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Abstract
Orbital angular momentum (OAM) beam generators have attracted tremendous interests recently due to their excellent performance and potential applications in wireless communication. However, the existing transmissive OAM generators suffer from several limitations, such as narrow bandwidth, high profile and low efficiency. In this study, a new wideband third-order meta-frequency selective surface (meta-FSS) for generating focusing vortex beam is developed. The proposed meta-FSS element is designed at X- band with a third-order band-pass filter property, which exhibits the merits of low profile, high transmissivity, and large angular stability. By employing the proposed meta-FSS element, prototypes of OAM generators for + 1 and −2 modes are designed, fabricated, and measured. Experimental results verify the ability of the proposed design to convert an incident left/right-handed circularly polarized (L/RHCP) spherical wave into a transmitted R/LHCP vortex carrying OAM wave from 9.0 GHz to 11.0 GHz with high mode purity. A good agreement is achieved between the experimental and numerical results, which demonstrates that the proposed structure paves the wave for generating desired OAM modes, and provides new possibility for designing novel low-profile wireless communication devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the rapid development of wireless communication systems, providing higher data transmission rates and offering a better-quality service within limited radio resources has emerged as an urgent challenge for researchers, even after adopting high density coding and channel sharing techniques. To solve this problem, orbital angular momentum (OAM) technology has garnered much attention recently due to its unique characteristics of modulating signal with phase distribution of electric field. An electromagnetic wave carrying OAM has a constant electric current (I0) and a helical transverse phase structure quantified by exp(ilϕ), where ϕ is the transverse azimuthal angle and l is the topological charge [1]. Owing to the distinct advantages of theoretically unbounded OAM eigenstates, low crosstalk, and orthogonality between different modes, a tremendous enhancement of channel capacity and transmission reliability can be achieved without needing additional frequency resources. Such vortex waves offer a potential solution to the rapidly increasing demand of wireless data transmission. Vortex waves carrying OAM were first introduced in the optical region [2–6] and experimentally demonstrated with Laguerre-Gaussian (LG) modes by Allen in 1992 [7]. Since then, the OAM concept has been explored extensively and has successfully extended to terahertz [8–10], millimeter [11–13], and radio frequency [14–18] regimes.
Various approaches for the generation of electromagnetic waves with OAM beams have been reported in the literature. Among them, uniform circular array antenna is established as the conventional method [19–21]. However, for a desired OAM mode, the number of antenna units must be larger than 2 l to satisfy the Nyquist’s theory and an intricate feeding network is inevitably required. The limited space between the antenna elements dramatically increases the complexity and cost of the feeding network, especially for large topological OAM modes. Moreover, the narrow bandwidth of the corresponding system is another drawback.
Spiral phase plate (SPP) is another representative method, which is widely used in the optical field [22,23]. The required phase compensation is achieved by changing the thickness of SPP device in proportion to the azimuthal angle φ around the center of SPP, and a constant thickness is maintained along the radial direction. Recently, researchers proposed a planar SPP to produce OAM waves in the radio frequency region by drilling different number of holes in different sectors [24]. However, the major disadvantages of single OAM mode and large beam divergence limits the practical application of SPP.
As the hollowness and divergence of OAM based EM waves become more severe with the increase of the topological charge and propagation distance, metasurface reflectors with spiral curves have been recently developed to generate focused OAM beams for long-distance communications [25]. However, the fabrication of non-planar structures is complicated and expensive. To overcome these limitations, several modified planar reflectors for OAM beam generations have been proposed based on the generalized laws of reflection and refraction [26–34]. Unfortunately, the feed blockage loss of reflectarray reduces their efficiency in communication systems and the narrow operation bandwidth is still an outstanding issue of the existing reflective OAM generators.
To circumvent the reflection deficiency, we present the design, simulation, and measurement of transmission-type focused OAM beam generator for long-distance communication across a wide frequency band based on a new third-order meta-frequency selective surface (meta-FSS) structure. The employed meta-FSS unit cell exhibits low profile, high transmissivity, and wide angular stability. An equation for determining the required phase compensation is derived and implemented for designing the OAM generator. Two prototypes of OAM beam generators that carrying vortex waves with + 1 mode and −2 mode are fabricated and characterized. In contrast to the existing transmissive OAM generators [35–45], no air space layer or less substrate layers are introduced. The robust numerical and experimental performance validate the broad bandwidth and high mode purity of the proposed OAM beam generator.
2. Design, simulation, and analysis of Meta-FSS unit cell
The schematic model of the proposed transmissive vortex generator is depicted in Fig. 1(a), and the three-dimensional topology of the utilized meta-FSS unit cell and a detailed view of each layer are presented in Fig. 1(b). The meta-FSS unit cell consists of three metal layers (with a thickness of 17 $\boldsymbol{\mu}\textbf{m}$) and is supported by two intermediate substrate layers. Both the top and bottom metal layers are designed with identical rectangular patch structure while the middle metal layer is composed of a square patch with a cross-slot and four rectangular apertures etched on it, resulting in the transmissive property. A cost-effective, high-frequency circuit material: F4B, with a thickness of 2.0 mm, permittivity of 3.5, and loss tangent of 0.002 at 10 GHz is employed as the substrate. A 0.08 mm-thickness resin adhesive with a permittivity of 4.2 is used as the bonding material, and the thickness can be ignored after lamination.
Fig. 1. (a) Schematic model of the transmissive vortex meta-FSS array and (b) geometry of the proposed meta-FSS unit cell.
As revealed in [46], the transmitted wave for a lattice unit cell illuminated by a left- handed circularly polarized (LHCP) incident wave along z-direction can be expressed as
To satisfy the above mentioned requirement of 180° phase difference and equal transmission magnitude between the orthogonal transmitted waves, the proposed meta-FSS element is elaborately designed and implemented using the CST full-wave simulation software. Unit cell boundaries are assigned along the x- and y- directions and Floquet ports are employed along the z-direction to emulate an infinite structure. TE mode (with E-field along the y-direction) and TM mode (with E-field along the x-direction) are set to obtain the responses of orthogonal components. The key parameters of the final optimized structure are indicated in Fig. 1(b), and the corresponding values are listed in Table 1.
Table 1. Geometrical parameters of the proposed unit cell (unit: mm)
The numerically calculated reflection coefficients are presented in Fig. 2(a), in which three obviously different reflection zeros at 6.35 GHz, 8.7 GHz, and 10.25 GHz for the TE incident wave and at 10.0 GHz, 11.9 GHz, and 13.55 GHz for the TM incident wave can be observed, representing a third-order band-pass filter response along both x- and y-directions. Further, the transmission coefficients of meta-FSS unit cell are plotted in Fig. 2(b), which shows a 3-dB overlapped frequency band between the outgoing TE and TM waves that ranges from 8.9 GHz to 10.65 GHz with an ideal phase difference of 180°.
Fig. 2. Numerical results of S-parameters. (a) Reflection coefficients. (b) Transmission coefficients.
For large-scale OAM generation, the edge cells are illuminated by non-normal waves and a deteriorated performance can severely influence the quality of OAM waves. Therefore, it is necessary to analyze the properties of the element at obliquely incident waves. The corresponding simulations are concluded using CST software, and the relevant results are shown in Fig. 3, in which it is evident that the transmission losses are less than 2.3 and 1 dB when the incident angle θ increases to 50° for the TE and TM waves within the frequency band of interest, respectively. The associated phase responses for different incident angles are plotted in Fig. 3, in which fluctuations less than 10° can be clearly observed. Such salient features facilitate that the utilization of the developed meta-FSS as an OAM generator with a wide range of the focal distance to the side-array dimension ratio.
Fig. 3. Numerical results of transmission coefficients under obliquely incident waves. (a) TE polarization. (b) TM polarization.
To validate the theory of passive element rotation, the unit cell is rotated around the geometric center with different angles (ψ) and illuminated by a LHCP wave. The numerically obtained amplitude and phase responses are shown in Fig. 4. It is evident in Fig. 4(a) that, when the rotational angle ψ is gradually increased from 0° to 90° with an interval of 30°, the magnitudes of co- and cross-polarized reflection coefficients at the frequency of 10.0 GHz are −11 dB and −15 dB, respectively, ensuring weak back lobe radiation. Meanwhile, the magnitude of cross-polarized transmission of the meta-FSS element is almost unchanged, which is better than −1 dB at each rotation angle as shown in Fig. 4(b). In addition, the corresponding transmission phase responses are exactly double of the rotation angles, which is in agreement with the aforementioned theory.
Fig. 4. Numerical results of (a) reflection coefficient and (b) transmission coefficient for different rotation angles. The superscripts, LL and LR, represent LHCP-LHCP and LHCP-RHCP, respectively.
3. Design, simulation, and evaluation of OAM generator
Using the proposed meta-FSS unit cells with pre-designed phase compensation, the incident spherical wave from the source antenna can be concentrated into the outgoing vortex beam carrying desired OAM mode at the broadside direction. The relationship between the position of the meta-FSS element and rotation angle is expressed as follows: [27,41]
Fig. 6. Snapshots of fabricated prototypes. (a) The top layer of + 1 mode. (b) The middle layer of + 1 mode. (c) The top layer of −2 mode. (d) The middle layer of −2 mode. The bottom metallic layer of the meta-FSS is exactly as same as the top layer.
To experimentally verify the broadband characteristic of the designed OAM generators, both the near-field and the far-field performances were measured. A LHCP helical antenna operating at X-band was designed, fabricated, and employed as the source antenna in the measurement. The structure of the helical antenna with detailed parameters and corresponding measurement performances are presented in Fig. 7, which shows a stable gain of 8.7 dBic at 10 GHz with approximately equal radiation patterns in the xoz and yoz planes. Furthermore, the experimentally obtained axial ratio is below 1.5 dB from 8.9 GHz to 11.6 GHz, which provides a salient circular polarization property to the OAM generator.
Fig. 7. Schematic model of the designed helical antenna and experimental results. (a) Side view of the helical antenna. The structural parameters are helix spacing (HS) = 6.6 mm, wire diameter (WD) = 2 mm, helix diameter (HD) = 9.5 mm, ground plane width (GPW) = 80 mm, and the number of turns is 1.4. (b) Experimentally measured radiation patterns at 10 GHz. (c) Experimentally realized gain and axial ratio versus frequency.
During the measurement process, the fabricated OAM generating panel was located at a distance of 72 mm from the panel center to the helical antenna and fixed by twelve nylon rods (ϕ = 4 mm), which was taken into account in our simulation as well. For the near-field measurement, a 300 × 300 mm2 plane was defined as the sampling plane at a distance of 0.2 m in front of the OAM generating panel. A standard linearly polarized probe antenna was used to scan and detect both the magnitude and phase of E-field with a sampling grid period of 3.0 mm. The experimental setup for near-field measurement is presented in Fig. 8. For far-field measurement, the radiation patterns were obtained in an anechoic chamber, where standard X-band L/RHCP horn antennas (HD-100SGACPH15NL/R, [47]) were connected to a vector network analyzer (Agilent N5227) and employed as the receiver antennas to record its co- and cross polarized radiation component. The OAM generator along with the center of the OAM generating panel.
Fig. 8. Experimental setup for the measurement of magnitude and phase distribution in the near field.
Numerical results of magnitude and phase distributions of E-field in + 1 mode and −2 mode in the near-field at the frequencies of 9.0 GHz, 10.0 GHz and 11.0 GHz are provided in Figs. 9(a)–9(d), while the corresponding experimental results are shown in Figs. 9(e)–9(h), respectively. The major feature of a clockwise helical phase front for + 1 mode and two anticlockwise helical phase fronts for −2 mode within the frequency range of 9.0 GHz to 11.0 GHz is clearly evident in the experimental results. Moreover, amplitude distributions with an obvious null in the center of the ring-shaped patterns are recorded for both the modes in Figs. 9(e) and 9(g). The simulated results exhibit a good agreement with the measured results, which validates the effectiveness of the OAM generator and broadband characteristic of the proposed meta-FSS structure.
Fig. 9. Simulated and experimental results of magnitude and phase distributions obtained by the near-field planar scanning technique at different frequencies. Simulated results of magnitude and phase distributions for (a-b) +1 mode and (c-d) −2. Experimental results of magnitude and phase distributions for (e-f) +1 mode and (g-h) −2 mode.
To characterize the quality of the OAM generator, the purity of the generated OAM mode was analyzed based on the phase sampled along the radius of the red dashed ring in Fig. 9, where distribution of the energy intensity is maximum. According to discrete Fourier transform (DFT) algorithm, the Fourier relationship between the OAM spectrum ${A_l}\; $ and the corresponding sampling phase ψ(φ) can be described as [48]
where ψ(φ) represents the discrete sampling phase value in the sampling plane and ${e^{ - jl\varphi }}$ is the harmonic related to the spiral phase front. Based on Eq. (4) and Eq. (5), the obtained OAM spectra are shown in Fig. 10, which proves that the dominant + 1 mode accounts for the highest proportion of 91.5%, 92.9% and 85.1% in experimental results at 9.0 GHz, 10.0 GHz, and 11.0 GHz, respectively. The corresponding weights for the −2 mode are 85.5%, 87.6%, and 90.2%. Experimentally measured spectra purity is slightly lower than the corresponding theoretical values. This discrepancy may be attributed to the measurement environment (e.g., environment noise) and fabrication tolerance. However, the high (low) percentage of major (parasitic) mode undoubtedly corroborates that our OAM generator can fairly preserve the mode cross-talk at a relatively low level.Fig. 10. Simulated and experimental results of OAM purity at 9.0 GHz, 10.0 GHz and 11.0 GHz. (a-c) +1 mode. (d-f) −2 mode.
The experimental results of the normalized 2-D far-field radiation patterns for + 1 mode are presented in Figs. 11(a)–11(c), and that for the −2 mode are shown Figs. 11(d)–11(f), respectively. Based on Fig. 11, the OAM generator can effectively convert the incident LHCP wave into RHCP outgoing wave from 9.0 GHz to 11.0 GHz with an amplitude null at the center of the vortex beam. For + 1 mode, the main lobe of the radiated OAM patterns points toward the direction of θ = 11° with the peak gain of 11.8 dBic, 13.1 dBic, and 14.6 dBic at 9.0 GHz, 10.0 GHz and 11.0 GHz, respectively. For −2 mode, the main lobe shifts toward the direction of θ = 18° while the peak gain decreases to 8.9 dBic, 9.6 dBic and, 10.9 dBic at the frequencies of 9.0 GHz, 10.0 GHz, and 11.0 GHz, respectively. Furthermore, the cross-polarization levels are lower than −15 dB in the main lobe direction at each frequency for both modes, (e.g., cross-polarization is −17.2 dB for + 1 mode and −16.1 dB for −2 mode at 10.0 GHz), which indicate a good axial ratio. In addition, a good agreement is achieved between experimental and numerical results.
Fig. 11. Simulated and experimental results of far field radiation patterns at xoz plane. (a-c) +1 mode. (d-f) −2 mode.
The transmission efficiency is evaluated and defined as the ratio between the energy carried by cross-polarized transmitted wave and that carried by incident wave, which can be expressed as [43,44]:
A comparison between the proposed and some recent publications on transmissive OAM generators are summarized in Table 2. Features of operation bandwidth, OAM mode, total thickness, number of substrate, measured mode purity, and measured peak efficiency are included in this table. The results confirm that the proposed OAM generator achieved a wider operation bandwidth compared with single-substrate-layer designs ([36,38–39]). Compared to multilayer-substrate-layer designs ([40,41,43–45]), this work exhibits low profile property and maintains a wider bandwidth (except [45]). In addition, the obtained higher than 85.1% mode purity and high transmission efficiency in the designed bandwidth are rarely reported by other works, which demonstrate the practicability of the proposed OAM generator.
Table 2. Comparison between the proposed and other reported transmissive OAM generators
4. Conclusions
We developed a novel transmission-typed wideband OAM generator with the proposed third order meta-FSS. Two panels carrying OAM vortex beams with + 1 mode and −2 mode were designed, simulated, and fabricated. Both near-field and far-field experimental characterizations validated the ability of the developed panels to convert the incident spherical phase front into helical phase front of OAM beam from 9.0 GHz to 11.0 GHz. Owing to its unique advantages of low profile (0.133 λ0), high transmissivity, wide bandwidth, planar structure, and low cost, the proposed configuration provides a potential solution to generate arbitrary OAM modes at radio frequencies, which can be extended to terahertz and optical frequency regions.
Funding
National Key Research and Development Program of China (2017YFA0100203); National Natural Science Foundation of China (61571130,U1637213).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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