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Abstract
In this paper, a single elliptical patch antenna is proposed to generate double-deflection orbital angular momentum (OAM) vortex beams. The physical mechanism of an equivalent uniform elliptical array (UEA) is constructed and analyzed by using the theory of characteristic modes. The elliptical patch antenna can be fed with a 3dB directional coupler to generate the double-deflection vortex beams with single OAM mode or mixed OAM modes. The simulation and measurement results verify that the proposed single elliptical patch antenna is a simple, miniaturized, and multifunctional generator for OAM vortex beams.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Vortex beams have received widespread attention in various electromagnetic bands because they can bring orbital angular momentum (OAM), and their infinite modes are mutually orthogonal in theory, all of these features show enormous potential in many fields [1–5]. Since the vortex beams were introduced into microwave bands [6], their potential applications in wireless communication, radar imaging and other fields have promoted the research and design of vortex beam generators [7,8], including uniform circular array (UCA) [9], reflective [10–13] or transmissive [14,15] antenna arrays, etc. For UCA, the number of array elements will increase with the increase of OAM mode, resulting a huge size of the array and a complex feeding network. For reflective and transmissive antenna arrays, they have a strict requirement on the relative position of feed and arrays. To deal with these disadvantages, a single antenna which is small in volume and requires only simple feeding network has been proposed to generate a single vortex beam [16–21]. The combination of these antennas can generate different vortex beams [22,23], which could be used in wireless communication [24,25].
This paper proposes an equivalent uniform elliptical array (UEA) model to analyze and design a single elliptical patch antenna based on the characteristic currents according to the theory of characteristic modes (TCM) [26]. Using the concept of projection and multiple vortex beams, the feeding and position of each element in the UEA can be designed to generate two inclined OAM vortex beams. Meanwhile, the characteristic currents of the UEA can be achieved by feeding with a 3dB directional coupler [27]. The antenna can generate two inclined vortex beams, which have the OAM modes of +1, −1 and ±1, respectively. As mixed OAM modes of ±1 are orthogonal at the same frequency, the single elliptical patch antenna has an ability to realize OAM mode multiplexing in different directions simultaneously.
2. Construction and analysis of equivalent uniform elliptical array (UEA) model
Figure 1(a) shows an elliptical metallic patch that has a major axis of 24mm and a minor axis of 20.7mm. The substrate thickness between the patch and the ground is 2mm. The characteristic mode analysis of this elliptical patch can be analyzed by using full-wave simulation software of FEKO. And thus two kinds of characteristic currents whose resonance frequency are around 5.8 GHz can be obtained, as shown in Figs. 1(b) and (c), respectively. Then these two complementary characteristic currents can be equivalent to two UEA models with 6 elements, respectively. If we could excite the characteristic currents simultaneously, a combining UEA model with 12 elements shown in Fig. 2(a) could be realized. The equivalent elements in the above models have equal amplitude but different phases, and the phase difference of the adjacent elements in each 6-element array is 180°. Furthermore, the phase difference between the two models can be adjusted by feeding source with $\Delta p$, so that the two 6-element UEA models can be distinguished by whether the elements have a phase shift $\Delta p$. To simplify the simulation of the models, we use electric dipoles instead of the equivalent elements. And the combining UEA model can be further decomposed into two orthogonal polarization models, as shown horizontal polarization in Fig. 2(b) and vertical polarization in Fig. 2(c), respectively.
Fig. 1. (a) Geometry of a single elliptical metallic patch, (b) characteristic current mode 1 of the elliptical patch, and (c) characteristic current mode 2 of the elliptical patch.
Fig. 2. Orthogonal polarization decomposition of the UEA model, (a) the equivalent model of total characteristic currents, (b) horizontal polarization current model, and (c) vertical polarization current model.
It should be noted that the position distribution of the equivalent elements and the phase difference $\Delta p$ can be adjusted to achieve the generation of the double-deflection vortex beams. As shown in Fig. 3, the inclined UCAs with a pitch angle of ${\theta _k}$ or ${\theta _l}$ in space can be projected into the UEAs on the xoy plane. And when the size of the UCAs and the pitch angles are designed reasonably, just like when there are two UCAs which are axisymmetric, the UEAs will become one UEA. Then the pitch angle ${\theta _k}$ of the deflected beams has the relationship with the axial ratio (AR) of the UEA, i.e., $AR = \cos ({\theta _k})$. Also, the size of the UEA needed to be designed and the position distribution of the UEA elements can be further determined. We can calculate the required feeding of each element by the following formula.
Fig. 3. Schematic diagram of the UEA model of an elliptical patch antenna projected by two inclined UCA models and generation of double-deflection vortex beams, simultaneously.
The phase difference $\Delta p$ is chosen to be 90°, which can be effectively achieved by using a 3dB directional couple feeding network in this paper. And the AR of UEA is determined as 0.86, so that the pitch angle of deflected beams is about 30°. Then the UEA model can be determined as shown in Fig. 4(a). Using this model, the double-deflection vortex beams with OAM mode of +1 can be generated, and the azimuth angles of the two beams are 0° and 180°, respectively. To observe the vortex beams, we can set two observation planes which are perpendicular to the beams with size of 10λ×10λ and with distance from the origin of coordinates of 10λ. Then the corresponding 3D radiation pattern of the UEA, and the E-field phase distribution diagrams of horizontal and vertical components can be obtained and shown in Figs. 4(b), (c), and (d), respectively.
Fig. 4. (a) Equivalent UEA model, (b) simulated 3D radiation pattern, (c) E-field phase distribution diagrams of horizontal component and (d) vertical component.
It can be seen from Fig. 4 that the UEA can generate double-deflection vortex beams simultaneously. As the E-field phase distribution diagrams for horizontal and vertical components are similar to each other. For the sake of simplicity, we just observe the result of the horizontal component in the rest of this paper. It is worth pointing out that if we change the AR to be 1, the UEA will become the UCA which is equivalent to a circular patch antenna. From the phase distribution of the UCA, it can be found that the circular patch antenna can only generate one single vortex beam that is perpendicular to the antenna surface with OAM mode of +2. Meanwhile, the UEA can provide not only the phase modulation of multiple beams, but also the phase modulation of the helical phases corresponding to the multiple beams. Therefore, comparing with the conventional UCA, the UEA has more advantages to adjust the number, propagation directions, and the OAM modes of the vortex beams.
3. Full-wave simulation and analysis of elliptical patch antenna
In order to verify the theoretical model, we fabricate the prototype of the elliptical patch antenna at 5.8 GHz. The dielectric substrate thickness is 2 mm with relative dielectric constant of 2.65, and the metal elliptical patch is attached to the top of the dielectric substrate. The elliptical patch dimension can be adjusted based on the structure shown in Fig. 1, and then it can excite the two required characteristic currents simultaneously by using two feeding points. To achieve the mode multiplexing, a 3 dB directional coupler [27] is designed and used, which is attached to the bottom dielectric substrate with thickness of 1 mm and relative dielectric constant of 2.65 as the feeding network. The two dielectric substrates can share one ground and the input ports of the patch are connected to the output ports of the 3 dB directional coupler through vias. The final model of the elliptical patch antenna with feeding network is shown in Fig. 5, and the corresponding dimensions of the generator are listed in Table 1.
Fig. 5. Geometry of the single elliptical patch antenna with a 3dB directional coupler as feeding network.
Table 1. Geometry dimension of the elliptical patch antenna (unit: mm)
The two feeding points of the antenna are named as Feed1 and Feed2, whose coordinates are (−13.4 mm, 6.3 mm) and (14.8 mm, 1.2 mm) in the Cartesian coordinate system, respectively. The two feeding ports of the 3 dB directional coupler are named as Port1 and Port2, as shown in Fig. 5. We can replace the UEA model shown in Fig. 4 with the elliptical patch antenna. The 3D radiation patterns of the antenna are simulated and shown in Figs. 6(a)-(c), which corresponds to the cases when only Port1 is fed, only Port2 is fed, and both Port1 and Port2 are fed, respectively. The E-field phase distributions of the vortex beams are displayed on the two observational planes in three corresponding cases are shown in Figs. 6(d)-(f). The mode spectrums of the vortex beams can be obtained by analyzing the amplitude and phase distribution of the E-field in the observation plane with the whole aperture sampling receiving scheme and discrete Fourier transform (DFT). The corresponding mode spectrums belong to the beam with the azimuth angle of 0° are shown in Figs. 6(g)-(i). The results of the beam with the azimuth angle of 180° are just similar to that of 0°. It can be seen that when Port1 is fed, the phase difference between Feed1 and Feed2 is +90° while the two deflected vortex beams have the OAM mode of +1. When Port2 is fed, the phase difference is −90° while the generated OAM mode is −1. Furthermore, when Port1 and Port2 are fed simultaneously, it is the superposition of two OAM states, which can achieve the multiplex communication based on the orthogonality of mixed OAM modes. As the simulation results show a high purity of the vortex beams, it is obviously that the antenna has excited the required characteristic currents. Without loss of generality, we can also use the elliptical patch antenna to excite higher-order characteristic currents, which can also be regarded as the higher-order TMn1 modes. As these characteristic currents can be equivalent to the UEA models with more array elements, the position and the excitation of these elements can also be designed to achieve the double-deflection vortex beams with higher-order OAM modes.
Fig. 6. Three kinds of vortex beams generation corresponding to three different feedings. 3D vortex beams radiation patterns of (a) OAM mode=+1, (b) OAM mode=−1, and (c) mixed modes +1 and −1. E-field phase distributions on observational planes of (d) OAM mode=+1, (e) OAM mode=−1, and (f) mixed modes of +1 and −1. Mode purity spectrums of (g) OAM mode=+1, (h) OAM mode=−1, and (i) mixed modes of +1 and −1.
4. Experimental results and discussion
In order to verify the correctness of the equivalent UEA-TCM theory and single antenna generator design, the prototype of the elliptical patch antenna is fabricated, and the measurement is implemented in microwave anechoic chamber, as shown in Fig. 7. The elliptical patch antenna is fed by the vector network analyzer (VNA, Agilent Technologies, PNA-X) through coaxial cable. And it is 10λ away from the receiving probe, which is a standard rectangular waveguide probe and operates from 5.38 GHz to 8.17 GHz. The antenna surface has an inclined angle of +30°, and the scanning plane has a size of 10λ×10λ.
Fig. 7. (a) Fabricated prototype of the elliptical patch antenna for OAM vortex beams generation and (b) the measurement scene in microwave anechoic chamber.
We measure the reflection coefficients of the two ports, and both of the simulated and measured results are shown in Fig. 8. It can be seen that both the simulated and the measured reflection coefficients are lower than −10dB from 5.7GHz to 5.9GHz, which is also the designed bandwidth that the antenna can generate the double-deflection vortex beams well. Comparing with the simulated results, the measured results have a slight frequency deviation, which is mainly caused by the error of the substrate dielectric parameters. As the trends of the curves are similar, we can find that the antenna can work normally and the results for measurement and simulation coincide with each other.
The near field scanning measurements are implemented in different cases. When Port1 of the antenna is fed, while Port2 is connected to a 50 Ω matching load, the measured E-field phase distribution of the generated vortex beam is shown in Fig. 9(a). When the excitation port is changed to Port2, the result is shown in Fig. 9(b). If we change the inclined angle to be −30°, the E-field phase distributions of the other vortex beam when Port1 or Port2 is fed are shown in Figs. 9(c) and (d), respectively. It is note that the E-field phase distributions shown in Figs. 9(a) and (c) satisfy the OAM mode of +1, while Figs. 9(b) and (d) satisfy the OAM mode of −1. Then the mode purity spectrums of the vortex beams can also be obtained with the same method that is used during the simulation, and the mode spectrums corresponding to the phase distributions shown in Figs. 9(a)-(d) are shown in Figs. 9(e)-(h). Comparing with the simulated results, the measured mode purity is still high enough, while it has a little decrease. This is because the actual measurement environment and the measurement errors will have a certain effect on the vortex beams. At the same time, as the data of E-field in the scanning plane is not sufficient, there will be a certain deviation when using the whole aperture sampling. Based on the measured results, we can find that the double-deflection OAM vortex beams are generated by the proposed elliptical patch antenna simultaneously.
Fig. 9. Measured E-field phase distributions (a) when the inclined angle is +30° and Port1 is fed, (b) when the inclined angle is +30° and Port2 is fed, (c) when the inclined angle is −30° and Port1 is fed, and (d) when the inclined angle is −30° and Port2 is fed. Measured mode spectrums (e) when the inclined angle is +30° and Port1 is fed, (f) when the inclined angle is +30° and Port2 is fed, (g) when the inclined angle is −30° and Port1 is fed, and (h) when the inclined angle is −30° and Port2 is fed.
5. Conclusion
In this paper, we propose a simply and miniaturized elliptical patch antenna to efficiently generate double-deflection OAM vortex beams. The single antenna can be equivalent to a UEA model based on the theory of characteristic modes. The theoretical analyses and full-wave simulations show the effectiveness and correctness of the UEA model of an elliptical patch antenna. The elliptical patch antenna is fed by a 3 dB directional coupler, so the OAM multiplexing of the vortex beams in two deflected directions can be effectively realized. Furthermore, the proposed analysis and design methods have an inspiration to single antenna generator and multiplexing for OAM vortex beams.
Funding
Outstanding Young Foundation of Shaanxi Province of China (2019JC-15); National Key Research and Development Program of China.
Disclosures
The authors declare no conflicts of interest.
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