The aim of this paper is twofold. On the one hand, to provide a better understanding of a composite right/left-handed (CRLH) waveguide, going into those aspects of interest for an antenna designer. A longitudinal slot as a radiating element has been considered to be studied and compared with its classic counterpart. On the other hand, to present the new design approach that is needed when using the CRLH waveguide technology to built array antennas. To that end, a slot array antenna has been designed, built, and measured. The simulations and measurements are in excellent agreement, confirming not only the backward-to-forward beam steering and broadband far-field performance, but also the validity of the design procedure used.
 The relatively recent appearance of the metamaterial concepts has attracted the attention of the scientific community, mainly tempted by the promising applications in different fields such as microwaves [Smith et al., 2000; Lai et al., 2004; Caloz and Itoh, 2006; Pendry et al., 1996; Eleftheriades and Balmain, 2005; Engheta and Ziolkowski, 2006], optics, and acoustics. Specifically in microwaves, the application of these novel concepts has given birth to guided wave structures showing a composite right/left-handed (CRLH) behavior, i.e., supporting both forward and backward waves, together with a zero-phase-constant mode [Caloz and Itoh, 2006]. The use of these CRLH structures has in turn made an impact in the conception of radiated wave devices [Caloz and Itoh, 2003]. Broadly speaking, the antenna engineers are being witness of newly invented prototypes with functionalities not offered by the classic technology, namely, the capability of providing a full-space dynamic scanning of the beam from the backward to the forward quadrant, passing through broadside, as the frequency ranges from the left-handed (LH) through the right-handed (RH) passbands [Caloz and Itoh, 2006].
 Nevertheless, as it is typical of any immature technology, the new advances are being rapid and diverse. A clear evidence is the increasing number of papers published to date [see, for instance, Lai et al., 2004; Hrabar and Jankovic, 2006; Weitsch and Eibert, 2007; Iwasaki et al., 2008; Pan et al., 2008; Navarro-Tapia et al., 2009; and Abielmona et al., 2011], each one making use of a different technology (in both planar structures and waveguides) to implement novel antenna prototypes. As a rule, the vast majority of these works focuses on the experimental verification of these scanning capabilities, and little effort has been done to go beyond the mere proof of concept. However, this tendency has been recently broken by the latest contributions that address the challenging problem of designing the “new” antenna prototypes. Particularly in CRLH waveguide technology, there are some achievements worthy of mention. The first one addresses the design of a slot array antenna resorting to an optimization process [Liao et al., 2010]; the second one proposes some guidelines to adopt an engineering approach to successfully design an antenna of the kind [Navarro-Tapia et al., 2012a]. However, despite these pioneering contributions in the design of slot array antennas on CRLH waveguides, some concerns on the subject still remain somewhat obscure and overlooked.
 The aim of this paper is twofold. On the one hand, to provide a better understanding of the CRLH waveguide technology going into those aspects that are essential for a designer of a slot array antenna, such as the properties of the radiating element. On the other hand, to present a true engineering approach to the design of a beam-steerable antenna in CRLH waveguide technology. To cope with this double target, this paper deals with the design of a slot array antenna on a CRLH waveguide fulfilling demanding requirements that concern the input matching, the side-lobe level (SLL) and the gain. Theoretical and experimental results are provided and discussed.
 The paper is organized as follows. The CRLH waveguide technology is presented and described in section 2, which addresses not only the technological aspects but also the dispersive behavior of the waveguide, its fundamental-mode field distribution, and surface current distribution. Section 3 deals with the model of the longitudinal slot on a CRLH waveguide as a lumped shunt element. The conditions for shunt representation and the validity are therein given. A parametric characterization of the slot in terms of an equivalent shunt admittance is also made. Section 4 obtains useful normalized information that fully characterizes the slot, by means of universal admittance curves, i.e., the resonant conductance and the resonant length. Finally, in section 5, an engineering approach to the design of a beam-steerable antenna is detailed. The experimental performances of such a type of antenna are shown.
2 CRLH Waveguide Technology
2.1 Description of the Technology
 Metamaterials are artificially manufactured structures showing, at a macroscopic level, effective constitutive parameters not present in nature. It means that the average size of the cells composing the medium has to be much smaller than the guided wavelength λg [Caloz and Itoh, 2006]. These metamaterial concepts, applied to waveguide transmission systems, have given birth to a new family of rectangular waveguides that can show a CRLH behavior, i.e., can support both forward and backward waves (the latter with antiparallel phase and group velocities), together with a zero-phase-constant propagating mode. When it occurs, they are commonly referred to as CRLH waveguides.
 When building a CRLH waveguide, many implementations are possible. They differ in the nature of the unit cell that gives the waveguide the metamaterial-like properties. Among the different possibilities [Marqués et al., 2002; Esteban et al., 2005; Eshrah et al., 2005a; Iwasaki et al., 2008], the solution proposed by Eshrah et al. [2005a] has been considered. With this technology, the CRLH behavior is achieved by machining corrugations onto one of the broad walls and filling them with a high-permittivity dielectric. This way, the upper broad wall is left free, which is very appropriate for slotted antenna applications. Although an explanation of its geometry can be found in Navarro-Tapia et al. [2012a], it has been also included here (see Figure 1) for the sake of completeness. The waveguide (inner dimensions a×b and wall thickness t) is air-filled. The corrugations have width wc, depth hc, and period pc, and the filling dielectric has a permittivity ϵc. According to these parameters, a corrugated waveguide prototype with an overall length of 284 mm has been built in aluminum with the dimensions listed in Table 1.
Table 1. Geometry and Dielectric Constant of a Rectangular Waveguide With Dielectric-Filled Corrugations
ϵc=2.17(1−j0.0009)ϵ0 (CuClad 217)
2.2 Dispersion Diagram
 A CRLH waveguide prototype has been designed to be operated within the monomode region, where the fundamental Bloch mode propagates. Although the dispersion diagram of the prototype has already been shown and explained in Navarro-Tapia et al. [2012a], this content is also herein reproduced for the sake of completeness. The measurements of the propagation constant of the fundamental Bloch mode have been carried out by means of the method proposed by Bianco and Parodi , which has been statistically improved by considering a large number of measurements [Navarro-Tapia et al., 2012b]. The propagation constant measurements are collected in Figure 2, where a superposition with the results theoretically predicted by a mode-matching analysis is made. Only the monomode region is displayed, where two bands of propagation are clearly distinguished. There is a LH band, where backward propagation occurs (β<0) and a RH band where the mode shows a forward wave behavior (β>0). Except for some increase in the attenuation constant with respect to the predicted value, at both ends of the frequency range, an excellent agreement is found. Note that the waveguide has been designed as “balanced” in the sense given by Caloz and Itoh , i.e., so as to avoid the presence of a stopband. The presence of a small, residual stopband around the balance frequency, i.e., 9.0 GHz, can be noted in Figure 2.
2.3 Modal Field Distribution
 In order to establish a comparison with the modal field distribution of the TE10 mode in a conventional waveguide, some qualitative comments on the fundamental Bloch mode distribution within the hollow part of the waveguide are given. A similar study was originally published in Eshrah et al. [2005b], in which a detailed spectral analysis can be found. Notice that only the electromagnetic field components at those transverse planes just centered over the dielectric laminates are discussed.
 In the LH passband, the main difference observed (with regard to the classic TE10) is the existence of a longitudinal component Ez which peaks in the corrugation interface. Ez gradually disappears as long as the y-coordinate increases, completely vanishing in the vicinity of the upper broad wall. Apart from that, the transverse electric field distributions, Ex and Ey, behave as the TE10 does in a classic waveguide. About the magnetic fields, similar remarks can be made. In addition to the expected Hx and Hz components, there is a Hy field contribution in close proximity to the capacitive surface, which also dies out toward the upper broad wall. In the RH passband, however, the previous additional components Ez and Hy are found to be nearly one order of magnitude lower than the other EM components. This is because in that frequency range, the corrugations do not behave as a capacitive surface any more, but rather act as a short circuit, being the environment of a conventional waveguide again restored.
 To sum up, there is evidence that the modal field distribution in a CRLH waveguide with dielectric-filled corrugations is similar to the TE10 mode of a classic waveguide, except for those “nonusual” contributions found in the LH passband in the proximity of the corrugated interface.
2.4 Surface Current Distribution
 The phenomenon of radiation of a slot machined onto one of the waveguide walls is related to the interruption of the surface current lines associated to the mode settled in the waveguide; hence, the importance of knowing the surface currents associated to the fundamental mode. Although this issue has been widely studied for the first-order modes in classic technology (specially for the TE10 mode), it has not been addressed yet for the fundamental Bloch mode in a CRLH waveguide.
 In order to obtain the surface current density, the knowledge of the magnetic fields on the upper broad wall will suffice. An analytic solution for the -field supported in the air-filled part of the corrugated waveguide is given by equations (9) and (11) in Eshrah and Kishk , for each one of the three (x, y, and z) components:
where , , and H0 is a constant. A simple look at these expressions reveals that only Hz is proportional to β, meaning that Hz will be reversed in the LH region (β<0) with respect to the RH region (β>0). Therefore, the negative sign of β will be responsible for a magnetic field on the upper broad wall somewhat different to the classic TE10 distribution on the standard waveguide.
 In order to illustrate this unusual phenomenon, the -field distribution onto the upper broad wall of the CRLH waveguide has been obtained for the prototype built by means of an analysis carried out with HFSS [HFSS, 2010]. Figure 3 offers an instantaneous distribution of , for two different frequencies (8.5 and 10.0 GHz), each one belonging to a different right/left-handed propagation regime. As the analytical formulae given by Eshrah and Kishk  suggest, the -field distribution is different for β values of opposite sign. When β<0, it can be observed how the Hz component experiences a change of sign with respect to its counterpart when β>0. Since only Hz suffers from an alternation in sign, the magnetic flow lines are altered in the LH band in such a way that they are not closed in the xz-plane any more, i.e., they do not appear in the form of closed loops in the upper broad wall.
 Once is known, the surface current lines can be computed, yielding the distribution shown in Figure 4. Whereas the current lines when β>0 adopt the usual TE10 distribution, these lines are particularly different when β<0. This phenomenon could warn about a different mechanism of radiation for a hypothetical slot machined onto the upper broad wall of the waveguide. However, while carefully watching a single point along a complete period of time, the lines at this point take the same values for both the LH and the RH frequencies, although at different instants along the period. So, if we deal with frequencies that belong to different bands, a slot will intersect different current lines, but the period-averaged effect will still be the same. Consequently, the global effect that a slot may experience is independent of the sign of β. Therefore, it can be concluded that the same kind of slot used in the classic waveguides can also be used in a design involving a CRLH waveguide, no matter if it works in the LH region or in the RH one.
3 The Slot as a Lumped Shunt Element
 It was A. F.Stevenson  who first concluded that the equivalent network for a longitudinal slot “is not of the most general type,” but a rather simple shunt element. Since then, this equivalence has been widely accepted by the engineering community, and most of the design procedures involving longitudinal slots are constructed upon this assumption. Due to the importance of handling an accurate lumped-element equivalent circuit for the slot, this section is to verify the validity of such a model when the waveguide involved has a CRLH behavior.
3.1 Conditions on the Slot Voltage Distribution
 Consider a rectangular aperture machined onto the upper broad wall of a waveguide, as shown in Figure 5 viewed from the outside. The slot has a length 2l and a width w, and lies parallel to the longitudinal z-axis. The slot is assumed to be narrow, i.e., 2l≫w. There is a displacement x of the aperture from the longitudinal symmetry plane. This displacement, also referred to as offset, makes the slot to interrupt the distribution of the current lines established on the structure, providing power radiation to free space. A coordinate system local to the slot has also been adopted. The axes (ξ, η) are defined through the center of the slot, the ξ-axis being along the slot.
 Let Eη(ξ,η) be the transverse electric field distribution in the slot aperture. By means of HFSS, Eη(ξ,η) is extracted for ξ values ranging from −l to +l along the longitudinal direction and η going along a transverse lineal path from −w/2 to +w/2. With such field data, the slot voltage distribution V(ξ) taken across the slot is defined as
 The shunt admittance representation for the longitudinal slot relies on the assumption that the forward and backward scattering off the slot for the dominant mode are equal and in phase, which in turn requires symmetry in the slot voltage distribution V(ξ) [Silver, 1984; Elliott, 1981; Huxley, 1947; Stevenson, 1948]. Some studies [Elliott, 1983; Josefsson, 1987] have shown that, under certain circumstances, e.g., if 2l≈λ0/2, the dominant component of V(ξ) for a longitudinal slot is a symmetrical standing wave. This classic statement is to be verified for a slot on a CRLH waveguide.
 An isolated slot has been placed onto the upper face of the prototype built under the circumstances of matched load and matched generator. The slot has a width w=1.0 mm, and an offset x=1.5 mm. A resonant slot has been tested for the first resonance (2lr≈λ0/2) at the two different frequencies previously studied, namely 8.5 and 10.0 GHz (for which β takes negative and positive values, respectively). The integral (4) has been done for the resonant slot at the corresponding frequencies. Figure 6 compiles the results where the abscissa axis has been normalized to the slot length (ξ/l). As shown for the offset x=1.5 mm, V(ξ) has a fundamental symmetrical (even) component, as well as an asymmetrical (odd) component. The latter, though, is only slightly noticeable, i.e., V(ξ)≈V(−ξ), which in turn ensures a symmetrical scattering. It is worth noting the quasi-uniform phase, which confirms that the slot can be viewed as a lumped equivalent circuit.
3.2 Validity of the Lumped Shunt Model
 Different studies in the past [Elliott, 1981; Josefsson, 1987; Stern and Elliott, 1985] concluded that the shunt model representation of the slot is far less accurate when the offset of the slot becomes significant. This subsection is to prove this statement for a longitudinal slot in a CRLH waveguide.
 In order to establish a comparison with the previous results, some tests have been made for resonant slots (2lr=λ0/2) at the frequencies 8.5 and 11.5 GHz. They all now have an offset x=6 mm, which is in fact closer to the outer end than to the center line of the waveguide (a=16.00 mm). The slot voltage distributions V(ξ) for x=6 mm have been computed and are shown in Figure 6, which also compiles the result formerly obtained for a slot with a modest offset (x=1.5 mm). When the offset is small, some asymmetry in the magnitude of V(ξ) can be seen, but slight enough to justify the assumption of the shunt model equivalence. In addition, the phase distribution of V(ξ) is nearly constant along the slot. However, when the offset is large, some different effects take place. At 8.5 GHz, the presence of a remarkably asymmetric component in the magnitude |V(ξ)| can be appreciated. At 10.0 GHz, the most significant effect is not an asymmetric magnitude but a nonconstant phase distribution. These two results suggest that the lumped shunt model is only valid for small offsets. For this reason, when very stringent requirements are demanded in a design of a slot array antenna, it may be necessary to model the slot by means of a more complex network, e.g., a T- or Π-circuit, so as to take into account the asymmetric scattering.
 Notice that the periodicity pattern of the corrugations below the slot does not interfere with this classic result, since the CRLH behavior implies that, at a macroscopic level, the structure can be seen as homogeneous [Navarro-Tapia et al., 2009].
3.3 The Slot Self-Admittance
 The lumped shunt admittance of the slot needs to be characterized. The quality and accuracy of the slot characterization is of paramount importance to guarantee a successful design of a slot antenna array. It is therefore a common practice to develop some design curves relating both the admittance and the slot physical parameters. The slot self-admittance depends on the slot geometry, namely, its length 2l, width w, depth t, and offset x.
 The self-admittance of a longitudinal slot is obtained by means of HFSS. An isolated slot, placed on the upper broad wall of the CRLH waveguide, is fed by the fundamental Bloch wave of the structure under matched terminations. Notice that, by using HFSS, the waveguide wall thickness is taken into account. By considering the slot as a two-port network, obtaining the normalized self-admittance is straightforward:
where G0is the characteristic admittance of the equivalent transmission line for the corrugated waveguide fundamental Bloch wave. The scattering parameters are customarily obtained with the assistance of a commercial solver. However, when dealing with periodic structures like this CRLH waveguide, these solvers are unable to give the S parameters referenced to the fundamental Bloch mode. To overcome this handicap, a method has been devised for the purpose [Navarro-Tapia et al., 2012b].
 The simulations of an isolated slot (width 1 mm) on the CRLH waveguide have been carried out at f1=8.5 and f2=10.0 GHz, with the assistance of HFSS. Figure 7 collects the slot admittance versus the length and offset. These results state that the essential behavior of such a slot is similar to that of a slot on a smooth wall waveguide [Elliott, 1981; Navarro-Tapia, 2011].
4 Design Curves
 When designing an antenna, the slot admittance values should be available at the design frequency for any given pair (x, 2l). However, the set of curves in Figure 7 only provides information for a few of different offsets. In practice, the information contained in Figure 7 is used in a more standardized and compact way.
4.1 Universal Curves
 The slot self-admittance can also be recast in the standard Stegen's form [Elliott, 1981]. For the sake of illustration, let us consider the curves in Figure 7a, obtained at 8.5 GHz (β<0). If these curves are properly normalized as Stegen did, a unique pair of curves is obtained. The result is reproduced in Figure 8, where the independent variable is given by the ratio l/lr. This pair of curves contains information of the behavior of every longitudinal slot at the same frequency. At different frequencies, the pair of curves will be slightly dissimilar to Figure 8, but nearly the same nearby the resonant length.
 This universal admittance curve can be viewed as a complex sum denoted by h(y) [Elliott, 1981]:
where y=l/lr represents the abscissa scale, and both h1(y) and h2(y) are the normalized conductance G and susceptance B, respectively. The pair of curves embodied by h(y) defines the behavior of a family of slots. However, to interpret the specific admittance value due to an offset x and a length 2l, the designer needs to know both the resonant conductance Gr and the resonant length 2lr of the corresponding slot.
4.2 Resonant Conductance
 Consider that g(x) represents the resonant conductance as a function of the offset x. Thus, the admittance values for the family of slots can be easily obtained as follows:
 The function g(x) at 8.5 GHz can be built from those admittance results shown in Figure 7a. After having picked the resonant conductance values for each offset analyzed, they are interpolated with a polynomial, giving rise to the continuous black line shown in Figure 9a. As expected, since the resonant conductance is related to the power radiated by the slot, g(x) is proportional to the slot offset.
 Bearing in mind that the admittance values are actually frequency dependent, the same process can be done for a family of slots at any other frequency f. By doing so, a collection of curves g(x,f) can be obtained, as shown in Figure 9a. For a given offset x, there is a decrease of the slot conductance with increasing frequencies. However, this phenomenon is only locally observed at either the LH or the RH passband. The existence of a tiny stopband (see section 2.2) in the vicinity of the transition frequency might be the explanation for it. It can be explained by means of Figure 9b, which collects the resonant conductance values Gr/G0 versus frequency picked from Figure 9a for x=2 mm. A coarse interpolation between these points has been done, showing the former prediction occurring separately at each passband. This representation evidences the presence of a discontinuous behavior around 9.0 GHz, which may be attributed to the fact that the waveguide is not perfectly balanced. If it were not for the residual tiny stopband of the dispersion diagram, a global monotonically decreasing tendency would be obtained, as the blue trace included in Figure 9b suggests.
4.3 Resonant Length
 In order to interpret the variable y=l/lr, the resonant length as a function of the offset, i.e., the function 2lr(x), must be known. By examining the admittance curves at 8.5 GHz in Figure 7a, 2lr(x) is just made up of those slot lengths for which the conductance peaks at every offset. Of course, it will also be a function of frequency. Figure 10 collects the results for a range of frequencies. It can be noticed how the resonant length of a slot increases with the offset, as well as with decreasing frequencies.
5 Antenna Design
 The antenna will be a traveling wave type, and a matched load will be placed at the forward end of the waveguide. All the slots will be lying on the same side of the center line and uniformly spaced along the waveguide at a distance d. This parameter d, together with the couplets of offsets x and lengths 2l for each slot, will completely define the slot array antenna.
5.1 Design Procedure
 The usability of Elliott's design procedure [Elliott, 1981] when the waveguide involved has a CRLH behavior will depend on the conditions upon which the method is constructed. One of them is the assumption of the TE10 monomode operation of the waveguide. This requirement is easily met by the CRLH waveguide since it has been designed for a single-mode operation. In addition, the study carried out in section 2 highlights that the field distribution for the fundamental Bloch mode is similar to that of the TE10, at least out of the vicinity of the corrugations. The other assumption is related to the equivalent circuit of the longitudinal slot, which is supposed to be modeled by a shunt admittance. Therefore, there is every indication that both the Elliott's method and design equations can be naturally used to tackle the design of a slot array antenna on a CRLH waveguide.
 A Dolph-Chebyshev pattern with a SLL better than −26 dB has been specified. The design frequencies are those at which the slot characterization has been carried out, i.e., f1 (LH region) and f2 (RH region). After applying the Elliott's design method at both frequencies, the offsets and lengths obtained for each case are shown in Figure 11. Note that the slots are numbered starting from the closest one to the matched load. The 13 slots are uniformly spaced a distance d=18.5 mm in both cases.
 Although both designs remain well matched and efficient at its own design frequency (see Navarro-Tapia et al., 2012a; and Navarro-Tapia, 2011), these features are unavoidably deteriorated when moving away from the working frequency. An attempt to enlarge the frequency band of operation has been made. Since the differences between both designs are somewhat slight, one may think of an array antenna whose slot dimensions are the arithmetic mean of the geometry of the design at f1 and the design at f2, as detailed in Figure 11 as well. Although the arithmetic mean design cannot be optimum at any of these frequencies, the input match and gain are now steadier over a wider bandwidth ranging approximately from f1 to f2.
5.2 Prototype and Measurements
 An antenna prototype has been built using the CRLH waveguide described in section 2. The 13 slots have been milled onto the upper broad wall in accordance with the dimensions of the arithmetic mean design given in Figure 11. A photograph of the antenna is shown in Figure 12.
 The radiation properties of the antenna prototype have been analyzed by means of HFSS. Figure 13 shows the simulated and measured far-field patterns for the H-plane at the frequencies under study. As expected, the main beam is shifted at θ=∓20° at f1 and f2, respectively. An excellent agreement between measurements and simulations can be observed, and the specified requirement of a SLL better than −26 dB is reasonably met. The narrow beam width (9° at 3 dB) makes the array good at discriminating different space directions.
 The full-space beam steering capability is illustrated in Figure 14, which shows that the broadside radiation is also achieved. The SLL and beam width remain acceptable from −30° to +30°. It is worth saying that the measured gain stays above 11 dBi from approximately f1 to f2, except for a small range around the balance frequency [Navarro-Tapia, 2011].
 As regards the S parameters of the antenna viewed as a two-port network, it stays essentially matched (|S11|<−20 dB) throughout the whole frequency range, despite the arithmetic operation (except around 9.0 GHz) [Navarro-Tapia et al., 2012a]. Therefore, the antenna provides a backward-to-forward steerable pattern, with the advantage of a broadband performance in terms of the SLL requirements, input match, and antenna efficiency.
 The study of the longitudinal slot as a radiating element in a CRLH waveguide has been fully addressed. The global effect that a slot experiments along a period of time turns out to be independent of the sign of β, meaning that the same kind of slots used in classic waveguides can be used in CRLH waveguides. Once known that a longitudinal slot can be used as a radiator in a CRLH waveguide, no matter what the sign of the β, the lumped shunt equivalent circuit of the slot has been subsequently studied. Despite the periodic nature of the waveguide, its homogenization at a macroscopic level makes the circuit model of the slot not dependent on the periodic lattice below. The admittance data have been presented in the standard form to which every slot antenna designer is used, paving the way to successfully tackle an antenna design.
 An engineering approach to deal with the design of a slot array antenna on a CRLH waveguide fulfilling real specifications has been proposed. Following the design guidelines given, a 13 slot antenna prototype has been designed, built, and measured. Not only does the excellent agreement between simulations and measurements confirm the reliability and accuracy of the slot characterization done, but also it proves the usability of the Elliott's method even for frequencies in the LH passband. The measurement results also highlight the distinguishing feature offered by the CRLH waveguide technology: a backward-to-forward steerable pattern that preserves the SLL requirements, input match, and antenna efficiency within a wide frequency bandwidth.
 To sum up, this paper has provided a better understanding of the CRLH waveguide technology, so that it can be seen by the antenna designers as one possible technology to be naturally used from now onward. In addition, the study made has contributed to the knowledge of the main properties and behavior of a longitudinal slot on a CRLH waveguide, a subject which still remained not investigated.
 This work was supported by the Spanish Ministry of Education and Science and by the European Regional Development Funds under grant TEC2006-04771, by the Spanish Ministry of Science and Innovation (Programa CONSOLIDER-INGENIO 2010) under grant CSD2008-00066 (EMET), and by the Junta de Andalucía (Spain) under grant P10-TIC-6883.