I. Introduction
Transmitarray antenna (TA) which is based on metasurface has great application prospects in wireless communication due to their high gain, planar structure, and feed-blockage-free characteristics [1, 2]. However, traditional TA requires a considerable focal length between the feed source and the aperture surface to ensure that the transmissive surface is uniformly illuminated by the incident wave, resulting in an overall increase in the profile of the antenna system. To overcome the limitation of the profile height, folded transmitarray antenna (FTA) has been proposed as an innovative solution [3, 4]. FTA reduces the profile height to one-third or less of the focal length F by folding the propagation paths several times, which is especially important in space-constrained applications with such a compact shape.
To achieve the low-profile characteristic, kinds of FTAs have been reported [5–11]. A magnetoelectric dipole structure with excellent radiation performance is utilized as the metasurface unit [5], while the reflective surface is replaced with a phase gradient distributed reflective surface to realize low height-to-diameter ratio. The metal-only transmission unit is also applicable for the low-profile architecture [6], which can reflect orthogonally polarized incident waves and transmit co-polarized ones. Bidirectional radiation could be readily generated with FTA. A dual-polarized feed source and partially reflective surfaces are utilized to enable electromagnetic waves to radiate from both the transmissive surface and the partially reflective surface [7]. A new architecture which is composed of the filtering surface, planar filtering illumination source and reflective polarization rotator is introduced for realizing a high-gain low-profile circularly polarized (CP) filtering transmitarray antenna [9]. In addition, the 3-dB gain bandwidth of FTA is equally crucial, and most FTAs achieve wideband by designing a transmission unit with wideband characteristic [12–15]. Two wideband tightly coupled bow-tie dipole antennas connected by a pair of differential microstrip-line phase shifters are designed to form a transmit/receive (T/R) array, which can achieve wideband characteristic through the element architecture [15]. The narrowband issue of high-gain circularly polarized antenna is addressed via the method of characteristic mode analysis, thereby realizing the wideband characteristic of the FTA [16]. The gain and bandwidth of aperture antennas are constrained by the electrical dimensions of the antenna. How to simultaneously achieve the wideband and low-profile characteristics of FTA has become a current research hotspot.
In this study, a wideband and low-profile FTA is proposed. The transmission unit consists of three layers of metal structure. By adjusting the size of the middle metal layer in the unit, the transmission phase can be flexibly controlled. Meanwhile, rotating the middle metal layer by 90° can obtain an additional 151° phase coverage. The wideband and wide-beam open-ended waveguide is used as feed source, which facilitates the realization of low-profile structures. By using genetic algorithm (GA) to weight and optimize the phase compensation error of edge frequency points, the gain bandwidth is significantly enhanced. The measurement results of the FTA prototype are in good agreement with the simulations.
II. Operating Principle
Fig. 1 shows the overall structure and operating principle of FTA. FTA consists of three parts: the upper transmissive metasurface, the lower reflective metasurface, and the feed source. The upper transmissive metasurface reflects the Y-polarized incident wave and converts the X-polarized incident wave into a Y-polarized transmitted wave, while enabling directional control of the transmitted beam. The lower reflective metasurface can achieve the conversion of Y- and X-polarized incident waves into X- and Y-polarized reflected waves respectively. The feed source is placed in the center of the lower reflective metasurface.
The Y-polarized wave emitted by the feed source irradiates the upper transmissive metasurface and directly reflected toward the lower reflective metasurface. On the lower reflective metasurface, the Y-polarized incident wave is converted into an X-polarized reflected wave, which then enters the upper transmissive metasurface and is converted into a Y-polarized transmitted wave. By controlling the phase distribution of the upper transmissive metasurface, high-gain plane waves are formed. In this antenna system architecture, the equivalent feed source is located at the intersection of the dashed lines, and the incident wave from the actual feed source undergoes two reflections in the upper and lower metasurfaces. Ray tracing theory indicates that the height H between the upper and lower metasurfaces is reduced to one-third of the actual focal length F. Under this architecture of FTA, the most suitable feed source is an open-ended waveguide. Compared to patch antennas, waveguides have a wider operating frequency band to meet the wideband requirement of FTA. Compared to horn antennas, its smaller aperture allows FTA to achieve lower sidelobe levels, and its 3dB beamwidth also meets the requirement for realizing a low-profile FTA.
III. UNIT Cell Design
1. Transmission Unit Design
The unit structure of the upper transmissive metasurface is shown in Fig. 2(a), which includes two dielectric layers and three metal layers. The upper and lower metal layers are polarization gratings with identical geometries but orthogonal orientations. The middle metal layer consists of four mirror-symmetric L-shaped branches and a dual-split ring, with its principal axis forming an angle of α = 45° with the x-axis as shown in Fig. 2(b). The structural parameters are summarized in Table 1. The dielectric layers are fabricated from FR4 substrate, which has a relative permittivity of 4.5.
As shown in Fig. 3, T and R denote the transmission and reflection coefficients, subscripts x and y denote the X-polarized wave and Y-polarized wave, respectively, and K denotes the multiple values of the middle metal layer’s dimensions. Fig. 3(a) shows that, in most cases, the transmission magnitude |Tyx| exceeds 0.8 in the frequency band of 18.0–27.0 GHz. In Fig. 3(b), it is evident that the transmission magnitude is highly sensitive to the different polarization states of the incident wave. The reflection magnitude |Ryy| is close to 0 dB, effectively suppressing the impact of Y-polarized incident wave. The reflection magnitude |Rxx| for X-polarized waves is less than −10 dB. Additionally, |Txx| is less than −30 dB, maintaining low transmission magnitude for co-polarized waves while ensuring high transmission magnitude for cross-polarized waves.
As shown in Fig. 4(a), by adjusting the K values of different multiples of the middle metal layer, a phase compensation of 151° can be obtained in the operating frequency band. Rotating the middle metal layer by 90° provides an additional 180° phase shift, as shown in Fig. 4(b). Therefore, the transmission unit can realize a total phase compensation of 302° by rotating the middle metal layer.
Fig. 5 shows the influence of different incident angles θ on the transmission magnitude and phase of the transmission unit. The transmission unit exhibits insensitivity to incident angle variations and has stable radiation performance. To further clarify the phase compensation mechanism of the transmission unit structure, Fig. 6 shows the electric field distribution under two states, with α = 45° and α = −45° respectively. After rotating the middle metal layer at a certain angle, the polarization state of the incident wave will change by 90° from the top to the bottom. When the middle metal layer rotates 90°, the electric field distribution of the top metal layer clearly reveals a 180° phase difference between the two unit states.
Table 2 summarizes different K multiple values, transmission phases, and transmission magnitudes of units under different array arrangements at 22.5 GHz. Although the transmission unit cannot achieve full phase compensation, quantifying the unit with six phase states can still ensure uniform phase compensation. Six phase states reduce the complexity of physical design while maintaining the excellent performance of the array.
2. Reflection Unit Design
The unit structure of lower reflective metasurface is shown in Fig. 7(a), which includes one dielectric layer and two metal layers. The upper metal layer consists of a square metal patch and a dual-split square ring as shown in Fig. 7(b), and the lower metal layer is a reflective ground plane. The dielectric layer is made of an F4B substrate, with a relative permittivity of 3.55 and a loss tangent of 0.0027.
The structural parameters of reflection unit are summarized in Table 3. Fig. 8(a) shows the frequency response of the reflection coefficient. In the K-band, the polarization of electromagnetic wave is orthogonally converted. Meanwhile, the reflection magnitude of the reflection unit for co-polarized waves is very low, which ensures the polarization conversion ability. Fig. 8(b) shows the reflection magnitude and reflection phase of the unit with different incident angles, indicating that the reflection unit is insensitive to incident angle variations.
As shown in Fig. 9, the polarization conversion characteristic of the reflective unit can be illustrated by the electric field vector decomposition method. The incident electric field Eiv is Y-polarized. The current excited on the reflective unit can be decomposed into u-polarized and v-polarized components. The polarization orthogonal decomposition of the incident electric field of Y polarization is carried out. The u-polarized component of the incident field will induce a u-polarized reflective component with equal magnitude and phase, and the v-polarized component of the incident field will induce a v-polarized reflective component with equal magnitude and reverse phase. Finally, the Y-polarized incident wave will be converted into the X-polarized reflected wave, which proves that the reflective unit has polarization conversion characteristic.
IV. Design and Optimization of FTA
1. Design of FTA
The phase compensation of the transmission metasurface, which is based on gradient distribution, is designed to control the transmitted wavefront. It converts the spherical wave after two reflections into a high-gain plane wave. Each unit provides a specific phase offset according to its own spatial position to offset the path difference generated in the propagation of spherical wave, so that the originally divergent phase distribution is compensated into an in-phase plane wave front. The transmission phase of the unit at the m-th row and n-th column can be calculated as given by Eq. (1):
Among them, k0 represents the wave number in free space. p represents the periodic size of the unit. F represents the focal length of the metasurface, and ϕ and θ represent the beam direction. The beam radiated by the antenna exhibits no deflection, so set ϕ = θ = 0°.
The feed waveguide applied in the FTA operates at 17.6–26.7 GHz, with a gain range of 5.2–7.2 dBi and a 3-dB beamwidth of 60°. The open-ended waveguide aperture size is only 11.7 mm × 5.3 mm (0.88 × 0.4 λ0). Since the aperture size is smaller than the operating wavelength, the integration of the open-ended waveguide into a reflective metasurface will not affect the polarization conversion characteristic of the reflective metasurface. The focal length F of the designed FTA is 60mm, corresponding to a profile height H of 20 mm (1.5λ0). Taking both gain requirements and aperture efficiency into account, the upper transmissive metasurface consists of 27 × 27 units with an area of 108 mm × 108 mm. The transmission phase compensation distribution of the metasurface is derived via theoretical calculations, as shown in Fig. 10(a). The lower reflective metasurface consists of 24 × 24 units with the area of 108 mm × 108 mm, ensuring full illumination of the upper transmissive metasurface while requiring no phase compensation design. Finally, the overall structure of FTA is shown in Fig. 10(b).
2. Optimization of FTA
Compared with the theoretical continuous phase distribution, phase error is inevitable in the design of FTA. Since the phase error is also a function of frequency, it is necessary to optimize the phase at the edge frequency points which have the most serious phase error to reduce its impact on the gain bandwidth. The introduction of reference phase ϕ0 can improve the phase compensation distribution at different frequency points and reduce the phase error [17]. Based on the deterioration of the phase compensation at the edge frequency points, two reference phases are introduced to the low frequency point and high frequency point in K-band respectively, and then the optimization method is employed to eliminate the phase error. To define the phase error function ϕerror, the weighting factor Amn is introduced. The weighting factor Amn is determined by two factors: the transmission magnitude of the transmission unit and the distance between the transmission unit and the feed phase center. After combining the weighting factor with the magnitude distribution extracted from the feed source at the aperture plane, the formula for optimizing the phase error at the two edge frequency points are derived as Eqs. (2)–(3):
where
φ m n n e e d M m n f e e d
To address the phase error of edge frequency points, low frequency point and high frequency point (19 GHz and 25 GHz) are selected as optimization targets. After obtaining two phase error functions ϕerror(i1 = 19) and ϕerror(i2 = 25), adding them together yields the fitness function, which is the objective function in the GA. Optimization is performed on this function to achieve the minimum phase compensation error. The fitness function is defined as Eq. (4):
As shown in Fig. 11, the GA is adopted to solve the optimal solution of the fitness function. In the algorithm parameter settings, the population size is 100. Based on Eq. (4), 50 iterative calculations are performed. The number of iterations is taken as the convergence criteria. When the iteration process reaches the preset 50 times, the stopping criterion is satisfied, and the algorithm terminates.
As shown in Fig. 12(a), before optimizing the phase compensation of the transmissive metasurface, the 3-dB gain bandwidth of the FTA is 26.6%, with 23.2% of this bandwidth (21.33–25.34 GHz, 25.78–27 GHz) falling within the operating frequency band. After optimizing the phase compensation, the original transmission unit is replaced by another discretized state unit. At the cost of a slight reduction in peak gain, the 3dB gain bandwidth of the optimized FTA is extended to 38% and 36.4% (18.8–27 GHz) is in the operating band. The optimized FTA maintains almost the same aperture efficiency as the pre-optimized FTA while realizing wideband characteristic. The optimized FTA is enabled to radiate electromagnetic waves in a wider frequency band by using its aperture efficiently. The phase compensation distribution of the optimized transmission unit is shown in Fig. 12(b).
V. Measurements and Discussion
To verify the performance of the designed antenna, the prototype was processed and measured. In Fig. 13, the printed circuit board technology was adopted to fabricate the transmissive surface and reflective surface. A slot was milled in the center of the reflective surface to mount the waveguide in it. By extending the boundary dimensions of the two dielectric layers, the distance between the upper and the lower metasurfaces can be fixed. Meanwhile, holes were drilled at the four corners of the dielectric layers, and plastic studs were inserted and secured with nuts, as shown in Fig. 13(d), thereby strictly controlling the FTA’s profile height.
The measurement of this prototype was completed in a standard microwave anechoic chamber. Before the measurement, a standard gain horn antenna was used to calibrate the measurement system to ensure the accuracy of the measurement platform. The antenna under measurement was installed at the center of the turntable by means of laser positioning, and the phase center of the antenna was aligned with the center of the measurement platform.
Fig. 14 shows the radiation patterns of the antenna prototype in the XOZ plane and the YOZ plane, respectively. The radiation patterns have good consistency from both the measured results and simulated results. The cross-polarization levels of the antenna prototype at the three frequency points are below −20dB. The sidelobe levels of the antenna prototype are less than −15 dB at both 19 GHz and 25 GHz. The sidelobe level is only slightly higher than −15 dB at 22.5 GHz. Affected by the feed waveguide and the turntable support, the sidelobe levels of the main polarization of the measured data have an error of 0.3–1.8 dB, while the maximum error of the cross polarization component is about 15–20 dB. The curve of the antenna’s gain and aperture efficiency versus frequency are shown on Fig. 15. At 23.5 GHz, the peak gain of 23.3 dBi and the peak aperture efficiency of 23.7% are achieved. The 3-dB gain bandwidth ranges from 18.8 GHz to 27 GHz, almost covering the entire K-band. Limited by the processing conditions, the error of the measured results mainly originates from the fabricating process. The gap between the transmissive and reflective metasurfaces in the prototype is fixed by plastic studs. Since the plastic studs are manually installed on the metasurfaces, there is a certain operational error. This error will affect the phase compensation accuracy, thereby resulting in a 0.2 dB reduction in gain.
To verify the advantages of the FTA, Table 4 lists the comparison results of previously reported FTA and the antenna’s performance. The FTA in [5, 9, 18–20] is obviously inferior to this antenna in 3-dB gain bandwidth and peak gain. Meanwhile, the peak aperture efficiency of the antenna is only inferior to that in [18], and the array size and height-to-diameter ratio are also smaller than most of previously reported FTA. The antenna features wideband, low-profile, high gain and miniaturization characteristics.
VI. Conclusion
This paper proposes a wideband and low-profile FTA. The prototype, which is composed of the upper transmissive metasurface, lower reflective metasurface, and open-ended waveguide, is designed and experimentally validated. The waveguide can help FTA realize the characteristics of low-profile and low sidelobe levels. With the combination of the GA and the phase error function, the FTA’s 3-dB gain bandwidth is improved to 36.4%. Moreover, the prototype has a low height-to-diameter ratio of 0.19 and a high gain of 23.3 dBi. The wideband and low-profile characteristics make the proposed FTA an attractive candidate for wireless communication systems and other practical applications requiring simultaneous wideband and low-profile operation.
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