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Abstract
Recently, considerable attention has been focused on orbital angular momentum (OAM) vortex wave, owing to its prospect of increasing communication capacity. Here, a single-layer metasurface is proposed to realize vortex beams with different OAM modes and polarizations carried at two distinctive bands. Both the resonant and geometric (Pancharatnam–Berry) phase cells are adopted to construct this metasurface for generating the desired phase profile, and each type of phase modulation cell can independently control the vortex beam at different frequencies. When a linearly-polarized wave is incident onto our metasurface, the resonant phase cells with spiral phase distribution can achieve OAM beam with topological charge of + 1 at 5.2 GHz. And under illumination of left-handed circular polarized (LHCP) wave, the rotated geometric phase cells assist the metasurface to generate the deflected OAM beam with topological charge of + 2 at 10.5~12 GHz. Both simulated and experimental results demonstrate good performance of the proposed single-layer metasurface at the above two frequency bands.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Orbital angular momentum (OAM) carried by vortex wave has attracted considerable interest due to its excellent performance and various application in optics and communication fields [1–10]. The OAM technology carries information on the phase distribution of electric field, which contains theoretically unbounded eigenstates. Since the eigenstates of OAM are mutually orthogonal to each other, using OAM can significantly improve the transmission capacity of optical communication system. So far, there have been many approaches to generate OAM wave, including spiral phase plate (SPP) [11,12], spiral parabolic antenna and circular antenna array [13–15]. More recently, metasurfaces based on catenary and other structures have been reported to generate vortex waves successfully, providing a novel route to achieve OAM beam [7,16–22]. Compared with the traditional methods above, metasurfaces have obvious advantages such as ultrathin profile, light-weight, and easy-fabrication, especially in the radio frequency domain [23–27].
Metasurface is generally composed of sub-wavelength cells that could tailor the wavefront of the incident EM wave by introducing abrupt phase changes across the interface [16,19]. By special design of phase distribution on the metasurface, the propagation direction of EM waves could be manipulated at will based on the generalized Snell’s law. This property promises a number of applications such as waveplates [28], flat lens [29,30], ultrathin cloak [31], orbital angular momentum generations [17–27] and low-scattering materials [32,33], etc. Typically, there are two approaches to modulate local phase with metasurfaces. One is based on the resonant phase modulation [34,35], which changes the phase information by varying the structural parameters of the meta-atoms. However, it usually leads to a narrow bandwidth due to the intrinsic dispersion of resonant meta-atoms. The other is the geometric phase modulation that is also called as the Pancharatnam–Berry (PB) phase modulation [36]. It can achieve the phase control with the rotation of the meta-atoms, and dispersionless phase responses can be obtained under illumination of circularly-polarized (CP) waves [18]. Numerous OAM beam generators based on metasurfaces have been proposed by using the resonant phase or PB phase modulation method [17–27]. Some researchers have also started to pay attention to the multiple OAM modes [37–41]. In [37], the shared-aperture antenna array concept was used to design the metasurface that is divided into subarrays (each subarray composed of particular PB phase cells supports a different OAM mode) for achieving the multiple OAM modes. However, since each subgroup only uses part of the metasurface aperture, the aperture efficiency is not high. In [38], the resonant phase cell was adopted to construct a single-layer metasurface for realizing two different OAM vortex waves in different directions. However, it is found that the existing multiple OAM metasurfaces are mainly limited to one frequency band. So the work in this paper focuses on the realization of the multiple OAM modes at two frequency bands. Here, we combine the resonant phase and PB phase cells into one single-layer reflective metasurface to generate the vortex beams at two microwave bands. By independently designing the resonant phase and PB phase distributions, the proposed metasurface is expected to achieve vortex beams with different OAM modes. Different from the subarray structure in [37], two kinds of the phase modulation cells are closely integrated into one meta-atom, and then they can use the whole metasurface aperture to realize the OAM beam at both two frequency bands. In addition, the reflected beam directions can be further controlled with additional phase modulation. This single-layer metasurface is numerically investigated, which shows that a + 1 mode OAM beam is generated at 5.2 GHz under illumination of linearly-polarized (LP) wave, while a + 2 mode OAM deflected beam is obtained at 10.5-12 GHz in response to incident CP wave. This vortex metasurface is fabricated, and the experimental results show good agreements with the simulation ones.
2. Theoretical design and analysis
Figure 1 shows the schematic model of the proposed vortex metasurface. Two kinds of metallic patterns made of 17μm thick copper are etched on one F4B substrate (h = 3 mm and ɛ = 2.65) backed by a ground plane. The I-shape pattern is used to construct the resonant phase cell, and by tuning its geometrical structures, different reflection phase can be obtained. Here, eight different topological patterns corresponding to eight different reflection phases are designed. The varying structure parameters including S, g1 and g2 are respectively listed in Table 1, while the left parameters are fixed as l = 10 mm, w1 = 0.2mm and w2 = 0.4mm.
Table 1. Structure parameters of the eight I-shape topological patterns.
The rectangular patch is adopted as a PB phase cell, and its parameters are set as a = 7.5mm and b = 4mm. When it is illuminated by a CP wave, a linearly varying phase shift range from 0 to 2π can be achieved by rotating the phase cell. The period of the whole unit cell is p = 12mm. In order to investigate the reflection characteristic of this vortex metasurface, numerical simulation is carried out by using CST Microwave Studio. The periodic boundaries are set to x and y sides, while the plane wave with different polarizations is incident onto the meta-atom.
Figure 2(a) shows the reflection magnitude and phase information of all the I-shape topological patterns. At this case, the meta-atom is illuminated by a LP wave, while the rotation angle of the PB phase cell is fixed as 60°. It is seen that all the topological cells have high reflectivity and their reflection losses are less than 0.2 dB. The reflection phase difference between each topological cell is about 45° at 5.2GHz, as shown in the inset of Fig. 2(a). To ensure independent operation of the resonant and PB phase cells, weak coupling is required between them. Here, we discuss the influence of the varying rotation angles of the PB phase cell on the reflection characteristic of the topological pattern 1 for the resonant phase cell. As Fig. 2(b) shows, the reflection magnitude and phase of the I-shape structure has no obvious variation when the rotation angles of the PB phase cell is varied from 0°to 150° with a step of 30°. Figure 2(c) presents the reflection characteristics of the PB phase cell with varying rotation angles under incidence of left-handed circular polarized (LHCP) wave. It is found that the incident LHCP wave is transformed into right-handed circular polarized (RHCP) wave at a wide band ranging from 10.5 GHz to 12.0 GHz where most of the reflection losses are less than 1 dB. In addition, the near-parallel phase response is obtained, which could be modulated from 0 to 360 degree with the rectangular patch rotating from 0 to 180 degree, as shown in the inset of Fig. 2(c). When changing the topological I-shape patterns from number 1 to number 8, we can see in Fig. 2(d) that the reflection phase of the PB phase cell is almost unchanged and its reflection loss variation is very weak, indicating that the resonant phase cell and PB phase cell has little crosstalk with each other.
Fig. 2 The reflection characteristics of the meta-atom at different situations. (a) The magnitude of the eight I-shaped topological patterns under LP incidence. Inset shows the reflection phase can almost cover 0° to −315° at 5.2 GHz. (b) The magnitude and phase of the I-shaped structure with topological pattern 1 for different rotation angles of the PB phase cell. (c) The magnitude of the cross-polarization components for the PB phase cells under LHCP incidence, while the rotation angle is changed from 0° to 150°. Inset shows the reflection phase can cover 0° to −360°. (d) The magnitude and phase of the PB phase cell with the rotation angle of 60° for the different I-shaped topological patterns.
Using the proposed metasurface cell, the vortex beams could be expected at two frequency bands via ingenious design of phase distribution. For generation of spiral phase profile, the phase shift of each point (x, y) should satisfy the relationship with the azimuthal angle around the center as
where l is the desired OAM mode number. Considering the influence of the feed source location, we add a converging phase profile to the spiral wave front, which can be written aswhere the incident wavelength is λ, and rf represents the distance between the feed horn and our metasurface. Therefore, the phase distribution of the resonant phase cells can be expressed as .If we need to deflect the vortex beam produced by the PB phase cells, an additional phase gradient along x-direction should be added to , and thus the total phase modulation at the higher band can be written as . Here the deflection angle of θ is set as 14 degree, so the additional phase gradient of according to the equation of .
To validate the OAM beam performance of our metasurface, an OAM-generating design with mode number + 1 is achieved with the resonant phase cells, while the PB phase cells take responsible for the generation of OAM beam with mode number + 2. As long as the above two kinds of the phase modulation cells satisfy the calculated phase distribution shown in Fig. 3, the dual-band OAM beams with different modes could be expected by our metasurface.
Fig. 3 Phase distribution and the calculation process for OAM generator at two separated bands. (a)The calculation process and phase distribution of our metasurface for generating + 1 mode OAM beam at f1 (5.2GHz) under y-polarized incidence. (b) The calculation process and phase distribution of our metasurface for generating + 2 mode OAM beam at f2 (10.5GHz) under LHCP incidence.
Next, all the phase modulation cells are designed to construct the desired phase profiles calculated above. Full-wave simulation is performed to investigate our vortex metasurface at the lower frequency band. The whole metasurface is designed to be composed of 41 × 41 meta-atoms and the overall dimension is 492 × 492mm2. The LP horn antenna (LB-187-15-C-NF, A-INFO.inc [42]) working at 3.9~5.9 GHz is set as the feeding source that is placed at a distance of 0.5m away from the metasurface. Figure 4(a) shows the far-field radiation pattern. There is an obvious OAM beam generated at 5.2 GHz, and the amplitude null caused by the phase singularity exists at its central region. From the near-field phase distribution shown in Fig. 4(b), it is found that the major feature of the spiral phase distribution is obtained, and its phase characteristics of topological charge l = + 1 is easily recognized. For the other OAM beam generated at the higher frequency, the vortex metasurface is illuminated by a LHCP plane wave. A vortex feature can be recognized from the far-field pattern displayed in Fig. 4(c), and the reflected beam is obviously deflected from the normal, and its outgoing angle is redirected towards about 14.0° at 10.5 GHz. The simulated phase distribution given in Fig. 4(d) shows the similar phase characteristic with the theoretically calculated result in Fig. 3(b). To characterize the efficiency of our device, we analyze the mode purity of the generated OAM beams based on the simulated phase profile given in Figs. 4(b) and 4(d). Generally, the purity of the optical vortex is calculated by decomposing its complex field on a complete basis set of optical modes with angular momentum, i.e. the Laguerre-Gaussian modes () [21,43]. In our metasurface, the mode purity for topological charge l = + 1 vortex beam at 5.2GHz is calculated to be 65%, and some phase noise is generated at other modes as shown in Fig. 5(a). The imperfect mode purity at 5.2GHz is mainly due to the quantization loss caused by the discrete I-shaped phase cells. For the PB phase cell, we can obtain arbitrary reflection phase value by tuning its rotating angle, and so the generated l = + 2 vortex beam OAM beam has higher mode purity that is about 83% at 10.5GHz as depicted in Fig. 5(b).
Fig. 4 Simulation results of the proposed vortex metasurface at two frequency bands. (a) Far-field pattern and (b) near-field phase distribution in the xoy plane of the vortex metasurface under normal incidence of the LP horn at f1 (5.2GHz). (d) Far-field pattern and (e) near-field phase distribution in the xoy plane of the vortex metasurface illuminated by LHCP plane wave at f2 (10.5GHz).
In order to verify the broadband behavior of the designed metasurface at the higher frequency band, the simulated far-field patterns at 10.5, 11, 11.5 and 12 GHz are respectively presented in Fig. 6. Each of the generated vortex beams exhibits an amplitude null across a wide band at its central region. Compared with the scattering magnitude of the LHCP wave at each frequency, the magnitude of the corresponding RHCP reflection patterns is much higher, indicating the excellent polarization conversion ratio. In addition, the topological charge l = + 2 can be easily observed from the phase profile of all the deflected OAM beams.
Fig. 6 Far-field patterns of the vortex metasurface illuminated by LHCP wave at 10.5~12GHz. (a) Cross-polarized component and (b) Co-polarized component. The incident LHCP wave is transformed into RHCP outgoing wave, and all the generated vortex beams are deflected from the normal when the observation direction is along -z axis. (c) Phase information pattern. The topological charge of l = + 2 can be distinguished from the phase profile, when the observation direction is set along the deflection direction.
3. Fabrication and measurement
To demonstrate the proposed vortex metasurface in experiment, we fabricate it using printed-circuit-board technology, as seen in Fig. 7(a). Two LP horns (LB-187-15-C-NF, A-INFO.inc) connected to a vector network analyzer are set as receiver and transmitter, respectively. The transmitting horn is placed at a distance of 0.5 m in front of the metasurface sample. Both the sample and the horn are fixed on a rotating equipment. When rotating the equipment, the sample is always illuminated by the normal incident wave produced by the transmitting horn. The reflected wave for the (- 90° to + 90°) rotating angles can be received by the receiving horn antenna. The measured far-field patterns are shown in Fig. 7(b), which also includes the simulation results as comparison. The amplitude null can be clearly seen at the center of the vortex beam. Compared with the simulation results, the measured amplitude in the center becomes high, which may be caused by the fabricated tolerance and the imperfection between the simulation and measurement environment. In order to measure the vortex characteristic of the sample at the higher frequency, the two LP horns are replaced by one pair of LHCP and RHCP horns, and using the same measurement method described above, we can obtain the OAM beam performance of the sample. Figures. 7(c)-7(f) shows the simulated and measured far-field patterns of the generated OAM beam. With modulation of the PB phase cells, the LHCP incident wave is converted into the RHCP wave at 10.5-12 GHz, and the deflection of the vortex beam can be clearly recognized, as seen in Figs. 7(c) and 7(e). The measurement results are in agreement with the simulation ones. The far field patterns of the LHCP waves are also measured, as seen in Figs. 7(d) and 7(f). The intensity of the LHCP field is relatively much lower than that of the RHCP field, and the cross-polarization suppression exceeds 15 dB. The magnitude and phase information of the two vortex beams were also measured at 5.2GHz and 10.5GHz by the near-field planar scanning technique. The vertical component of the reflected electrical field Ev was detected by using a standard measuring probe, as seen in Fig. 8(a). The near-field sampling plane is set at a distance of 3.0m away from our sample, and the reflected field magnitude and phase were measured on the sampling plane. To observe vortex phase information, the sampling plane is set to be perpendicular to the outgoing vortex beam. So when measuring the vortex beam generated at 10.5 GHz, the sample is rotated by 14° to keep the scanned surface perpendicular to the vortex beam. The sampling grid period is set as 20 mm at 5.2 GHz and 10mm at 10.5GHz. It is seen in Fig. 8(b) that the two doughnut-shaped field intensity maps are obtained at both 5.2 and 10.5 GHz. In addition, the major feature of the spatial phase distribution for the + 1 mode and + 2 mode vortex beams can be also identified in Fig. 8(c), although there is a little phase distortion in the center of the vortex beam because of the shielding effect of the feeding horn in front of the sampling plane. Therefore, the proposed single-layer metasurface has been verified to generate the two vortex beams with different OAM modes at two frequency bands.
Fig. 7 (a) Photography of the fabricated vortex metasurface. (b-f) Measured and simulated far-field radiation patterns of the vortex metasurface. (b) Co-polarized component under LP incidence at 5.2 GHz. (c, d) Cross-and co-polarized components under LHCP incidence at 10.5GHz and (e, f) Cross-and co-polarized components under LHCP incidence at 12GHz.
Fig. 8 Measured magnitude and phase distributions by near-field planar scanning technique (a) Near-field planar scanning setup and the standard measuring probe. (b) Measured magnitude distributions of the vortex beams at 5.2GHz and 10.5GHz. (c) Measured phase distributions of the vortex beams at 5.2GHz and 10.5GHz.
4. Conclusion
In summary, we have proposed a single-layer metasurface which can generate two vortex beams with different OAM modes at 5.2 and 10.5-12 GHz. Two types of phase modulation cells are adopted to construct the whole vortex metasurface, and each type of phase modulation cell takes responsible for the generation of one OAM mode. Both the simulated and experimental results show good performance of our vortex metasurface. Since all the phase cells are printed on one single-layer dielectric substrate, it is a convenient and low-cost way to generate beams carrying OAM at two separated bands. The proposed method could be developed for potential application in radio and microwave wireless communications.
Funding
National Natural Science Foundation of China (NSFC) (61475160, 61605213, 61775218).
Acknowledgments
Chen Ji and Jiakun Song contributed equally to this work.
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