impedance

of 50 .

III. VIA-FREECOUPLEDCRLH LW-TL

A. Geometrical Realization

In this section, a 25-cell via-free coupled microstrip CRLH

LW-TL is introduced. Fig. 4 is a photograph of the fabricated

25-cell via-free coupled CRLH LW-TL. Each unit-cell, as

shown in Fig. 1(a), has ten pairs of interdigital capacitors

(fingers) divided into two five-pair groups connected to each

end of the LH stub inductor. Each finger is 6.3 mm in length

and 0.15 mm in width, and the gap between the fingers is 0.1

mm. The dimensions of the stub inductor are 16.0 mm in length

and 1.0 mm in width. The period of the unit-cell is 7.4 mm. The

substrate used for this structure is Rogers RT/Duroid 5870 with

dielectric constant of and thickness of

mm. The extracted equivalent circuit model parameters of the

coupled CRLH unit-cell are reported in Table I.

B. Unit-Cell Characteristics

The dispersion diagrams, the attenuation constant, and theBloch impedance of the via-free unit-cell for the common-mode

Fig. 6. Common-mode (red curve) and differential-mode (blue curve) disper-sion diagram of the via-free coupled CRLH unit-cell from (a) full-wave simula-tion and (b) equivalent circuit model. (SW stands for slow-wave and FW standsfor fast-wave regions.)

Fig. 7. Common-mode (red curve) and differential-mode (blue curve) attenu-ation constant of the via-free coupled CRLH unit-cell for (a) 1 GHz GHz and (b) 2.5 GHz GHz (zoomed).

Fig. 8. Bloch impedance of the via-free coupled CRLH unit-cell: (a) common-mode and (b) differential-mode. The blue solid curve corresponds to real partand the red dashed curve is the imaginary part.

and the differential-mode excitations are obtained using (2)(4)

and are shown in Figs. 6, 7, and 8, respectively.

Fig. 6(a) is the dispersion diagram of the via-free coupled

CRLH unit-cell obtained from full-wave simulation of the unit-

cell using Ansys Designer. Similarly, Fig. 6(b) is the dispersiondiagram of the unit-cell obtained from the extracted equivalent

circuit model of the unit-cell shown in Fig. 1(b). In these fig-

ures, the red curve is associated with the dispersion curve of the

common-mode and blue curve is for the differential-mode. The

jumps in the dispersion curves obtained from the full-wave sim-

ulation are caused by the self-resonances of the interdigital ca-

pacitors. These self-resonances are created by the physical con-

figuration of the interdigital capacitors that have two resonant

paths with the electrical length of at GHz and

GHz. To confirm this phenomenon, the frequency re-

sponse of the interdigital capacitor section of the proposed cou-

pled CRLH unit-cells are obtained and shown in Fig. 9. There-

fore, the dispersion diagrams of the unit-cell obtained from theequivalent circuit model, which is based on the lumped element

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Fig. 9. Frequency response of the interdigital capacitor section of the proposedcoupled CRLH unit-cells.

Fig. 10. Common-mode (red curve) and differential-mode (blue curve) disper-siondiagram of the dualpolarizedCRLH unit-cell from(a) full-wave simulationand (b) equivalent circuit model. (SW stands for slow-wave and FW stands forfast-wave regions.)

values, cannot predict these self-resonances. Also, the slope of

the common-mode dispersion curve and that of the differen-

tial-mode are different as a result of the effective elimination

of in the case of common-mode excitation.

From the red curve in Fig. 6, it is clear that this structure

supports both RH guided and leaky-wave under its funda-mental mode of operation when common-mode is applied. The

common-mode excitation results in a RH leaky-wave region

of 3.6 GHz to 4.2 GHz and a RH guided-wave region above

4.2 GHz. On other hand, this structure does not support guided

or leaky-wave in the frequency region below 3.6 GHz which

correspond to the LH region under common-mode excitation.

This confirms that the via-free CRLH LW-TL supports only RH

waves as the LH waves are cut off under the common-mode.

The blue curve in Fig. 6 corresponds to the differential-mode

excitation and indicates that the via-free CRLH unit-cell be-

haves as a conventional CRLH unit-cell supporting both LH

and RH waves while differential-mode is applied. This unit-cellis a nearly balanced one with a transition frequency of 3.7 GHz

when differential-mode is applied. Under differential-mode,

this unit-cell has a LH guided-wave region: GHz,

a LH leaky-wave region: 2.92 GHz GHz, a RH

leaky-wave region: 3.7 GHz GHz, and a RH

guided-wave region: GHz.

Fig. 7 is the attenuation plots obtained from (3a) and (3b). The

red dashed curve corresponds to the common-mode and blue

curve is the differential-mode one. Based on the red curve, the

large -values below 3.7 GHz confirms that the LH waves are

cutoff under common-mode excitation. Also, the jumps in the

red and the blue curves in Fig. 7(a) at 4.8 GHz and 6.18 GHz

are due to the self-resonance of the interdigital capacitors. Basedon Fig. 8(a), the Bloch impedance value of the via-free CRLH

Fig. 11. Common-mode (red curve) and differential-mode (blue curve) atten-uation constant of the dual polarized CRLH unit-cell for (a) 1 GHz GHz and (b) 2.5 GHz GHz (zoomed).

Fig. 12. Bloch impedance of the via-free coupled CRLH unit-cell:(a) common-mode and (b) differential-mode. The blue solid curve corre-sponds to real part and the red dashed curve is the imaginary part.

unit-cell rises from 0 to 37 near the transition frequency under

common-mode excitation. Similarly, Fig. 8(b) shows that the

via-free CRLH unit-cell has Bloch impedance value of 45

near the transition frequency when differential-mode excitation

is applied.

C. S-Parameters

The proposed 25-cell via-free coupled CRLH LW-TL is

simulated using Ansys Designer. For measurement purposes,

two Rat-Race couplers are designed having a bandwidth of 30%

and the center frequency of 3.7 GHz, to provide common-mode

and differential-mode excitation over the frequency band

GHz. This frequency band covers the

LH and RH leaky-wave regions, fulfilling the requirement

for the in-phase and the 180 out-of-phase condition for

common-mode and differential-mode excitations consequently.

Using the measured and simulated single-ended -pa-

rameters in (1), the measured and simulated common- anddifferential-mode -parameters are obtained and shown in

Fig. 13. In order to validate the coupled-line approach dis-

cussed in Section II, the common- and differential-mode

-parameters obtained from measurement of the 25-cell CRLH

LW-TL integrated with two of the designed Rat-Race couplers

are also plotted in Fig. 13 in blue.

Based on Fig. 13, there is good agreement between the mea-

sured (red dot-dashed curve) and simulated (black solid curve)

, obtained from (1). On the other

hand, Fig. 13 shows that the measured common- and differen-

tial-mode -parameters obtain from (1) and those from mea-

surement of the TL with the Rat-Race couplers (blue curve)

match well in the frequency region 3.0 GHz GHz.The small discrepancy due to over-etching causes a 100 MHz

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Fig. 13. Common/differential-mode -parameters for the via-free CRLHLW-TL, black solid curve represents the simulated results, the red dot-dashedcurve is associated to measurement obtained from (1) and the blue dashedcurve is the measurement of the TL integrated with two Rat-Race couplers.

shift in the measured results compared to the simulated ones.

Based on Fig. 13(a) the level of is near 0 dB in the fre-

quency region below 3.7 GHz. Also according to Fig. 13(b)the level of in this frequency region is below dB,

indicating that the structure is operating in the cutoff region.

In contrast, the level of and , are nearly below

dB from 3.7 GHz to 7 GHz. Therefore, it is apparent that

the via-free coupled CRLH LW-TL supports RH guided-wave

mode under common-mode as dB and also sup-

ports forward radiation as dB. Conversely, based

on F ig. 1 3(c) and (d), t he l evels o f and for t he d if-

ferential-mode are below dB from 2 GHz to 7 GHz except

at 3.7 GHz, as the unit-cell in use may not be fully balanced.

Therefore, the proposed coupled CRLH LW-TL supports both

LH and RH guided-wave modes under differential-mode exci-

tation as dB and also support backward and for-ward radiation as is near dB.

Fig. 14. Common/differential-mode -parameters for the dual polarizedCRLH LW-TL, black solid curve represents the simulated results, the reddot-dashed curve is associated to measurement obtained from (1) and the bluedashed curve is the measurement of the TL integrated with two Rat/Races.

D. Current Distributions

In order to understand the behavior of the via-free CRLH

LW-TL, the current distribution along the TL is obtained for

three frequencies of 3.1, 3.7, and 4.3 GHz corresponding to LH

region, transition frequency, and RH region, respectively for

both common-mode and differential-mode excitations. These

current distributions are shown in Fig. 15 for common-mode

and Fig. 16 for differential-mode. From Fig. 15(a) the level of

current distribution indicates that at GHz the TL is

operating in cutoff region as common-mode is applied. From

Figs. 15(b) and (c) it is clear that the dominant current is flowing

along the interdigital capacitors and the currents flowing into the

stub inductor are in the opposite direction under common-mode

excitation, which results in a virtual open-circuit along the sym-metry plane of the TL and effective elimination of .

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Fig. 15. Current distribution of the 25-cell via-free coupled CRLH LW-TL under common-mode at (a) 3.1 GHz, (b) 3.7 GHz, and (c) 4.3 GHz.

Fig. 16. Current distribution of the 25-cell via-free coupled CRLH LW-TL under differential-mode at (a) 3.1 GHz, (b) 3.7 GHz, and (c) 4.3 GHz.

Fig. 17. Current distribution of the 25-cell dual polarized coupled CRLH LW-TL under common-mode at (a) 3.1 GHz, (b) 3.7 GHz, and (c) 4.3 GHz.

Fig. 18. Current distribution of the 25-cell dual polarized coupled CRLH LW-TL under differential-mode at (a) 3.1 GHz, (b) 3.7 GHz, and (c) 4.3 GHz.

Fig. 16 demonstrates that under the differential-mode excita-

tion the currents that are flowing along the stub inductors are

stronger than those along the interdigital capacitors. In fact the

direction of the current distribution along the upper set and the

lower set of the interdigital capacitors are in the opposite direc-

tion as a result of 180 out-of-phase excitation. Fig. 16 also con-

firms the CRLH nature of the via-free coupled CRLH LW-TL

under differential-mode excitation as current flow is observedalong both the interdigital capacitors and stub inductors.

E. Radiation Characteristics

To demonstrate the RH beam steering capability of thevia-free coupled CRLH LW-TL under common-mode excita-tion, three frequencies 3.8, 4.0, and 4.3 GHz are chosen in theRH fast-wave region and the radiation patterns are shown inFig. 19. These radiation patterns are obtained by feeding port1 and port 3 of the via-free coupled CRLH LW-TL shown in

Fig. 4 in-phase, using a designed Rat-Race coupler and termi-nating ports 2 and 4 with 50 loads. From Fig. 19 it can be

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Fig. 19. Common-mode measured (solid curves) and simulated (dashed curves) radiation patterns of the via-free coupled CRLH LW-TL at (a) 3.8 GHz, (b) 4.0GHz, and (c) 4.3 GHz.

Fig. 20. Differential-mode measured (solid curves) and simulated (dashed curves) radiation patterns of the via-free coupled CRLH LW-TL at (a) 3.1 GHz, (b)3.7 GHz, and (c) 4.3 GHz.

seen that the radiated main beam is steered from 32 to 60 asfrequency scans from 3.8 to 4.0 GHz. Moreover, assuming thatthe TL is laying in the -plane and interdigital capacitors areoriented along -direction as shown in Fig. 4, it is evident fromFig. 19 that the dominant radiated field is the component.This is due to the fact that the dominant current distribution is

along the interdigital capacitors for common-mode as can beseen from Fig. 15. The comparison between the measured andthe simulated patterns reveals good agreement. The differencebetween the measured and simulated patterns is caused by theusage of infinite ground plane in the full-wave simulations.Conversely, to show the backfire to endfire beam steeringcapability of the via-free coupled CRLH LW-TL when it isoperating in the fast-wave region while differential-mode isapplied, three frequencies of 3.1 GHz (backward radiation), 3.7GHz (broadside radiation), and 4.3 GHz (forward radiation)are selected. The radiation patterns for these three frequenciesare shown in Fig. 20. These radiation patterns are obtained byfeeding port 1 and port 3 of the TL, 180 out-of-phase using a

designed Rat-Race coupler and terminating ports 2 and 4 with50 loads. Based on Fig. 20 the beam is steered fromto 30 as frequency scans from 3.1 to 4.3 GHz. In addition thedominant radiated field in these patterns is the component.This is the result of the dominant current distribution beingalong the stub inductor under differential-mode excitationas can be seen from Fig. 16. Good agreement is achievedbetween the measured and simulated radiation patterns and thedifference between the patterns is caused by the infinite groundassumption in the simulations. Table II summarizes the mea-sured and the simulated radiation characteristics of the via-freecoupled CRLH LW-TL under common-mode excitation forthe chosen frequencies. Similarly, Table III summarizes the

measured and the simulated radiation characteristics of this TLunder differential-mode excitation for the chosen frequencies.

IV. DUALPOLARIZEDCOUPLEDCRLH LW-TL

A. Geometrical Realization

In this section, a 25-cell dual polarized coupled mi-crostrip-type CRLH LW-TL is introduced. Fig. 5 is a pho-tograph of the fabricated 25-cell dual polarized coupled CRLH

LW-TL. The dual polarized coupled CRLH unit-cell is obtainedby inserting a ground (GND) via along the symmetry plane ofeach via-free unit-cell providing a physical short-circuit fromthe stub inductor to the ground plane. The dimension of theunit-cell components remains the same as the via-free coupled

CRLH unit-cell and the ground via has a radius of 0.3 mm. Theproposed dual polarized coupled CRLH unit-cell is shown inFig. 2(a). The ground via introduces an inductance to theground. Fig. 2(b) shows the equivalent circuit model of the dual

polarized CRLH unit-cell and the extracted circuit parametersare summarized in Table I.

B. Unit-Cell Characteristics

Thedispersion diagrams of the dual polarizedCRLH unit-cellfor common-mode and differential-mode obtained from full-wave simulation are shown in Fig. 10(a) and those from the

equivalent circuit model are plotted in Fig. 10(b). In these fig-ures, the red curve corresponds to the common-mode and thedifferential-mode is plotted in blue. The jumps in the dispersion

curves obtained from full-wave simulation at 4.8 and 6.18 GHzare caused by the self-resonance of the interdigital capacitors.

From Fig. 10, it is apparent that the unit-cell is nearly bal-anced when differential-mode is applied and unbalanced under

common-mode excitation with a small stopband from 3.36 to3.55 GHz. This stopband is caused by the additional induc-

tance, that is introduced by the ground via. Both excita-tion modes support LH and RH waves. The transition frequency

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TABLE IIRADIATION CHARACTERISTICS OF THEVIA-FREECOUPLEDCRLH LW-TLFOR COMMON-MODEEXCITATION

TABLE IIIRADIATION CHARACTERISTICS OF THEVIA-FREECOUPLEDCRLH LW-TLFOR DIFFERENTIAL-MODEEXCITATION

Fig. 21. Common-mode measured (solid curves) and simulated (dashed curves) radiation patterns of the dual polarized coupled CRLH LW-TL at (a) 3.1 GHz,(b) 3.7 GHz, and (c) 4.3 GHz.

of the unit-cell for the differential-mode is GHz.

The 25-cell dual polarized coupled CRLH LW-TL is LH atGHz, while at GHz it is RH. In addition this

CRLH-TL is in the LH guided-wave region below 2.92 GHz;

similarly, this CRLH-TL operates in the RH guided-wave re-gion above 5.51 GHz. In contrast, this structure supports LHradiation in the frequency region of GHz,and RH radiation in the frequency region of

GHz. There is a shift of 0.2 GHz in the LH branch of the

common-mode dispersion curve compare to that of the differen-tial-mode which is the result of additional LH inductance, ,introduced by the ground via and the unit-cell being unbalancedunder common-mode excitation.

Attenuation constants of the dual polarized coupled CRLHunit-cell are obtained from (3a) and (3b) and are shown inFig. 11 for common-mode and differential-mode. The red

dashed curve corresponds to the attenuation constant of thecommon-mode and the blue curve is that of the differen-tial-mode. The jumps in Fig. 11(a) at 4.8 and 6.18 GHz aredue to the self-resonance of the interdigital capacitors. Also,

the peak seen in the common-mode attenuation constant plotof the dual polarized CRLH unit-cell shown in Fig. 11(b) near

3.55 GHz is due to the unbalanced nature of this unit-cell undercommon-mode excitation.

The Bloch impedance of the structure for common-mode and

differential-mode can be seen in Fig. 12(a) and (b), respectively.The unit-cell has a Bloch impedance of 42 and 44 nearthe transition frequency when common-mode and differential-

mode excitations are applied, respectively.

C. S-Parameters

Using the measured and simulated single-ended -pa-rameters in (1), the measured and simulated common- and

differential-mode -parameters are obtained for the 25-celldual polarized coupled CRLH LW-TL and are shown inFig. 14. In order to validate the coupled-line approach dis-cussed in Section II, the common- and differential-mode

-parameters obtained from measurement of the 25-cell CRLHLW-TL integrated with two designed Rat-Race couplers arealso plotted in Fig. 14 in blue. A good agreement between the

measurement (red dot-dashed curve) and the simulated (blacksolid curve) of , using (1), canbe observed. On the other hand, Fig. 14 shows that the measuredcommon/differential-mode -parameters obtained from (1) and

those from measurement of the TL with the Rat-Race couplersmatch well in the frequency region Hz GHz.

The small discrepancy is caused by over-etching resulting inabout 100 MHz shift in the measured data in comparison to the

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Fig. 22. Differential-mode measured (solid curves) and simulated (dashed curves) radiation patterns of the dual polarized coupled CRLH LW-TL at (a) 3.1 GHz,(b) 3.7 GHz, and (c) 4.3 GHz.

TABLE IVRADIATION CHARACTERISTICS OF THEDUALPOLARIZEDCOUPLEDCRLH LW-TLFOR COMMON-MODEEXCITATION

TABLE VRADIATION CHARACTERISTICS OF THEDUALPOLARIZEDCOUPLEDCRLH LW-TLFOR DIFFERENTIAL-MODEEXCITATION

simulated ones. Furthermore, Fig. 14 indicates that the level

of -parameters for both excitation modes are below 10 dBfrom 2 to 7 GHz, except for the common-mode at frequencyband of 3.36 to 3.55 GHz which corresponds to the stopbandas a result of being unbalanced. Therefore, it is apparent thatthe proposed coupled CRLH LW-TL supports both LH and RH

guided-wave modes under both excitation as dBand dB, it also supports backward and forwardLW radiation under both excitations as dB and

dB.

D. Current Distributions

The behavior of the 25-cell dual polarized coupled CRLH

LW-TL is better understood through the current distributionalong the TL. To this end, common-mode current distributionsand differential-mode current distribution are obtained for the

chosen frequencies, 3.1 GHz (LH region), 3.7 GHz (transitionfrequency), and 4.3 GHz (RH region), using Ansys Designer.Figs. 17 and 18 show the common-mode and differential-modecurrent distributions, respectively. Wave propagation can be ob-

served for all three chosen frequencies for both common-modeand differential-mode. This confirms the CRLH nature of

the coupled CRLH LW-TL under both modes of excitation.Moreover, based on Fig. 17, it is evident that in the case of

common-mode excitation the dominant current distribution is

along the interdigital capacitors as the currents flowing in thestub inductor are in the opposite direction and end up cancelingeach other. Conversely, in the case of differential-mode exci-tation shown in Fig. 18 the dominant current distribution isalong the stub inductors and in this case current flow is in the

opposite directions along the interdigital capacitors. So whenTL is laying in the -plane oriented in the -direction andcommon-mode is applied the -plane can be considered as the

-plane. But for the differential-mode the -plane is orientedin -plane. This yields to two orthogonal modes of operation;therefore, the coupled CRLH LW-TL has two orthogonalpolarization states under common-mode and differential-mode

excitation.

E. Radiation Characteristics

To confirm the dual polarization nature of this coupled CRLHLW-TL, radiation patterns are obtained for the three chosenfrequencies: GHz (backward radiation),GHz (broadside radiation), and GHz (forward radi-

ation) and are plotted in Fig. 21 for the common-mode andFig. 22 for the differential-mode. To measure the radiation pat-

terns, the CRLH-TL is integrated with a designed Rat-Racecoupler through its port 1 and port 3 for in-phase and 180

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out-of-phase excitations and the two remaining ports are ter-

minated with 50 loads. In the case of common-mode exci-tation, the component is the dominant radiating componentfor all three frequencies. The radiation beam is steered from

24 to 34 as frequency scans from 3.1 to 4.3 GHz. It is worthnoting that due to the unbalanced nature of the unit-cell under

common-mode and the dispersion diagram being shifted downon frequency axis as shown in Fig. 10, the beam at 3.7 GHzis slightly shifted to the RH direction. Conversely, the dom-inant radiating component under differential-mode is the

component for all three chosen frequencies while the beam issteered from 24 to 30 by scanning the frequency, as shownin Fig. 22. Therefore, the proposed coupled CRLH LW-TL is

indeed a novel dual polarized coupled CRLH LW-TL. Figs. 21and 22 show a decent agreement between the measurement andsimulation. In Fig. 21(b), we see a widening of the beam as thebeam is scanned through broadside, while in Fig. 22(b) the beam

maintains its shape fairly well as the beam scans through broad-side. This is evidently due to the fact that the common mode has

a fair amount of stopband behavior at broadside while the differ-ential mode does not, which in turn is due to the fact that the dif-

ferential mode is almost perfectly balanced while the commonmode is not.

A summary of the measured and simulated radiation charac-teristics of the 25-cell dual polarized CRLH LW-TL is shown in

Tables IV and V for common-mode and for differential-mode,respectively.

V. CONCLUSION

A via-free coupled CRLH LW-TL and a dual polarizedcoupled CRLH LW-TL are analyzed using the common/differ-

ential-mode excitation. It is shown when the common-mode

excitation is applied the via-free coupled CRLH LW-TL sup-

ports both RH guided and radiated waves. The forward beam

steering capability of the via-free TL is demonstrated under the

common-mode. The LH waves are cutoff when common-mode

is applied as a virtual open-circuit is created along the symmetry

plane of the structure and LH stub inductors are effectively

eliminated. It is shown that the dominant current distribution is

located along the interdigital capacitors for this mode of opera-

tion. Under differential-mode excitation, a virtual short-circuit

is created along the symmetry plane of the structure and CRLHbehavior is observed. In this case the dominant current distri-

bution is located along the stub inductor. Beam scanning from

backward to forward direction including broadside is demon-

strated for differential-mode excitation. For the dual polarized

CRLH LW-TL it is shown that the structure has a CRLH nature

under both common-mode and differential-mode of excitations.

This is achieved by modifying the via-free CRLH unit-cell by

inserting ground via at the center of the stub inductor along the

symmetry plane. It is also revealed that this structure exhibits

dual polarized nature, as the dominant current distribution in

the case of common-mode excitation is orthogonal to that of the

differential-mode. Current distribution and radiation patterns

are used to show the dual polarization nature of the structure atthree chosen frequencies.

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Mohammed Reza M. Hashemi(M07) received theB.S. degree in electrical engineering with minors inmathematics from the University of Nevada, Reno,in 2004 and the M.S. degree from The PennsylvaniaState University, University Park, in 2006. He is cur-rently a Ph.D. candidate at the University of Cali-fornia, Los Angeles (UCLA) and a member of theMicrowave Electronic Laboratory.

His research interests include microwave andmillimeter-wave devices, metamaterial and CRLHstructures and their applications, leaky-wave an-

tennas, and computation electromagnetics.Mr. Hashemi was the recipient of numerous fellowships and scholarships in-

cluding the Melvin P. Bloom Memorial Graduate Fellowship.

Tatsuo Itoh (S69M69SM74F82LF06)received the Ph.D. degree in electrical engineeringfrom the University of Illinois, Urbana, in 1969.

After working for the University of Illinois, SRI,and University of Kentucky, he joined the facultyat The University of Texas at Austin in 1978, wherehe became a Professor of Electrical Engineeringin 1981. In September 1983, he was selected tohold the Hayden Head Centennial Professorship ofEngineering at The University of Texas. In January1991, he joined the University of California, Los An-

geles as Professor of Electrical Engineering and holder of the TRW EndowedChair in Microwave and Millimeter Wave Electronics (currently NorthropGrumman Endowed Chair). He has 375 journal publications, 775 refereedconference presentations, and has written 43 books/book chapters in the areaof microwaves, millimeter-waves, antennas, and numerical electromagnetics.He generated 70 Ph.D. students.

Dr. Itoh received a number of awards, including IEEE Third MillenniumMedal in 2000, and IEEE MTT Distinguished Educator Award in 2000. He

was elected as a member of National Academy of Engineering in 2003. He is amember of the Institute of Electronics and Communication Engineers of Japan,and Commissions B and D of USNC/URSI. He served as the Editor of IEEETRANSACTIONS ONMICROWAVETHEORY ANDTECHNIQUESfor 19831985. Hewas President of the Microwave Theory and Techniques Society in 1990. Hewasthe Editor-in-Chiefof IEEE MICROWAVE AND GUIDED WAVE LETTERS from1991 through 1994. He was elected as an Honorary Life Member of the MTTSociety in 1994. He was the Chairman of Commission D of International URSIfor 19931996. He serves on advisory boards and committees of a number oforganizations. He served as Distinguished Microwave Lecturer on MicrowaveApplications of Metamaterial Structures of IEEE MTT-S for 20042006.

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