Low-Dispersive Leaky-Wave Antennas for mmWave Point-to-Point High-Throughput Communications

In this article, we present two efficient leaky-wave antennas (LWAs) with stable radiation pattern, operating at 60 GHz. Both antennas exhibit attractive properties such as significantly reduced beam-squint, low loss, low sidelobes, high directivity, and simple manufacturing. The beam-squint of conventional LWAs is reduced by refracting the leaked waves in a dispersive lens and the low sidelobe levels are achieved by tapering the leakage rate along the aperture. Since the antennas are implemented in groove gap waveguide technology, the losses are low. The two antennas are different in terms of their asymmetric/symmetric leakage tapering with respect to the broadside direction. Both designs are optimized for low sidelobes, but since symmetry is enforced in one, the resulting performance in terms of sidelobes is suboptimal. However, in the symmetric design, multiple stable beams can be obtained, simultaneously or independently. Twenty percent bandwidth is obtained with less than ±0.5° beam-squint. In this frequency range, the gain is stable at 17 and 15 dBi for the asymmetric and symmetric designs, respectively. The designs are intended for point-to-point links in mmWave communication networks where low losses, directive beams, and low sidelobes are expected to be key features.

compared to conventional technologies. The high frequency translates into a need for fully metallic structures and small manufacturing details. Due to the intrinsic layered nature of gap waveguides, 2-D array solutions, in which multiple layers are used to construct the feeding network and radiating elements, were initially proposed as a means of achieving high gain [6], [7]. While resulting in relatively simple and reliable manufacturing, the complex and cumbersome design of the feeding network, which is obstructed by the space required for the electromagnetic band gap (EBG) structure at the lateral sides of the waveguides, results in large interelement distance in the array which produces high sidelobes.
Recently, gap waveguide leaky-wave antennas (LWAs) were proposed [8], [9]. The main benefit of LWAs, especially in high frequency applications, is their ability of producing directive radiation with a very simple feeding structure, contrary to the previously proposed 2-D arrays. Moreover, it has been shown that an increased control of the aperture fields can be exerted in this type of antennas [10]. This additional control can be used to produce desired far-field properties, such as low sidelobes or broad beamwidth. However, the inherent dispersion of the feeding waveguide causes the radiated beam to scan with frequency [11]. While sometimes desired (for instance, in radar and imaging applications), this beam scanning limits the applicability of LWAs in many scenarios, e.g., highfrequency point-to-point communications. Moreover, as directivity increases, the beamwidth decreases, and the scanning becomes more detrimental, which further limits the effective bandwidth of the antenna.
The beam scanning of LWAs is well known and several techniques to reduce or cancel it completely have been proposed [12]- [23]. The reported techniques can be divided into five categories. First, in [12], it is demonstrated that a reduced scanning in the radiation pattern can be obtained if the radiating aperture is divided into several subapertures, each responsible for the radiation in a narrow frequency range. However, since the aperture is divided, this results in reduced directivity. The same concept is used in [13] and [14], resulting in similar deterioration. Second, in [15], a technique for reduced beam-squint, which does not suffer from reduced directivity, is proposed. The authors demonstrated that a wideband squintfree radiation of energy can be obtained if a nondispersive guided wave is traveling at the interface between two medias. A "leaky-lens" can be designed by printing a slot on the back of a dielectric and the guided wave in the slot is leaked into the dielectric. However, since the leakage only occurs in the pres-This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/ ence of a dielectric, this technique is inherently lossy, especially at high frequencies. Third, in [16] and [17], the beamsquint is reduced by coupling the leaked energy through one or multiple cavities, placed in-front of the radiating aperture. While significantly reducing the beam-squint, the resulting radiation pattern is distorted and high sidelobes appear. Fourth, in [18], non-Foster circuits which can be used to eliminate the beam-squint in a finite frequency range are proposed. This method is quite general and can be applied to arrays as well as LWAs, but active components and biasing are required, resulting in decreased overall efficiency of the system. Finally, several attempts to reduce the beam scanning using metamaterials/metasurfaces have been reported. In [19], a 1-D nonreciprocal transmission line was proposed, in which the beam-squint reduction is achieved through the radiation of two waves traveling in opposite directions on the line, with different phase velocities (due to non-reciprocity). However, since nonreciprocal materials are required, the realization of such a system is difficult. Similarly, in [20], squint-free radiation is achieved by combining two leaky waves traveling in opposite directions along a 1-D transmission line. However, while the main beam is squint free, the radiation pattern changes over the operation bandwidth. Mehdipour et al. [21] proposed a method of reducing the dispersion of an LWA by refracting the radiated fields through a Huygens' metasurface. The dispersion of the metasurface must be such that waves of different frequencies, impinging from different directions, are refracted into one direction at the other side of the metasurface. Although it is theorized that a complete squint-free radiation is possible, the beam-squint is only reduced by a factor of 2 in [21]. In [22] and [23], a similar concept is applied, but instead of a Huygens metasurface, a dispersive lens is placed in front of the radiating aperture. The lenses are implemented using metasurfaces. Again, the dispersion of the lens must be such that the refracted fields in the lens are focused into one direction. In these works, an almost full cancellation of the beam squint is achieved.
In this article, we apply the same concept as in [22] and [23] in the design of two directive antennas at mmWave frequencies. Similar to [23], the antennas are implemented in groove gap waveguide technology, resulting in low losses. The novelty of this work is threefold. First, we demonstrate how reduced sidelobes can be obtained simultaneously to reduced beam-squint. Second, we demonstrate how the technique in [22] and [23] can be used to design directive multibeam antenna systems. Third, we have significantly increased the operational frequency, compared to [23], which implies technological and manufacturing challenges. The intended application for the proposed systems is point-topoint communications for future mobile communication networks (5G and beyond), where high directivity, low sidelobes, low losses, and multibeam capabilities are desired [24]. This article is outlined as follows: in Section II, the operational principle of the antenna is explained. In Section III, two design examples are detailed. In Section IV, the design examples are experimentally verified, and finally, in Section V, conclusions are drawn.

II. DESIGN PRINCIPLES OF LOW-DISPERSIVE LWAs WITH REDUCED SIDELOBE LEVELS
An illustration of the design used for both antennas is presented in Fig. 1, and it consists of two main components: the leaky waveguide (in yellow) and the dispersive prism (in blue). The design procedure is similar to the one in [22] and [23] but, for completeness, the important steps are repeated below. The additional techniques employed in order to improve the radiation performance are indicated in the following as well. First, the technique used for the reduction of sidelobes is discussed (Section II-A). Second, the reduction of the beamsquint is presented (Section II-B).

A. LWA With Reduced Sidelobe Levels
In point-to-point communications, a low sidelobe level (SLL) is desired in order to reduce interference. Such characteristics in the far-field pattern can be obtained by illuminating the aperture with a sinusoidal distribution [11]. The relationship between the magnitude of the complex aperture distribution, A(z), and the imaginary part (α) of the complex propagation constant in the leaky guiding structure (β − j α) is given by [25] |A(z)| = α(z)e − z 0 α(t )dt (1) where z is the position along the aperture. By solving (1) for α/k 0 (as is done in [26]) under the assumption that a sinusoidal aperture distribution (i.e |A(z)| = sin(πz/L A )) is desired, we obtain where L A is the length of the leaking aperture and k 0 is the free-space propagation constant. In order to efficiently radiate over some bandwidth, the radiation efficiency η is set to 90%-95%. Additionally, the real part of the propagation constant, β, must remain fixed throughout the aperture in order to radiate coherently from every section of the structure. The desired aperture distribution for reduced sidelobes and the corresponding α/k 0 (z)and β-profiles are illustrated in Fig. 2. The tapered leakage can be obtained by gradually changing the dimensions of the waveguiding structure along the aperture. Therefore, this leakage is structure independent and low-sidelobe LWAs can be implemented in different technologies, e.g., gap waveguide [10], substrate integrated waveguide (SIW) [27], and microstrip [28]. Far-fields with other properties, for instance, near-field focusing, control of the radiation nulls, and broad beamwidth, can be obtained if other leakage profiles are employed [25], [27].

B. LWA With Reduced Beam-Squint
In this article, the beam-squint of conventional LWAs is reduced by coupling the leaked energy through a dispersive prism-lens. A similar approach was followed in [22] and [23]. Prisms are structures that, for impinging waves of different wavelengths, refract the light in different directions. This spatial division of the spectral components of the impinging light occurs due to the frequency-dependent refractive index in the prism. Prisms can operate in one of two modes. In the first operational mode, prisms split the spectral components of white light (i.e., light with a wide range of wavelengths) incident from a single direction into several directions depending on frequency. In the second operational mode, prisms gather a colored light (i.e., light concentrated in a narrow range of wavelengths) impinging from different directions into white light traveling in one direction. In this article, the employed prism is operated in the second mode. Although prisms exist in a variety of shapes, we will focus our analysis to triangular prisms. The operating principle of the antenna is illustrated in Fig. 3.
In conventional LWAs, the beam-squint arises from the dispersive nature of the waveguide mode. The direction of maximum radiation is given by where β l and k 0 are the propagation constants in the leaky waveguide and free-space, respectively. The scanning of the leaky-wave radiation is illustrated in Fig. 3 (left). There, the radiation from the leaky structure is spatially divided into its spectral components, and in conventional LWAs, the direction of maximum radiation scans from broadside to endfire Fig. 3. Illustration of working principle for reduced beam-squint. For a range of frequencies, the dispersive radiation from the leaky waveguide is refracted into a single direction with a dispersive prism. The prism inclination, δ p , is chosen so there is no refraction at the edge of the prism and hence, when the frequency increases. By placing a prism in front of the leaky aperture, this scanning can be canceled. The required characteristics of the prism can be found through the Snell's law, which describes the refraction through an interface where n 1 and n 2 are the refractive indices on each side of the interface and θ i and θ t are the impinging and refracted angles, respectively. n 1 and/or n 2 may be, in general, frequency dependent. For this analysis, the first medium is assumed to be air (n 1 = n 0 = 1). The second medium corresponds to the prism, which we will assume is frequency dependent (n 2 = n p ( f )). The impinging angle is given by the direction of maximum radiation of the leaky waveguide, i.e. θ i = θ l ( f ). By substituting these assumptions in (4), we obtain It is clear that, since the impinging angle varies with frequency, the light of different wavelengths is refracted into one single direction, given that the refractive index in the prism neutralizes this variation. For conventional LWAs, sin[θ l ( f )] increases with frequency, and hence, in order to reduce the beam-squint, the refractive index of the prism must also increase with frequency. Furthermore, in order to avoid to again spatially divide the spectral components of the light at the second interface of the prism, the prism inclination, δ p , is chosen so that θ t (i.e., the refracted angle) is normal to the second interface. In conclusion, if a prism can be devised with the correct frequency behavior of the refractive index n p ( f ), a non-squinting LWA can be realized. Noteworthy is that, throughout this analysis, no assumption on the type of guiding structure has been made, and thus, this technique is structure independent, contrary to, for instance, the technique used in [15]. In fact, it has been used successfully for both SIW LWAs [22] and groove-type gap waveguide LWAs in the X-band [23].

III. DESIGN EXAMPLES
Two LWAs are designed using the procedures outlined in Section II. In this article, denoted as asymmetric and symmetric. The two designs differ in the implemented leakage profile. The asymmetric LWA is designed to have the lowest possible sidelobes with a single fixed beam. The symmetric LWA, on the other hand, is designed to have low sidelobes with a symmetric leakage tapering with respect to the broadside direction. Thus, the symmetric design enables beam-switching by feeding from either end of the leaky waveguide (P 1 and P 2 in Fig. 1). Both antennas have a center frequency of 60 GHz. The realized prototypes are shown in Figs. 4 and 5 for the asymmetric and symmetric designs, respectively.

A. Leaky Groove Gap Waveguide
Since the target is mmWave communications, the antennas are implemented in groove gap waveguide technology [1], [2], [29]- [31]. Due to the high operating frequency, the EBGstructure in the groove gap waveguide, opposite to the prisms as showed in Fig. 1, consists of a 2-D periodic repetition of glide-symmetric holes [32], [33]. A glide-symmetric structure is, contrary to purely periodic structures, composed of two subunit cells. The geometrical operation, applied to the subunit cells in a glide-symmetric structure, consists of a translation of p/2, where p is the translational period of the full unit cell, and a mirroring [34]. In the case of Cartesian glide symmetry, which is the symmetry employed here, the mirroring is done with respect to a plane. Glide-symmetric metasurfaces have shown attractive properties such as very low-frequency dispersion [35], [36], increased equivalent refractive index [37], [38] (extremely large indices reported [39]), and huge stop bands at selected frequencies [32], [33]. Moreover, glide-symmetric holey EBG structures have larger unit cells, are less expensive to manufacture, and are more robust, compared to a bed-ofnails structure [5], [32], [33]. These interesting properties of glide symmetry have been extensively studied over the last few years and several numerical methods have been reported which give valuable physical insight on this technology [40]- [43].
Due to their larger physical dimensions, glide-symmetric EBG structures are especially attractive at high frequencies (submillimeter wavelength). As a matter of fact, gap waveguides employing a glide-symmetric holey EBG structure operating up to 170 GHz have been presented [44]. Additionally, by decreasing the undesired gap between the two parallel plates, the width of the stopband increases while remaining centered at the same frequency, which further simplifies manufacturing and assembly [32], [45]. In [33], it was shown that a single row of a glide-symmetric holey EBG is enough to suppress the leakage in a straight waveguide. The unit cell of the EBG-structure used in the gap waveguide is shown in Fig. 6(a) (red), together with the dispersion diagram (red curve). The dimensions used for the simulation are r h = 1.3 mm, d h = 1.1 mm, g = 0.05 mm, and p EBG = 3.2 mm. A full stopband is obtained, ranging from 45 to 80 GHz. In Fig. 6(a), only the first part of the Brillouin diagram is presented. However, the full stopband (i.e., for the full irreducible Brillouin diagram) is marked by the red area.
In [9], it was shown that a groove-type gap waveguide can be transformed into a leaky-wave antenna by removing the EBG-structure on one of the sides of the groove. Furthermore, if the removed EBG-structure is instead replaced with a longitudinal structure (with respect to the waveguiding direction), the leakage can be controlled along the aperture, and the profile necessary for reduced sidelobes can be obtained. In this work, similar to the designs presented in [9], [10], and [23], periodically repeated square pins, placed along the groove, are employed to control the leakage (in order to reduce the sidelobes). These pins are here denoted leaky pins and are marked with green in Figs. 1 and 6(a). The leakage rate is mainly determined by the height, ph l , and periodicity, p l , of the leaky pins. The control of propagation constant of the waveguide mode, β l , is mainly exerted through the width of the leaky waveguide, w wg . Since the geometry of the waveguide is varied, the dispersion diagram changes along the structure, but for reference, the dispersion diagram for one sample of the leaky mode, β l , is presented in Fig. 6(a) (yellow curve). For this sample, the dimensions are h wg = 2.39 mm, pw l = 0.7 mm, p l = 1.5 mm, ph l = 1.5 mm, and w wg = 4.8 mm.
The dependencies of α/k 0 and β l on these parameters are obtained through curve-fitting of simulation data. More specifically, in this analysis, the parameters are assumed to be independent. This allows us to write α/k 0 and β l as a sum of four terms where κ(·), ν(·), τ (·), γ (·), χ(·), and ψ(·) are curve-fit with a suitable function and c 1 − c 8 are obtained through multivariate linear regression. More details can be found in [46]. The correct aperture illumination is obtained by mapping the desired α/k 0 -and β-profiles to the corresponding waveguide

B. Metasurface Prism
In Section II-B, the requirements on the refractive index inside the prism were outlined. Ideally, it should follow that of the effective refractive index of the leaky mode, which is rapidly increasing close to the cutoff of the guiding structure and then converges to 1 at high frequencies. However, such prisms are difficult to conceive in reality and we will therefore, in this article, limit the targeted bandwidth in which a reduced beam-squint is obtained. Moreover, we will allow for a small variation of the direction of maximum radiation (±0.5 • ) after the waves are coupled through the prism. Taking these last two considerations into account, the constraints on the prism's refractive index are alleviated since the only requirement is to have a proper derivative of the refractive index with respect to frequency, in some frequency range.
An index-profile consistent with the above requirements is readily achieved using a metasurface. Moreover, since metasurfaces can be made fully metallic, they are attractive for high-frequency applications such as the one considered. In this article, the metasurface is implemented in a parallel plate bedof-nails structure. Again, a holey metasurface could be used for increased robustness and decreased cost. However, due to the small air gap needed in the holey structure, which both requires accurate manufacturing and sophisticated impedance matching (to match to free-space), the bed-of-nails structure is preferred here.
The unit cell of the prism is depicted in Fig. 6(a) (in blue), together with the dispersion diagram (blue curve). The dimensions for the simulation are: h wg = 2.39 mm, ph p = 0.7 mm, pw p = 0.7 mm, and p p = 1.3 mm. From the dispersion curve, the effective refractive index of the prism is calculated as n eff,prism = β p /k 0 , where β p and k 0 are the propagation constants in the prism and in free-space, respectively. The effective refractive index of the leaky waveguide (for one sample along the waveguide) and the prism is presented in Fig. 6(b). For a range of frequencies (indicated with green in the figure), the ratio between the two indices remains approximately constant. Using (5), the final direction of maximum radiation (calculated based on infinite structures) is found, as illustrated in Fig. 6(c). A stable radiation, allowing ±0.5 • squinting, is obtained in the range 54-64 GHz and hence, roughly 20% bandwidth is achieved.

IV. ANTENNA PERFORMANCE
The two designs are simulated in a full-wave solver. The asymmetric structure is only excited from one end of the leaky waveguide, while the symmetric structure is excited from both ends, sequentially (although simultaneous excitation is possible for a dual-beam radiation pattern). The waves travel along the leaky waveguide, slowly leaking their energy into the  prism. The remaining energy at the far side of the waveguiding structure (P diss = P in |S 21 | 2 ) is dissipated in a matched load. The length of the leaky waveguides is L A = 100 mm (= 20λ) and the prism inclination is, in both designs, δ p = 45 • . The remaining dimensions are as defined in the unit cell simulations and are given in Figs. 6-8.
The S-parameters are presented in Fig. 9(a) and (b) for the asymmetric and symmetric structures. For clarity, only the response from one port is shown in the symmetric design. The other port behaves the same due to the symmetry. A good matching is obtained throughout the band, with an |S 11 | below −15 dB in both designs. The periodic ripples in the |S 11 | are attributed to the presence of internal reflections in the antennas. The periodicity of the ripples, p ripple , gives the distance from the excitation to the location at which the reflection occurs where c is the speed of light. In our case, d refl corresponds to the interface between the prism and free-space. The power transfer between the two ends of the waveguide, i.e., |S 21 |, is below −15 dB (≈3% power dissipated in the second port) throughout the band in both designs. Such a low value is usually not desired in LWAs since it might result in inefficiently used aperture (i.e., too fast leakage). However, since a leakage tapering is performed, the aperture is well illuminated in both designs, as illustrated with the x-component of the electric field in Figs. 10 and 11. Additionally, a low |S 21 | results   in higher radiation efficiency, as the power is not dissipated in the load at the second port. In the measurements of the S-parameters, the effect of the transitions from waveguide to coaxial cable has been calibrated away since they introduced significant reflections in the upper part of the frequency band. The discrepancies between measurements and simulations in the |S 21 | are attributed to increased metallic losses due to the surface roughness (not included in simulations).
The normalized H-plane far-fields are presented in Figs. 12 and 13 for the asymmetric and symmetric designs, respectively. By comparing the results in Fig. 12(a) with  Fig. 13(c), which corresponds to the simulated cases of a leaky waveguide with and without prism, for the asymmetric and symmetric designs, respectively, it is clear that the beam-squint is significantly reduced by coupling the radiation through a prism. The measurements of the far-field, presented in Figs. 12(b) and 13(b) for the two designs, corroborates the simulations. The radiation pattern at a specific direction, normalized to the peak value, is presented in Figs. 14 and 15, for the two designs, together with the realized gain and sidelobe level. Again, it is clear that by coupling the radiation through a prism, decreased beam-squint is obtained. At 45 • , a maximum of 0.5 and 1 dB scan-loss is obtained in the asymmetric and symmetric designs, respectively. Moreover, the realized gain is stable at roughly 17 and 15 dBi for the two designs throughout the band. The observed ripples in the S-parameters are small and they have no noticeable effect on the gain. Sidelobes below −20 and −17 dB are obtained in the asymmetric and symmetric designs, respectively. In the asymmetric design, the measured sidelobes are higher than the simulated in the upper part of the operating band. A similar increase in the sidelobes is observed in simulations for higher frequencies (66-70 GHz). Due to the high reflections from the transitions at the higher frequencies, the gain is not measured at frequencies above 62 GHz. A small drop in the measured gain is observed at 58 GHz. Other than that, the measurements agree well with simulations in all the far-field characteristics. The obtained total efficiency for the two antennas.   Table I. Almost 90% efficiency is achieved throughout the band.

V. CONCLUSION
In this article, two novel nondispersive LWAs are presented, operating at 60 GHz. The antennas utilize a dispersive lens to cancel the dispersion of the feeding leaky waveguide, thus, obtaining a nonsquinting radiation pattern with respect to frequency. Unlike previous works, a leakage tapering is performed along the aperture which results in reduced sidelobe levels. One asymmetrically and one symmetrically tapered antenna is designed and manufactured. The asymmetric antenna is optimized for the lowest possible sidelobes with a single-beam operation and the symmetric antenna is optimized for the lowest possible sidelobes, under the constraint of symmetric tapering with respect to broadside. The symmetry in the latter design results in slightly increased sidelobes, compared to the asymmetric design, but enables two beams that can be obtained either independently or jointly. To the best of our knowledge, this is the first multibeam low-dispersive LWA reported in the literature. High efficiency and low losses are achieved at 60 GHz by implementing the antennas in groove gap waveguide technology. Both antennas achieve a beam squint smaller than 1 • over a 20% bandwidth and the total efficiency is almost 90% throughout the band in both designs. A stable gain of 17 and 15 dBi is achieved in the asymmetric and symmetric designs, respectively. The antennas are manufactured and measurements corroborate simulations. No LWA with similar or better performance in terms of radiation pattern stability, SLL, bandwidth, and efficiency (90%) has been reported in the literature, especially considering the high operating frequency. The antennas are intended for mmWave point-to-point links in future communication systems (5G and beyond). In 2019, he joined the Department of Electromagnetic Engineering, KTH Royal Institute of Technology. He has authored and coauthored over several journal and conference articles. His current research interests include transformation optics, lens antennas, metamaterials possessing higher symmetries, and leaky-wave antennas.
Mr. Zetterstrom has been awarded the first price in the Student Design Competition at APS/URSI 2016 in Puerto Rico and the IEEE Eugene F. Knott Research Grant for his works.