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Abstract
Vortex beam generators carrying orbital angular momentum (OAM) with both transmission and reflection modes has broad application prospects in full-space high data capacity communication and orbital angular momentum multiplexing systems. In this work, we proposed a vanadium dioxide (VO2) assisted metasurface to independently produce and manipulate focused vortex transmission-reflection modes with different number of beams and focal lengths under right-handed circular polarized (RCP) wave incidence. The proposed metasurface generates the diagonal vortex beams, four vortex beams, and focused vortex beam for transmission mode at 1.26THz and reflection mode at 1.06THz by changing phase state of the VO2. Our work may find many potential applications in future high data capacity information multiplexing communication systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, metasurfaces have been widely implemented in polarization converters [1–5], holographic lenses [6,7] and absorbers [8–12], etc. The devices can be classified as transmission mode [13–15] and reflection mode [16] in terms of electromagnetic wave transmission direction. However, once the structure parameters of these reported devices are fixed, their functions and capabilities can not be regulated flexibly. The occurrence of coding metasurface provides a simplified and convenient method for tunable device performance [17]. In recent years, a few full-space metasurfaces have been developed to manipulate electromagnetic wave in both transmission and reflection modes simultaneously [18–21]. Nevertheless, the above-mentioned metasurfaces can only deal with the orientation or amplitude of electromagnetic waves, and have not to improve the channel capacity of electromagnetic wave. Recently, vortex beams carrying orbital angular momentum (OAM) have attracted great attention due to their enhancing channel capacity in communication systems [22–25]. In 2018, Bai et al. proposed [26] an encoded metasurface consist of three parts metal patterns to generate reflected vortex beams. Zhang et. al. [27] designed an encoded metesurface consists of single metal pattern to control transmission-focused vortex beams. However, all previously reported vortex beam metasurfaces only operate in reflection mode or transmission mode. More recently, the metasurface for both transmission and reflection modes vortex beam has been demonstrated [28]. Due to the advantage of making full use of space resources, full-space terahertz vortex beam generator with orbital angular momentum is worth developing in both transmission and reflection spaces by using the same metasurface.
In this article, we proposed a transmission and reflection modes focused vortex beam controller, which consists of a periodic silicon cylinder with middle notch on top of vanadium dioxide (VO2) bottom film layer. The designed structure realizes diagonal vortex beams, four vortex beams, and focused vortex beam in both transmission and reflection modes at different frequencies. By controlling the phase transition of VO2, the designed metasurface realizes to switch transmission and reflection modes flexibly. Our work will have a great application prospect in future high data capacity information multiplexing communication systems.
2. Device design
Figure 1 illustrates functions schematic diagram of the proposed full-space vortex beam metasurface, which has ability to generates transmission and reflection modes diagonal vortex beams, four vortex beams, and focused vortex beam. The top layer is silicon (ɛ=11.9) cylinder with middle notch. The period of the unit cell is P = 100 µm in both x and y directions. In order to achieve a relatively fixed phase difference by rotating coding elements, we split the cylinder into two halves. By optimizing the height and radius of the silicon column, the proposed structure generates high amplitude, which meet the requirement of focused vortex beam. The optimized geometrical parameters are set as: R = 40 µm, d = 20 µm, and h1 = 150 µm. The substrate material is polyimide with dielectric constant of ɛ=3.5, loss tangent of tanδ=0.02 and thickness of h2 = 40 µm. The bottom layer is VO2 film with h3 = 0.2 µm. The VO2 phase state can be switched by employing a microheater to change the temperature. Recover insulator state of VO2 is by natural cooling. The proposed coding element is simulated by CST simulation software. We use the method of rotating the semicircular silicon column coding element by the angle of α° to achieve stable phase difference. Figure 2 gives the cross-polarization amplitude and phase of 16 kinds of coding elements for transmission mode at 1.26THz and for reflection mode at 1.06THz by switching VO2 phase state (i.e. VO2 conductivity of 200S/m at room temperature, and VO2 conductivity of 200000S/m at 68°C). In this paper, we mainly focus on the control of terahertz wave focused vortex beam at transmission and reflection modes. Therefore, as long as the medium has two phase transition, it can meet the design requirement. Moreover, the phase transition temperature of vanadium dioxide is only 68°C, which is relatively easy to control and has ultra-fast respond speed [29]. Therefore, we designed a vanadium dioxide hybrid metasurface. When the VO2 is in insulating state, the dielectric constant and conductivity of the VO2 are ɛ=9 and σ=200S/m, respectively. When the VO2 is in metallic state, the dielectric constant of the VO2 can be characterized by Drude model [30]
Fig. 1. Functions schematic diagram of the proposed full-space vortex beam metasurface, which produces diagonal vortex beams, four vortex beams, and focused vortex beam in both transmission and reflection modes
Fig. 2. Amplitude and phase responses of the proposed coding element, (a) transmission mode at f = 1.26THz, (b)reflection mode at f = 1.06THz under right circularly polarized (RCP) wave incidence.
3. Results and discussions
3.1 Diagonal vortex beam modulation
The 16 kinds of coding unit cells with a phase evenly distributed the whole 360° are named as “0, 1, 2… 15”, as shown in Table 1. Figures 3(a) and 3(b) display metasurface (marked S1) with coding sequence: “0 4 8 12…/4 8 12 0…/8 12 0 4…/12 0 4 8…” and metasurface (marked S4) with coding sequence: “8 4 0 12…/4 0 12 8…/0 12 8 4…/12 8 4 0…”, respectively, where the “/” represents a line break. As can be seen from Fig. 3, the gradient phase of the S1 metasurface increases along the predesigned arrow direction. Similarly, the gradient phase of the S2 metasurface also increases along the arrow direction. The designed coding metasurface is divided into N equal segments. The relationship among the phase difference Δφ, topological charge l and the number of segments N of the silicon medium metasurface can be given by N·Δφ=2πl. Figure 3(c) illustrates vortex metasufaces (marked S2) arrangement with topological charge of l = 2. Figure 3(d) shows the metasurface S3 which is obtained by S1 and S2 convolution operation. Similarly, Fig. 3(e) gives metasurface S5 by convolving metasurface S4 with S2. At last, metasurface S6 is obtained by S3 and S5 superposition operation, as displayed in Fig. 3(f). By combing the convolution theorem with Fourier's convolution theorem, we can obtain the corresponding convolution coding element phases [31]. By using the superposition theorem, the same metasurface can produce different effects [32]. A simple schematic of the superposition principle is shown in the Fig. 4. The pitch angle can be calculated by θ = arcsin(λ/Γ), where λ is the vacuum wavelength of the electromagnetic wave and Γ is the coding period. The azimuth angle is expressed as φ = ± arctan(Dx/Dy), φ = π ± arctan(Dx/Dy), where Dx and Dy are the length and width of the encoding period.
Fig. 3. Schematic diagonal vortex metasurface arrangement, (a) Metassurface S1 with coding sequence: “0 4 8 12…/4 8 12 0…/8 12 0 4…/12 0 4 8…”, (b) Metassurface S4 with coding sequence: “8 4 0 12… /4 0 12 8…/0 12 8 4…/12 8 4 0…”, (c) Metassurface S2 with coding sequence: “12 8 4 0/0 4 8 12”, (d) Metassurface S3 convolved by S1 and S2, (e) Metassurface S5 convolved by S4 and S2, (g) Metassurface S6 superimposed by S3 and S5.
Fig. 4. Principle schematic of the superposition theorem, (a) 3-bit coding units, (b) operations performed according to the superposition theorem
Table 1. Coding particles and phase response vs. rotation angle.
When VO2 is in dielectric state (i.e. at temperature of 25°C), the metasurface S6 works at transmission mode. Here, the working frequency is set as 1.26THz (The corresponding vacuum wavelength is λ = 238µm), and the corresponding encoding period is Γ = 400√2µm and Dx = Dy = 800µm. Subsequently, we obtain the deflection angle of θ = 24.88°, and the azimuth angles φ1 = 135° and φ2 = 315°. Figure 5(a) plots the calculated azimuth curve at cut angle of 155°, which are consistent well with the theoretical predictions. Figure 5(b) displays the top view of the two diagonally deflected vortex beams with topological charge number l = 2 in z < 0 space and the phase distribution of the vortex beam. The two-dimensional (2D) electric field far-field diagram in Fig. 5(c) indicates that the two main vortex beams are deflected with angle of 25°. The energy amplitude of the vortex beam has a hollow circular shape, which proves the generation vortex beam. Figures 6(a-b) illustrate the OAM mode purity in transmission and reflection modes, respectively. It can be seen from the figure that the mode purity of the vortex beam is larger than 85%.
Fig. 5. Normalized transmission amplitude, 3D far-field of diagonal vortex beams and 2D electric field distribution of the transmission mode metasurface (Marked S6) at 1.26THz, (a) normalized transmission amplitude at cut angle of 155°, (b) 3D far-field of the transmission diagonal vortex beam and phase distribution, (c) 2D electric field distribution of the deflected diagonal vortex beam.
When VO2 is in metallic state (i.e. at temperature of 68°C), the metasurface S6 changes from transmission mode to reflection mode. When S6 is illumined by RCP terahertz wave at 1.06 THz, the reflected far-field diagrams are shown in Fig. 7. As expected in Figs. 7(a)∼7(c), the incident LCP wave are split symmetrically into two dominating reflected diagonal vortex beams in z > 0 space. Meanwhile, we give the pitch angle of the vortex beam is close to 30° (see in Fig. 7(c)). The deflection angle is calculated as θ = 30.02°, which agrees well with the simulation results. In addition, vortex beam metasurfaces with different diagonal deflection angles and different topological charges are designed. In transmission mode, when the RCP wave is vertically incident in the front of the metasurface at 1.26THz, the far field and electric field diagrams are shown in Figs. 8(a, c). It can be noted that the deflection angle of vortex beam with topological charges of l = 2 and l=−1 are θ = 24.88° and θ = 16.26°, respectively. Similarly, for reflection mode, when the RCP wave is vertically incident from the back of the metasurface at 1.06THz, the far field and electric field diagrams are shown in Figs.8(b, d). It can also be noted that the deflection angle of vortex beam with topological charges of l = 2 and l=−1 are θ = 30.02° and θ = 19.49°, respectively.
Fig. 7. Normalized reflection amplitude, 3D far-field of diagonal vortex beams and 2D electric field distribution of the reflection mode metasurface (Marked S6) at 1.06THz, (a) normalized reflection amplitude at cut angle of 30°, (b) 3D far-field of the reflected diagonal vortex beam and phase distribution, (c) 2D electric field distribution of the reflected diagonal vortex beam.
Fig. 8. 3D far-field of the diagonal vortex beam and phase distribution in (a) transmission mode at1.26THz and (b) reflection mode at 1.06THz; 2D electric field distribution of the diagonal vortex beam (c) transmission mode at 1.26THz and (d) reflection mode at 1.06THz.
3.2 Four-beam vortex control
We designed the checkerboard coding metasurface with the coding sequence S7 as “0 4…/4 0…”, as shown in Fig. 9(a). In order to reduce the coupling reaction between adjacent unit cells, 3 × 3 coding elements are used as super coding elements. Meanwhile, a vortex metasurface with topological charge number l = −2 is arranged in Fig. 9(b). Then, metasurface S9 can be obtained by convolution of the S7 and the S8. Similarly, when metasurface S9 works at transmission mode, it generates four deflected vortex beams in transmission mode at 1.26 THz under LCP incidence, as shown in Fig. 10. It can be seen from the Fig. 10(a) and Fig. 10(c) that the designed metasurface realizes the generation and manipulation of vortex beams. Figure 10(b) plots the azimuth curve with the cut angle of 146°. Apparently, the azimuth angles of the four vortex beams are φ1 = 45°, φ2 = 135°, φ3 = 225° and φ4 = 315°, and the pitch angle is 180°−34°=146°, as depicted in Fig. 10(c). According to the generalized Snell's law, the deflection angle (encoding period of Γ=300√2µm) is θ=34.12°. which is in good agreement with the theoretical calculation of 34°. At 68°C, S9 metasurface converts from transmission mode to reflection mode. Figure 11(a) shows the 3D far-field scattering patterns and phase profiles of the 1.06 THz under RCP wave incidence. It can be seen from figure that the reflection normalized amplitude curve (see Fig. 11(b)) is consistent with that of the transmission mode (see Fig. 10(b)). The reflection pitch angle can be calculated as θ = 41.84°, which is consistent with the simulation result of 42° (see Fig. 11(c)). Obviously, the proposed metarsurface realizes the switchable transmission mode and reflection mode.
Fig. 9. Schematic diagram of four-beam vortex metasurface based on the convolution theorem. (a) Checkerboard metasurface (Marked S7), (b) Vortex metasurface (Marked S8) with topological charge l = −2, (c) Four-beam vortex metasurface (Marked S9) obtained by S7 and S8 with convolution operation
Fig. 10. 3D far-field, normalized reflection amplitude, vortex beams and 2D electric field distribution of the transmission mode metasurface (Marked S9) at 1.26THz, (a) 3D far-field scattering patterns of four vortex beams and phase distribution, (b) normalized transmission amplitude at cut angle of 146°, (c) 2D electric field distribution of four vortex beams.
Fig. 11. 3D far-field, normalized reflection amplitude, vortex beams and 2D electric field distribution of the reflection mode metasurface (Marked S9) at 1.06THz, (a) 3D far-field scattering patterns of four vortex beams and phase distribution, (b) normalized reflection amplitude at cut angle of 42°, (c) 2D electric field distribution of four vortex beams.
3.3 Focused vortex regulation
Figures 12(a-c) shows the phase distribution principle of the focused vortex metasurface (see Fig. 12(c)), which is formed by adding the focusing lens phase (see Fig. 12(a)) and the vortex phase (see Fig. 12(b)), and the corresponding phase arrangement is according to the relation of $\Phi (x,y)\textrm{ = }l \bullet arctan(y/x) + 2\pi /\lambda [\sqrt {({x^2} + {y^2} + {F^2})} - F]$. Figures 12(d, e) present the 2D cross-sectional electric field intensity profiles in x-z and x-y plane for transmitted focused vortex beam (z = −1500µm) with topological charge number l = −1 at 1.26THz LCP under RCP wave incidence when the VO2 is in dielectric state (at 25°C). The simulated phase distributions for RCP wave are illustrated in Fig. 12(f). From the figure, one can see clearly that the focused vortex spiral phase carrying OAM with topological charge of l = −1. When the VO2 is in the metallic state (at 68°C), the function of the designed metasurface turns into focused vortex beam of reflected mode at 1.06 THz under LCP incidence, as shown in Figs. 12(g, h). From the intensity profiles in x-z section (see Fig. 12(g)), the focused vortex position is converted from z=−1500µm to z = 1200µm (i.e. transmission mode converts to reflection mode). We note that the designed metasurface generates a ring-shaped intensity distribution with a hollow center, which is a good agreement with the characteristic profile of vortex beams carrying OAM with topological charge of l=−1. The corresponding phase distributions of the reflection mode focused vortex is illustrated in Fig. 12(i). The efficiency of the designed focused vortex metasurface is 72.73%. Furthermore, convolution the vortex metasurface phase arrangement with topological charge of l=−1 (see Fig. 13(a)) and focusing lens phase with transmission focal length of 1000µm (see Fig. 13(b)), we arrange a focused vortex metasurface phase distribution, as shown in Fig. 13(c). When the VO2 is in dielectric state, x-z 2D electric field diagram for transmission mode at y = 0µm and x-y profile 2D electric field distribution at z = −1200µm are shown in Figs. 13(d, e). Figure 13(f) displays the transmission mode focused vortex phase at 1.26THz under LCP incidence, which is consistent with the designed focused vortex prediction. When the VO2 is in the metallic state, the designed metasurface serves as a reflection mode. The x-z profile 2D electric field distribution for reflection mode at y = 0µm and x-y profile 2D electric field distribution at z = 1000µm at frequency of 1.06THz under LCP incidence are given in Figs. 13(g, h). The x-z electric field at y = 0µm identifies the focal length of the focused vortex and the efficiency is 76.07%. The reflection focused vortex phase is shown in Fig. 13(i). Apparently, the results appear that the metasurface can be used as transmission-reflection mode vortex beam controller of terahertz wave.
Fig. 12. Phase arrangement, focused vortex electric field and vortex phase, (a) vortex metasurface phase arrangement with topological charge of l = −1, (b) focusing metasurface phase arrangement with transmission focal length of 1500µm, (c) focused vortex metasurface phase arrangement. When VO2 is in dielectric state at frequency of 1.26THz, (d) x-z 2D electric field diagram for transmission mode at y = 0µm, (e) x-y profile 2D electric field distribution at z = −1500µm, (f) transmission focused vortex phase. When VO2 is in metallic state at frequency of 1.06THz, (g) x-z profile 2D electric field distribution for reflection mode at y = 0µm, (h) x-y profile 2D electric field distribution at z = 1200 µm, (i) reflection focused vortex phase.
Fig. 13. Phase arrangement, focused vortex electric field and vortex phase, (a) vortex metasurface phase arrangement with topological charge of l = −1, (b) focusing metasurface phase arrangement with transmission focal length of 1000µm, (c) focused vortex metasurface phase arrangement. When VO2 is in dielectric state at frequency of 1.26THz, (d) x-z 2D electric field diagram for transmission mode at y = 0µm, (e) x-y profile 2D electric field distribution at z = −1200µm, (f) transmission focused vortex phase. When VO2 is in metallic state at frequency of 1.06THz, (g) x-z profile 2D electric field distribution for reflection mode at y = 0µm, (h) x-y profile 2D electric field distribution at z = 1000 µm, (i) reflection focused vortex phase.
Figure 14(a) shows the phase distribution of transmission mode focused vortex metasurface with focal length F = 1500µm (marked as S9 metasurface, which is able to generate a focused vortex beam with l = −2). Figure 14(b) displays the phase distribution of reflection mode focused vortex metasurface with focal length F = 1000 µm (marked as S10 metasurface). The phase distribution of full-space focused vortex metasurface (marked as S11 metasurface) superimposed by transmission mode and reflection mode metasurfaces are shown in Fig. 14(c). When the VO2 is in insulating phase, S11 metasurface achieves the transmission mode focused vortex beam at 1.26THz under LCP incidence, as shown in Fig. 15. Figure 15(a) depicts the 3D electric field scattering patterns at y = 0 under RCP wave normal incidence. The focal length of the focused vortex beam is F = 1500µm in x-z plane profile. The x-y section 2D electric field diagram and phase profiles at z = −1500 µm are displayed in Fig. 15(b) and the efficiency is 70.15%. While the VO2 is in metallic state, the 3D electric field scattering patterns of the reflection mode focused vortex beam and phase distribution of the S11 metasurface illuminated by terahertz wave at 1.06THz, as depicted in Fig. 16. From Fig. 16(a), one can see that the focal length of the focused vortex is 1000µm in x-z electric field profile at y = 0, which is consistent with the designed S11 metasurface arrangement prediction. In addition, we can also find that a focused vortex beam at z = 1000µm displays a ring shape intensity profile having a hollow center with the efficiency of 71.28%, as exhibited in Fig. 16(b). Apparently, a switchable transmission-reflection modes focused vortex beam of the same metasurface can be achieved by changing external operating temperature at different frequencies. Table 2 shows a comparison with some previous works, in which our designed metasurface has relatively good vortex beams manipulation performance and multi-function.
Fig. 14. Phase distribution of full-space focused vortex metasurface superimposed by transmission mode and reflection mode metasurfaces, (a) Phase distribution of transmission mode focused vortex metasurface with focal length F = 1500µm, (b) Phase distribution of reflection mode focused vortex metasurface with focal length F = 1000 µm, (c) phase distribution of the full-space focused vortex metasurface.
Fig. 15. Transmission mode focused vortex beam and phase distribution of metasurface S11 under RCP wave incidence at 1.26THz, (a) x-z profile of the focused vortex at y = 0, (b) x-y profile at z = −1500 µm and phase distribution.
Fig. 16. Reflection mode focused vortex beam and phase distribution of metasurface S11 under RCP wave incidence at 1.06THz, (a) x-z profile of the focused vortex at y = 0, (b) x-y profile at z = 1000 µm and phase distribution.
Table 2. Performance comparison between the proposed multifunctional metasurface and some previous works
4. Conclusion
To summarize, we proposed a multifunction terahertz vortex beam generator for control vortex beam in both transmission and reflection modes. The proposed metasurface not only produces diagonal vortex beams, four vortex beams, and focused vortex beam of transmission mode at 1.26THz, but also achieves the same functions of reflection mode at 1.06THz by switching dielectric state to metallic state transition of the VO2 layer. Although, the presented metasurface can only respond to the electromagnetic wave of a specific frequency, and the operating frequency band also has a space to expand by switching the operating temperature. The fabrication of these proposed structures can be fabricated according to the steps in Ref. [37]. Our presented metasurface realize the transmission and reflection modes focused vortex beam, which can efficiently improve the channel capacity expansion and communication efficiency in the future.
Funding
National Natural Science Foundation of China (61831012, 61871355, 62271460); Talent project of Zhejiang Provincial Department of Science and Technology (2018R52043); Zhejiang Key R & D Project of China (2021C03153, 2022C03166); Research Funds for the Provincial Universities of Zhejiang (2020YW20).
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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