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Abstract
This paper proposes a novel metasurface that can simultaneously generate orbital angular momentum (OAM) beams with pre-designed different reflection directions, multi-beam and multi-mode under x-(y-) polarized terahertz wave incidence. The configuration of unit cell is made up of a hollow cross of Jesus structure as top layer, a PTFE substrate layer and a gold metal bottom plate. Theory of phase gradient distribution is derived and used to design multifunctional OAM metasurface. The proposed metasurface generates two OAM beams with OAM mode l = 1 and four OAM beams with l = -1 at frequency of 1 THz, respectively. Similarly, at frequency of 1.3 THz, the designed metasurface produces two OAM beams with l = -2 and an OAM beam with l = 2 for x-(y-) polarized wave incidence, respectively. Since each OAM mode can be used as an independent digital information coding channel, the designed multifunctional OAM metasurface has a wide application prospect in future terahertz communication.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
It is well known that the frequencies and polarizations of electromagnetic waves can effectively increase the information transmission capacity of communication systems. Time division multiplexing (TDM), wavelength division multiplexing (WDM) and frequency division multiplexing (FDM) have been widely used in various communication systems [1–3]. Recently, orbital angular momentum (OAM), another electromagnetic wave parameter, has been widely concerned by researchers because it can infinitely enhance the capacity of communication system. As we all know, OAM technology originates from optical frequency band, and then extends to microwave frequency band [4–7]. For example, in 2007, Thide et al. used a loop antenna array to generate an OAM beam at a frequency of 1 GHz [8]. Since then, different structures have been proposed to generate OAM beams, including spiral phase plates [9], phased antenna arrays [10], gratings [11], metasurface [12] and so on. In 2016, Yu et al. designed a single-layer square metasurface structure to produce two OAM beams in different directions at 5.8 GHz [13]. In 2018, Ran et al. demonstrated the double-arrow structure to generate an OAM beam with l = 2 in the range of 12 GHz to 18 GHz [14]. Zhang et al. introduced of a lens into a single-layer structure for generating a single small-aperture microwave vortex beam [15]. Zhang et al. designed a dual-band metasurface to generate two independent vortex beams [16]. In 2019, Meng et al. produced two vortex beams with different directions and topological charges at 15 GHz [17], In 2020, Zhang et al. extended this work to the 40GHz-70 GHz frequency band [18]. In 2021, Zhang et al. designed a dual-polarization metasurface, which produces vortex beams with l = 1 and l = 2 [19].
Recently, vortex beam with OAM has been expanded to the terahertz frequency region. In 2013, He et al. realized a terahertz vortex beam with a topological charge of l = 1 by using a V-shaped structure [20]. In 2019, Li et al. used an orthogonal I-type structure to generate an OAM beam under circular polarization incidence [21]. In 2020, Fan et al. employed a three-layer transmissive metasurface to achieve linearly polarized OAM beams [22]. In 2021, Pan et al. used a single-layer square groove structure to achieve an offset OAM beam and mult-beam OAM beams generation [23]. Most recently, due to the advantages of small size and easy integration, the metasurface is widely used for generating OAM vortex beams. However, most of existing metasurfaces can only produce a vortex wave beam carrying with OAM at a single operating frequency. In order to generate multifunctional OAM, the reported metasurfaces need re-design metasurface structure and re-arrange the metasurface pattern. In fact, multi-vortex wave beams of different frequencies and polarizations are of great important in improving the capacity and quality of communication systems. Therefore, a single metasurface generating vortex wave with multi-beam and multi-mode OAM under different polarization and frequency modes becomes a research hotspot.
In this letter, a multi-functional OAM generator based on a single metasurface is developed to generate multi-beam and multi-mode OAM beams for different frequencies and polarization terahertz waves. The design of the metasurface unit cells is analyzed and the orbital angular momentum generation mechanism is studied.
2. Metasurface structure design and theoretical analysis
Figure 1 shows schematic of the multi-beam, multi-mode orbital angular momentum of different polarized and frequencies terahertz beams realized by the designed metasurface structure. In the figure, ${\vec{\boldsymbol u}}$. n is the direction of the nth vortex beam generation, θ is the angle of the nth vortex beam along z-axis and φ is the angle of the nth vortex beam along x- axis. The configuration of unit cell is made of a hollow cross of Jesus structure with thickness of 0.2 μm as top layer, a Poly tetra fluoroethylene (PTFE, ε = 2.1, tanδ = 0.0002) substrate layer with thickness of 35 μm and a gold metal bottom plate with a thickness of 0.2 μm. The hollow cross of Jesus structure and surrounding metal of unit cell that are orthogonal to each other are used to facilitate independent phase adjustment under different polarized waves incidence. The a and c affect the phase of the metasurface under x-polarized wave incidence. The b and d affect the phase of the metasurface under y-polarized wave incidence. This makes the unit cell have the ability to regulate the phase in dual-polarization and dual-frequency modes. In order to generate a single offset vortex beam in a specified direction, the required phase distribution for each unit cell can be calculated by
Fig. 1. Schematic diagram of the proposed orbital angular momentum generator with different polarized vortex beams
Among them, ${\vec{u}_m}$ = (sinθmcosφm, sinθmcosφm, cosθm) is the mth beam direction, which is one of the n beams. By adjusting the parameters appropriately, the phases of the dual frequency under x- and y- polarized terahertz waves illumination achieve the anticipated value.
The proposed metasueface is simulated by using full-wave numerical simulations by using CST Microwave Studio [24]. In simulation, the surrounding boundary condition was set as the periodic boundary and an open boundary condition was set along z direction. The structure is illuminated by a linearly-polarized terahertz wave along + z direction. The reflection amplitude and phase distributions at the frequency range from 0.7 THz to 1.6 THz are calculated under x and y polarized terahertz wave irradiation, as shown in Fig. 2. Figure 2(a) displays the phase distribution of 16 types of metasurface unit cells illuminated by x-polarized terahertz wave. At frequency of 1 THz, the gradient phase of the proposed metasurface unit satisfies the distribution of 0, π/2, π and 3π/2 for x- polarized incidence wave. Similarly, at frequency of 1.3 THz, the designed metasurface unit cells meet the demand of the gradient phase distributions of 0, π/2, π and 3π/2. Likewise, for y- polarized incidence terahertz wave, the metasurface unit cells still meet a phase gradient distribution at frequency of 1 THz and 1.3 THz, respectively. It can also be seen from Fig. (2) that at frequency of 1 THz, the gradient phase of four metasurface unit cells is 0, but at frequency of 1.3 THz, the gradient phases of the same metasurface unit cells are of 0, π/2, π and 3π/2, respectively. This phenomenon occurs because the preset different vortex phases at frequencies of 1 THz and 1.3 THz. Figure 2(c) and Fig. 2(d) show the reflection amplitudes of 16 kinds of the proposed metasurface unit cells in the frequency range of 0.7 THz to 1.6 THz under x and y polarized incidence terahertz waves, respectively. One can see that the reflection amplitudes of the proposed metasurface unit cells are higher than 0.8 at 1 THz and 1.3 THz. The optimized geometry parameters for the 16 types of unit cells are shown in Table 1. The metasurface unit cell is made of a hollow cross of Jesus structure. The 16 kinds of metasurface unit cells have the same geometry with different hollow cross size parameters.
Fig. 2. Reflection amplitude and phase distribution of the 16 kinds of metasurface unit cells, (a) and (c) are reflection amplitude and phase distribution for x-polarized terahertz wave incidence, (b) and (d) are reflection amplitude and phase distribution for y-polarized terahertz wave incidence (Marked line is at operating frequencies of 1THz and 1.3THz), (e) Simulation model and boundary conditions
Table 1. 16 kinds of metasurface unit cells and size parameters
3. Performance analysis and discussion
According to the principle of formula (2), 32×32 unit cells are arranged to design a dual-polarization dual-frequency terahertz wave OAM metasurface with an expected reflection direction, beam number, and OAM mode, as shown in Fig. 3. In the synthesized metasurface structure, the number of different unit cells is decided by the phase gradient. Each unit cell has four channels (dual frequency and dual polarization) to produce independent phase distribution. The smaller phase gradient of each channel is, the more unit cell numbers are required to cover the range of 2π. Since the phase distribution at different frequencies is the same value under different polarization modes, the phase gradient in this letter is preset as 90°. The far-field characteristics of the designed metasurface under orthogonal linear polarized terahertz waves incidence are simulated by using CST software at 1 THz and 1.3THz, as shown in Fig. 4 and Fig. 5, respectively. Figure 4(a) shows four OAM beams under y-polarized incidence wave. The azimuth angles of the four beams are (l1 = -1, θ1 = 21°, φ1 = 45°), (l2 = -1, θ2 = 21°, φ2 = 135°), (l3 = -1, θ3 = 21°, φ3 = 180°) and (l4 = -1, θ4 = 21°, φ4 = 225°). Figure 4(b) illustrates two OAM beams distributed along y-axis with azimuth angles are (l1 = 1, θ1 = 14°, φ1 = 90°) and (l2 = 1, θ2 = 14°, φ2 = 270°) under x-polarized incidence wave. At frequency of 1 THz, under x-polarized wave incidence, the metasurface structure generates two OAM beams with OAM mode l = 1. When the incident wave changes as y polarization, the same metasurface structure produces four OAM beams with OAM mode l = -1.
Fig. 3. Topology pattern of the multifunctional OAM generator based on the proposed metasurface unit cells, (a) Four-channel multi-function OAM generator pattern, (b) Channel 1: The vortex phase under y-polarized wave incidence at 1THz, (c) Channel 2: The vortex phase under x-polarized wave incidence at 1THz, (d) Channel 3: The vortex phase under x-polarized wave incidence at 1.3THz, and (e) Channel 4: The vortex phase under y-polarized wave incidence at 1.3THz.
Fig. 4. Far-field radiation patterns and phase of the designed metasurface for different OAM modes l = -1 (a), and l = 1 (b) with different OAM beam numbers and directions under x and y polarized terahertz waves incidence at frequency of 1.0THz
Fig. 5. Far-field radiation patterns and phase of the designed metasurface for different OAM modes l = -2 (a), and l = 2 (b) with different OAM numbers and directions under x and y polarized terahertz waves incidence at frequency of 1.3 THz
From the Fig. 5(a), one sees that the designed metasurface structure produces two OAM beams distributed along x-axis under x-polarized terahertz wave illumination. The azimuth angles of the two OAM beams are (l1 = -2, θ1 = 10°, φ1 = 0°) and (l2 = -2, θ2 = 10°, φ2 = 180°). According to Fig. 5(b), it can be noted that the designed metasurface structure produces an OAM beam (l = 2) under y-polarized wave incidence. At frequency of 1.3 THz, under the incidence of x-polarized waves, the proposed metasurface produces two OAM beams with OAM mode l = -2. If the incident wave is changed as y polarization, the metasurface structure produces an OAM beam with OAM mode l = 2. It can be clearly observed that an amplitude null area of each OAM beam in the far-field radiation produces at the center region generated by the phase singularity. The far-field radiation results verify that the designed single metasurface structure generates multiple functional OAM beams. Figure 6 shows the electric field phase, amplitude and OAM mode purity of the proposed metasurface illuminated by terahertz wave. The proportion of the OAM mode purity of topological charge l=2 is of 31.5% at frequency of 1.3 THz (see Fig. 6 (c)). A comparison between the described metasurface in this article and the recently reported device in different literatures is presented in Table. 2. From the table, one can find that the proposed structure offers more multi-beam and multi-mode orbital angular momentum in comparison with the designs in literatures [17,19].
Fig. 6. (a) Electric field phase, (b) amplitude and (c) OAM mode purity when the proposed metasurface is illuminated by terahertz wave
Table 2. Comparison between the described metasurface in this article and the reported metasurface in the literatures.
4. Conclusion
To sum up, we proposed a new single metasurface which can produce multi-beam, multi-mode OAM beams with required reflection directions under different polarized terahertz wave beams incidence at frequencies of 1THz and 1.3THz without change the metasurface arrangement. The simulation results are in good agreement with the those of the theoretical calculation anticipation. A single metasurface realizes the multifunctional regulation OAM, which previously required a variety of preset metasurface patterns [see Refs. 25–26]. The designed dual-polarization dual-frequency multi-beam and multi-mode orbital angular momentum generator has good potential application prospect in future terahertz wireless communication.
Funding
National Natural Science Foundation of China (61831012, 61871355); Zhejiang Key R & D Project of China (2021C03153); Fundamental Research Funds for the Provincial Universities of Zhejiang (2020YW20); Zhejiang Lab (2019LC0AB03).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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