Dual-polarized reflectarray for generating dual beams with two different orbital angular momentum modes based on independent feeds in C- and X-bands

Xiangshuai Meng; Jiaji Wu; Zhensen Wu; Tan Qu; Lin Yang

doi:10.1364/OE.26.023185

1. Introduction

In 2007 [1], Thide introduced the notion of OAM from devices in the optical communication regime to those in the wireless radio frequency regime, using circular array antennas for the first time, which generated significant interest from researchers in the field, and led to a flurry of research on this topic. Many methods for generation of OAM waves, also called vortex waves, have been suggested, such as circular array antennas [2–6], spiral phase plates [7–9], spiral reflectors [10–12], and planar air-fed array antennas (reflectarrays [13–18] and transmittarrays [19–22]). These approaches provide a variety of solutions to the problem of blocks that are encountered during the generation of vortex waves. In addition, using circular arrays based on the idea proposed by Thide for introducing large topological numbers into OAM, the compatibility between the sizes of the elements on these circular arrays and their spatial distribution can be limited. Furthermore, because different phases required for different elements in circular arrays [23,24], feed networks (power dividers) and phase shifters should be considered in practical applications, increasing the design complexity and inducing an additional insertion loss, which reduces the efficiency in the system. Furthermore, spiral reflectors can be obtained through bending on traditional reflectors. Especially, in the microwave to millimeter wave domains, the highly accuracy parameters need to be calculated, resulting in a fairly complex design. However, instead of the above two, planar air-fed array antennas that use the printed circuit technology for stable and low cost fabrication are considered to be the practical way for generating vortex waves in the radio frequency domain. As is known, the development of air-fed array antennas was motivated by microstrip patch antennas suffering from narrow bandwidth performance, which negatively affects their application in communication systems. Thus, with a better performance with respect to waves carrying the OAM obtained using the predesigned concept, the bandwidth should be improved for further practical applications. In [19], broadband all dielectric microwave lenses were presented for generating electromagnetic waves with the OAM resonation spanning from 8 to 16 GHz. In addition, simulated radiation patterns of OAM waves were observed to characterize the features of OAM waves. Because different lens areas have different permittivity distributions, it is quite challenging to design practically fabricable systems. In [25], a Panchatatnam–Berry metasurface was proposed for expanding the wideband to a broad range, from 6.95 to 18 GHz, along with the polarization conversion of incident circularly polarized waves. The above two methods for bandwidth expansion were demonstrated through the characterized radiation patterns resonating at the corresponding frequency instead of obtaining the phase and intensity distributions in the near field; thus, the feasibility of the methods for bandwidth expansion could not be verified without calculating the purity of the desired OAM number. In [26], an achromatic electromagnetic metasurface for generating a vortex wave with OAM was proposed to increase the polarization efficiency and expand the bandwidth. Moreover, the above-mentioned methods for bandwidth expansion cannot be generalized to other two or three discontinuously specified bands. Here, for bandwidth expansion of air-fed reflectarrays utilized for generating dual beams corresponding to two different OAM modes, we propose two elemental cells operating in two different bands orthogonally arranged on a reflectarray with suppressed coupling in each linearly polarized direction. Owing to this predesigned concept based on interleaved orthogonal unit-cells, this reflectarray can be decomposed into two reflectarrays operating in two independent bands with orthogonal polarization. Therefore, by properly manipulating the length related to the resonant frequency in the unit-cells, a reflectarray that generates OAM and operates in two specified bands can be realized. In addition, the designed reflectarray has been validated for operation at the center frequency of the C- and X-bands, which lays a solid foundation for multi-band OAM reflectarrays to be employed in base station communication system based on the polarization diversity technology.

2. Element cell design

The difficult part in the element cell design amounts to decreasing the coupling between the elements operating in the two bands; at the same time, avoidance of physical interference given a limited space is also need to be considered. To realize a system with predesigned operation performance in two bands and to achieve a proper layout of orthogonally interleaved units with suppressed coupling shown in Fig. 1(a), a novel reflective element cell consisting of two separately independent element units corresponding to the operation in the C-band in the horizontal polarization and in the X-band in the vertical polarization is described in Fig. 1(b) and 1(c). The design of the proposed element cell is based on the orthogonal characteristic of the currents flowing on the orthogonally arranged elements in the reflectarray, which causes the coupling to be suppressed. The periodicity of the two element cell was set to 21 mm. The designed element cell was etched on the both sides of the substrate F4B, with the dielectric constant of 2.65, the loss tangent of 0.001, and the thickness $H_{s}$ of 0.8 mm. Moreover, there exists an air gap $H_{a}$ of 7 mm between the lower side of the substrate and the metallic plate functioning as the ground plane for wave reflection.

Fig. 1 (a) Interleaved geometry of the dual-band element. (b) Geometrical construction of the C-band element. (c) Geometrical construction of the X-band element.

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Compared with one resonator layer, the phase variation of the two-layer resonators is very linear in 360-degree range and the behavior is similar at the three frequencies. This means a significant improvement in the bandwidth of the element. More importantly, the phase slope versus dimensions is much lower than in the phase response for one resonator layer, which means a low sensitivity to manufacturing tolerances. In this scenario, a good bandwidth and a more than $360 °$ phase response range to be provided for compensation without physical interference in the two bands can be obtained, as shown in Fig. 2(a) and 2(b). Next, both phase response curves are independently decided by only one parameter in each band with the finally optimized parameters listed in Table 1, which significantly reduces the need for the parameter sweep and the computation time for the desired result. In addition, element cell simulations were performed using the commercial simulation software HFSS based on the method of finite elements, with master-slave boundary conditions and Flouqent port excitation. For an x-/y-axis polarized plane wave incident on the X-/C-band element, the x-/y-axis polarized response phase and magnitude versus the length of the X-/C-band element operating at 6/10 GHz, is shown in Fig. 2(c) and 2(d), which reveals that there exists a slight fluctuation caused by the X-/C-band element’s length, leading to a negligible effect to the phase response with respect to the C-/X-band element’s length. Besides, it is worth noting that the energy radiation of the microstrip can be realized through the resonance of the antenna because the microstrip antenna is a resonant antenna. The simplest way to enable the microstrip unit cell not to radiate energy is to make it not resonant. The resonant current in the dipoles along the one polarization direction can only be excited by the incident wave with the same polarization direction. Without resonant current excited, the coupling between the two elements orthogonally interleaved on the reflectarray surface can be weak. In addition, the reflective phase response curves versus the element length operating in the C-band and X-band for different incidence angles are shown in Fig. 2(e) and 2(f). Considering a slight fluctuation compared with the results for normal incidence, a large array within the incidence angle of 25° can be constructed.

Fig. 2 (a) Phase response of the C-band element. (b) Phase response of the X-band element. (c) Effect on the C-band element of the X-band element variation when performing at 6 GHz. (d) Effect on the X-band element of the C-band element variation when performing at 10 GHz. (e) Phase response versus the X-band element length, for different offside angles. (f) Phase response versus the C-band element length, for different offside angles.

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Table 1. Parameter Values of the Unit Cell

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3. Reflectarray design

To utilize the desired reflectarray for generating dual beams carrying two different OAM modes in each polarization direction in the corresponding band, we designed and fabricated a reflectarray composed of up to $21 \times 21$ elements, operating in the X-band in the vertical polarization direction corresponding to the area of 441 mm × 441 mm, and $20 \times 20$ elements performing in the C-band in the horizontal polarization direction with the whole configuration of 420 mm × 420 mm, with two separate linearly polarized horns functioning as the feed located at the focal length (at the normal distance of 500 mm from the designed reflectarray). According to the focal length $f$ and the reflectarray size $D$ , the $f / D$ ratio was estimated as 1.13 and 1.19, for the X-band and C-band, respectively. In addition, to achieve the desired reflectarray performance, the required compensation phase of the two element cells in both corresponding polarization directions orthogonally arranged on the reflectarray was calculated based on [3]

ϕ_{f_{1}}^{m n} = - k_{1} | {\overset{⇀}{r}}_{m n} - {\overset{⇀}{r}}_{f} | + \arg {\sum_{i} \exp [j (k_{1} {\overset{⇀}{r}}_{m n} \cdot {\hat{u}}_{i} \pm l_{i} φ_{i})]}

ϕ_{f_{2}}^{m n} = - k_{2} | {\overset{⇀}{r}}_{m n} - {\overset{⇀}{r}}_{f} | + \arg {\sum_{i} \exp [j (k_{2} {\overset{⇀}{r}}_{m n} \cdot {\hat{u}}_{i} \pm l_{i} φ_{i})]}

where

k_{1}

,

k_{2}

respectively refer to the wavenumbers operating at the center frequency of the X-band and C-band,

{\overset{⇀}{r}}_{m n}

denotes the position vector of the

m n^{t h}

element,

{\overset{⇀}{r}}_{f}

is the position vector of the phase center of the feed, and

{\hat{u}}_{i}

is the radiation direction of the

m n^{t h}

beam carrying the corresponding OAM modes

l_{i}

.

In addition, the designed reflectarray is considered to reflect spherical waves coming from the feed into two beams at each band, as shown in Fig. 3, with Beam1, Beam2 operating in the C-band pointing to ( $θ = 30 °, φ = 0 °$ ), ( $θ = 30 °, φ = 180 °$ ) carrying the OAM mode of $l = 1$ , $l = - 1$ , respectively, and Beam1, Beam2 operating in the X-band pointing to ( $θ = 30 °, φ = 90 °$ ), ( $θ = 30 °, φ = 270 °$ ) carrying the OAM mode of $l = 1$ , $l = - 1$ .

Fig. 3 Directions of the OAM beam in the two bands.

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With the formula for the phase required to compensate the phase difference between the feed and the element cell located on the reflectarray derived from Eq. (1) and Eq. (2), the two-dimensional (2D) phase difference patterns that should be compensated at 6 GHz and 10 GHz are given in Fig. 4(a) and 4(b), respectively. Therefore, considering the compensation phase calculated from Eq. (1) and the reflective phase response curves with respect to the element length shown in Fig. 2, the corresponding sizes of the element cells distributed at the different positions of the reflectarray can be computed quickly. Furthermore, the designed dual-polarization dual-band OAM generation reflectarray is fed by two separated horn antennas featuring linear polarization with the aperture of 37 mm × 47 mm in the X-band, the aperture of 63 mm × 83 mm in the C-band, and the radiation patterns of the E-plane and H-plane of the feed operating in the C-band and X-band are approximately equal to each other, which satisfies the condition as a feed. In addition, it should be emphasized that the entire reflectarray structure comprising the predefined PCB and the standard feeding horn should have a precise assembly support frame, to guarantee the alignment between the reflectarray and the feed source.

Fig. 4 (a) Compensation phase for the C-band reflectarray at 6 GHz. (b) Compensation phase for the X-band reflectarray at 10 GHz.

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4. Simulation and measurement results

To further experimentally demonstrate the proposed theory, the assembled reflectarray suggested in Fig. 5 was tested in an anechoic chamber. First, for the near-field measurement process at 6 GHz, the horizontal polarization horn at the center frequency of 6 GHz with the standard gain of 10 dB is set as the feeding antenna, and the center of the whole assembled antenna is aligned to the center of the probe at the initial calibration position. In addition, the sampling plane of 2.025 m × 2.025 m with the step of 25 mm is used to obtain the near-field dates which are employed to calculate the far-field radiation. Next, the turntable move backward to the position where the distance between the probe and the center of the designed reflectarray is set as 2 m, and it takes twice the measurements to obtain the magnitude and phase of the two beam with different OAM modes when the turntable rotates $+ 30 °$ and $- 30 °$ , respectively, and the scanning plane is perpendicular to each radiation beam with an area of 1.525 m × 1.525 m, covering the main radiation region at 6 GHz. Similar to the method at 6GHz, the size of the sampling plane set as 1.515 m × 1.515 m with the sampling interval 15 mm is considered to obtain the near-field dates which are applied to calculate far-field radiation pattern at 10GHz, the size of the sampling plane situated at 2 m over the reflectarray is 0.915 m × 0.915 m with the step of 15 mm.

Fig. 5 (a) Configuration of the experimental system for the designed reflectarray using the near-field scanning technology. (b) Photograph of the fabricated reflectarray.

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From the far-field measured radiation patterns calculated based on the near-field sampling dates presented in Fig. 6, the measured radiation patterns are concluded to be in a good agreement with the results of simulations in dual-band (DB) and single-band (SB) element reflectarray, and there exists a null in $\pm 30 °$ that matches the hollow characteristics of energy transmission for the desired wave carrying OAM. Besides, at X-band, the reflectarray has the maximum gain of 19.9 dB for $l = 1$ and 19.8 dB for $l = - 1$ , obtaining the aperture radiation efficiency of 7.1% at 10 GHz. For C-band, the maximum gain is 18.8 dB for $l = 1$ and 17.7 dB for $l = - 1$ , with the aperture radiation efficiency of 13.8% at 6 GHz.

Fig. 6 (a) Far-field radiation pattern at 10 GHz. (b) Far-field radiation pattern at 6 GHz.

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Moreover, the simulated 2D far-field normalized radiation patterns in DB element refectarray, with resonances at 5.5 GHz and 6.5 GHz respectively, are shown in Fig. 7(a) and 7(b) for a typical OAM wave. The simulated 2D far-field radiation patterns operating at 9.5 GHz and 10.5 GHz are shown in Fig. 7(c) and 7(d), revealing energy nulls in $\pm 30 °$ .

Fig. 7 (a) Simulated far-field radiation pattern at 9.5 GHz in DB element reflectarray. (b) Simulated far-field radiation pattern at 10.5 GHz in DB element reflectarray. (c) Simulated far-field radiation pattern at 5.5 GHz in DB element reflectarray. (d) Simulated far-field radiation pattern at 6.5 GHz in DB element reflectarray.

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In addition, the measured 2D planar far-field intensity distribution achieved using the Discrete Fourier Transform have a typical doughnut-shaped amplitude with singularity in the intensity, as shown in Fig. 8(a) and 8(b), respectively. Furthermore, from the results in Fig. 9, it can be seen a phase wave front with an obvious spiral shape along with the phase singularity causing the amplitude null at the center of the desired beam, which completely conforms to the unique characteristics of the vortex wave.

Fig. 8 (a) Measurement of 2D far-field intensity distribution at 10 GHz in DB element reflectarray. (b) Measurement of 2D far-field intensity distribution at 6 GHz in DB element reflectarray.

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Fig. 9 Simulated intensity and phase in the first row in SB element reflectarray. Simulated intensity and phase in the second row in DB element reflectarray. Measured intensity and phase in the third row in DB element reflectarray.

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The 2D simulation phase and intensity pattern for 5.5 GHz, 6.5 GHz within the C-band and those for 9.5 GHz, 10.5 GHz within the X-band are respectively shown in Fig. 10. The simulation results in Fig. 9 and Fig. 10 present the spiral-shaped phase and the doughnut-shaped intensity pattern, which strongly suggests the obtained wave carrying the desired OAM modes in the designed directions. Specially, the purity of the orbital angular momentum generated by the designed reflectarray can be taken into account to be more convincing in practical applications.

Fig. 10 Simulated intensity and phase in the first row in DB element reflectarray operating at X-band. Simulated intensity and phase in the second row in DB element reflectarray operating at C-band.

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Next, we calculated the OAM spectrum using the Discrete Fourier Transform algorithm based on the phase sampled at the radius of a black ring where the energy intensity distribution is the largest. From [11,27], the Fourier relationship between the OAM spectrum $P (α)$ and the corresponding sampling phase $ψ (φ)$ can be expressed by

P (α) = \frac{1}{2 π} \int_{0}^{2 π} ψ (φ) d φ \exp (- j l φ)

ψ (φ) = \sum_{- \infty}^{+ \infty} P (α) \exp (j l φ) .

Here, $ψ (φ)$ refers to the discrete sampling phase value in the sampling plane, while $\exp (- j l φ)$ is the harmonics related to the spiral phase front. Henceforth, the normal weight of the OAM modes is obtained by applying Eq. (3) and Eq. (4).

Considering the simulated phase distributed at the maximal intensity position simulated using DB element reflectarray, we obtain the simulated OAM spectrum with the predesigned OAM modes of $l = 1$ , $l = - 1$ at 5.5 GHz and 6.5 GHz, and the desired OAM numbers of $l = 1$ , $l = - 1$ at 9.5 GHz and 10.5 GHz, as shown in Fig. 11. From the simulated OAM spectrum shown in Fig. 11, the dominating OAM modes account for more than 60%. It is worth pointing out that, as shown in Fig. 12, based on the measurement results by DB element reflectarray, the desired OAM modes have dominant weights, including the OAM modes of $l = 1$ , $l = - 1$ operating at 6 GHz with the weights of 70.05%, 62.41%, and the OAM modes of $l = 1$ , $l = - 1$ operating at 10 GHz with the weights of 84.26%, 63.22%, respectively. However, parasitic modes with the weight of less than 20% slightly affect the other predesigned dominant OAM modes; thus, the modes generated by the designed reflectarray feature good purity. In addition, the weight difference between the SB and DB simulated result is less 7% shown in Fig. 12, which means the purity of the OAM modes performing in one band can be slightly affected by another band in DB element reflectarray.

Fig. 11 (a) Simulated OAM spectrum of $l = 1$ at 9.5 GHz. (b) Simulated OAM spectrum of $l = - 1$ at 9.5 GHz. (c) Simulated OAM spectrum of $l = - 1$ at 10.5 GHz. (d) Simulated OAM spectrum of $l = 1$ at 10.5 GHz. (e) Simulated OAM spectrum of $l = 1$ at 5.5 GHz. (f) Simulated OAM spectrum of $l = - 1$ at 5.5 GHz. (g) Simulated OAM spectrum of $l = - 1$ at 6.5 GHz. (h) Simulated OAM spectrum of $l = 1$ at 6.5 GHz.

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Fig. 12 (a) Simulated and measured OAM spectra of $l = 1$ at 10 GHz. (b) Simulated and measured OAM spectra of $l = 1$ at 10 GHz. (c) Simulated and measured OAM spectra of $l = 1$ at 6 GHz. (d) Simulated and measured OAM spectra of $l = 1$ at 6 GHz.

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5. Conclusion

To sum up, a novel dual-band dual-polarized reflectarray for generating dual-beams carrying two different OAM modes in each band with two separate feeds was designed, fabricated, and validated. The predesigned element cell consists of two orthogonally arranged units corresponding to two resonating bands in two orthogonal polarization directions, which can independently compensate the required phase with suppressed coupling without physical interference owing to the orthogonal current flowing. Based on the reflective phase response with respect to the elements’ dimensions and the spatial phase difference between the feed and the elements’ distributed on the reflectarray, a practical reflectarray can be implemented. Moreover, simulation results are in a good agreement with the results of measurements, and the calculated OAM spectrum based on the sampling data reveals dominant weights for the designed OAM modes pointing to different directions in the two bands, compared with parasitic modes. Furthermore, from the far-field radiation pattern shown in Fig. 6, the intensity and phase displayed in Fig. 9, and the purity of the OAM modes calculated in Fig. 12, we conclude that the coupling between the two elements orthogonally distributing on the reflectarray can be neglected, resulting in a good polarization isolation. This presented reflectarray pave a way to generate the multi-band OAM waves for radio and microwave wireless communication application.

Funding

National Natural Science Foundation of China (NSFC) (No. 61601355, 61775175 and 61571355); China Postdoctoral Science Foundation (2016M602770); Postdoctoral Science Foundation in Shaanxi Province.

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Parameters	Values	Parameters	Values	Parameters	Values
$R$	3.7 mm	$W_{y}$	1 mm	$L_{y 4}$	$0.48 * L_{y 1}$
$W_{x}$	0.3 mm	$G_{y}$	3 mm	$P$	21 mm
$G_{x}$	0.4 mm	$L_{y 2}$	$0.8 * L_{y 1}$	$H_{s}$	0.8 mm
$L_{x 2}$	$0.8 * L_{x 1}$	$L_{y 3}$	$0.6 * L_{y 1}$	$H_{a}$	7 mm

Dual-polarized reflectarray for generating dual beams with two different orbital angular momentum modes based on independent feeds in C- and X-bands

Abstract

1. Introduction

2. Element cell design

3. Reflectarray design

4. Simulation and measurement results

5. Conclusion

Funding

References

Cited By

Figures (12)

Tables (1)

Equations (4)

Optics Express