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Abstract
A coding transmissive metasurface is presented for −1 mode quad-OAM-beam generation in 9.2–9.4 GHz. The 3bit metasurface is designed based on Pancharatnam−Berry (PB) phase principle, which is fed by a linear horn antenna. To satisfy the phase requirement of quad-OAM-beam, the phase compensation is introduced in the design for transmitting spherical waves into plane waves and promoting the directionality of incidence. The prototype of the metasurface is fabricated and measured. The experimental results coincide with theoretical analysis. Additionally, the OAM efficiency and purity are calculated to reveal the perfect performance of the metasurface. The proposed method has potential application in multi-channel wireless communication systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Vortex beam carrying orbital angular momentum (OAM) has attracted great interest in many fields due to the characteristics of infinite orthogonal topological charge [1–3]. It is expected to expand communication capability and promote the efficiency of the frequency spectrum in a way. It is reported that the vortex beam has been widely used in imaging, micro-machining, detection, and other fields [4–6]. Recently, several methods have been presented for OAM generation such as spiral phase plate (SPP), spiral and twisted reflectors, circular phased antenna array, metasurface, and so on [7–9].
For the classical method in OAM generation, numerous works have been studied [10–20]. Reference [10] proposed a structure of spiral phase plate made of material with varying thickness and constant refractive index. By increasing the additional phase factor, the OAM is achieved in 60 GHz with low loss, but it is limited to harsh fabrication standards. A spiral reflector is proposed for OAM generation illuminated with a Yagi antenna in 2.4-2.5 GHz [11]. The phased antenna array is also an effective method in OAM generation. A circular phased antenna array is proposed in 10 GHz which can generate OAM mode l=±2, ±1 simultaneously by shifting the fed pattern [12]. The system using the phased array is presented to generate seven sorts of OAM modes in the X-band [13]. Moreover, the circular patch is analyzed by the characteristic mode theory for dual-frequency [14]. To expand the OAM topological charge, the four-mode antenna array with independent feeding networks is present in Ref. [15]. The circular phased antenna array can realize different OAM modes. However, both of them have shortcomings such as intricate design processes, complex feeding networks, and limited beam quantities.
As a two-dimensional artificial structure with periodic or non-periodic arrangement, metasurface has strong capability of manipulating electromagnetic waves with the characteristics of low loss, easy fabrication, and low cost [21–39]. Previous studies are indicated that it can be utilized for OAM generation. For the reflective metasurface, the loss of absorption is usually negligible because of its metallic ground. A reflective metasurface is designed for single-beam OAM generation based on the geometry phase principle, the metasurface can work in wide bandwidth and generate the vortex beam with high purity [21]. The reflective nature-inspired metasurface in 13.1-20.5 GHz is illuminated to generate high purity OAM with the bandwidth of 44%, which is designed based on the circularly polarized incidence and sunflower PB elements [22]. Different from the reflective metasurface, the transmissive metasurface can avoid the occlusion effect which has profound application in wireless communication systems. It is reported that a bilayer metasurface with dual-operating modes are proposed to realize different OAM beam [23]. A three layers dual-mode transmissive metasurface is devised with different polarized incidences which can respectively engender OAM beam with l=+2 and l=+4 for x-polarized and y-polarized incident waves [24]. Multi-OAM-beam can promote communication channels which have profound applications. Recently, a multiplexing scheme for OAM in terahertz is presented to reach four multi-beam OAM [25]. However, for the microwave domain, the design scheme is difficult to generate the OAM beams because the wavelength is much longer than that in terahertz and the diffraction phenomenon is more obvious in that of microwave frequency band.
In this manuscript, a coding transmissive metasurface is designed for quad-OAM-beam generation in 9.2-9.4 GHz. The phase compensation is introduced to transmit spherical wave into plane wave. Moreover, the 3bit coding metasurface is assembled based on the PB phase principle. By calculating the coding sequence of quad-OAM-beam, the prototype of metasurface is fabricated and measured in the microwave anechoic chamber. The proposed method is validated by numerical simulations and practical experiments. The designed quad-beam OAM metasurface has potential application in wireless communication systems.
2. Design and fabrication
For fulfilling the requirement of OAM phase, the transmissive element should satisfy the high transmission coefficients and 360deg phase shift simultaneously. The principle of PB phase has been introduced to reach continuous phase shift. It is applicable to multi-bit phase coding, whose phase is regulated by rotation of two metal bi-symmetrical arrow patches for the unit cell. To elaborate the mechanism of the PB phase principle, a right-hand circular polarization (RHCP) wave is incident along -z direction. The electric field vector of the incident wave ${\overrightarrow E ^i}$ and transmissive wave ${\overrightarrow E ^t}$ can be expressed as:
Due to the element is irradiated with a circularly polarized wave, the transmissive phase shift and transmissive coefficients in u-axis have the equal tendency in x-axis, which means Φx=Φu and Tx = Tu. The analogous results can be obtained that Φy=Φv and Ty = Tv. Then transmissive wave in x-y coordinate system is expressed as:
It is a notice that ${\overrightarrow E ^t}$ could be divided into two components including ${\overrightarrow E ^t}_{(LHCP)}$ and ${\overrightarrow E ^t}_{(RHCP)}$:
From Eqs. (1)-(8), it is concluded that only the LHCP component of transmissive wave has −2φ phase shift when it is irradiated by RHCP wave. To acquire perfect transmissive wave with circular polarization, the cross-polarized wave should be restrained which is available for co-polarized wave generation. Therefore, the co-polarized transmission txx and tyy should approximate one while the phase difference of ΔΦ=Φxx-Φyy could be close to 180deg.
On account of the analysis mentioned above, a three-layer with single substrate coding transmissive metasurface (CTMS) is designed as element in Fig. 2. The microstructure is composed of two metallic patches shaped of arrow and a dielectric substrate with the thickness of 2.5 mm. The metallic patches are on both side of substrate to satisfy the phase requirement. The dielectric substrate is Rogers 4350B (ɛr = 3.66 and tanδ=0.0037). The metallic patches are all copper with the conductivity of 5.8×107S/m which have been printed on both sides of the dielectric substrate as shown in Fig. 2(a, b). All parameters are optimized and 3bit coding elements have been designed by rotating metallic patches. Optimized parameters are p = 10 mm, h = 2.5 mm, l = 7 mm, w = 1.08 mm, l1 = 4.06 mm, l2 = 1.2 mm, α=130deg, respectively. The relationship between the 3bit coding elements and the rotating angles of metal patches are shown in Table 1.
Fig. 2. Schematic of the PB phase elements: (a) perspective view. (b) Top view. Optimized parameters of the elements are p = 10 mm, h = 2.5 mm, l = 7 mm, w = 1.08 mm, l1 = 4.06 mm, l2 = 1.2 mm, α=130deg.
Table 1. The 3bit coding elements of metasurface
For demonstrating the transmission coefficients of proposed elements, full-wave analysis is realized by CST Studio Suite 2020. From Fig. 3(a, b), it can be observed that the transmission coefficients of txx and tyy in x-polarized or y-polarized incidence are close to 0.83 and the phase difference ΔΦ= Φxx-Φyy is near 180deg in the highlight frequency band, which tends to meet the requirement of PB phase principle. tcp is utilized to express transmission illuminated by the circularly polarized wave. LHCP wave and RHCP wave are indicated as - and + in subscript. To further explore the characteristics of elements, the amplitude and phase responses of transmission coefficients for 000-111 elements are simulated with circularly polarized incidence. It is worth noting that the transmission coefficients are higher than 0.8 in 9.2-9.4 GHz while the phases of 000-111 elements shift from 0deg to 360deg as shown in Fig. 3(c, d). It can be seen that when the rotation angle θ shifts from 0deg to 180deg with the step size of 22.5deg, the 2θ phase response is achieved covering 360deg which coincides with the PB phase principle. The simulated results indicate the well performance of the elements which can be used to assemble metasurface.
Fig. 3. The amplitude and phase results of transmission coefficients for proposed CTMS. (a) The transmission of txx and tyy with x-polarized or y-polarized incidence. (b) The phase response of Φxx, Φyy, and phase difference ΔΦ with x-polarized or y-polarized incidence. (c) The transmission of 000-111 elements with circularly polarized incidence. (d) The LHCP and RHCP phase response of 000-111 elements with circularly polarized incidence.
To investigate the mechanism of the designed metasurface, the surface current distribution at 9.3 GHz with x- or y-polarized incidence has been simulated as shown in Fig. 4. The surface current distribution with y-polarized incidence is shown in Fig. 4(a), as it is clearly observed that the current mainly flows along the vertical metallic rod and short stubs in a circular period. The current distribution on the top layers has the same flow direction as the bottom layers, which can hardly change the transmissive phase. Nevertheless, the surface current distribution with x-polarized incidence is revealed in Fig. 4(b). The current primarily flows along oblique rods and stubs in a circular period. Conversely, the current distribution on the top layers has opposite flow direction to the bottom layers. It is indicated that the metasurface element can convert x-polarized incidence with 180deg phase difference which tends to satisfy the conditions of the PB phase principle.
Fig. 4. The surface current distribution of proposed metasurface elements at 9.3 GHz. (a) The surface current on the top layer and bottom layer with y-polarized incidence. (b) The surface current on the top layer and bottom layer with x-polarized incidence.
To elaborate the concept of quad-OAM-beam metasurface, the CTMS is fabricated to reach the function. In this manuscript, the performance of 9.3 GHz are listed which has better transmission coefficients in the working frequency band. Similar results can be realized in 9.2 GHz and 9.4 GHz. The linear polarized horn antenna is designed as the feeding source as shown in Fig. 1. The 3D far-field radiation pattern of the proposed horn antenna at 9.3 GHz is demonstrated in Fig. 5(a). The |S11| curve in Fig. 5(b) displays that the −10 dB bandwidth of the horn antenna covers 8-12 GHz, Fig. 5(c, d) shows the far-field radiation pattern in the XOY and YOZ plane, the half power null size of the antenna is 37.6deg with the max gain of 13.2dBi, which can satisfy the requirement of feeding source. Moreover, the cross-polarized components are less than −85 dB for the horn antenna at 9.3 GHz in Fig. 5(c, d).
Fig. 5. The performance of linear polarized horn antenna. (a) The 3D far-field pattern of linear polarized horn antenna at 9.3 GHz. (b) The |S11| and gain curves of linear polarized horn antenna. (c) The far-field radiation pattern in XOY plane for the linear polarized horn antenna. (d) The far-field radiation pattern in YOZ plane for the linear polarized horn antenna.
Generally, the proposed linear polarized horn antenna may generate the spherical wave. To achieve the function of OAM, the phase compensation is introduced to transmit spherical wave into plane wave. As shown in Fig. 6(a), the origin of coordinates is located on the top layer of the metasurface, the feeding antenna is simplified as the point source with coordinates of (0, 0, zh). Subsequently, the compensation phase ϕij is calculated as follows:
Where k0 is the wave vector defined as k0 = 2πf0/c, xi and yi correspond to the coordinates (xi, yi, 0) of each metasurface element. For the design of metasurface for OAM generation, each element should rotate at a certain angle. It can be fulfilled by an additional phase factor eilφ for the Gaussian beam. However, to realize the function of multi-beam, the coding sequence of Px and Py are introduced in the design. In combination with the required function, the final phase distribution can be described as:Fig. 6. The schematic of coordinate system and coding pattern for quad-beam OAM generation. (a) The schematic of coordinate system of quad-beam OAM antenna. (b) Phase compensation coding sequence. (c) Quad-beam OAM coding sequence. (d) The final coding sequence.
To illustrate the proposed quad-OAM-beam metasurface, the CTMS is designed and simulated with 40×40 elements. The simulated magnitude and phase distribution of the quad-OAM-beam are revealed in Fig. 7(a, b) and the simulated near-field magnitude and phase distribution for one of the main beams is shown in Fig. 7(c, d). It can be observed that the quad-OAM-beam is located on the spherical coordinate system with azimuth angle φ=45°, 135°, 225°, and 315° respectively. Compared with the incident horn antenna, the simulated gain of the quad-OAM-beam is 15.3dBi which promotes 2.1dBi in 9.3 GHz due to the coding sequence of phase compensation is introduced for beam focus. Furthermore, to observe the perfect vortex distribution of OAM, the detection plane must be perpendicular to each OAM beam. The near-field magnitude for quad-OAM-beam is detected which has apparent characteristics of doughnut shape and the corresponding phase distribution displays a helical wavefront which is accorded with the theoretical analysis.
Fig. 7. Simulated results of quad-OAM-beam. (a, b) The simulated magnitude and phase distribution in spherical coordinate system. (c, d) The simulated near-field magnitude and phase distribution for one of the main beams in the perpendicular plane.
3. Results and discussion
A prototype of metasurface with 40×40 elements is fabricated by PCB (print circuit board) technique to verify the proposed the function of quad-OAM-beam. The metasurface is located on the side of horn antenna with focus diameter ratio of 0.75 as shown in Fig. 8(a), the distance between the horn antenna and metasurface is 300 mm. The near-field testing environment is revealed in Fig. 8(b). The testing facilities include a received horn antenna, a number of RF coaxial cables, and a vector network analyzer of Agilent N5230C. All the testing is fulfilled in the microwave anechoic chamber.
Fig. 8. Testing environment and experimental results of CTMS. (a) Schematic of far-field testing environment. (b) Schematic of near-field testing environment.
Experimental results of quad-OAM-beam is shown in Fig. 9(a-d). The quad-OAM-beam is located in the plane with azimuth angle of phi = 45deg, 135deg, 225deg and 315deg. To intuitively display the performance of generated quad-OAM-beam, the far-field patterns in phi = 45deg and 135deg are measured including all beams as shown in Fig. 9(a, b). The symmetrical beams are observed in 34deg with the gain of 14.9dBi. Figure 9(c, d) illustrates the near-field magnitude and phase distribution of OAM beams at 9.3 GHz, the observation plane is located in the plane perpendicular to one of the main beams with the distance of 10 mm. It can be noticed that the obvious energy loss appears in the center of the observation plane, which is similar to the shape of cyclic annulus. The phase reveals spiral gradient phase distribution with a spiral shifting from 0deg to 360deg.
Fig. 9. The simulated and experimental results of quad-OAM-beam metasurface. (a, b) Simulated and experimental far-field radiation pattern with phi = 45deg and 135deg at 9.3 GHz. (c, d) Experimental near-field magnitude and phase distribution of −1 mode OAM beam at 9.3 GHz with distance of 10 mm.
The OAM efficiency is introduced to measure the transmission performance of proposed metasurface, which is defined as the ratio of the transmissive energy and incident energy which is given as follows:
Fig. 10. The OAM purity and efficiency. (a) The simulated and measured OAM efficiency at 9.3 GHz. (b) The simulated and measured OAM purity in 9.3 GHz.
To evaluate the quantities of generated quad-OAM-beam, the OAM purity is calculated based on Fourier-transform, which is defined as follows:
In Eq. (14), Al is the OAM weight for each mode component, the angular distribution is represented as Ψ(φ). The OAM spectrum can be calculated as follows:
Figure 10(b) shows the simulated and measured OAM purity. It is worth noting that the simulated OAM purity of −1 mode OAM is closed to 77.3%, the measured results for OAM purity of 73.4%. Moreover, the proposed method for quad-OAM-beam generation is verified and the experimental and simulated results illustrate the well performance of CTMS.
4. Conclusion
A quad-OAM-beam coding transmissive metasurface is designed in microwave band based on PB phase principle. Quad-OAM-beam is emerged by mixing multi-function coding sequence appropriately. The prototype is fabricated and measured in microwave chamber. To evaluate the performance of the proposed antenna, the OAM efficiency and purity are calculated in the manuscript. The OAM efficiency is close to 79% while the OAM purity is near 73%. The simulated results are a bit lower than that of the simulation which is accorded with theoretical analysis. Moreover, the designed metasurface for quad-OAM-beam generation may pave the way for multi-channel wireless communication systems and OAM imaging systems.
Funding
Natural Science Basic Research Program of Shaanxi Province (2020JM-350, 20200108, 20210110); National Natural Science Foundation of China (61801508, 62171460); Young Innovation Team at Colleges of Shaanxi Province (2020022); National Postdoctoral Program for Innovative Talents (BX20180375); China Postdoctoral Science Foundation (2021T140111, 2019M650098, 2019M653960); Postdoctoral Research Funding of Jiangsu Province (2019K219); The Graduate Innovation Foundation of Air Force Engineering University (CXJ2021060).
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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