Broadband Polarization-Decoupled Metasurface for Generating Tailored Dual-Polarization Conical Beams

Yang, Lingjun; Ying, Beier; Sun, Sheng

doi:https://doi.org/10.1155/2023/3599970

International Journal of RF and Microwave Computer-Aided Engineering

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Abstract Introduction Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 3599970 | https://doi.org/10.1155/2023/3599970

Broadband Polarization-Decoupled Metasurface for Generating Tailored Dual-Polarization Conical Beams

Lingjun Yang,¹Beier Ying,²and Sheng Sun¹

Academic Editor: Morteza Shahpari

Received15 Feb 2023

Accepted17 Aug 2023

Published14 Oct 2023

Abstract

Conical beam antenna plays a significant role in providing stable access to satellite signals for moving communication terminals. Although metasurfaces have been used to generate conical beams, most of them can only reflect conical beams with identically distributed and mirror-symmetric phase responses for left-hand circular polarization and right-hand circular polarization, which can hinder the dual-polarization applications of metasurfaces. In this study, a metasurface is designed to independently manipulate dual-polarized excitations in broadband. To achieve the broadband control of conical beams, broadband conditions for both geometric and propagation phases are developed. Differently, metasurface designed in this study consists of three types of distinguishingly shaped elements, which can provide more degree of freedom in dual-polarization broadband design. In addition, a design method is developed for metasurface to generate the cone angle tailorable conical beams. Via fabricating a metasurface following the proposed method, the designed metasurface is verified in theorem, simulation, and experiment that it can generate desired conical beams with tailored divergent angles and phase responses covering a bandwidth from 12.5 GHz to 17 GHz.

1. Introduction

In today’s communication systems, humans, vehicles, and various moving objects performing unregular movements have become the carriers of satellite-based communication terminals [1–5]. However, this moving characteristic makes it difficult for these terminals to keep relatively still with satellites to have stable access to satellite signals. To maintain a qualified performance between terminal antennas on moving objects and satellites, a circumferential radiation pattern is expected for terminal antennas. Conical beam antenna with its strongest radiation on a conical surface deviating a certain angle from the normal and covering a large area has been proposed to guarantee stable access to satellites for moving objects [4, 5], particularly, the orbital angular momentum (OAM) beam, a kind of conical beam with identical polarization along the conical surface. Unlike vector conical waves with different polarization [6, 7], OAM conical beams can promote stable reception and communication while the receiver moves. Meanwhile, OAM conical beams have been widely used in nanoparticle manipulation [8], superimaging resolution [9], and data communications [10, 11].

For many years, methods have been developed on generating conical beams such as antenna arrays [12, 13], traveling-wave antennas [10, 11], holographic plates [14], elliptical patch antennas [15], and spiral phase plates [16]. However, generating conical beams with these traditional methods usually depends on complex feeding networks and bulky structures. In recent years, metasurfaces composed of elements with artificially engineered two-dimensional structures are applied in electromagnetic wave manipulation [17–19], which shows an advantage in generating and controlling conical beams. For example, metasurfaces based on resonant structure can generate vector conical beams [6, 7] and OAM conical beams [20–23] in a narrow bandwidth. Moreover, metasurfaces satisfying the Pancharatnam-Berry (PB) phase can introduce a frequency-independent abrupt phase, which can benefit broadband fabrication for circularly polarized (CP) beams [24–26]. Nevertheless, PB-phase-only metasurface cannot present independent phase responses for both left-hand circular polarization (LHCP) and right-hand circular polarization (RHCP) excitations. The propagation phase is introduced into metasurface design to solve this problem. The propagation phase, an additional variable, makes it possible to independently control phase responses for both RHCP and LHCP excitations (so-called polarization-decoupled strategy) [27–35]. Normally, in most published work, only a single type of element was used for propagation phase adjustment, which can provide a limited degree of freedom to achieve the required broadband phase responses. Therefore, different types of elements are proposed in this study. On the other hand, efforts should be put into designing dual-polarization conical beams with tailored divergent angles or OAM mode in broadband.

In this paper, we investigate the relationship between metasurface and generated conical beams aiming at generating tailored conical beams with expected phase responses (OAM modes) or cone angles for LHCP and RHCP incidences via a single metasurface shown in Figure 1(a). Specifically, this work can be categorized into three aspects. Firstly, we propose the constraints of phase responses for broadband polarization-decoupled elements. Secondly, we develop three broadband polarization-decoupled elements displayed in Figure 1(b) to compose a metasurface, which can realize the broadband polarization decoupling. Thirdly, we establish a theory to tailor the generated conical beams over dual polarization. To verify the effectiveness of proposed elements and theories, we fabricate a metasurface that generates cone angle independently tailored OAM conical beams for dual polarization, illustrating a good conformity with desired cone angle and OAM mode for both LHCP and RHCP excitations.

(a)

(b)

2. Phase Responses for Broadband Polarization-Decoupled Elements

For PB phase reflective elements with a self-centered rotation angle of , the designed phase responses can be ideally expressed by [36] in which is the orientation angle of a specific element and the two-letter index refers to the polarization states of reflected and incident waves. From (1a)–(1d), a good performance of a reflective polarization-decoupled element can be achieved by suppressing the cross-polarized reflection coefficients into zero, which is achieved by using mirror-symmetric elements and adjusting the magnitude of and copolarized reflection coefficients into unity with a 180° phase difference between them (). Therefore, the reflection coefficients for LHCP and RHCP can be described as

From (2a) and (2d), phase responses of LHCP and RHCP are and . This means that arbitrary phase distributions of and can be independently designed by controlling the propagation phase and the orientation angle or so-called geometric phase of each element [28].

Here, we aim to analyze the frequency-related phase responses. Based on (2a)–(2d), the geometric phase and the propagation phase response or termed initial phase of a element, denoted as in (2a)–(2d), can be described as

To achieve the broadband control of LHCP and RHCP conical beams, we propose two necessary conditions for both geometric and propagation phases. First, both geometric and propagation phases should cover a range. Second, the phase gradient between neighbored elements should remain the same within desired bandwidth. For geometric phase, the phase coverage can be fulfilled by rotating the orientation angle of each element indicated by (3a) if the broadband 180° phase difference of and copolarized reflection coefficients has been satisfied (, or ). Additionally, the CP phases of elements related to geometric phase are orientation-related-only and frequency-unrelated as indicated in (3a), which can benefit the broadband design. Regarding to propagation phase design, if different elements are used to discrete the propagation phase, phase responses of the elements should satisfy the relationship in which is the propagation phase of the th different element and is the phase gradient between neighbored elements.

3. Elements for Broadband Polarization Decoupling

In this study, the phase gradient is 60°, so six types of elements are required according to (4a). From (2a) and (2d), elements satisfying PB phase conditions have the same reflective amplitude but attach a 180° phase difference after a 90° self-centered rotation (). Therefore, we only need to propose three types of elements, and another three types of elements can be obtained by rotating 90° of original ones. As depicted in Figure 1(b), all these elements are designed to be a single-layer dielectric substrate (F4B, , mm, and mm) with a metal ground and a metallic sheet mounted on the two hexagonal surface sides of dielectric substrate. The only difference among elements is the shape of metallic sheets mounted on the upper side of the dielectric substrate shown in Figure 1(b). The designed parameters are , , , , , , , , , , , and (unit mm).

Figure 2 shows the characteristics of proposed elements simulated in commercial software high-frequency structural simulator (HFSS) under Floquet port and periodic boundary condition. As presented in Figure 2(a), the magnitude of reflection coefficients for these elements can reach approximately 0.80 or even higher value covering frequencies from 12.5 GHz to 17 GHz with a 30.5% fractional bandwidth. Figure 2(b) depicts the initial phases of proposed elements from 12.5 GHz to 17 GHz, which gives that at any frequency, different elements can cover a phase range together satisfying constraints in (3a). The six initial phase lines in Figure 2(b) show a good parallel characteristic with an almost uniform phase gradient 60° among neighbored lines, satisfying the proposed broadband condition (3b). These evenly distributed initial phase responses could be attributed to the multielement designs, since the obviously different shapes can provide more freedom in designing desired results.

(a)

(b)

4. A Design Method of Metasurface to Generate Tailored Conical Beams

For metasurface, each element performs as an electromagnetic radiator. According to antenna theory, for a circular metasurface composed of elements, the far-field radiation pattern with circular polarization can be calculated by [37] in which is the field’s position vector, is the position vector of the th element observing from cylindrical coordinate, is the wavevector in free space, and is the inclination factor satisfying derived from the Huygens-Fresnel principle. The phase profile of the th element is where is the azimuth angle of the th element (, , 0) observed from cylindrical coordinate.

Once the arrangement, the period, and the size of metasurface are determined, the far-field radiation pattern and the cone angle , the angle of θ with maximum far-field radiation energy, can be calculated based on (5) and (6). The triangular arrangement is applied in our metasurface since it has better isotropy [38]. The period of element is 10 mm. Based on (5) and (6) calculated with different metasurface sizes, we uncover the relationship among cone angle , OAM mode , and the size of metasurface depicted in Figure 3(a), in which the cone angle increases with the increasing of OAM mode under a certain size of metasurface, while it decreases with the increasing of radius under a specific OAM mode. The quantitative relationship in Figure 3(a) is essential to tailor conical beams featuring expected cone angles or OAM modes. The OAM beam will be poor if the size of metasurface is too small, so we force when the results of in Figure 3(a) become inaccurate for small .

(a)

(b)

Based on previous discussions, a metasurface can be designed as follows. First, the desired phase profiles and (for LHCP and RHCP) should be determined according to the expected cone angle in Figure 3(a). Then, for every element, it should be arranged according to phase profile and rotate a specific angle according to phase profile . For example, we aim to generate conical beams for LHCP and RHCP with cone angles 10° and 20°, respectively. According to Figure 3(a), to generate conical beams with angles 10° and 20°, the relationship between OAM mode and the size of metasurface is extracted to Figure 3(b). Normally, the size of metasurface is determined by needs. In this example, the size of the designed metasurface is 12 times of the element period (), so referring to dash lines in Figure 3(b), the corresponding OAM mode is ±4 when the expected cone angle is 10° for LHCP and the OAM mode is ±9 when the expected cone angle is 20° for RHCP. Following the fabricating procedure, the desired phase responses (for LHCP, ) and (for RHCP, ) are firstly depicted in Figure 4. Then, phase profiles of and are illustrated in Figure 4. Finally, the proposed elements are arranged and rotated in accordance with the given phase profiles to compose the metasurface depicted in Figure 4. Once the phase profile is determined, the theoretical far-field radiation patterns at 15 GHz can be calculated by (4a), (4b), and (5), which are revealed in Figure 5. For both LHCP and RHCP cases, the maximum energy of the reflected beams covers a circumferential range from 0° to 360° at cone angles 10° and 20°, respectively, which demonstrates that the designed phase profiles can generate conical beams with tailored cone angles.

5. Simulation and Experiment

In this part, the proposed metasurface in Figure 4 is simulated in HFSS. The reflected fields are obtained under LHCP and RHCP plane wave excitations at 15 GHz. Regarding to copolarized -field patterns in Figure 5, for both LHCP and RHCP excitations, the maximum energy has covered 360° in the azimuth plane at exactly 10° and 20°, respectively. The number of phase-changing spirals along dash lines denoted on phase pattern () in Figure 5 shows that the OAM mode is 4 for LHCP and -9 for RHCP. These simulated results conform with the theoretical results, which can verify the effectiveness of the proposed theories. Moreover, as depicted in Figure 5, the cross-polarization patterns for both LHCP and RHCP excitations are low enough, which is significant for the metasurface to reach a high conversion efficiency, . in which is the area of upper space. In this case, the proposed metasurface can obtain a high enough (with 77.6% for LHCP and 76% for RHCP, respectively).

To verify the broadband (from 12.5 GHz to 17 GHz) characteristic of the proposed metasurface, copolarized far-field radiation patterns at -plane and -plane produced by (4a) and (4b) and HFSS simulations are compared at 13 GHz, 15 GHz, and 17 GHz. Figure 6(a) is the far-field patterns under LHCP excitation. The conical-shaped pattern could be found at both - and -planes with cone angle . Figure 6(b) shows the far-field patterns under the excitation of RHCP wave, where broadband conical beams are generated. The cone angles are strictly consistent with the expected values at designed frequency (15 GHz). Although cone angles are not a strictly fixed value within the desired bandwidth due to the frequency dependence, an intrinsic characteristic, of the OAM pattern, the generated radiation patterns also show a conical-shaped beam with near -10 dB side lobes and can be accurately predicted by theoretical results.

(a)

(b)

To verify the proposed metasurface experimentally, we build a specific experiment setup to generate the aforementioned conical beams. Figure 7 shows the front and side views of the experiment setup, where the metasurface is placed at a 3D-printed stand and two Archimedes spiral antennas are located at the position vector and on the stand referring to the center of metasurface (unit mm). The upper antenna is a right-hand spiral antenna, which is normal to the metasurface, and the lower antenna is a left-hand spiral antenna which is oriented to the center of the metasurface. In this case, additional compensated phases should be imparted into each element to compensate the sphere waves nonideally generated by these two implemented antennas. For the th element in the metasurface, the compensated phase could be obtained by [39] in which is the propagation constant, is the position vector of the th element, and is the position vector of the antenna. Therefore, phase responses used to design the fabricated metasurface are

The far-field radiation patterns of both simulated and measured results under the excitations of LHCP and RHCP spiral antennas at 13 GHz, 15 GHz, and 17 GHz are shown in Figure 8. Although the far-field patterns are not as symmetric as those with plane wave incidences in Figure 6 due to the nonideal excitation and the offset design, the copolarized measuring results at 15 GHz in Figures 8(a) and 8(b) can still show the expected conical beams with near -9 dB side lobes and fit the simulated results at both -plane and -plane. For both RHCP and LHCP excitations, the magnitude of cross-polarized patterns is almost -6 dB lower than that of the corresponding copolarization patterns, which verifies the high efficiency of the proposed metasurface. For broadband performance, experiments are conducted at 13 GHz and 17 GHz with the results presented in Figure 8(c), in which conical beams can be found in copolarized far-field patterns under LHCP and RHCP excitations. The experiment results confirm that we can generate broadband cone angle-tailored conical beams with LHCP and RHCP waves using the proposed metasurface. Moreover, better experiment results could be achieved if a broadband dual-polarization antenna with high performance was used and placed normal to metasurface rather than applying two antennas requiring offset feed in our experiment.

(a)

(b)

(c)

6. Conclusion

In this work, we have proposed a metasurface to independently generate cone angle-tailored OAM conical beams with both LHCP and RHCP. The designed metasurface has been verified in theorem, simulation, and physical experiments resulting in reasonable conformity with expectations. The cone angle of generated conical beams can be tailored independently with LHCP and RHCP excitations from 12.5 GHz to 17 GHz covering a broad bandwidth. Compared with traditional conical beams, we can achieve dual-polarized conical beams with LHCP and RHCP excitations. In particular, we propose three types of elements, which can provide more degree of freedom in dual-polarization decoupling and broadband design. In addition, depending on the found relationship among cone angle, OAM mode, and the size of metasurface, the generated conical beams or OAM modes are tailorable, which can be expanded to the applications of beam steering and tailored OAM beams. Although we conducted the experiment at 12.5 GHz to 17 GHz, the broadband theory of polarization-decoupled elements and the design process are also suitable in terahertz and optical fields.

Data Availability

No underlying data was collected or produced in this study.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grants 61721001 and 61971115.

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Copyright © 2023 Lingjun Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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