Generation of Mode-Reconfigurable and Frequency-Adjustable OAM Beams Using Dynamic Reflective Metasurface

Recently, much attention has been paid to beams carrying orbital angular momentum (OAM) for radio communication, which faces a great challenge of dynamic generation of OAM with different topological charges. In this paper, a novel reflective metasurface is designed to generate mode-reconfigurable OAM beams in radio frequency domain. Each unit cell of the proposed metasurface consists of an octagonal ring slot and a varactor diode. The response of each element to incident radio field can be engineered individually by controlling the voltage of the corresponding varactor diode, thereby dynamically producing OAM with different modes. Full-wave simulations show that the designed reflective metasurface can generate frequency-adjustable OAM beams with different topological charges of $l = +1$ , +2, −1, −2 over a frequency range of 5.2 GHz~5.8 GHz. An OAM purity analysis further verified the reliability of OAM beams generated by the proposed metasurface. The obtained results are in good agreements with the theoretical analyses, demonstrating a good prospect of practical application.


I. INTRODUCTION
In 1992, Allen et al. first found the fact that the Laguerre-Gaussian (LG) light beams can carry a certain mode of orbital angular momentum (OAM) [1], and proposed that light beams with a helical phase front have the potential to benefit the relevant applications in optical manipulation. In addition, OAM modes are orthogonal to each other, making it possible to increase the channel capacity of wireless communication system without additional frequency resources [2], [3]. In the past decades, the OAM vortex beam has become an important research topic due to its excellent physical nature and the potential applications [4]- [9]. In 2007, Thidé extended the investigations on OAM from optics to microwave and proposed to generate OAM using phased array antennas [10], promoting the development of OAM in microwave communication [11].
A variety of methods have been reported to generate OAM vortex waves in microwave range, including spiral phase The associate editor coordinating the review of this manuscript and approving it for publication was Giovanni Angiulli . plate (SPP) [12] and phased array antenna [13]- [18]. The structure of SPP is simple, but it can only obtain the OAM beam with a single mode, restricting the practical application. In addition, it is not easy to precisely fabricate a SPP with a screwed structure, resulting in the divergence and mode purity reduction of generated OAM beam. The circular phased array antenna could precisely control the phase distribution and generate OAM mode with high purity. However, it usually needs to employ complex feeding network with phase shifters, and the gain is not high due to the loss of complicated feeding circuits. To solve these problems, there have been some new ways to generate OAM vortex waves such as holographic plate [19], travel-wave antenna [20]- [24] and dielectric resonator antenna [25], [26]. Holographic plate and dielectric resonator antenna can produce OAM beams with small divergence angle, but they have relatively low gains. The circular travel-wave antenna can generate multiple OAM modes simultaneously, but it has large size and high profile. Very recently, metasurface has been introduced to microwave range to generate OAM beams owing to its advantages such as low profile, high gain, and flexible capability of modulating electromagnetic waves [27]- [38]. However, the previous studies of microwave metasurface rarely produced OAM beams possessing the characteristics of reconfigurable mode and adjustable working frequency simultaneously, which greatly hinders its applications.
In this paper, we propose a novel reflective metasurface to generate mode-reconfigurable and frequency-adjustable OAM beams in microwave range. Each unit cell of the proposed reflective metasurface can actively engineer the phase profile by a varactor diode. The proposed metasurface is illuminated by a horn antenna and introduces an azimuthal phase profile of e jlϕ (ϕ is the azimuthal angle) into the reflect electromagnetic waves, generating vortex waves. Numerical simulation results show that the proposed reflective metasurface can generate mode-reconfigurable OAM beams with high purities in the bandwidth. Our proposed method has potential application in future wireless communication system.  Figure 1(a) schematically shows the proposed reflective metasurface, which is normally illuminated by a horn antenna and transform the incident waves into reflected OAM vortex waves. The substrate of the metasurface is TMM13i with dielectric constant of ε r = 12.2, loss tangent of tanδ = 0.0019, and thickness of 1.5 mm. The substrate with high dielectric constant can be helpful to miniaturization of the structure since higher dielectric constant results in lower resonant frequency [39]. Considering the specific phase profile of vortex beam and the cost, the metasurface totally consists 120 units arranged in five circles. From inner to outer, these circles has radius of 20 mm, 30 mm, 40 mm, 50 mm and 60 mm, and contains 8, 16, 24, 32, and 40 uniformly distributed unit elements, respectively. Our design can be read from Fig. 1(a). Therefore, to simplify the structure and avoid disturbing, the structure is designed as a ring, whose inner and outer radius is 15 mm and 70 mm, respectively. It is because that space of the central part of the metal plate is not enough to accommodate unit elements for OAM beam generation, and the reflected field from this area will interfere with that from unit elements, disturbing the generated OAM beam. To ensure the metasurface working at frequency range of 4.5GHz∼6.5GHz, the geometric parameters have been numerically optimized. The unit structure of the proposed metasurface is shown in Fig. 1(b-d) and its parameters are given in Table 1. In the top layer, an octagonal slot is cut into a metal patch, and a varactor diode is inserted into the slot to connect the inner and outer metal patches. Note that we choose octagonal ring rather than circular and square rings since octagonal ring slot is more feasible to insert varactor diode than the circular case and provides larger reflection area of antenna than the square case. The inner metal patch is connected to a metal column through a via inside the substrate, through changing the voltage applied between the metal column and the outer metal patch, the diode capacitance can be well controlled. The metal column is not connected to the bottom ground, therefore we can manipulate the varactor diode individually by using the field programmable gate array (FPGA). This method minimizes the outer disturbing on the reflection field. As a result, the capacitance of the varactor diode can be changed by applying a voltage to the inner and outer metal patches, therefore changing the responses of metasurface to incident electromagnetic field. This concept may allow us to dynamically engineer the phase distribution of reflective field and generate mode-reconfigurable OAM beams with a unique metasurface.

II. PRINCIPLE AND DESIGN OF REFLECTIVE METASURFACE
To demonstrate, simulation models of the designed element are built by using a commercial software High Frequency Structure Simulator (HFSS) which is based on the finite element method. In the simulations, the floquet port excitation is adopted as the incident source and perfect electrical conductor condition is used as ground, as shown in Fig. 1(b). To simulate the response of each unit element, master-slave boundary condition is set at the boundaries in both x-and y-direction to save the computing memory and time. To simulate the designed metasurface, radiative boundary condition is used in horizontal boundaries instead. We set incident source as a spherical wave with y-polarization, which can be generated by Vivaldi antenna and horn antennas in 75524 VOLUME 8, 2020 microwave regime [29], [30]. This kind of source will not block the reflection aperture. In our design, the parameter of varactor diode is chosen as MAVR-000120-1411 from MACOM [40], whose capacitance value ranges from 0.14 pF to 1.1 pF. In the simulation, we consider an ideal case and the capacitance value is described by an equivalent RLC boundary, in which the resistance and inductance are not taken into consideration. Even though loss from resistance may affect the reflected wave, luckily, it has been demonstrated that its influence on reflection phase can be negligible [41]. The unit element, which is composed of the octagonal slot, metal patch, and varactor, can be represented with an equivalent LC circuit. The metallic part and varactor can be modeled by inductance L and capacitance C, respectively. The load impedance can be calculated by Z eff = jwL+1/jwC. By utilizing the tunable capacitance of varactor, we can manipulate the load impedance to create different surface impedance of the unit element. It is known that the electromagnetic response can be described by the impedance Zs as E = Z S n × H , wheren is a unit vector. Thus, the capacitance value changes the surface impedance of the unit element, providing us with an opportunity to engineer the reflected electric field. In this method, the radio-frequency performance can be dynamically altered through simple low-cost bias voltage, and the coupling between investigated radio-frequency and dc voltages is negligible [35], [39].  Figure 2 shows the simulated magnitude and phase of reflected wave from a unit element as functions of varactor diode capacitance and incident frequency. Note that, we are trying to achieve mode-reconfigurable OAM beams by using varactor diode. Thus, it is not considered to change the geometry parameters, such as the position and size of the varactor diodes. Instead, we dynamically tune the capacitance value of the varactor diode from 0.14 pF to 1.1 pF and the incident frequency is over a broadband range from 4.5 GHz to 6.5 GHz. It can be seen from Fig. 2(a) that the amplitude changes abruptly at specific frequency when the capacitance value changes, indicating the unit element could resonantly interact with the incident electromagnetic field at this frequency. In addition, the resonance frequency decreases as the capacitor value increases. It means that interaction between the unit element and the incident field will change when the capacitance has different value, and it may result in phase shift of reflected wave at fixed frequency. Figure 2(b) shows that the reflected phase could shift from 0 to 2π by controlling the capacitances of varactor diode, which could satisfy the requirement of OAM beams generation. According to these results, we choose 5.2 GHz to 5.8 GHz for two reasons: first, variation of the reflected amplitude is smaller than 0.5 dB in this frequency range when the capacitance changes; second, beyond this range it either cannot cover entire phase shift of 0-2π or is difficult to precisely control the capacitance. Similar experiment of precisely controlling the capacitance value of varactor can be referred to [41].
To generate an OAM beam, the phase distribution at metasurface generally consists of two parts: one is the helical phase distribution of the form e jlϕ along the azimuthal axis, where l represents the topological charge of an OAM beam, and the other one is the compensation for the phase of incident wave, which is determined by the source. In our case, the phase shift could be represents by [31], [33] ϕ where (x, y) is the coordinate in the metasurface plane, λ 0 is the wavelength in vacuum, r xy is the distance from the center of horn to the location (x, y). Here, the incident spherical wave is 75 mm away from the metasurface. The phase value of compensation for each unit element can be calculated. Figures 3(a-d) show the phase distributions of the designed metasurface to generate OAM beam with topological charge of l = −1, +1, −2, +2, respectively, which are calculated from Eq. (1). In the following, we demonstrate the performance of the proposed metasurface to generate mode-reconfigurable OAM beams.

III. RESULTS AND DISCUSSION
As discussed above, the reflected phase response of the proposed structure varies with the capacitance and the results in Fig. 2 suggests us to generate OAM beams in the frequency VOLUME 8, 2020 ranging from 5.2 GHz to 5.8 GHz. Therefore, a reconfigurable OAM mode can be effectively achieved by the metasurface through electrically controlling the capacitance of varactor diodes.  show the amplitude distributions of electric field in x-y plane, which is observed in a circle with radius of 250 mm at a distance of 300 mm (about 5 times of wavelength) from the metasurface. These generated electric field exhibit the characteristics of OAM beams with ring-like amplitude distributions, which are caused by phase singularity at the central region. In addition, the central dark zone grows larger when the topological charge l of the OAM beam increases. The non-uniformly distributed amplitude may be attributed to the difference in reflected amplitude between unit elements in the designed metasurface. The features of spiral phase distribution are also obvious. As shown in Figs. 4(a2)-(d2), the phase variation of −2π, 2π , −4π and 4π , respectively, happens in a circle along the azimuthal direction, which also confirms the characteristics of OAM beam. Figures 4(a3)-(d3) show the corresponding far-field radiation patterns with amplitude nulls existing at the central regions. From both the near-field and far-field performances, it is found that the major feature of the OAM beam is successfully obtained, and different OAM modes can be dynamically achieved, verifying the good performance of the mode reconfiguration.
As mentioned above, this proposed metasurface has another advantage of frequency-adjustable characteristic. To demonstrate, we simulate the generation of OAM beams with topological charges of l = −1, +1, −2 and +2 at frequency of 5.8 GHz, as shown in Fig. 5 (from left to right). It is also observed in x-y plane within a circle with radius of 250 mm at a distance of 300 mm (about 6 times of wavelength) from the metasurface. It can be seen that the results are similar to the case of 5.2 GHz, exhibiting the key features To further verify the reliability of the proposed method, the power spectrum of these OAM beams generated by the designed metasurface is calculated using the discrete Fourier transform algorithm. The Fourier relationship between the OAM spectrum P(α) and the corresponding sampling phase ψ(ϕ) can be expressed as [22] where ψ(ϕ) refers to the discrete sampling phase value in the sampling plane, exp(-jlϕ) is the harmonic related to the spiral phase front. We simulated the generation of OAM beams with topological charges of l = +1, −1, +2, and −2 at frequencies of 5.2 GHz, 5.4 GHz, 5.6 GHz and 5.8 GHz and calculated the power spectra. In these cases, the propagation distance of OAM beams is set to be 300 mm (about 5∼6 times of wavelength), and the radius of a circular observation area is 150mm. The chosen area is the main radiation direction of wave propagation, so the model purity is most accurate in this area. As shown in Figs. 6(a)-(d), the power spectra of the generated OAM beam with topological charges of l = −1, +1, −2, and +2 are calculated at the frequencies of 5.2GHz, 5.4 GHz, 5.6 GHz and 5.8 GHz. It can be seen that most of the power is concentrated within the generated OAM 75526 VOLUME 8, 2020 mode, meanwhile, there is part of the power extending to the neighboring OAM channels. It is in a good agreement with the result of field distributions above.
From the experimental point of view, the fabrication inaccuracies, for example the capacitance error, may have influence on the generated OAM beams. It is because the phase of reflected wave highly depends on the capacitance values, especially around the resonance frequencies. To demonstrate, we performed simulations at frequency of 5.8GHz, randomly selecting half of the unit elements and introducing errors to their capacitance values. When the error is 0.02pF, the mode purities of OAM beams with l = −1, 1, −2 and 2 are calculated to be 0.60, 0.61, 0.63, and 0.59, in contrast, the corresponding mode purities of ideal cases are 0.62, 0.64, 0.68, and 0.65, respectively. By optimizing the capacitance values in experiment, the fabrication errors may be compensated and the generated OAM beam can be improved.
We additionally studied the mode purities of these OAM beams at frequency of 5.2GHz with propagation distances of 200mm, 250mm and 300mm, as summarized in Table 2. Due to the divergence of OAM beam, the observation area varies to ensure most of the energy can be involved. It can be seen that the calculated mode purities do not vary significantly with the propagation distance. In addition, the mode purities of OAM beams with l = ±1 are more stable than that with l = ±2 since the divergence is more obvious for the latter cases. Because different capacitance values bring changes in both phase and amplitude of reflection, resulting in difference in reflected amplitude between unit elements in the  designed metasurface, and finally leading to the mode impurity. Fortunately, the calculated spectrum purities for all generated OAM modes are higher than 60% at all frequencies, as summarized in Fig. 7. Therefore, it is demonstrated further that proposed method could dynamically generate the OAM beams with good purity over the frequency range of 5.2 GHz∼5.8 GHz. Table 3 summarizes different techniques to compare the results of our proposed scheme with that of the other state-ofthe-art techniques. From the view of mode purity, our scheme are comparable with the state-of-the-art techniques. While considering the mode-reconfigurable and frequency-tunable properties, our results are better than most reported cases.

IV. CONCLUSION
In conclusion, we propose a novel reflective metasurface with varactor diodes, which can generate mode-reconfigurable and frequency-adjustable OAM beam in microwave range by tuning the capacitance of varactor diode. Simulation results demonstrated that the designed reflective metasurface can generate OAM mode of l = −1, −2, +1 and +2 with mode purity over 60% in the frequency ranging from 5.2 GHz to 5.8 GHz. The proposed reflective metasurface has the advantages of small size, low profile, mode reconfiguration and VOLUME 8, 2020 frequency-adjustable characteristics, which has great importance in future wireless communications system. KAI