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Abstract
In this paper, a dual-band metasurface (MS) generating multiple orbital angular momentum (OAM) beams independently in full polarizations is proposed. First, the design principle of controlling full polarizations independently is analyzed. Second, the frequency selective surface is introduced to the meta-atom design that ensures the meta-atom operates at Ku- and Ka-band independently, while, at each band, sixteen optimized meta-atoms realize the high reflection amplitude and enough phase coverage. Next, the optimized dual-band meta-atom controlling full polarizations independently is utilized to design the MS, which could generate eight independent OAM beams including the x-polarized, y-polarized, left hand circularly polarized, and right hand circularly polarized OAM beams at dual-band. Finally, the MS is designed, fabricated, and measured. Both simulated and measured results verify that the proposed MS could generate multiple OAM beams in full polarizations at dual-band, showing the perspective in the OAM-based area, such as the wireless communication, target detection, and security encryption.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Vortex waves with the helical phase term of eilφ, l is the topological charge of orbital angular momentum (OAM) mode and φ is the azimuth angle, possess the spiral wave-fronts along the propagation direction [1]. In radio frequency domain, the current researches and applications of the vortex wave mainly focus on three areas: First, for the OAM-based wireless communication, because the orthogonal OAM modes are infinite in theory, showing the promising prospect in the high-capacity wireless communications [2]. Recent research has demonstrated that the OAM-based mode multiplexing is limited by the physical size of aperture [3], so in a fixed aperture, combining full polarizations regulation and dual-band operation, which would be positive to the complicated OAM-based wireless communication systems. Second, for the OAM-based encrypted holography, the typical OAM-based encrypted holography is first realized at the optical frequencies, which utilizes the angular momentum selectivity of the metasurface (MS) to reconstruct different images [4,5]. Subsequently, recent research has shown that at the microwave frequencies, correct holographic images can be reconstructed when the MS is illuminated by the vortex beams with definite OAM mode and polarization [6]. Third, for the OAM-based target detection, multiple vortex beams with unique wave-front structures have attracted great attention in the target detection and microwave imaging [7–9], by extracting phase information from scattered echoes of different vortex beams, the azimuth can be reconstructed. Therefore, combining the OAM multiplexing, polarization multiplexing and multi-band operation show the powerful potential in the wireless communication systems, target detection, and security encryption.
Up to now, some typical methods are proposed to generate the OAM beam, such as the spiral reflector [10], holographic diffraction grating [11], circular traveling wave antenna [12], helical slot antenna [13], and patch antenna [14–16]. Apart from these methods generally generate the single OAM mode or operate at single frequency band, another two typical methods including the antenna array and MS are utilized to generate multifarious OAM beams as:
- (1) For the antenna array, adopting multiple types of feeding networks generates multiple OAM beams, which operate in single polarization at single frequency band [17,18] or dual frequency bands [19]. Employing the opposite phase differences on the dual circular polarization (CP) element generates the opposite OAM modes in left-hand circular polarization (LHCP) and right-hand circular polarization (RHCP) [20]. In addition, considering the complex feeding network especially for more OAM beams generation, Rotman lens-fed antenna array is proposed to simplify the feeding network and generate multiple OAM beams in single polarization at single frequency band [21].
- (2) For the MS, adopting different sections of the MS [22,23], or synthesizing the phase patterns [24], or utilizing the holographic strategy [25] could generate multiple OAM beams in single polarization at single frequency band. Besides, controlling multiple polarized channels to generate multiple OAM beams at single frequency band [26–30] and generating the respective OAM beam at dual-band [31,32] correspond to the polarization multiplexing and OFDM, respectively. Moreover, recent research combining the polarization multiplexing and OFDM is also proposed [33–35], while only two orthogonal liner or circular polarizations are designed independently and thereby polarization-based multiplexing is not fully utilized.
Therefore, there are few works that generate multiple OAM beams with full polarization operation and multiple frequency bands operation, in other words, the current works hardly realize the OAM mode multiplexing, polarization multiplexing, and OFDM by single OAM generator.
In this paper, a dual-band MS generating multiple OAM beams independently in full polarizations is proposed, as shown in Fig. 1. To be specific, at both Ku- and Ka-band, the deflection angle of the x-polarization, y-polarization, LHCP, and RHCP vortex beams are set as (25°, 270°), (25°, 180°), (25°, 0°), (25°, 90°), respectively. Herein, the first and second angle denotes the elevation angle and azimuth angle of the beam directions, and the beam directions are also expressed as (θ, φ). Meanwhile, the corresponding OAM mode numbers of the x-polarization, y-polarization, LHCP, and RHCP are set as −2, + 2, −1, + 1 at Ku-band and +2, −2, + 1, −1 at Ka-band, respectively.
Fig. 1. The schematic of the designed MS for generating multiple OAM beams in full polarizations at Ku / Ka-band. Herein, the feed source operates in linear polarization (LP).
Therefore, the designed shared aperture MS realizes multiple OAM beams generation, full polarizations operation, and dual-band operation, which is positive to the complicated OAM-based wireless communication systems, such as improving the channel capacity and transmitting or receiving multiple information in different polarizations at dual-band. Furthermore, the designed OAM MS regulating full polarizations would further enhance the capability of OAM-based encrypted holography, and one can expect that the capability of OAM-based encrypted holography would be further improved by combining the dual-band operation, such as that different holographic images can be reconstructed at different frequencies. In addition, the designed MS generating multiple OAM beams also show the potential in the target detection.
2. Design of dual-band meta-atom operating in full polarizations independently
In order to design the dual-band meta-atom operating in full polarizations independently, in this section, the corresponding design principle for controlling full polarizations independently is introduced [29], meanwhile, the dual-band meta-atom is designed and its performance is analyzed. Therefore, combining the design principle of controlling full polarizations independently and the dual-band meta-atom would be favorable to the next MS design.
2.1 Design principle for controlling full polarizations independently
The desired reflective E-field from the mn-th meta-atom in each polarization (u-LP, v-LP, LHCP and RHCP) can be expressed in a general form [29,36]:
Each meta-atom on the MS realizing the independent phase control for full polarizations ($\varphi _u^{mn}$, $\varphi _v^{mn}$, $\varphi _l^{mn}$, $\varphi _r^{mn}$) ensures that the designed MS could generate the respective OAM beam in different polarizations. From Eq. (2) one can see that the independent phase control in full polarizations ($\varphi _u^{mn}$, $\varphi _v^{mn}$, $\varphi _l^{mn}$, $\varphi _r^{mn}$) could be realized by controlling the LHCP (the first item in Eq. (2)) and RHCP (the second item in Eq. (2)) independently. Subsequently, the recent research proposed a spin-decoupled strategy, which could be utilized to control the LHCP and RHCP E-field independently, and the corresponding reflected E-field is given as
Therefore, the independent phase control for full polarizations ($\varphi _u^{mn}$, $\varphi _v^{mn}$, $\varphi _l^{mn}$, $\varphi _r^{mn}$) could be realized by controlling the x-polarized reflection phase $\varphi _x^{mn}$, y-polarized reflection phase $\varphi _y^{mn}$, and rotation angle ${\alpha ^{mn}}$ of the mn-th meta-atom.
2.2 Meta-atom design and its performance analysis
The designed dual-band meta-atom [33] is shown in Fig. 2, where each metal layer is printed on the Rogers4350b substrate with permittivity of 3.66 and loss tangent of 0.004. Specifically, the designed meta-atom is composed of the Ka units operating at Ka-band located in layer I (shown in Fig. 2(c)), frequency selective surface (FSS) located in layer II (shown in Fig. 2(d)), and Ku units operating at Ku-band located in layer III (shown in Fig. 2(e)). The detailed parameters of the designed meta-atom are summarized and tabled in Table 1.
Fig. 2. The configuration of the designed meta-atom. (a) Perspective view. (b) Side view. (c)–(e) The detailed configuration of the meta-atom on layer I, layer II, and layer III, respectively. Herein, the subscripts ux / uy and bx / by represent that the top unit and the bottom unit operate in x-polarization / y-polarization, respectively.
Table 1. The detailed parameters of the designed meta-atom. (all in millmeters)
Herein, the FSS is introduced to suppresses the mutual influence between the Ku- and Ka-units. To illustrate the operating mechanism of the proposed FSS, the electric field distributions of the meta-atom at different frequencies are shown in Fig. 3. As shown in Fig. 3(a) corresponding to the electric field distributions in the yoz surface, it can be clearly seen that the incident wave could pass through the upper Ka units and arrive at the bottom Ku units at 12.55 GHz (Ku-band), meanwhile, the incident wave could be reflected when striking on FSS at 30 GHz (Ka-band). Therefore, FSS is acted as a band-pass filter at Ku-band and metal ground at Ka-band. Correspondingly, as shown in Fig. 3(b), one can clearly see that the Ku (Ka) units only operate at Ku (Ka) band and have negligible coupling on the Ka (Ku) units.
Fig. 3. (a) Simulated electric field distributions at 12.55 GHz and 29 GHz in the yoz cutting surface. (b) Simulated electric field distributions at 12.55 GHz and 29 GHz in the xoy cutting surface.
Moreover, the mutual influence between the Ku and Ka units is further analyzed, as illustrated in Fig. 4. From Fig. 4(a), (b) one can see that the Ka units with different unit length Lux, Luy and different rotation angle αu have very low influence on the Ku units. On the other hand, from Fig. 4(c), (d) one can draw the similar conclusion that the Ku units with different unit length Lbx, Lby and different rotation angle αb have very low influence on the Ka units. Hence, from the above analysis, one can conclude that the FSS efficiently suppress the mutual influence between the Ku and Ka units. Similarly, for the y-polarized incident wave, one can obtain the same conclusion.
Fig. 4. The x-polarized reflection phase and amplitude responses of the periodic meta-atom when (a), (b) operating at Ku-band with different Lux, Luy and different αu, respectively, and (c), (d) operating at Ka-band with different Lbx, Lby and different αb, respectively.
Finally, the detailed geometries of sixteen Ku and Ka units are optimized and then shown in Fig. 5 and Fig. 6, respectively. Note that the Ku unit 9, 10, 11, 12, 13, 14, 15, 16 could be obtained by rotating the Ku unit 1, 2, 3, 4, 5, 6, 7, 8 by 90°, respectively, similarly, vice versa for the Ka units 9-16. Correspondingly, the x-polarized reflection amplitude and phase responses of the sixteen meta-atoms are shown in Fig. 7, where the Ku and Ka units realize the 360° phase coverage with 22.5° steps and the reflection magnitude of the Ku and Ka units are higher than −0.63 dB and −0.78 dB, respectively. The designed sixteen well performed meta-atoms with high amplitude and enough phase coverage at dual frequency bands would be favorable to the final MS design. Finally, combining with Eq. (4), for the mn-th meta-atom, the independent phase control for full polarizations could be realized by controlling the x- and y-polarized reflection phase (given in Fig. 7) and regulating the rotation angle.
Fig. 5. The detailed geometries of sixteen Ku units with rotation angles αb = 0° to realize 360° phase coverage for x- and y-polarized waves. The geometrical parameters for Ku unit 1 - unit 8 are optimizes as: Lbx1 / Lby1= 9.2 / 6.92, Lbx2 / Lby2= 9.45 / 7.25, Lbx3 / Lby3 = 9.67 / 7.5, Lbx4 / Lby4 = 2.85 / 7.7, Lbx5 / Lby5 = 4.38 / 8, Lbx6 / Lby6 = 5.34 / 8.25, Lbx7 / Lby7 = 6 / 8.75, Lbx8 / Lby8 = 6.55 / 9, all in millimeters. Besides, the radio rx and ry for Ku unit 1 - unit 8 are optimizes as: rx1 / ry1 = 0.6 /0.7, rx2 / ry2 = 0.6 / 0.7, rx3 / ry3 = 0.6 / 0.7, rx4 / ry4 = 0.7 / 0.7, rx5 / ry5 = 0.7 / 0.66, rx6 / ry6 = 0.7 / 0.65, rx7 / ry7 = 0.7 / 0.6, rx8 / ry8 = 0.85 / 0.6.
Fig. 6. The detailed geometries of sixteen Ka units with rotation angles αu = 0° to realize 360° phase coverage for x- and y-polarized waves. The geometrical parameters for Ka unit 1 - unit 8 are optimizes as: Lux1 / Luy1 = 1.58 / 1.15, Lux2 / Luy2 = 1.6 / 1.32, Lux3 / Luy3 = 1.64 / 1.39, Lux4 / Luy4 = 1.69 / 1.44, Lux5 / Luy5 = 1.78 / 1.48, Lux6 / Luy6 = 1.95 / 1.5, Lux7 / Luy7 = 2.3 / 1.53, Lux8/ Luy8 = 1.55 / 0.6, all in millimeters.
Fig. 7. The x-polarized reflection amplitude and phase responses of the meta-atoms at 12.55 GHz and 29 GHz. Herein, the rotation angles are set as: αu=αb = 0°.
3. Design of dual-band multiple OAM MS operating in full polarizations
By combining the principle of controlling full polarizations independently and the designed dual-band meta-atom, thereby, in this section, the dual-band multiple OAM MS operating in full polarizations is designed, as shown in Fig. 1. Specifically, the designed MS aperture is square with the side length of 220 mm, and the feed source is located in the MS center position and 220 mm away from the MS. Meanwhile, at both Ku- and Ka-band, the x-polarization, y-polarization, LHCP, and RHCP vortex beams are deflected at (25°, 270°), (25°, 180°), (25°, 0°), (25°, 90°), respectively. The corresponding OAM modes for x-polarization, y-polarization, LHCP, and RHCP vortex beams are set as −2, + 2, −1, + 1 at Ku-band and +2, −2, + 1, −1 at Ka-band, respectively.
For generating the abovementioned multiple vortex beams in the designed direction (θ, φ), the required phase distribution of each meta-atom (x, y) on the MS should satisfy the following Equation as
Fig. 8. The required phase distributions on MS for generating full polarizations independently at dual band. (a)–(d) x-polarization, y-polarization, LHCP and RHCP at 12.55 GHz, respectively, and (e)–(h) x-polarization, y-polarization, LHCP and RHCP, at 29 GHz respectively.
Subsequently, combining the above full-polarized phase distributions, meanwhile, utilizing the design principle for controlling full polarizations independently shown in Eq. (4), finally, the corresponding x- and y-polarized phase distributions of the meta-atom on MS are shown in Fig. 9(a)-(d), meanwhile, the corresponding rotation angles and unit numbers on MS are shown in Fig. 9(e)-(h), respectively.
Fig. 9. The required phase distributions on MS for (a), (b) x- and y-polarization at 12.55 GHz and (c), (d) x- and y-polarization at 29 GHz, respectively. (e), (f) The rotation angle αb on layer III and rotation angle αu on layer I, respectively. (g), (h) The unit number for Ku units on layer III and for Ka units on layer I, respectively. Note that each pixel represents one of the MS meta-atom.
Subsequently, the simulated near-field amplitude and phase distributions and the corresponding OAM mode purity are shown in Fig. 10 and Fig. 11. Herein, all observations are rotated by 25° at Ku- and Ka-band to make the observe direction parallel to the vortex beam direction. From Fig. 10 and Fig. 11 one can clearly see that the simulated results are well consistent with the our expect, specifically, the designed MS generates the well performed vortex beams with amplitude null at the center area and spiral phase ±2π (2π / −2π represent OAM mode l = + 1 / l = -1) or ±4π (4π / −4π represent OAM mode l = + 2 / l = -2) in the clockwise direction, and the OAM modes for x-polarization, y-polarization, LHCP, and RHCP vortex beams are −2, + 2, −1, + 1 at Ku-band and +2, −2, + 1, −1 at Ka-band, respectively.
Fig. 10. Simulated near-field amplitude and phase distributions and calculated OAM mode purity at 12.55 GHz for (a) x-polarization with OAM mode l = -2, (b) y-polarization with OAM mode l = + 2, (c) LHCP with OAM mode l = -1, and (d) RHCP with OAM mode l = + 1.
Fig. 11. Simulated near-field amplitude and phase distributions and calculated OAM mode purity at 29 GHz for (a) x-polarization with OAM mode l = + 2, (b) y-polarization with OAM mode l = -2, (c) LHCP with OAM mode l = + 1, and (d) RHCP with OAM mode l = -1.
Moreover, the dominant OAM mode purities for both co-polarization and cross-polarization are calculated and the calculation process are described as follows:
The vortex electric field can be characterized as the summation of a series of spiral harmonics, which can be expressed as follows:
where Al indicates the amplitude of each spiral harmonic and is defined asFrom Eq. (6a) and Equation (6b) one can see that the OAM mode spectrum could be computed by performing the Fourier transforms on the electric fields [37]. Herein, the electric field could be obtained by extracting the near-field results along the white dashed circle, as shown in Fig. 10 and Fig. 11. Finally, the dominant OAM mode purity could be obtained by calculating the ratio of the dominant OAM mode power to all OAM modes power:
Herein, during the process of calculating OAM modal purity, the finite and consecutive OAM modes are utilized instead of considering unbounded OAM modes. Besides, for comparing the co- and cross-polarized OAM mode purities clearly, the summation of the co-polarized OAM modes power, $\sum\nolimits_{l ={-} \infty }^{l ={+} \infty } {|{A_l}{|^2}} $, is adopted when calculating the co- and cross-polarized OAM mode purities.
Following the above calculation process of the OAM mode purity, thereby the dominant OAM mode purities for the co-polarization are calculated and higher than 85% at Ku-band and higher than 96% at Ka-band, respectively, and the OAM mode purities for the cross-polarization are lower than 5% at Ku-band and lower than 2% at Ka-band, respectively.
4. Experiment results
For demonstrating the abovementioned MS that generating multiple OAM beams in full polarizations at dual-band, thereby the corresponding prototype is fabricated and measured, and the measured configuration is shown in Fig. 12. Herein, considering the available experimental equipment, two LP horns operating at Ku- and Ka-band respectively are selected as the feed source and these two LP horns are alternately assembled to simplify the feed system. The near-field scanning plane is set as 360mm × 360 mm at Ku-band and 240mm × 240 mm at Ka-band, respectively, and the distance between the scanning plane and MS is fixed as 625 mm. Besides, the prototype is rotated by 25° at Ku- and Ka-band to ensure the observe direction parallel to the vortex beam direction.
Fig. 12. The measured planar near-field scanning configuration. Insets: the local enlarged photograph of the fabricated MS.
The measured near-field amplitude and phase distributions for all polarizations at Ku- and Ka-band are shown in Fig. 13 and Fig. 14. From Fig. 13 and Fig. 14 one can see that compared with the simulated results shown in Fig. 10 and Fig. 11, the measured vortex beams show the similar results as: spiral phase ±2π or ±4π in the clockwise direction, amplitude null at the center area, and high dominant OAM mode purity at Ku- and Ka-band. Therefore, according to the simulated results and the measured results, we can conclude that the designed MS could generate multiple OAM beams in full polarizations at Ku- and Ka-band.
Fig. 13. Measured near-field amplitude and phase distributions and calculated OAM mode purity at 12.55 GHz for (a) x-polarization with OAM mode l = -2, (b) y-polarization with OAM mode l = + 2, (c) LHCP with OAM mode l = -1, and (d) RHCP with OAM mode l = + 1.
Fig. 14. Measured near-field amplitude and phase distributions and calculated OAM mode purity at 29 GHz for (a) x-polarization with OAM mode l = + 2, (b) y-polarization with OAM mode l = -2, (c) LHCP with OAM mode l = + 1, and (d) RHCP with OAM mode l = -1.
Herein, the minor differences observed between the simulated and measured results can be attributed to two reasons: Firstly, the misalignment between the MS prototype center and the receiving horn center during the measurement process. Secondly, the misalignment between the MS prototype center and the feed horn center during the assembly process, as well as the air gap error of the MS prototype during the assembly process.
Moreover, the simulated and measured OAM mode purities for all polarizations are summarized and tabled in Table 2, which shows that the simulated and measured dominant OAM mode purities all remain at a high level. Besides, the generated vortex beams possess the high OAM mode purity for the co-polarization and very low OAM mode purity for the cross-polarization at dual frequency bands.
Table 2. Simulated and measured OAM mode purities at 12.55 GHz and 29GHz
The comparisons between the proposed MS and other relevant reported works are summarized and tabled in Table 3. Compared with other MSs operate at single frequency band [30,31] or in single / dual polarization [33–35], our proposed MS in this paper could generate multiple vortex beams in full polarizations at dual frequency bands, and all OAM beams possess high OAM mode purity, therefore, the proposed MS shows the prospective in the wireless communication system, target detection, and security encryption.
Table 3. Comparison between the proposed MS in this paper and other relevant reported works
5. Conclusion
In conclusion, by introducing the design principle of controlling full polarizations independently and the well performed dual-band meta-atom, we propose a dual-band MS that generating multiple OAM beams in full polarizations, meanwhile, each polarization is controlled independently. Then, eight OAM beams (x-polarization, y-polarization, LHCP, and RHCP vortex beams at dual-band) are generated independently in the respective direction. The measured results are well consistent with the simulated results, verifying the designed correctness of the proposed MS. The proposed MS, which generates multiple OAM beams in full polarizations at dual-band, shows the powerful potential in some OAM-based applications, such as the wireless communication, target detection, microwave imaging, and security encryption.
Funding
National Natural Science Foundation of China (62288101).
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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