Realization of Deep Tilt Angle, High Aperture Efficiency, and Low Sidelobe Using a Single Metaplate and a Patch Antenna

A beam-forming system for a patch antenna is proposed to realize a deeply tilted beam with high-gain, high aperture efficiency, and low sidelobe level. The proposed system uses only one novel metaplate, where the total system height is less than one wavelength. Firstly, a T-shaped metatwin is created as an element for the metaplate. It is revealed that the metatwin can provide a phase shift of more than 450° with change in the metatwin arm length. Based on this, secondly, a simulation is performed where a normally incident plane wave is refracted at a deep angle of 65° using a single metaplate. Thirdly, the incident plane wave is changed to a quasi-spherical wave using a small patch antenna. It is found that a 65° tilted beam is formed by virtue of a newly designed single metaplate. It is also found that a gain of 18.1 dBi is realized with an aperture efficiency of 49% and a maximum side lobe level of −14.6 dB. Fourthly, all simulated results, including the frequency response of the gain and S11, are validated using measured results.


I. INTRODUCTION
The radiation beams from patch antennas [1]- [3], loop antennas [4]- [6], and spiral antennas [7]- [10] are usually set to have their maximum intensities in the direction normal to the antenna plane (broadside direction), as shown in Fig. 1(a). For more effective communications, the antenna is often tilted, thereby directing the radiation beam toward a target, as shown in Fig. 1(b). Mounting such an antenna on, for example, a wall or a roof, causes the antenna to protrude into the air, resulting in a bulky, space-consuming arrangement.
However, the research in [11]- [17] has provided a solution for this antenna tilting issue, where a feed antenna is with N metaplate dielectric plates on which parasitic elements are printed. Such a dielectric plate is called a metaplate or metasurface. It has been found that a broadside radiation beam generated by the feed antenna is changed into a new beam whose maximum intensity is in the direction of the target specified by depression angle θ = θ 2 (the elevation angle is 90 • − θ 2 ) by virtue of the metaplates, as shown in Fig. 1(c): up to θ 2 ≈ 50 • for N metaplate = 2 [15] and up to θ 2 ≈ 60 • The associate editor coordinating the review of this manuscript and approving it for publication was Tutku Karacolak .
for N metaplate = 3 [16]. Thus, if multiple metaplates are used, there is no need to tilt the antenna. It is inevitable that, as N metaplate is increased, the flatness of the beam-forming system is deteriorated. This causes a system height issue.
In addition to realizing system flatness, evaluation of aperture efficiency η aperture is also important for, in particular, a system using flat plates (such as metaplates). Generally, as tilt angle θ 2 becomes deeper, the gain is decreased with increase in the side lobe level, resulting in the reduction of η aperture . In fact, η aperture = 40% in [14], 9.8% in [15], and 9% in [16]. In such a case, a physical antenna size must be larger to hold the required gain. This needs a larger space and raises an installation issue.
Then, questions arise as to whether a single metaplate (N metaplate = 1) can realize a tilted beam whose direction is close to or greater than the current deep value of θ 2 = 60 • [16], [19], [21] with low sidelobe level; and at the same time, whether this beam-forming system can exceed a current aperture efficiency of η aperture = 40%. If these questions are resolved with constructive results, the cost of design and fabrication will be drastically reduced, and the potential for application to modern communication systems is increased.  [14], 2 [15], and 3 [16].
Based on the abovementioned background, this paper presents a solution to the questions by proposing a novel beam-forming system. The system is composed of a single novel metaplate (N metaplate = 1) and a feed patch antenna to achieve challenging items; deep tilt angle (θ 2 > 60 • ) and high aperture efficiency (η aperture > 40%). In addition, the proposed system is designed to meet all the following requirements: gain ≈ 18 dBi, maximum sidelobe level (MSL) < −10 dB, and total system height H total < one wavelength (1λ DSN ).
This paper consists of five sections. Section II presents the proposed metaplate composed of T-shaped metatwins. The fundamental characteristics, S11 and S21, are investigated. Variation of the phase of S21 with change in the arm length of the T-shaped metatwin is discussed.
Section III is devoted to beam formation. Firstly, a case where a normally incident plane wave is refracted at a deep angle by a metaplate is considered. The design of the metatwins for this case is based on an equation that describes the phase required for each metatwin. Secondly, a case is considered where a small patch antenna illuminates the designed metaplate. An extension of the equation for the phase of the metatwins is derived by regarding the small patch antenna as a point source and using optical ray tracing between the source point and each metatwin. A beam with a tilt angle of 65 • is obtained by simulation.
To confirm the validity of the simulation results, a lowprofile patch-metaplate beam-forming system is fabricated and measured. The measured results for the radiation beam, S11, and gain of the beam-forming system are discussed in Section IV. Section V presents the conclusions, indicating that the antenna system meets all design requirements for N metaplate , θ 2 , η aperture , gain, MSL, and H total .
Note that, in Table 3 of the Appendix, the proposed beamforming system is compared with previous work [14]- [21] to reveal its novelty and usefulness. The previous systems are not found to meet all the challenging requirements specified in this paper. In [14], [17], [18], θ 2 > 60 • is not met, although N metaplate = 1 is met. In [15], [16] and [19]- [21], the number of metaplates is N metaplate ≥ 2, which is against the main requirement of N metaplate = 1, and the aperture efficiency is low, i.e., it does not reach η aperture > 40%, despite of N metaplate ≥ 2.
Also, note that the simulations throughout this paper are performed using an electromagnetic wave analysis solver based on a finite integration technique [22].

A. METASURFACE BEHAVIOR
To meet the required specification regarding the number of metaplates (N metaplate = 1), a single dielectric substrate of relative permittivity ε r and thickness B is used, where multiple pairs of T-shaped elements are printed on its top and bottom surfaces, as shown in Fig. 2: 2M + 1 pairs in the x-direction and 2N +1 pairs in the y-direction, with neighboring distance p (periodicity). The single pair of T-shaped elements on the top and bottom surfaces, which occupies a square area of side length 2L and a thickness/depth of B, is designated as the metatwin; it is specified by a central arm of length L c , an x-directed side arm of length L x , and a y-directed arm of length L y , where the width of all the arms is w.
First, we investigate whether the metatwin has a transmission coefficient whose amplitude is unity, and a reflection coefficient that is extremely small. For this, we reveal the frequency response of the metatwin when a plane wave of an x-polarized electric field (parallel to the center arm of length L c ) impinges on it. Fig. 3(a) shows the calculated results regarding the normalized values of Z 0 Y es and Z ms /Z 0 [23], where Z 0 is the intrinsic impedance in free space; Y es and Z ms are the electric sheet admittance and magnetic sheet impedance of the metatwin, respectively; and T and R are the transmission and reflection coefficients (both complex), respectively. Arm lengths (L x , L y ) = (1.8 mm, 3.8 mm), VOLUME 10, 2022 together with the parameters summarized in Table 1, are used to evaluate Eqs. (1) and (2).  According to Eqs. (1) and (2), a Huygens surface [23]- [26] appears at a frequency where Y es Z 0 and Z ms /Z 0 are equal and purely imaginary. Such a case is observed at two frequencies, f 1 and f 2 , where the real parts are regarded as zero and the imaginary parts are nearly equal: (Y es Z 0 , Z ms /Z 0 ) = (0.04 − j1.897, 0.016 − j1.886) at f 1 = 11.43 GHz and (Y es Z 0 , Z ms /Z 0 ) = (0.005 − j1.827, 0.017 − j1.838) at f 2 = 20.03 GHz. Fig. 3(b) shows the simulated scattering parameters, |S21| and |S11|, for the metatwin. The results show that, at f 1 ' and f 2 ', the absolute value of the transmission coefficient is 0 dB (unity), with an extremely small reflection coefficient of less than −30 dB. Note that f 1 ' and f 2 ' are the same as the abovementioned equation-based frequencies f 1 and f 2 : It is also found that the metatwin has a wideband transmission characteristic across a frequency range from f 1 = 11.43 GHz to f 2 = 20.03 GHz (54.7%). Fig. 4 shows the simulated current distribution along the T-shaped metatwin over one time period, T , where the working frequency is f 1 = 11.43 GHz. The x-directed current on the top T-shaped element, DoC top , changes with a time step of T /4: +x, +x, −x, and −x directions; meanwhile, the x-directed current on the bottom T-shaped element, DoC bottom , changes as follows: +x, −x, −x, and +x directions. In other words, (DoC top , DoC bottom ) = (+, +) at t = 0, (+, −) at t = T /4, (−, −) at t = T /2, and (−, +) at t = 3T /4. Note that a fictitious small magnetic current in the y-direction is generated at T /4 and 3T /4 by the two electric currents along an overlapping section of the top and bottom center arms. Also note that the y-directed currents on the top T-shaped element (red arrows) flow in the direction opposite to each other, and hence the y-directed electric fields (cross polarized fields) are canceled; the same happens for the y-directed fields generated by the currents on the bottom T-shaped element (blue arrows).

B. EFFECTS OF METATWIN ARM LENGTH
We further investigate the transmission coefficient S21 of the metatwin when the arm length is changed. Fig. 5(a) shows the simulated amplitude |S21| when the arm length L L is increased from L L = L c through L L = L c +L to L L = L c +3L within a square loop area of side length 2L = 7.6 mm. Note that the length L L is illustrated in the inset of this figure. It is found that a good transmission characteristic is obtained from 10.8 GHz to 12.5 GHz for a criterion of |S21| > −3 dB. It is also found that phase S21 at 11.5 GHz shifts up to approximately 450 • with change in length L L , as shown in Fig. 5(b). It follows that the metatwin has a phase shift of more than the 360 • that is needed for beam formation.

III. BEAM FORMATION A. REFRACTION OF A PLANE WAVE
For preparation of the design goal, a fundamental situation is considered here, where a plane wave (TE mode to the yz plane) impinges a metaplate from θ 1 = 0 • and is refracted in a direction of θ 2 , as shown in Fig. 6 [23]- [25].
For the refraction at θ 2 , phase φ mn is defined for the center point of metatwin mn as follows: where k DSN is the wave number: k DSN = 2π/λ DSN with λ DSN being the free-space wavelength at design frequency f DSN (≡ 11.5 GHz). Eq. (3) means that neighboring metatwins have a phase relationship of φ (m+1)n − φ mn = −pk DSN sinθ 2 in the x-direction and φ m(n+1) − φ mn = 0 in the y-direction. Note that the required φ mn can be realized by selecting the appropriate L-shape length L L from Fig. 5(b).
We evaluate Eq.    As shown in Fig. 9, the patch antenna used here is square with a small side length of S p = 7.0 mm = 0.268 wavelength at design frequency f DSN (= 11.5 GHz). The dielectric substrate (of relative permittivity ε r−p and thickness B p ) and ground plane supporting the patch are also square with side lengths S sub and S GP , respectively. The small patch is fed by a 50-ohm coaxial line, where the feed point is shifted away from the center point by d FD for impedance matching. The parameters are summarized in Table 2. Fig. 10 shows the radiation pattern of the patch antenna at design frequency f DSN : the half-power beamwidth is HPBW/xz ∼ = 99 • in the xz-plane and HPBW/yz ∼ = 67 • in the yz-plane, and the gain is approximately 7.2 dBi in the z-direction. Note that E θ and E φ denote the θand φ-directed electric radiation field components, respectively.
We start with forming a broadside beam (θ 2 = 0 • ) at f DSN . L-shape length L L is selected to obtain phase φ mn in Eq. (4), where 13 × 13 metatwins are used (M = N = 6).      11 shows the simulation results for the radiation pattern in the xz-plane, where the distance between the patch and metaplate, h, is chosen to have small values near 3λ DSN /4: 1λ DSN /2, 3λ DSN /4, and 5λ DSN /4. It is found that, as distance h is increased, the wave front of radiation from the patch antenna becomes quasi-spherical. This means that the patch antenna radiation characteristic increasingly resembles that of a point source. It is also found that a broadside beam is formed by the metaplate, as designed. In the following discussion, we use a distance of h = 0.75λ DSN , leading to a total system height of H total = B p + h + B sub = 23.57 mm = 0.90λ DSN , so that it meets the required total system height specification (H total < 1λ DSN ) described in the Introduction.
Next, we design a beam with a deep tilt of θ 2 = 65 • in the xz-plane to meet the required specification of θ 2 > 60 • . Simulation is performed on the basis of Eq. (4) using Fig. 5 for L-shape length L L . Such a deep tilt beam is formed based on near-field phase correction [27]- [33] for the metaplate. As shown in Fig. 5, the proposed metatwin realizes large transmission amplitude (|S21| > −3 dB) with an arbitrary transmission phase S21. This contributes to a high-gain beam when S21 for metatwin mn is adjusted such that it generates in-phase radiation in a θ 2 = 65 • direction. In other words, the radiation field is confined around the θ 2 = 65 • direction. For better understanding of the high-gain, first, Fig. 12(a) shows S21 for metatwin mn to form a 65 • -tilted beam, when a plane wave impinges on the metaplate. Second, Fig. 12(b) shows S21 given by Eq. (4), which takes into account the phase delay from a point source to metatwin mn. Fig. 13(a) illustrates the wave propagation behavior. The arrow shows a wave front direction of θ 2 = 65 • . Fig. 13(b) shows the simulated 2D and 3D radiation patterns, which confirm that a tilted beam is formed as designed. The gain in the θ 2 = 65 • direction is 18.1 dBi, resulting in an aperture efficiency of η aperture = 49.0%. The maximum side lobe is found to be MSL = −14.6 dB. Note that these simulation results meet the required specification values.

IV. FABRICATION AND MEASUREMENT
The beam-forming system composed of the patch antenna and the metaplate in Section III is fabricated, as shown in Fig. 14, to confirm the deep beam tilt of θ 2 = 65 • . Fig. 15 shows the measurement setting in an anechoic chamber. The radiation pattern is measured by rotating the antenna system on the turntable, while a transmitting pyramidal horn antenna is fixed. The radiation pattern for the system, shown in Fig. 13(b), is measured at frequency f DSN = 11.5 GHz and illustrated by dots in the 2D pattern. For additional information, the measured radiation pattern for the isolated small patch antenna (i.e., the patch antenna without the metaplate) is added in Fig. 10. It is found that the measured and simulated results are in good agreement. Fig. 16 shows the frequency response of the input characteristic in terms of S11. Note that S11 for the isolated small patch antenna is also presented for comparison. It is revealed that S11 with the metaplate and S11 without the metaplate have no remarkable difference. S11 of the patch together with the metaplate has a simulated bandwidth of 4.0% for     a criterion of S11 = −10 dB (VSWR ≈ 2) and 6.2% for a criterion of S11 = −6 dB (VSWR = 3). These bandwidths are acceptable for practical application.
The deviation of the tilted beam from θ 2 = 65 • and the gain in the direction of θ 2 = 65 • are shown as a function  of frequency in Figs. 17 and 18, respectively. The simulation results reveal that the beam deviation and gain drop are small across the frequency range for a S11 = −10 dB criterion. Note that the bandwidth for a 3-dB gain drop criterion is 8.3%.
Thus, the measured results confirm the simulation results. It follows that the proposed beam-forming system answers the main question of whether a θ 2 greater than 60 • can be obtained under certain conditions, since the results show values of θ 2 = 65 • , N metaplate = 1, gain = 18.1 dBi, η aperture = 49%, and MSL = −14.6 dB. It also follows that the requirement on the total system height is met with the value of H total = 0.90λ DSN .

V. CONCLUSION
It has been found that a patch-metaplate system can realize a radiation beam that meets the following characteristics: deep tilt angle of more than 60 • , high gain of approximately 18 dBi, and high radiation aperture efficiency of approximately 50%. These values have been realized under the two required conditions of the use of a single metaplate (N metaplate = 1) and a small system height of less than one wavelength at the design frequency of 11.5 GHz.
The design for the beam-forming system is performed in four steps. Firstly, a T-shaped metatwin is proposed and investigated. It is revealed that the metatwin has a wide frequency band of 14.6% (10.8 GHz to 12.5 GHz) for a −3 dB transmission coefficient criterion. It is also revealed that the VOLUME 10, 2022 phase shift across this frequency region is extremely wide: 450 • , which exceeds the 360 • needed for beam forming. Secondly, a metaplate using T-shaped metatwins is designed to refract the wave front of a normally incident plane wave in a 65 • direction. After the confirmation of the validity of this design, thirdly, the final metaplate is designed such that the quasi-spherical radiated wave from a small patch antenna forms a high gain beam in the 65 • direction. The simulation for a system composed of the patch antenna and the designed metaplate shows that a 65 • tilted beam is formed with a gain of 18.1 dBi, an aperture efficiency of 49%, and the maximum sidelobe level of −14.6 dB, where the total system height is small: 0.90λ DSN .
Fourthly, the beam-forming system is fabricated, and measurements are performed. The measurements validate that the specified characteristics are all realized. . His significant contributions are the development of five integral equations for line antennas in free space and printed on a dielectric substrate, the invention of an L-shaped wire/strip antenna feeding method, and the realization of numerous wideband antennas, including curl, metaspiral, metahelical, and body of revolution antennas. His other accomplishments include design of antennas for GPS, personal handy phones, space radio, electronic toll collection, RFID, UWB, and radar. He has been awarded 78 patents, including ''A curl antenna element and its array'' (Japan). His research interests include numerical methods for lowand high-frequency antennas and optical waveguides.