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Abstract
In this paper, an ultrathin Huygens’ metasurface is designed for generating an orbital angular momentum (OAM) beam. The Huygens’ metasurface is a double-layered metallic structure on a single-layer PCB. Based on induced magnetism, the Huygens’ metasurface achieves the abilities of available near-complete transmission phase shift around 28 GHz. According to the principle of vortex wave generation, a Huygens’ metasurface is designed, implemented and measured. The simulated and measured results show that the dual-polarized OAM transmitted waves with the mode l = 1 can be efficiently generated on a double-layered Huygens’ metasurface around 28 GHz. The measured peak gain is 23.4 dBi at 28 GHz, and the divergence angle is 3.5°. Compared with conventional configurations of OAM transmitted beam generation, this configuration has the advantages of high gain, narrow divergence angle, and low assembly cost. This investigation will provide a new perspective for engineering application of OAM beams.
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1. Introduction
With the rapid development of modern communication technology and the rapid expansion of channel capacity, wireless spectrum resources have become very scarce. Due to their unique spiral phase factor [1] and mutual orthogonality between different modes [2], OAM beams can greatly increase channel capacity and spectrum utilization, and then have potential applications such as data coding [3–5], confidential communication [6–8], detection of rotating objects [9,10] and passive positioning [11]. OAM beams can be generated by introducing different spatial phase delays to transform the incident waves into the vortex waves carrying OAM. In microwave band, the generation of OAM beams was first proposed by Thidé et al. [12]. Since then, several methods of generating OAM waves have emerged including spiral phase plate [13,14], circular phase-shifted array [15] and spiral reflecting surfaces [16]. However, all these methods have disadvantages such as bulky, difficult to manufacture, and low efficiency.
In recent decades metamaterials and metasurfaces have been widely studied and emerged as an efficient platform for EM manipulation. From effectively medium approach [17–19], to hyperbolic EM modes [20–22], chirality and anisotropy [23–25], as well as metamaterials and metasurfaces integrating 2D materials [26], etc., diverse EM manipulation approaches have been demonstrated. Particularly, as a two-dimensional form of metamaterials, metasurfaces can conveniently manipulate the phase, amplitude and polarization of electromagnetic (EM) waves within ultrathin layers, which provides new degrees of freedom for exploring fantastic physics phenomena and realizing next-generation EM devices [27–31]. Metasurfaces also can be used for the generation of OAM beams by properly designing the phase distribution on surface. Because reflective metasurfaces are easier to implement, the generation of OAM beams on reflective metasurface are widely explored [32–37]. By comparison, there are far fewer studies on the generation of transmitted OAM waves [38–40]. Due to the difficulty of simultaneously achieving high transmission and complete phase coverage on single- or double-layer frequency selective surface (FSS) structures [41], these configurations use either multilayer structure or metallic vias, which makes their structure complex and difficult to implement.
As an important branch, Huygens’ metasurfaces can achieve resonant transmission by tailoring the impedance matching between electric and magnetic dipoles [42]. This crucial capability of the Huygens’ metasurface provides an advanced solution for transmitted wave manipulation, from the fascinating physical phenomena [43–49] to antenna engineering applications [50–52]. In particular, double-layer Huygens’ metasurfaces can be used to simplify the structure complexity and reduce the assembly cost, thereby promoting engineering applications. Various double-layer structures have been developed for metalens antennas and abnormal refraction, including antisymmetric metallic elements [53,54], symmetric dual-polarized metallic elements [55,56] and electric dipole pairs [57,58]. These studies provides extra opportunities for conveniently generating transmitted vortex waves with OAM.
In this paper, we demonstrate the efficient generation of transmitted OAM waves with mode l = 1 on double-layer transmissive metasurface at 28 GHz. We believe that this research will greatly promote the engineering application of OAM vortex waves in the fields of wireless communications.
2. EM responses of unit cell
The surface equivalence principle is an approach that is used to analyze the radiated behaviors from infinitely thin structures. Recently it has been developed for the design of ultrathin EM surfaces [42]. Here we will discuss the EM responses of Huygens’ unit based on the surface equivalence principle. Firstly we assume that a linearly polarized wave is incident on an EM surface and is transmitted and reflected from the surface. Based on the surface equivalence principle, the incident wave will excite the electric and magnetic surface currents on the surface which can be characterized as the electric surface admittance Yes and the magnetic surface impedance Zms, respectively. Then the transmission coefficient T and reflection coefficient R of EM wave can be expressed as [42,57]
For conventional FSS structures, there is only electric resonance and no magnetic resonance, so |Yes| >> 1 around the electric resonant frequency and |Zms| → 0 in the considered frequency region. Assuming Yes = iαeff and then Eq. (1) is rewritten as
Equation (2) exhibits two properties of conventional FSS structures. On the one hand, it is easy to see that the transmission phase φT cannot be 180° because this requires Yes to be a real number. In other words, the transmission phases around the value of 180° are unavailable and thus the available transmission phase coverage will be much less than 360°. On the other hand, at the electric resonant frequency (i.e. αeff >> 1), it can be got that |T| → 0 and φT = -90°. In brief, for conventional FSS structures, the incident EM wave will be reflected strongly with transmission phase of -90° at the electric resonant frequency.
To obtain the available transmission phase coverage close to or beyond 360°, we need to get the available transmission phase around the value of 180°. In Eq. (1) we set R = 0 and then get Yes = Zms. That is to say, ideally zero reflection occurs at the case that Yes and Zms are equal. Provided that both electric and magnetic resonances exist on the surface and Ye = Zm = iαeff (αeff >> 1), we can obtain
The results show that, at the resonant frequency, the incident EM wave can pass through the EM surface with |T| → 1 and φT ≈ 180°. Such resonance, the so-called Huygens’ resonance, give rise to resonant transmission phenomenon. It is the result of the impedance matching between electric surface admittance and the magnetic surface impedance [42]. Thus, when the conventional FSS structure is replaced by a Huygens’ surface, the propagation of EM waves at the resonant frequency changes from strong reflection to perfect transmission, and the transmission phase changes from -90° to -180°. The unavailable transmission phase around the value of 180° becomes available. This is the essence of Huygens’ surface enabling complete transmission phase coverage at a certain frequency.
We will investigate the Huygens’ resonance in our structure based on above analysis. The configuration of Huygens’ units is given in Fig. 1, which consists of a dielectric substrate and a pair of symmetric notched square rings on two surfaces. The dielectric substrate material is Rogers RO4003C with dielectric constant ${\varepsilon _r}$ = 3.55, loss tangent $tan\delta \;$ = 0.0027, and thickness h = 1.524 mm. The metal patches are made of 18 µm thick copper sheets. The width of all metal rings is w = 0.2 mm. The period of unit is p = 5 mm. The size of the notched square ring on both surfaces is s = 4.8 mm. The top metallic layer is a square ring with notches symmetrically distributed on all four sides, and the notch length is g. The bottom metallic layer is four metal bars symmetrically distributed on the surface with length l. Due to symmetry, the frequency response of unit is dual-polarized. For convenience, we only discuss the frequency responses of unit for y polarization. The commercial software CST Microwave Studio is used for the simulation of frequency response.
Fig. 1. The configuration of Huygens’ unit cell. Yellow and brown colors manifest the top and bottom metallic layer. (a) 3-D view. (b) Side view.
Both the top and bottom metallic layer on the metasurface can be regarded as electric dipoles, with their own resonant frequencies. If the resonant frequencies of the two electric dipoles are not the same, the magnetic resonance in the structure can balance at most one of the electric resonances to stimulate a Huygens’ resonance, but not both. For this we choose the condition of “g + l = 4.4 mm” so that the top and bottom metallic layers have the same or similar resonant frequencies. Then the magnetic resonance in the structure is expected to balance both two electric resonance simultaneously. The transmission amplitude and phase spectra of unit are illustrated in Fig. 2(a) and 2(b). When l = 3.2 mm, we can see that a transmission peak appears at 26.5 GHz with |T| ≈ 0.92 and φT = 174°. Obviously, it’s a resonant transmission peak where impedance matching occurs between the electric dipole and the magnetic dipole. It should be point out that there is no separate magnetic dipoles component in the unit. The magnetic dipole essentially is induced by a current loop formed between the top and bottom metallic surfaces. Such effect is so-called induced-magnetism [55]. Induced magnetism makes the magnetic element super-latticed with electric element in one double-layer metallic unit, providing a more convenient route for the manipulation of broadband transmitted waves.
Fig. 2. (a) The transmission amplitude spectrum of the unit for different parameters. (b) The transmission phase spectrum for different parameters. (c) The transmission amplitude and phase shifts at 28 GHz.
The transmission peak shifts to lower frequencies with an increase of the length l or shifts to higher frequencies with a decrease of the length l. For example, the transmission amplitude is |T| ≈ 0.95 with φT = 173° at 27.7 GHz when l = 3 mm, and |T| ≈ 0.97 with φT = 178° at 25.1 GHz when l = 3.4 mm, etc. All the transmission peaks are resonant transmission because their transmission phases are near 180°. In results, around 28 GHz, the unit is always transparent for the parameters considered, and the continuously varying phases cover the value of 180°.
The transmission amplitude and phase of unit at 28 GHz as functions of the parameter l are illustrated in Fig. 2(c). On the one hand, when l = 2.95 mm, the peak value of transmission amplitude appears with the value of |T| ≈ 0.97 and φT = 180°. Near-perfect transmission is obtained. This is a resonant transmission caused by Huygens’ resonance. On the other hand, when l is varied from 0.4 to 4 mm, all the transmission amplitudes are greater than 0.83 and the transmission phase shifts about 320°. It is shown that near-full available transmission phase coverage at 28 GHz can be obtained by utilizing the Huygens’ resonance.
3. Design, implement and measurement of Huygens’ metasurface for OAM wave generation
To effectively generate the OAM transmitted waves, we built a space-fed antenna system combining a horn feed and a metasurface lens, as illustrated in Fig. 3. The horn feed source is placed directly above the Huygens’ metasurface which is used to radiate the spherical phase front of EM waves. The Huygens’ metasurface is used for efficient conversion of the spherical phase wavefront into a spiral phase wavefront. The distance between the feed source and the meta-lens is F.
Fig. 3. The sketch of the Huygens’ metasurface antenna system. The incident electric field marked by double E labels indicates dual-polarization.
To obtain the desired phase conversion, the phase compensation on metasurface can be divided into two parts. The first part is the focused phase compensation. In this part the spherical phase wavefront is converted into a planar phase wavefront. The second part is the OAM phase factor which presents the conversion of the planar phase wavefront into an OAM spiral phase wavefront. The phase compensation of metasurface on the first part is defined as φ1(m, n), which satisfies the following expression
where fc is the operating frequency, c is the speed of light in free space, and m (n) is the number of cells in the x (y) direction. The second part, i.e. the OAM phase factor, is defined as φ2(m, n) and satisfies the following expression where l is the OAM mode. The total phase compensation Δφ(m, n) is the sum of these twoIn the above design, we choose fc = 28 GHz, F = 128 mm and a square array with size of A = 135 × 135 mm2 (27 × 27 units). For clearly observing the effective generation of OAM transmitted waves, we only consider the mode of l = 1. The distributions of the focused phase compensation φ1(m, n), OAM phase factor φ2(m, n) with l = 1 and the total phase compensation Δφ(m, n) are calculated in Fig. 4(a)-(c) according to Eqs. (4)-(6), where Fig. 4(a) typically is a phase distribution of transmitarray and Fig. 4(b) is the phase distribution of OAM waves. In addition, It can be observed from Fig. 4(c) that there is a spiral phase distribution for the OAM beam with the mode of l = 1. The total phase distribution in Fig. 4(c) is the superposition of the classic transmitarray and the classical OAM phase. The actual phase distribution for the generation of OAM transmitted wave with the proposed Huygens’ unit is illustrated in Fig. 4(d). It can be seen that the results of Fig. 4(d) is similar with those of Fig. 4(c). Their difference is always maintained within the range of ±20°, which is shown in Fig. 4(e). Furthermore, the transmission amplitude distribution on the Huygens’ metasurface is in the range of -0.5 to -1.63 dB, which is illustrated in Fig. 4(f). Thereby, we can think that the proposed Huygens’ units can well meet the requirements of generation of OAM transmitted waves.
Fig. 4. Transmission phase and amplitude distributions of the designed Huygens’ metasurface at 28 GHz. (a) Focused phase compensation φ1(m, n). (b) OAM phase factor φ2(m, n). (c) The total phase compensation Δφ(m, n). (d) The actual phase distribution for the generation of OAM transmitted wave with the proposed Huygens’ unit. (e) The Difference between the actual phase distribution and the theoretical phase distribution. (f) The actual transmission amplitude distribution.
The generation of transmitted OAM vortex waves at 28 GHz using the Huygens’ metasurface is simulated in Fig. 5. It can be seen from Fig. 5(a) that this is a ring-shaped radiation pattern along the transmission direction with a deep null in its center. The gain of ring-shaped radiation reaches 24 dBi. On the other hand, there is a divergence angle in the ring-shaped pattern with a small value of ±3.6°, as shown in Fig. 5(b). Investigations have shown that the phase gradient in the radial direction is beneficial to decrease the divergence angle of OAM [59]. Here the focusing effect of Huygens’ metasurface gives rise to the phase gradient in the radial direction, effectively reducing the divergence angle of OAM beam. High gain and small divergence angle present good conversion performance of Huygens’ metasurface.
Fig. 5. (a) The simulated 3D far-field radiation for the generation of OAM transmitted vortex waves at 28 GHz. (b) the electric distribution (Ey) in E-plane.
Fig. 6. The simulated far-field transmission phase and amplitude distributions for generation of OAM transmitted waves with mode l = 1. (a), (b) and (c) are the phase distributions at 27, 28 and 29 GHz, and (d), (e) and (f) are the amplitude distributions at 27, 28 and 29 GHz, respectively.
In order to determine that the ring-shaped radiation pattern converted by Huygens’ metasurface is an OAM beam indeed, we further observe the simulated phase and amplitude distributions in the far-field region. We choose xoy plane at the distance of 450 mm (∼42λ at 28 GHz) from the metasurface in the transmission region, and the observed area is 240 × 240 mm2. The phase and amplitude distributions of the transmitted beams at 27, 28 and 29 GHz are simulated in Fig. 6. On the one hand, as illustrated in Fig. 6(a)–6(c), the phase distributions present the vortex shapes with total 360° phase changes. On the other hand, the amplitude distributions present the “doughnut” patterns with central singularity, which is given in Fig. 6(d)–6(f). The main features of the typical spatial wavefront for OAM beams with mode l = 1 are satisfied. The simulated results reveal that the proposed Huygens’ metasurface effectively generates an OAM transmitted vortex wave with mode l = 1.
For experimental verification, we implement this Huygens’ metasurface and measure its far-field radiated performance in a microwave anechoic chamber. The measurement environment is shown in Fig. 7. For determining the dual-polarized properties of this Huygens’ metasurface, the far-field radiated performance for both polarizations are measured. In the setup, a 15 dBi standard gain horn antenna is used as a feed source to illuminate the Huygens’ metasurface. A planar near-field measurement system is used to measure the phase and electric field intensity distributions of the transmitted wave. The area of the scanning plane is set to 210 × 210 mm2 with a measured step of 5 mm. The distance between the scanning plane and the metasurface is 450 mm.
The phase and amplitude distributions at 27, 28, and 29 GHz for both polarization, are shown in Fig. 8 and Fig. 9. It can be clearly seen that the measured results in both polarization cases are similar to the simulated results. The transmission phase distribution varies 360° clockwise around the center of metasurface. The amplitude distribution has a “doughnut” shape with an amplitude zero point at the center of array. These are the main features of the typical spatial phase wavefront of mode l = 1. From the measured results, it can be easily concluded that the designed Huygens’ metasurface can successfully generate dual-polarized OAM vortex waves of mode l = 1.
Fig. 8. The measured y-polarized far-field transmission phase and amplitude distributions for generation of OAM transmitted waves with mode l = 1. (a), (b) and (c) are the phase distributions at 27, 28 and 29 GHz, and (d), (e) and (f) are the amplitude distributions at 27, 28 and 29 GHz, respectively.
Fig. 9. The measured x-polarized far-field transmission phase and amplitude distributions for generation of OAM transmitted waves with mode l = 1. (a), (b) and (c) are the phase distributions at 27, 28 and 29 GHz, and (d), (e) and (f) are the amplitude distributions at 27, 28 and 29 GHz, respectively.
The simulated and measured results of far-field radiated patterns at 27, 28 and 29 GHz are given in Fig. 10. Because the dual-polarization properties of the metasurface have been verified in Fig. 8 and 9, here we just process the measurement for y polarization. At these three frequencies, the simulated and measured far-field radiated patterns are both split double-peak shapes. The simulated divergence angles at 27, 28, 29 GHz are 3.8°, 3.7°, 3.6° for E-plane, and 3.7°, 3.6°, 3.5° for H-plane, respectively. The corresponding measured values of divergence angles are 3.7°, 3.5°, 3.5° for E-plane, and 3.6°, 3.5°, 3.4° for H-plane, respectively. The simulated and measured peak gain at 28 GHz are 24 dBi and 23.4 dBi. The measured and simulated results are in good agreement, and the very narrow divergence angles present good directivities of the OAM vortex waves.
Fig. 10. The simulated and measured far-field radiated patterns. (a) 27 GHz. (b) 28 GHz. (c) 29 GHz.
The gains spectrum and the aperture efficiency for the OAM beam generation with Huygens’ metasurface are given in Fig. 11. The simulated and measured maximum gains are 24 and 23.4 dBi at 28 GHz, and the simulated and measured 3-dB gain bandwidth is 25.16∼29.3 GHz (14.8%) and 25.17∼29.2 GHz (14.8%). The measured and simulated results are in good consistent. In addition, the aperture efficiency is the ratio of the maximum effective area of the antenna to the aperture area, which is calculated through the expression η = Gλ02/(4πA) × 100%, where G is measured gain. The maximum of simulated aperture efficiency is 14.95%, and that of measured aperture efficiency is 10.97% at 28 GHz.
The important performance indicators of OAM beam generation in this work are compared with those of existing work. As shown in Table 1, multilayer FSS structures are used in most studies, which increases their fabrication and assembly cost [39,60–62]. Reference [63] reported a double-layer structure with vias for OAM beam generation, but its aperture efficiency is the lowest among these studies. Moreover, the OAM generation in most studies exhibit a large divergence angle, and the 3-dB bandwidth fails to provide. By comparison, our work exhibit the merits of small divergence angle, wide 3-dB bandwidth, the high aperture efficiency and the simplest structure. The OAM beam generation based on double-layer Huygens’ metasurface in this work has important value of engineering application.
Table 1. Comparison of existing OAM beam generationa
4. Conclusion
An ultrathin Huygens’ metasurface is proposed for efficient generation of dual-polarized OAM transmitted vortex wave with mode l = 1. By utilizing the induced magnetism, the Huygens’ resonance can be achieved on a double-layer metallic structure, which exhibits more convenient manipulation abilities of transmitted EM waves. The simulated and measured results verify the validity of generating the dual-polarized OAM transmitted vortex wave with this Huygens’ metasurface. The resulting OAM vortex waves has excellent radiation performance such as small divergence angle and high gain. We believe that the Huygens’ metasurface for OAM beam generation will greatly promote the engineering application of OAM vortex waves.
Funding
Innovation Project of Guangxi University of Science and Technology (GKYC202224); Key Program of Natural Science Foundation of Guangxi Province (2019GXNSFDA245011, 2021GXNSFDA220003); National Natural Science Foundation of China (62001102, 62071133).
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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