1. Introduction

The orbital angular momentum (OAM) [1,2], developed along with spin angular momentum (SAM) [3,4], has been studied extensively in recent years [5–8]. In quantum communications, the OAM of photon has been used to achieve the three-dimension entanglement and superdense coding [5,6]. The OAM has also been used in astrophysics to detect the rotation of large astronomical objects [7,8]. OAM waves with different mode indexes are orthogonal to one another [9] and therefore each OAM mode can be used to obtain an independent communication channel. This interesting property has attracted much attention of communication researchers and engineers, from acoustic communications [10] to optical communications [11–13]. The first free-space communication using an OAM light beam was demonstrated in 2004 [14]. In 2012, Wang et al. did the first experiment achieving a terabit free-space data transmission by using the OAM multiplexing [15]. Meanwhile they also did a similar experiment with optical fiber [16]. Recently, Mario Krenn et al. [17] successfully demonstrated a very long OAM free-space transmission of over 143 km using a laser beam.

As the potential applications, the OAM also have been introduced to the area of radio wireless communications. Thus far, all OAM radiators have been excited up to two OAM modes only, giving no more than two wireless communication channels for each radiator. In 2007, Thide et al. designed the first microwave OAM radiator using a circular distributed radiator array [18]. After that, many different methods have been proposed to generate and detect the OAM waves. The metamaterials and metasurfaces, which consist of sub-wavelength unit structures, have been widely investigated to generate the OAM waves. In [19–24], the phase-engineered metasurfaces have been used to generate the OAM mode at microwave band. In [25], a complementary metasurface with ultrathin thickness for the OAM generation has been investigated. Using a similar approach, a generation method based on the frequency selective surface has been studied [26]. The all-dielectric material has been introduced for the OAM generation at microwave band [27,28]. In addition, the metalenses with switchable functionalities has been used for the OAM generation [29]. In most of the cases, the multiple radiators were used to simultaneously transmit multiple microwave signals, with each radiator element transmitting a single signal only [29,30]. There are also some studies in which only a single OAM radiator was considered, including the traveling wave loop antenna [31], patch antenna [32], horn antenna [33], whispering gallery mode resonator [34] and hemispherical dielectric resonator antenna [35]. In 2014, Yan et al. multiplexed 8 OAM signals generated by four OAM antennas, with each antenna radiating two orthogonal OAM signals only [36]. The multiplexed signal was transmitted through a single aperture of a lens. In 2016, the multi-mode OAM multiplexing method was investigated using a shared-aperture antenna array [37,38], not a single radiator. Very recently, Zheng et al. demonstrated a microwave OAM-mode multiplexing communication system [39]. In their work, four independent signals were transmitted using a reflector antenna, which is fed by two radiators for generating four OAM modes. In other words, each radiator, again, has two OAM modes only. The lens and reflector of these studies are merely used as a focusing component for the OAM beam, not as a radiator that generates OAM modes. Thus far, more than one OAM radiator have still been required to obtain more than two channels.

Since multiple radiators can be used to increase the channel capacity, it has been widely queried about the usefulness of OAM radiators because no obvious advantages can be seen when compared with multiple-input-multiple-output (MIMO) systems [40–43]. This paper presents the single OAM radiator that can multiplex more than two wireless signals. Our radiator is a cylindrical dielectric resonator antenna (DRA) [44–46] simultaneously excited in two degenerate HEM_21δ modes and the TM_01δ mode. The former and latter are OAM modes of l = ±1 and l = 0, respectively. The three OAM modes work at the same frequency of 2.6 GHz, which was achieved by carefully designing the dimensions of the DRA and the feed network. In the next section, the phase pattern and intensity distribution of the tri-mode DRA are measured and simulated in both the near- and far-field regions. Finally, an experimental near-field communication link is setup to demonstrate that our DRA can provide three independent wireless channels.

2. Antenna configuration and working principle

Figure 1(a) shows the tri-mode DRA with three OAM modes of l = ±1 and l = 0. The structure has two substrates and the details are given in Appendix B and Appendix C. The DRA, made of low-loss composite material, has a relative permittivity of ɛ_r = 10, radius of r, and height of h. It rests on the upper substrate. The resonators were made of a low-loss material by Laird Technologies. They were accurately machined using the computer numerical control method. The detailed dimensions of the antenna are shown in Fig. 8 of Appendix B. In this antenna, Probe 1 and Probe 2 touch the side wall of the DRA, exciting the l = ±1 OAM modes. Figure 1(b) shows a photo of the DRA with the two probes, which are connected to the two output ports of a hybrid coupler printed on the lower substrate, as shown in Fig. 1(c). The remaining two ports of the hybrid coupler are connected to Ports 1 and 2 of this three-port radiator. When only Port 1 is excited, the phase difference between Probes 1 and 2 is + 90°, exciting the l = +1 OAM mode. But when only Port 2 is excited, the phase difference between the two probes is −90° and the l = –1 OAM mode will be excited. Port 3 is connected to the planar cross patch for exciting the TM_01δ mode of the DRA [47], giving a conventional linear-polarized wave (l = 0). The details of the hybrid coupler and planar cross patch feed are shown in Fig. 9 of Appendix C. Between the upper and lower substrates is the ground plane of the antenna, as shown in Fig. 1(b) and Fig. 8(c). The upper and lower dielectric substrates of the antenna are RT/duroid 6006 and RT/duroid 6002, respectively, provided by the Rogers corporation. Because of the property of the hybrid coupler, Ports 1 and 2 are isolated from each other. Port 3 is also isolated from Ports 1 and 2 because its field is orthogonal to those of Ports 1 and 2. Also, by using the probes and cross patch, the mutual coupling between the HEM_21δ modes and TM_01δ mode can be further suppressed. It should be mentioned that although multiple OAM modes can be simultaneously generated using metasurface [19–29,48–51], their OAM modes have been generated from a single port and therefore all of them carry the same information. It is different from our design that three ports are used and therefore three different sets of information can be sent at the same time.

 

Fig. 1. Schematic and internal field of OAM DRA. (a) Schematic of OAM DRA radiating three different OAM modes of l = 1, l = –1 and l = 0 excited at Port 1, Port 2, and Port 3, respectively. (b) Photo showing the perspective view of OAM DRA prototype. (c) Photo showing the hybrid coupler printed at the bottom of OAM DRA prototype. (d) Internal H-fields of OAM DRA at the xoy-plane for OAM modes of l = +1, l = −1, and l = 0.

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In designing the OAM DRA, the most challenging task is to excite the proper DRA mode that can be used to generate a twisted (OAM) wave. Here, the higher-order DRA mode was used to generate the twisted wave. Below is a simple analysis of the DRA. For the HEM_mnδ mode of a cylindrical DRA, its radiation field can be written as E_θ ≈ A_n(θ, r)cos(mφ), E_φ ≈ B_n(θ, r)cos(mφ), and E_r=0, where A_n and B_n are functions of θ and r only, and m and n denote the mode indexes in the azimuthal and radial directions, respectively [44]. Suppose the DRA is excited by two quadrature sources of equal amplitude with an angular displacement of α=(b + 1/2)π/m from each other, where b is arbitrary integer, the superimposed field components of the two sources can be given in the Cartesian coordinate as E_x= C_n(θ, r)e^{−j(m−1)φ}, E_y= D_n(θ, r)e^{−j(m−1)φ}, E_z= 0, where C_n and D_n are functions of θ and r only. The superimposed wave is a twisted wave with an OAM index of l, where l = m –1. When the HEM_21δ mode is excited by the two sources (i.e., m = 2), two OAM modes of l = ±1 can be generated. It should be noted that since the two excitation sources (Probes 1 and 2) are fed by the hybrid coupler, the signals at the two probes have a constant phase difference. In other words, the two HEM_21δ modes excited by the two probes are coherently superposed, generating an OAM wave with l = +1 or − 1. A third wave (l = 0), which is a conventional linear-polarized wave, is associated with the TM_01δ mode of the DRA. Figure 1(d) shows the internal H-fields of the different DR modes on the xoy-plane (equatorial plane). As mentioned before, the feeds of Probes 1 and 2 have a phase difference of 90° when Port 1 is fed, exciting the HEM_21δ mode with an OAM index of l = +1. With reference to the figure, the H-field pattern shows a quadrupole characteristic in the equatorial plane [52], showing that the azimuthal factor cosmφ has a variation of m = 2. When Port 2 was fed, similar field distributions were found with different field directions (l = −1). Finally, when Port 3 is excited, the H-field forms a single loop, verifying that it is the TM_01δ mode of the DR (l = 0).

3. Results

3.1 Antenna characteristics

To verify the theory, the cylindrical DRA operating at 2.6 GHz was fabricated and measured. The simulation and measurement setup is discussed in Appendix A. Figures 1(b) and 1(c) show the fabricated DRA and more details can be found in Fig. 8 of Appendix B and Fig. 9 of Appendix C. Figures 2(a)–2(d) shows the simulated and measured S-parameters of the DRA. With reference to the figure, good agreement between the measured and simulated results can be observed. It can be found from the figure that Ports 1, 2 and 3 are all matched very well (|S|< –10 dB). Also, across the operation band (2.59–2.61 GHz), a good isolation of higher than 14 dB is obtained between any two ports. Since the material has a high dielectric constant of 10, the operating bandwidth of the antenna is not very wide. The bandwidth can be increased by using a lower dielectric constant, but the dielectric constant cannot be too low or a weak resonant mode will be obtained. Figures 2(e)–2(g) and 2(h)–2(j) show the measured near-field phase pattern at z = 330 mm (3λ₀) and power density, respectively, where λ₀ is the wavelength at 2.6 GHz in air. They were measured with an ORBIT/FR near-field measurement system (as shown in Fig. 7(a)) having a measurement aperture of 300×300 mm². With reference to Fig. 2(e), Port 1 has an OAM mode of l = +1 because the phase of the E-field rotates (starting from the origin) in the counterclockwise direction as the wave propagates. For Port 2 (Fig. 2(f)), an OAM wave with l = –1 is generated and the phase rotates in the clockwise direction. In both cases, the phase change is 2π after one rotation. Port 3, however, is very different from Ports 1 and 2 because it generates a conventional EM wave (or OAM wave of l = 0) with zero phase change after one rotation (Fig. 2(g)). The near-field amplitudes of the three waves are now discussed. As can be observed from Figs. 2(h) and 2(i), each OAM wave (l = ±1) has a null field at the center of the beam, as expected. The results are similar to those of the twisted optic OAM beams [2]. It was found that its maximum field is stronger than the minimum field by at least 18 dB. The case of l = 0 also has a null field at the center of its beam, which is expected for the TM_01δ mode [53]. Its corresponding simulated results are shown in Fig. 10 of Appendix D. It can be observed that the simulated results reasonably agree with the measured results.

 

Fig. 2. Results of OAM DRA. The results were simulated with the software ANSYS HFSS, which is based on the finite element method. The detailed dimensions of the prototype can be found in Fig. 8 of Appendix B and Fig. 9 of Appendix C. (a-d) Simulated and measured S-parameters at the three ports. (e-g) Measured phase diagram of OAM modes with l = ±1 and l = 0. (h-j) Measured field intensity of OAM modes with l = ±1 and l = 0. (k) Measured mode purity using the spiral spectrum algorithm.

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The purity of the OAM waves is analyzed using the spiral spectrum algorithm [54–56], which is a quantitative study of the mode index for OAM beams. Figure 2(k) shows the measured mode index spectrum from l = –3 to l = +3 extracted from our measured OAM beams. With reference to the figure, for the measured result of the l = –1 mode, the mode-index purity is highest for l = –1 but very low (ideally zero) for others (l = –3, –2, 0, 1, 2, 3), as expected. Similar results are observed for the measured results of l = 0, 1. It was found that for each OAM wave (l = ±1), over 90% of the total power is carried by the azimuthal component (e^±jφ). For the l = 0 case, the spectrum purity is more than 91%. Again, reasonable agreement between the measured and simulated results can be observed by comparing Fig. 2(k) with Appendix D Fig. 8(g).

Next, the polarizations of the generated waves are discussed. In our design, two HEM_21δ modes are used to generate an OAM mode. These two degenerate modes generate a circularly polarized wave, excited by two quadrature sources with the same amplitude. In other words, both mode 1 (l = + 1) and mode 2 (l = –1) give circularly polarized waves. For port 3, the mode with l = 0 generates a linearly polarized wave, which has been widely studied in the open literature. Figure 3 shows the vector near-field distributions of the different modes at different times in one period. With reference to the figure, the black arrow at an arbitrary location refers to the main direction of the electric field. It can be seen from the figure that the direction of the mode-1 field (l = +1) changes anticlockwise, indicating that the wave is right-hand circularly polarized (RHCP). For the mode-2 field (l = –1), the direction of the field changes clockwise and the wave is left-hand circularly polarized (LHCP). In contrast, the direction of the field of port 3 changes linearly, showing that mode 3 generates a linearly polarized wave.

 

Fig. 3. Simulated vector near-field distributions of different modes at different times in one period T. (a-d) Simulated vector field distributions of mode 1 (l = +1). (a) t = 0. (b) t = T/4. (c) t = T/2. (d) t = 3T/4. (e-h) Simulated vector field distributions of mode 2 (l = –1). (e) t = 0. (f) t = T/4. (g) t = T/2. (h) t = 3T/4. (i-l) Simulated vector field distributions of mode 3 (l = 0). (i) t = 0. (j) t = T/4. (k) t = T/2. (l) t = 3T/4.

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To further verify the polarizations of the waves, the axial ratios (ARs) of these modes at the φ = 0 plane are studied in Fig. 4. It is known that the ARs of the perfect circular and linear polarizations are 0dB and ∞, respectively. With reference to the figure, the ARs of both mode 1 and mode 2 are lower than 3 dB, whereas that of mode 3 is much higher than 3 dB, as expected.

 

Fig. 4. Simulated axial ratios (ARs) of different modes in the φ = 0 plane.

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The far field characteristics of the DRA were measured using a Satimo Starlab measurement system. Figures 5(a)–5(c) and 5(d)–5(f) show the measured 3D and 2D normalized far-field radiation patterns of the DRA, respectively. The results are presented using the coordinate system defined in Fig. 1(a). A null field can be observed in the far field for all the cases of l = 0, ±1, as expected. In each case, the maximum field is stronger than the minimum field by more than 20 dB. It is worth mentioning that for the two degenerate HEM_21δ modes, the cross-polarized (X-pol) fields can be suppressed by using a differential feed [57]. This can be done by using four vertical probes instead of two vertical probes with proper phase shifts between the probes. Figures 5(g) and 5(h) shows the measured peak gain and total efficiency (mismatch included) of the radiator, respectively. It was found that the peak gains are obtained at θ = 35° and 37° for l = ± 1 and l = 0, respectively. As can be observed from the figure, the peak gain of the radiator for l = ±1 is about 5 dBi, whereas that for l = 0 is about 4.3 dBi. The total efficiency of the radiator is higher than 80% at 2.6 GHz. The corresponding simulated field pattern and radiator gain is shown in Fig. 11 of Appendix E and they are in reasonable agreement with the measured results.

 

Fig. 5. Measured radiation characteristics of OAM DRA. (a-c) Measured normalized 3D far-field radiation pattern. (d-f) Measured 2D far-field radiation pattern at different planes. (g) Measured radiator gain with mismatch included. (h) Measured total radiator efficiency with mismatch included.

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3.2 Communication link measurement

The multimode OAM DRA can be deployed to transmit three independent signals. For demonstration, a communication link was setup as shown in Fig. 6(a). In the setup, two identical DRAs excited in the three modes (l = 0, ±1) are used as the transmitting and receiving radiators. For the transmitting DRA, each of the three ports was input a signal of 0 dBm (1 mW) and a bandwidth of 20 MHz (2.59–2.61 GHz). The transmitting and receiving DRAs are placed face-to-face, separated by a distance of 160mm (∼1.5λ₀ at 2.6 GHz), operating in the near-field region

 

Fig. 6. Measured signal-to-noise ratio (SNR) and decoding rate of wireless communication system deploying two three-port OAM radiators. (a) Communication system setup. (b) measured SNR of the OAM antenna-based commutation system. (c) Measured decoding rate using two identical three-port OAM DRAs as the transmitting and receiving radiators. (d) Measured decoding rate using two identical three-port diversity DRAs as the transmitting and receiving radiators for comparison.

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Figure 6(b) shows the measured signal-to-noise ratio (SNR) of the OAM antenna communication system, recoded at every second. With reference to the figure, almost all of the measured SNRs are higher than 30 dB, showing a good communication quality. The decoding rate of the communication systems are shown in Figs. 6(c) and 6(d). With reference to the figure of decoding rate, the three independent signals can be decoded successfully, with the peak and average decoding rates given by 100% and 89%, respectively. Here the decoding rate is defined as the ratio of the amount of the successfully decoded data to that of the total transmitted data in a unit time (1 second here). The successful decoding shows that the three signals can be distinguished from each other at the receiving end. It means that the radiated signals are orthogonal to each other, which is an important characteristic of OAM waves. For comparison, two identical reference three-port diversity DRAs [58] that only radiate linearly polarized fields were also designed at 2.6 GHz and used in the same setup. The original three input signals were used to feed the three ports of the diversity DRA and the measured results are shown in Fig. 6(c). As compared with the OAM DRA system, the three-port diversity DRA system has zero decoding rate for most of the time. Its peak and average decoding rates are only 64% and 8%, respectively. This poor result is not surprising because the three EM waves radiated by the diversity DRA are not orthogonal and therefore cannot be distinguished properly from one other at the receiver end. Finally, it should be mentioned that the transmission system can be extended to some extent by adding a lens [59] to the system. In this case, the communication distance can be enhanced although the antenna may still operate in its near field region.

4. Summary and discussion

This paper has presented a single OAM radiator that simultaneously transmits three independent EM waves in air at a single frequency. The design has been based on the theory of DRA. Three resonant modes of the cylindrical DRA were excited at 2.6 GHz, namely two degenerate HEM_21δ modes and the TM_01δ mode. The DRA has three ports for transmitting/receiving three different EM waves. A hybrid coupler has been used to provide a quadrature dual feed for Ports 1 and 2, causing the two degenerate HEM_21δ modes to become two OAM modes of l = +1 and l = −1. For Port 3, a planar feed has been used to excite the DRA and generates a linearly polarized wave (l = 0). The DRA was simulated with commercial software. To verify the simulation, a prototype was fabricated and its reflection coefficient, near- and far-field patterns, radiator gain, and total efficiency were measured. It has been found that the measurements agree reasonably well with the simulations. Also, a wireless communication system using two identical three-port OAM DRAs was setup to test the simultaneous transmission and reception of three independent signals.

Compared with the previous OAM-based systems that multiplex EM waves using a multi-antenna system or an antenna array, our OAM DRA is a single radiator being able to transmit three independent signals at a single frequency. The DRA is excited in its three resonant modes at the same frequency, with each resonant mode corresponding to an OAM mode that gives an independent wireless channel. It is different from the previous cases [37,38] in which the fields of several antenna elements are combined. As discussed above, two degenerate higher-order modes of the cylindrical DRA can be used to generate the OAM mode. The HEM_mnδ mode can generate an OAM mode with a mode index of l, where |l| = m – 1. Therefore, the degenerate HEM_21δ modes can be used to generate the OAM modes with l = ±1. Similarly, the degenerate HEM_31δ modes can be used to generate the OAM modes with l = ±2. It is worth mentioning that different DRA modes generally have different resonance frequencies. Therefore, the DRA can also be used to generate different OAM modes at different frequencies.

It should be mentioned that since the working principle of our design is independent of frequency, our microwave design, in principle, can be extended to work in millimeter-wave band, THz band, and even optical band. In THz and optical bands, it needs to substantially miniaturize the radiator and the nano-fabrication or other fabrication methods are needed. Also, to improve the radiator efficiency, low-loss materials in THz and optical bands should be considered, such as the crystalline silicon (c-Si), GaAs, and titanium dioxide. In addition, a low-loss feed network using the coplanar waveguide [60] and nanostrip line [61] should be deployed.

Appendix A Experimental methods

a) Calculation and simulation method

The calculated results of the paper were obtained using MATLAB software. Commercial package ANSYS HFSS (High Frequency Structural Simulator), based on the finite element method, was used to design and optimize the OAM DRA. In the simulation, each port was excited by a wave-port with a characteristic impedance of 50 Ω.

b) Configuration of OAM DRA

Based on the optimized design, two identical OAM DRA prototypes were fabricated and the dimensions of each DRA are given in Fig. 8. They are made of composite material with a relative permittivity of 10. The structure has two microwave substrates that are stacked together (Fig. 9); the lower substrate (left part of Fig. 9) provides the hybrid coupler for Ports 1 and 2, whereas the upper substrate provides the planar cross-patch feed (right part of Fig. 9) for Port 3. Their ground planes are located at the interface of the two substrates and touch each other. The upper and lower substrates have relative permittivities of 2.94 and 6.15, and dissipation factor of 0.0012 and 0.0025, respectively.

c) S-parameters measurement

The S-parameters were measured with Keysight network analyzer 8361A.

d) Phase pattern and field intensity measurement

The phase pattern and field intensity of the OAM DRA were measured with an ORBIT/FR near-field measurement system as shown in Figs. 5(a)–5(b). In the measurement, an open-ended waveguide was used as the probe to detect EM waves. In the measurement, only one port of the DRA was excited at a time with the remaining two ports terminated with 50-Ω loads.

e) Far-field measurement

The far-field characteristics were measured with a Satimo Starlab near-field measurement system, as shown in Figs. 5(c)–5(d). There are 16 probes in the measurement system. Each probe has two dipole antennas to obtain the near-field data of the radiator under test. A near-field to far-field transformation is done by software to obtain the far-field characteristics of the radiator, including the radiation pattern, radiator gain, and radiation efficiency. Again, only one port was excited at a time and the remaining two ports were terminated with 50-Ω loads.

 

Fig. 7. Photographs of experimental set up for measuring phase and field density and far field characteristics. (a)–(b) ORBIT/FR near-field measurement setup for measuring the phase and field density. (a) Measurement setup. (b) Location of OAM DRA. (c)–(d) Satimo StarLab system for measuring radiation pattern, radiator gain, and total radiator efficiency. (c) Perspective view. (d) Measurement probes and OAM DRA.

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Appendix B Detailed demensions of the radiator

 

Fig. 8. Geometry of OAM DRA. (a) Perspective view. (b) Top view. (c) Side view. The dimensions of the radiator are given by W_f = 1.94 mm, L₁ = 26 mm, W₁ = 5 mm, L₂ = 16.5 mm, W₂ = 3.35 mm, L₃ = 16.5 mm, W₃ = 2 mm, R₁ = 10.4 mm, R_g = 70 mm, r = 24 mm, R_{sma_in} = 0.65 mm, h_sub1 = 0.76mm, h_sub2 = 0.63 mm, h_cop = 0.018 mm, h_pin = 11 mm, h = 18 mm, and α = 135°

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Appendix C Photo of OAM DRA prototype and feed network

 

Fig. 9. Photo of OAM DRA prototype and feed network.

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Appendix D Simulated results of OAM DRA

 

Fig. 10. Simulated results of OAM DRA. (a)–(c) Simulated phase diagram of OAM modes with l = +1, l = –1, and l = 0 at a distance of z = 330mm (3λ₀). (d)–(f) Simulated field intensity of OAM modes with l = +1, l = –1, and l = 0 at a distance of z = 330mm. (g) Simulated mode purity using the spiral spectrum algorithm.

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Appendix E Simulated far-field results of OAM DRA

 

Fig. 11. Simulated far-field results of OAM DRA. (a)–(c) Simulated normalized 3D radiation patterns of OAM modes with l = +1, l = –1, and l = 0. (d)–(f) Simulated normalized 2D radiation patterns of OAM modes with l = +1, l = –1, and l = 0 at different planes. (g) Simulated radiator gain.

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Funding

National Natural Science Foundation of China (61361166010); Research Grants Council (N_CityU134/13); Fundamental Research Program of Shenzhen City (JCYJ20170818094814530).

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