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Abstract
Generating multiple beams in distinct polarization states is promising in multi-mode wireless communication but still remains challenging in metasurface design. Here, we theoretically and experimentally demonstrate a concept of broadband receiving-transmitting metasurface and its application to the generation of multi-polarization multi-beam. By employing U-slot patch, an efficient receiving-transmitting element with full phase coverage is designed within a wide bandwidth. Based on this architecture, a methodology is proposed to generate dual spin-decoupled beams and then developed into the strategy of generating multiple beams at different linear polarizations. To verify our strategy, two lens antennas, respectively radiating dual-spin dual-beam and quad-polarization quad-beam, are devised. With multi-polarization multi-beam radiated, the two lens antennas are both with whole aperture efficiency above 40% within the bandwidth of 10.6–12.3 GHz (14.8%), firmly validating our strategy and design.
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1. Introduction
Metasurfaces, the two-dimensional equivalent of metamaterials, are periodic arrays of subwavelength engineered inclusions that can locally manipulate waves over a subwavelength thickness [1–8]. As one intriguing analogy of metasurfaces, transmissive metasurface (TMS) has no disadvantage of interference between incident and outgoing waves [5–8], thus showing great application potential in many devices. However, the design of TMS is more challenging as compared to its reflective counterpart. This is because insertion loss must be considered to achieve the required phase range [5,6] while it is not necessary to consider magnitude response in reflective metasurface. Besides, TMSs also suffer from narrow bandwidth due to their resonance feature [7,8].
To solve aforementioned bottlenecks, TMSs with orthogonal bars are developed [9–13]. Aided with Fabry-Pérot-like resonance [9], such a kind of metasurface is generally with high transmission rate within a broad bandwidth, and has been widely used in wideband polarization converter [9], lens antenna (LA) [10,11], folded transmitarray [12,13], et al. Despite of high transmission efficiency and wide operation bandwidth, the metasurface with orthogonal bars only works under linearly polarized (LP) illumination. In addition, outgoing wave from such a metasurface is locked to the orthogonal polarization of incident wave. To break those restrictions, receiving-transmitting metasurfaces [14–17] are usually employed to response for wave of arbitrary polarization incidence with high transmission efficiency in microwave region. For example, circularly polarized folded LAs are realized by using linear-to-circular [14] and circular-to-circular [15] receiving-transmitting meta-atoms. Besides, a dual-band dual-linear polarization transmitarray is realized by employing receiving-transmitting elements operating in linear-to-linear scheme [16]. Although receiving-transmitting metasurface is widely used in LA design [17], it is still challenging for such a metasurface to simultaneously obtain full phase coverage with high transmission efficiency in wide bandwidth.
As of today, an explosive growth of interest has been devoted to the application of TMSs in multi-beam LAs [18–24] due to their merits of high gain and wide beam coverage. Traditional method of generating multi-beam in a LA is by employing intelligence algorithms [18,19], which is complex and time-consuming. The developed addition theorem provides a simple and convenient methodology to generate multi-beam on a single aperture [20,21]. However, neither the intelligence algorithm nor the addition theorem are effective for generating multi-beam in multiple polarizations. To implement multi-polarization multi-beam for multimode wireless application, linearly birefringent metasurface [22,23] is usually used to generate dual-beam in orthogonal polarizations. In fact, the two beams in orthogonal polarizations are induced by polarization decomposition of incident wave [24]. As a result, only two polarization statuses are available for multiple beams even if the addition theorem is simultaneously employed [25]. To date, it is still a blank to acquire wideband multiple beams in more than two working polarization states by using TMSs.
To fill the gap, here we propose an architecture of wideband receiving-transmitting metasurface with high efficiency and full phase coverage to generate multi-polarization multi-beam. Based on the receiving-transmitting scheme, a methodology is proposed to generate dual spin-decoupled beams and then developed into the strategy of generating multiple beams in different linear polarizations. Two lens antennas, namely lens antenna 1 and lens antenna 2, are designed to generate dual-spin dual-beam and quad-polarization quad-beam, respectively. Both simulation and measurement results coincide well in both cases and showcase high performances, firmly validating the effectiveness of proposed methodology in multi-polarization multi-beam generation.
2. Broadband high efficiency meta-atom design
As shown in Fig. 1, the element is designed with a period of p = 10 mm and composed of three metallic layers printed on two identical substrates (F4B, h = 2 mm, εr = 3.5, tanδ = 0.002). Both substrates are bonded using an Arlon CuClad6700 film (hf = 0.114 mm, εr = 2.35, tanδ = 0.0025). The first metallic layer, namely reception layer with lable ① in Fig. 1(a), is used for receiving incident wave from lower half-space and converting the wave into current along the metallic via hole, whereas the third metallic layer, also called radiation layer marked with ③, is introduced for converting the current into radiation wave in upper space. To enable wideband phase manipulation, two identical U-slot patches [26], with parameters of (a, b, l, w) as depicted in Fig. 1(b), are employed as the reception and radiation layers, respectively. The second metallic layer is a ground plane with an etched hole (diameter dh = 0.6 mm), and the reception and radiation layers are connected by a metalized via hole with a diameter of d = 0.3 mm.
Fig. 1. Layout and performance of the meta-atom. (a) Perspective view and (b) top view of the meta-atom. Co-polarized transmission (c) amplitude and (d) phase of the chosen elements versus frequency. Co-polarized transmission (e) amplitude and (f) phase change of the 10th cell versus frequency and incident angle.
Apparently, two mirrored radiation patches can excite completely opposite electromagnetic field, which implies that the process to design full phase coverage of the meta-atom can be simplified and divided into two steps: first, optimizing parameters (a, b, l, w) of the U-slot patch to achieve a phase range of 180◦ of transmissive wave, and second, rotating radiation patches to their mirror counterparts to acquire the other 180◦ phase coverage. In this way, eighteen meta-atoms numbered from 0 to 17 as listed in Table 1 are finally selected to cover phase range of 180◦ with a phase step of 10◦. The rest atoms numbered from 18 to 35 are correspondingly acquired by mirroring radiation layers of the elements numbered from 0 to 17. Under x-polarized excitation in CST Microwave Studio, amplitude and phase of the co-polarized transmission coefficient are calculated and depicted in Figs. 1(c) and (d), respectively. It is clear that all of the elements are with high transmission amplitude of more than 0.9 within 9.5 GHz – 12.5 GHz, and a full phase coverage in steps of 10° is achieved across 10 GHz to 12 GHz by using the devised meta-atoms. Besides, the relatively parallel phase curves at different frequencies are responsible for the meta-atom’s ability of broadband wave manipulation of transmission wave. The angular stability of the meta-atom (the 10th cell is selected as an example herein) is investigated as shown in Figs. 1(e) and 1(f). With incident angle varied below 30◦, the co-polarized transmission amplitude can always maintain above 0.92 and transmission phase fluctuates within 25°, showing a good angular stability within ±30◦ incident angle.
Table 1. Parameters of The Phased Elements
3. Generation of dual-spin dual-beam
To generate two distinct beams in the two spins, it is necessary to find a methodology to impose two different phase profiles on the two spins. To this end, we start by analyzing the transmissive wave from elements with receiving-transmitting architecture. The transmissive wave from such a meta-atom, propagating along + z direction, can be described as ${\vec{\boldsymbol{E}}_{\boldsymbol{t}}} = {e^{j\mathrm{\Phi }}}{\vec{\boldsymbol{e}}_{\boldsymbol{x}}},$ in which Φ represents the propagation phase induced from structure variation of the patch on the meta-atom. When rotating the radiation patch of the meta-atom with an orientation angle of β in anticlockwise direction, the transmissive wave becomes ${\vec{\boldsymbol{E}}_{\boldsymbol{t}}} = {e^{j\mathrm{\Phi }}}({\cos \beta {{\vec{\boldsymbol{e}}}_{\boldsymbol{x}}} + \sin \beta {{\vec{\boldsymbol{e}}}_{\boldsymbol{y}}}} )$. If described under circularly polarized basis, the transmissive wave will be ${\vec{\boldsymbol{E}}_{\boldsymbol{t}}} = ({{e^{j(\mathrm{\Phi } + \beta )}}{{\vec{\boldsymbol{e}}}_R} + {e^{j(\mathrm{\Phi } - \beta )}}{{\vec{\boldsymbol{e}}}_L}} )/\sqrt 2$. It is clear that independent phase distributions are achieved for left-hand circular polarization (LCP) and right-hand circular polarization (RCP). Besides, the propagation phase of Φ and orientation angle of β should be
Herein, ${k_0} = 2\pi /\lambda$ is the wavenumber at the reference frequency, and $\xi$ is the gradient to tilt the radiation beam. With distinct gradients of ${\xi _R} ={-} x\sin ({{{20}^ \circ }} )$ and ${\xi _L} ={-} y\sin ({{{30}^ \circ }} )$ imposed on RCP and LCP channels, phase profiles of ФR and ФL can be easily figured out as shown in Figs. 2(a) and 2(b). The propagation phase (Ф) and orientation angle (β) of meta-atoms are then accordingly mapped out as depicted in Figs. 2(c) and 2(d) by using Eq. (1). Converting propagation phase profile into structure mapping according to the phase data in Fig. 1(d) and then rotating meta-atoms against the orientation angle distribution, the metasurface lens is finally actualized and fabricated by using standard PCB technology.
Fig. 2. Phase distribution of the metasurface lens in LA1. Phase profiles of (a) RCP and (b) LCP imposed on the lens. Correspondingly calculated (c) propagation phase and (d) orientation angle distribution of the lens.
Lens antenna 1 (LA1) is then assembled by setting a horn source (waveguide cross section of 13.5 × 23.6 mm2 and radiation aperture size of 27 × 34 mm2) at the focal point of the lens, as shown in Fig. 3(a). Performances of LA1 are characterized with Time Domain Solver in CST Microwave Studio and measured in a microwave anechoic chamber. Figure 3(b) presents simulated 3D radiation pattern at 11 GHz in circular polarization basis. Unambiguously, dual pencil beams deflected to + x and + y directions are generated, which coincides well with the predictions using Eq. (2). The simulated and measured radiation patterns of LA1 on the two principal planes (xoz and yoz planes) are also plotted in Figs. 3(c) and 3(d). Apparently, experimental radiation patterns are in good agreement with numerical ones, both indicating a RCP and a LCP pencil beam deflected to + x direction with θ = 20° and to + y direction with θ = 30°, respectively. Besides, the RCP radiation beam is with a measured gain of 22.4 dB, beamwidth of 8° and axial ratio below 1 dB, whereas the LCP radiation beam possesses a measured gain of 22.3 dB, beamwidth of 9° as well as axial ratio below 1 dB.
Fig. 3. Prototype and performance of LA1. (a) Fabricated prototype and (b) the simulated 3D radiation pattern of LA1. Simulated and measured far-field patterns at 11 GHz on (c) xoz and (d) yoz planes. Simulated and measured gain and aperture efficiency for (a) RCP and (b) LCP beams across 9–13 GHz.
To show operation bandwidth of LA1, realized gain and aperture efficiency of the radiated RCP and LCP beams are portrayed in Figs. 3(e) and 3(f). It should be noticed that the aperture efficiency herein is calculated by
in which θ represents the deflection angle of the shaped beam whereas Scosθ is the effective aperture. Since the phase in Eq. (2) is dispersive, deflection angle of the shaped beam is frequency dependent, which can be calculated byHerein, f0 is the reference frequency and θ0 represents the deflection angle of the shaped beam at f0. With this method, aperture efficiency varied with frequency can be easily figured out. Clearly, the RCP beam achieves a measured peak gain of 23.1 dB at 11.8 GHz, peak aperture efficiency (AE) of 28.7% at 11.6 GHz, 1 dB gain bandwidth (BW) of 10.8–12.4 GHz (13.8%) and BW of AE above 20% across 10 GHz–12.4 GHz (21.4%). In addition, the LCP beam achieves a peak gain of 23 dB at 11.8 GHz, peak AE of 30.2% at 11.6 GHz, 1 dB gain variation BW of 10.8–12.4 GHz (13.8%) and BW of AE above 20% across 10 GHz – 12.4 GHz (21.4%).
4. Generation of quad-polarization quad-beam
As introduced in [27], electromagnetic wave characterized by arbitrary polarization can be expressed as a linear combination of two orthogonal CP components
Herein, the symbol of “$\angle$ “ is the phase of a complex variable. Similarly, if a phase profile of ΦL expressed as
Fig. 4. Phase distribution of the metasurface lens in LA2. Phase profiles of (a) RCP and (b) LCP imposed on the lens. Correspondingly calculated (c) propagation phase and (d) orientation angle distribution of the lens.
Based on above methods, the metasurface lens is fabricated as shown in Fig. 5(a) and then assembled with the feeding horn to form LA2 as shown in Fig. 5(b). With identical setup of LA1, far field radiation pattern of LA2 is calculated as shown in Fig. 5(c). It is clear that quad beams are generated from the lens antenna, which exactly coincides with theoretical predictions of the four beams from F1 to F4. By altering polarization vector in far-field plot properties, polarization of the four shaped beams can be easily recognized in simulation software. Furthermore, rotating the reception probe around its axis can help identifying polarization of the radiation beams in practical measurement setup. In this way, simulation and measurement radiation patterns characterized by x/y-polarizations on xoz plane are portrayed in Fig. 5(d), whereas the simulation and measurement counterparts characterized by ±45°-polarizations on yoz plane are plotted in Fig. 5(e). Clearly, x/y-polarized beams tilt to ± x directions with deflection angles of 30° and 20° whereas ±45°-polarized beams deviate toward ± y directions with deflection angles of 20° and 30°. This is quite in accordance with theoretical predictions.
Fig. 5. Prototype and performance of LA2. (a) Fabricated prototype of the metasurface lens. (b) Schematic view of LA2. (c) The simulated 3D radiation pattern of LA2. Simulated and measured far-field patterns at 11 GHz on (d) xoz and (e) yoz planes. (f) Comparison of the aperture efficiency of LA1 and LA2 across 9–13 GHz.
To show bandwidth of LA2, we use the whole aperture efficiency, which is denoted by as introduced in [18], to evaluate bandwidth of a multi-beam antenna. For comparison, Fig. 5(f) shows the simulated and measured whole aperture efficiencies of LA1 and LA2. It is clear that the whole aperture efficiencies of the two lens antennas are all above 40% within the bandwidth of 10.6 – 12.3 GHz (14.8%), further validating merits of wideband and high efficiency of the proposed metasurface. Besides, the whole aperture efficiency of LA2 is lower than that of LA1. This is due to the fact that LA1 is not a strict case of multi-beam generation but a special case of orthogonal polarization separation.
5. Conclusion
In conclusion, two broadband lens antennas (LA1 and LA2), which can generate dual-spin dual-beam and quad-polarization quad-beam, are comprehensively presented. The designed antennas, featuring high efficiency, broad operation bandwidth, undistorted high gain pencil beam and low cross-polarization level, is very promising in many engineering scenarios, for instance, satellite communication system, and the next generation communication system, et al. Furthermore, the proposed strategy of multi-polarization multi-beam generation is especially conducive to designing multi-mode high gain antennas and is readily extended to higher frequency regime.
Funding
China Postdoctoral Science Foundation (2022M723864).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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