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Abstract
In this paper, a Luneburg lens-based multi-beam orbital angular momentum (OAM) antenna is proposed to achieve the 2D beam scanning capability of dual-mode OAM beams. The proposed design is composed of nine compact dual-mode antennas as sources, and a 3D-printed Luneburg lens. The sources, i.e., octagonal patch antennas, can radiate both right-handed circularly polarized (RHCP) and left-handed circularly polarized (LHCP) OAM beams with mode number l = ±1 by switching the input ports. Then, the sources are put at multiple focal points of the Luneburg lens to generate the OAM beams in different directions, and the directivities of the OAM beams are also enhanced by the Luneburg lens. The proposed design can realize nine dual-mode OAM beams with ±30° beam scanning range in two orthogonal planes. It should be noted that the proposed design can be expanded to achieve a larger number of beams with a periodic extension of the source antennas, also a wider beam scanning range with a Luneburg lens of a larger radius.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the growing requirements of spectral efficiency and channel capacity in wireless communication, the generation of microwave vortex beams with orbital angular momentum has been widely studied to achieve different radiation characteristics in the recent decade, e.g., multi beams [1–8], active and passive OAM modes switching [9–17], and transmission–reflection integration [18,19]. However, the beam scanning capability of the OAM is rarely discussed. The inherent hollow of the OAM beams will limit the field coverage range. Hence, integrating the beam scanning capability with the OAM beam is an effective method to ensure the coverage of OAM communication.
In order to achieve steerable OAM beams, the phased array is a convenient solution [20–22]. The flexible phase and amplitude modulation of the transmit/receive (TR) components can realize arbitrary wavefronts. However, the high cost of the TR components makes phased arrays hard to be used for commercial applications, especially for a large-size array. To realize the OAM beam scanning capability without TR components, several passive beam scanning methods have been proposed, e.g., bifocal transmitarray and reflectarray [23–25], multi-beam antenna [26], leaky-wave antenna [27], and reconfigurable metasurface [28,29]. In [24], a bifocal transmitarray is designed based on the combination of the bifocal principle and the OAM beam phase distribution, where the sources at different positions can excite the OAM beam in different directions. The transmitarray can achieve good OAM beam scanning performance, but the sidelobe level (SLL) and the mode purity are not ideal for large-angle beam scanning. In [26], a planar pillbox reflector based multi-OAM beam antenna is designed with the linear OAM beam scanning ability, where the OAM beam is realized by the slotted waveguide antenna and dielectric phase elements, and the beam scanning capability is provided independently by the pillbox reflector. Similar to the bifocal transmitarray, the switching of the sources will realize the OAM beam scanning. The compact full-metal guide wave structure of the pillbox reflector can achieve extremely high radiation efficiency, but the antenna cannot achieve the 2D beam scanning capability, due to the limitation of the planar pillbox beam forming network (BFN). The SLL and the beam scanning range of the design are also limited. For the above passive steerable OAM beam generations, the required phase distribution of the OAM beams is realized by the array factor. The multiplication of the steered OAM array factor and the element factor will generate the steered OAM beam with a large SLL for the passive OAM beam scanning designs, as shown in Fig. 1(a), which will reduce the directivity and degenerate the mode purity of the OAM beam, thus increasing the interference.
Fig. 1. Schematic diagram of (a) the OAM beam scanning method based on array factors; (b) the OAM beam scanning method based on element factors in the proposed design.
To overcome this limitation, a Luneburg lens-based topology is proposed in this paper to realize the steerable OAM beams with stable sidelobe levels and high mode purity, as shown in Fig. 1(b). In the proposed design, the vortex radiation characteristic is provided by the compact source antenna. The Luneburg lens is used to achieve the passive beam scanning capability and gain enhancement, and its spherical structure could steer the beams with almost identical performance when fed by source antennas at different positions. It should be emphasized that the compact source is the key point of the proposed design, i.e., an octagonal patch antenna, and its two resonant modes are combined with a phase shift to achieve the OAM beams. Furthermore, by switching the input ports of the antenna, different phase combinations are applied to achieve OAM beams with mode number l = ±1. The combination of the compact source antennas and the Luneburg lens achieves good OAM beam scanning capability, low SLL, and high purity. To verify the performance of the proposed design, a prototype with nine source antennas is fabricated and positioned at different focal points of a 3D-printed Luneburg lens. Then the beam scanning range is simulated and measured, which demonstrates its capability for future OAM communications and sensor systems.
2. Design procedure
The schematic diagram of the proposed design is shown in Fig. 2, composed of nine dual-mode OAM source antennas and a 3D-printed Luneburg lens, where the sources are placed at different positions on the focal plane of the lens, thus it can generate the dual-mode OAM beams in different directions. Two layers of B300A (εr = 3.0, tanδ = 0.0015) printed circuit boards (PCBs) with the thickness of 0.762 mm (top) and 0.508 mm (bottom) are used as the substrates of the source antennas. The Luneburg lens is manufactured by stereo lithography apparatus (SLA) 3D printing technology, using SPR6000B (εr = 2.8, tanδ = 0.002) as material.
2.1 Operating principle of the source antenna
To achieve the OAM beams by a compact source antenna, two resonant modes of an octagonal patch are excited simultaneously, which is inspired by [30]. Characteristic mode analysis (CMA) is used to analyze the operating characteristics of the octagonal patch, and the simulated current distributions of the first six modes of the octagonal patch antenna are presented in Figs. 3. It can be seen that the currents of Mode1 and Mode2 concentrate on the edges of the patch and the resonant modes have eight-fold symmetry. The simulated modal significances and characteristic angles of the first six modes are shown in Figs. 4. The results show that Mode1 and Mode2 have almost exactly the same modal significance and characteristic angle, due to their 45° rotational symmetry. Hence, Mode1 and Mode2 can be excited at the same frequency with the same characteristic angles.
Fig. 3. Current distribution of the first six modes of the octagonal patch antenna at 5.8 GHz. (a)-(f) Mode1-Mode6
Fig. 4. (a) Modal significances and (b) characteristic angles of the first six modes of the octagonal patch antenna.
Next, to realize the required OAM source, Mode1 and Mode2 are excited with a phase difference of 90°, as shown in Fig. 5 (a) to (c). The orthogonal and parallel decompositions of the currents in Fig. 5(c) are shown in Fig. 5(d), where the reintegration of the orthogonal current distribution on the edges is shown in Fig. 5(e). It can generate eight LHCP current distributions with the same phase but different rotation angles, as shown in Fig. 5(f). Consequently, the LHCP current distributions in Fig. 5(f) can be regarded as different phases, thus generating the l = -1 OAM beam, as shown in Fig. 5(g). Similarly, the octagonal patch can also generate the l = + 1 RHCP mode OAM beam by combining Mode1 and Mode2 with a phase difference of -90°, due to its symmetry. However, it should be emphasized that different current decomposition methods of Mode1 and Mode2 will generate a magnitude difference. As shown in Fig. 5(c) to Fig (d), the current of Mode1 is decomposed into two parallel components, while the current of Mode2 is decomposed into two orthogonal components, which will undesirably increase the cross-polarization and thus deteriorate the mode purity of the OAM beam. Hence, the excitation magnitudes of Mode1 and Mode2 should be optimized in the antenna feeding network design.
Fig. 5. Analysis of the OAM beam generation. (a) Current of Mode1 with 0° phase; (b) current of Mode2 with 90° phase; (c) combination of Mode1 and Mode2 with a phase difference of 90°; (d) orthogonal decomposition of the currents; (e) reintegration of the orthogonal currents; (f) LHCP current distributions with the same phase but different rotation angles; (g) LHCP current distributions with different phase differences (generating the required OAM beam).
2.2 Design of the source antenna feeding network
Based on the combination of Mode1 and Mode2, the octagonal patch can generate the OAM beams with modes l = ±1. Next, a compact antenna feeding network is designed to excite the beams. The schematic diagram of the source antenna is presented in Fig. 6(a). The antenna is composed of two-layer substrates. The ground layer is located in the middle of the two substrates. The octagonal patch is placed on the top substrate, fed by a coupler, and two power dividers on the bottom substrate. The power dividers are used to generate the balanced excitation of Mode1 and Mode2 for symmetric radiation patterns. The balanced excitation can suppress Mode3 and Mode4, which have the modal significances around 0.1, thus guaranteeing the mode purity of the OAM beams. For Mode5 and Mode6, the minor modal significance (below 0.02) will not affect the mode purity. Next, to excite Mode1 and Mode2 with ±90° phase difference, a coupler is used to feed the two power dividers. Hence, the switching of input ports of the coupler can excite the OAM beams with modes l = ±1. The meander microstrip line between the coupler and the power divider is designed to guarantee the same phase delay from the output ports of the coupler to the power dividers. It should be noted that the sizes of the coupler are optimized to compensate for the magnitude difference for the decomposed components, as we discussed at the end of Session 2.1. The geometric relationship of the octagonal patch and the antenna feeding network is shown in Fig. 6(b), and the parameters are summarized in Table 1.
Fig. 6. (a) Schematic diagram and (b) geometric relationship of the source antenna and the feeding network; (c) simulated S-parameters of the source patch antenna.
Table 1. Dimensions of the proposed design. (Unit: mm)
The simulated S-parameters of the source antenna are shown in Fig. 6(c). It can be seen that the -10 dB isolation coefficient is approximately 75 MHz at the center frequency of 5.8 GHz and the reflection coefficients of the input ports are below -17.9 dB. In fact, the bandwidth of the source antenna depends on the bandwidth of the two presented resonant modes. However, the application of the coupler results in that the reflected currents from the two output ports of the coupler will be in-phase added to the input ports when the operating frequency is off the bandwidth of the patch, thus generating poor isolation. To further illustrate the performance of the source antenna, the simulated phase and magnitude of the 2D U-V coordinate system radiation patterns are presented in Figs. 7. The relationship between the Cartesian coordinate system and the U-V coordinate system is as follows:
Fig. 7. Simulated magnitude of the 2D co-polarized radiation patterns excited by (a) Port1; (d) Port2; simulated magnitude of the 2D cross-polarized radiation patterns excited by (b) Port1; (e) Port2; simulated phase of the 2D co-polarized radiation patterns excited by (c) Port1; (f) Port2.
The required phase and magnitude distributions of OAM beams with l = ±1 can be clearly observed in Fig. 7(a), (c), (d) and (f). The simulated cross-polarizations of the source antenna are shown in Fig. 7(b) and (e). The maximum cross-polarization is below -15.0 dB within the 3 dB beamwidth of the OAM beams in the azimuth planes. The results prove that the source antenna can achieve the dual-mode OAM radiation characteristic with low cross-polarization and a compact structure.
2.3 Design of the Luneburg lens and the multi-OAM beams
In order to achieve the passive OAM beam scanning capability, a spherical Luneburg lens is used as the multi-beam beamforming network. The Luneburg lens is a spherical device with a refractive index that varies continuously in the radial direction. The refractive index distribution of the Luneburg lens [31] is as follows:
where R is the radius of the lens and r is the distance in the radial direction. Since the continuous refractive index variation is hard to achieve for practical applications, several 3D-printed cylindrical [32,33] and spherical [34–37] Luneburg lenses with discrete refractive index distribution are proposed to achieve the passive beam scanning capability, but they are not suitable for the proposed design, due to the fact that the lens unit needs to be 90° rotational symmetry to ensure the same phase variation of the horizontal and vertical fields. The schematic diagram of the Luneburg lens is shown in Fig. 8(a). The lens is composed of ten-layer lens units with an equivalent refractive index of 1.414 to 1.087. The selection of the layer number mainly depends on the precision of the 3D printer, which is 0.1 mm in our implementation. In the Luneburg lens design, more lens layer numbers can achieve better focusing characteristic of the Luneburg lens with the constant radius. However, if more layer numbers are used, the size of the lens unit will be decreased, and the 3D printer will be difficult to distinguish the position of air and resin, thus introducing extra error. The lens unit is realized by three mutually orthogonal cuboids with a cube at its center. The length of the lens unit is below 0.2λ0. The sub-wavelength lens unit can guarantee the approximately isotropic equivalent refractive index. Different sizes of the center cube can change the equivalent refractive index of the lens unit, which is extracted by the periodic simulation, as shown in the top right of Fig. 8(a). The simulated refractive index of the proposed ten-layer Luneburg lens is presented in Fig. 8(b). It can be seen that the simulated results and the ideal refractive index fit well. The parameters of the lens units are summarized in Table 1.Fig. 8. (a) Schematics of the 3D-printed Luneburg lens and the lens unit; (b) refractive index of the ideal Luneburg lens and the proposed 10-layer Luneburg lens.
Next, nine source antennas are placed at different focal points of the Luneburg lens, the distances between the center of the Luneburg lens and the source antennas are 110.0 mm. The relative position between the source antennas and the Luneburg lens is shown in Fig. 9. The input ports RP1 to RP9 and LP1 to LP9 are marked on the left of Fig. 9. The included angles between the adjacent sources are 30° both in elevation and azimuth planes. It should be noted that the phase center of the source antenna is located at the focal points of the Luneburg lens to achieve the ideal conversion from a spherical wave to a plane wave. However, the OAM beam does not have the equivalent phase center, due to its anisotropic phase distribution. Hence, the aperture of the proposed OAM source antenna should be sufficiently small to guarantee that the circularly polarized currents in Fig. 5(g) are almost concentric. Then, the circularly polarized currents can be regarded as being positioned at the focal point, thus achieving the gain enhancement of the OAM beam.
The simulated magnitude and phase of the 2D radiation patterns with l = + 1 are shown in Figs. 10 and Figs. 11. The results prove that the proposed design can achieve the dual mode OAM beams with ±30° beam scanning range in both elevation and azimuth planes. In addition, the antenna can be expanded to achieve more beams and larger directivity, due to its periodic topology.
Fig. 10. Simulated magnitude (a)-(i) and phase (j)-(r) of the 2D radiation patterns with mode l = + 1, excited by input ports RP1-RP9.
Fig. 11. Simulated magnitude (a)-(i) and phase (j)-(r) of the 2D radiation patterns with mode l = -1, excited by input ports LP1-LP9.
3. Fabrication and measurement
To verify the performance of the proposed design, an antenna prototype is fabricated and measured. The fabricated source antenna and the 3D-printed Luneburg lens are shown in Fig. 12(a) and (b). The assembled antenna prototype is shown in Fig. 12(c). A 3D-printed fixture is used to place the source antennas in the appropriate positions. The planar near-field antenna measurement environment is presented in Fig. 12(d).
Fig. 12. Schematics of the (a) source antenna; (b) 3D-printed Luneburg lens; (c) assembled antenna prototype; (d) planar near-field antenna measurement environment.
The simulated and measured S-parameters are compared in Figs. 13. The results are partially presented due to the symmetric design. It can be seen that the measured -10 dB isolation bandwidth of a source antenna is from 5.77 to 5.86 GHz. The isolations between adjacent sources are larger than 23.5 dB, which proves good isolation between the beams in different directions. The slight frequency offset of the simulated and measured results should result from the minor fabrication error, e.g., the air gap between the top and bottom PCBs. The air gap can be regarded as an open cavity, which can generate an extra loss to the source antenna, thus reducing the value of the isolation coefficient. Moreover, the air gap will also introduce a reflection to the input port, and change the reflection coefficients. For the isolation between the adjacent source antennas, the fabrication error can slightly affect the resonant frequencies of the source antennas, thus affecting the isolations.
Fig. 13. Simulated and measured (a) S-parameters of the source antenna; (b) isolation between the adjacent source antennas.
The simulated radiation patterns of ports RP4 to RP6 and LP4 to LP6 are shown in Figs. 14 and Figs. 15 at 5.8 GHz. The results show that the proposed design can achieve ±30° beam scanning range with a gain of approximately 13.5 dBi for both RHCP and LHCP beams. The axial ratio of the beams is below 3 dB within the 3 dB beamwidth of the steered beams. Moreover, the SLLs of the steered beams are stably below -9.8 dB, which is much better than the array factor based multi OAM antenna designs [23–29].
Fig. 14. Simulated and measured (a) radiation patterns; (b) axial ratio of the RHCP beams in the horizontal plane.
Fig. 15. Simulated and measured (a) radiation patterns; (b) axial ratio of the LHCP beams in the horizontal plane.
The measured near-field magnitude and phase distribution of the OAM beams are shown in Figs. 16 and Figs. 17. The near-field measurement setups are shown in Figs. 18. In the measurement environments, the antenna is rotated for the corresponding angle (e.g. 30° in the azimuth plane and 30° in the pitch plane for RP7 and LP7) to ensure that the probe can receive the field distribution with the same distance. Hence, the hollow energy rings of the steered beams are also located in the center of magnitude intensity planes. The size of the reference plane is 400 mm × 400 mm, and the distance between the antenna and the reference plane is 250 mm. Due to the symmetric structure of the proposed design, the results of ports RP1 to RP4 and RP8 to RP9 are omitted, the same rules apply to the LHCP ports. The measured results show the RHCP and LHCP ports can excite the clockwise and counterclockwise phase distributions, thus proving that the OAM beams are realized. In order to quantify the purity of the OAM beams, the Fourier transform is used to decompose the OAM beams into different OAM modes [38,39]. The decomposition method is shown as follows:
Where Al is the Fourier coefficient of the OAM beams with mode number l, ψ(φ) is the discrete E-field distribution along the circumference of the OAM beam’s null location, and the E-field distribution is the maximum value along the radius direction. In the purity calculation, the OAM beams with mode number l = −2 to 2 are considered. The purity of the OAM mode l is defined as follows:Fig. 16. Measured magnitude distribution of the OAM beams with mode l = + 1, excited by input ports (a) RP5; (b) RP6; (c) RP7, measured phase distribution of the beams excited by (d) RP5; (e) RP6; (f) RP7.
Fig. 17. Measured magnitude distribution of the OAM beams with mode l = -1, excited by input ports (a) LP5; (b) LP6; (c) LP7, measured phase distribution of the beams excited by input port (d) LP5; (e) LP6; (f) LP7.
Fig. 18. Near-field measurement setups for (a) LP5 and RP5; (b) LP6 and RP6; (c) LP7 and RP7 excitation.
The purity of the measured OAM beams is shown in Figs. 19. It can be seen that the purity is larger than 0.68 for the steered beams. In the antenna measurement, direction alignment can greatly affect the measured phase and magnitude distribution of the OAM beams, thus affecting the purity calculation. Hence, the purity of RP6, RP7, LP6, and LP7 is not as good as the center ports RP5 and LP5, but the measured result can prove that the proposed design is feasible.
Fig. 19. Purity of the measured OAM vortex beams excited by input ports (a) RP5 to RP7; (b) LP5 to LP7.
To highlight the advantages of the proposed design, several existing OAM antennas are compared with the proposed design in Table 2. It can be seen that the active transmitarray based designs [40,41] can achieve the multi OAM mode and beam switching. However, the loss of the diodes will greatly limit the transmission efficiency of the transmitarray unit, thus limiting the gain of these designs. The bifocal OAM transmitarray [24] and multi-beam antenna [26] based on frequency-independent quasi-optical mechanism can achieve the steered OAM beams with relatively wide operating bandwidth, but their phase modulation methods make them hard to achieve mode switching and 2D beam scanning. For the frequency scanning leaky-wave OAM antennas [27,43], the mode switching and beam scanning capabilities can be achieved. However, the frequency beam scanning characteristic is not suitable for most communication applications. Moreover, it should be noted that the beam scanning capability of all the previous designs is realized by their array factors. Hence, the SLLs of the referred designs are not ideal for the steered beams. In contrast, the proposed design can realize the 2D OAM beam scanning capability, low SLL, and dual OAM mode switching simultaneously, due to its element factor and Luneburg lens based OAM beam generation topology.
Table 2. Performances of the proposed antenna and the previous OAM antenna designa
4. Conclusion
In this paper, a dual-mode multi-OAM-beam antenna is proposed. By combining the compact dual mode (l = ±1) OAM source antennas and a spherical Luneburg lens, the proposed design can achieve the passive dual mode OAM beam scanning. The novelty of this design lies in the generation of l = ±1 mode OAM beams using a compact source antenna, which greatly helps to achieve the source miniaturization. The proposed design can be easily expanded to achieve more beams and directivity due to its periodic structure. The advantages of the proposed design include low cost, passive beam scanning capability, and high extensibility, making it a suitable candidate for future wireless OAM communication and sensor applications.
Funding
National Key Research and Development Program of China (2019YFB1803205); Key Research and Development Projects of Shaanxi Province (2022GY-114).
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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