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Abstract
Here, we propose a new encoded metasurface with different predesigned coding sequences to dynamic manipulate terahertz wavefront and realize various functionalities including beam splitting, anomalous beam deflection, vortex beam generation, angle controlled single-beam deflection, angle controlled multi-beam deflection, angle-controlled vortex beam generation and multi-vortex beam generation. The far-field scattering patterns obtained by CST Microwave Studio demonstrate the behavior of the terahertz wave in each case and shows a high consistency with our theoretical prediction results. Due to the excellent properties of the diversified functionalities in a single structure at terahertz frequencies, the proposed encoded metasurface provides promising applications in terahertz multiple-input, multiple-output (MIMO) communication.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In 2014, T. Cui et al. [1] proposed the concept of coding metasurface for controlling the propagation of electromagnetic wave. The coding metasurface unit cells with 0 and π phase difference are expressed as binary coding particles 0 and 1, respectively. Owing to suitable for efficient regulation of microwaves, the digital coding metasurfaces have attracted considerable attention [2–6]. Recently, in order to control electromagnetic wave more freely, the digital coding metasurface conception has been extended to higher order coding such as 2-bit, 3-bit coding, etc [7–10]. However, most of the reported coding metasurfaces are still operating at the microwave frequency region [11–12]. More recently, some digital coding metasurfaces at terahertz frequencies are investigated [13–17]. Nevertheless, these previous coding metasurfaces are suffering from high ohmic dissipation due to using metallic resonators. In recent years, researchers have found that high-permittivity dielectrics are suitable for design digital coding metasurfaces by using its Mie resonance effects [18–21]. Furthermore, the dielectric coding metasurfaces have capability of achieving high efficiencies manipulation of electromagnetic wave without metal’s intrinsic nonradiative losses, especially within terahertz wave regime. In addition, it is beneficial for practical applications to structure a coding metasurface with multiple diversified functions for terahertz wave manipulation.
In this letter, we propose a design scheme of simple coding metasurface to realize diverse functions. The coding unit cell is composed of a high refractive index silicon particle and bottom metal plate layer. Eight coding particles across the 360° phase coverage with 45° interval are remarked ‘0’, ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, ‘6’, and ‘7’ to represent the ternary states ‘000’, ‘001’, ‘010’, ‘011’, ‘100’, ‘101’, ‘110’, and ‘111’, respectively. By predesigned several different coding strategies, we demonstrate that the proposed dielectric coding metasurfaces have the capability to flexibly manipulate reflected terahertz wave with seven distinct functions such as beam splitting, anomalous beam deflection, vortex beam generation, angle controlled single-beam deflection, angle controlled multi-beam deflection, angle-controlled vortex beam generation and multi-vortex beam generation. These are numerically simulated by using the commercial software, CST Microwave Studio, which are in accordance the theoretical analysis prediction results.
2. Dielectric unit cell design
Figure 1 represents the sketch representation of the proposed a single dielectric terahertz metasurface with diversified functions and the designed basic unit cell, which is composed of silicon dielectric layer with two different sizes of square grooves, and a bottom metal plate layer. The period of the silicon dielectric unit cell is P=100µm and the thickness of silicon substrate (ε=11.9) is h0 = 70µm. The bottom metal plate layer is selected as aluminium (Al) with thickness of 1µm to impede the terahertz energy transmitting through the sample and then produce reflection wave. The height of the two kinds of square grooves is h=30µm. The terahertz metasurfaces are constructed by utilizing square particles with different widths square grooves arranged periodically. The coding unit array can be fabricated by large-scale mask, lithography and etching techniques, and the electron beam lithography can be employed to produce the subwavelength unit cell.
Fig. 1. (a) Three-dimensional schematic diagram of terahertz metasurface with diversified functions, (b) Designed unit cell with the relevant geometric parameters
To obtain the eight distinct coding unit cells required by the 3-bit terahertz coding metasurface, the size of the unit cell is scanned in the commercially available Computer Software Technology (CST) Microwave Studio. In our simulation, periodic boundary conditions are applied in both x- and y- directions, and z-axis is set as Floquet-port excitation. Figures 2(a) and 2(b) describe the reflection amplitudes and phases for the eight coding unit cells labeled with numbers “0” to “7” from 0.7 to 1.3 THz, respectively. One can clearly see from Fig. 2(a) that the reflection amplitudes at 1.0THz for the eight coding unit cells labeled with numbers “0” to “7” exceed 0.97. Figure 2(b) shows the eight coding unit cells fully cover the 360° phase range with a 45° interval by changing geometric parameters (i.e. d1 and d2). Note that the phase for the coding unit cells from “0” to “7” are optimized as −366.39°, −411.55°, −457.17°, −500.03°, −544.44°, −590.42°, −636.71°, −681.05°, respectively, as shown in Table 1. One can notice that the eight coding unit cells with sufficient reflection was readily achieved across 360° phase coverage by a single silicon dielectric structure with a metallic ground sheet. In order to reduce the influence of the coupling effect among adjacent unit cells, a super unit cell is composed of N×N unit cells. Furthermore, the coding metasurface consists of M×M super unit cells.
Fig. 2. Reflection amplitudes (a) and (b) phases of eight coding unit cells with different size parameter d1 and d2
Table 1. Coding particles shape and corresponding phase vs. size parameters.
3. Diversified functions of the structured terahertz metasurface
3.1 Beam splitting
According to the generalized Snell's law and the far-field function of metasurface scattering, the azimuth angle (φ) of the reflected beam and the length and width (Dx and Dy) of the unit cell have the following relation as
Fig. 3. Terahertz beam splitting, (a) and (b) are the three-dimensional far-field scattering patterns with different coding sequences; (c) and (d) are the normalized electric field scattering patterns of (a) and (b), respectively. (Theoretical calculation results (θ=22.02°, φ=0°, 90°, 180°, and 270°), and simulation results (θ=22°, φ=0°, 90°, 180°, and 270°))
3.2 Anomalous reflection
Here we demonstrate the ability of the proposed terahertz metasurface to refract the normally incident terahertz waves in anomalous directions under different coding sequences. The example is a coding metasurface having a gradient coding sequence: 0 2 4 6 0 2 4 6 0 2 4 6 …, as shown in Fig. 5(a). N is the number of the unit cells, which is composed of super unit cell. A period coding sequence along x direction is composed of 4 kinds of supercells. By using different N=2 (i.e. Г=4×2×100 µm=800 µm), N=3 (i.e. Г=4×3×100 µm=1200 µm), and N=4 (i.e. Г=4×4×100 µm=1600 µm), we can simulate the three-dimensional far-field scattering patterns, as plotted in Fig. 5(b). The deflection angles are of θ1=22°, θ2=14°, θ3=10°, which are in accordance with the theoretical predictions (calculated according to above Eq (2)). In order to clearly observe the effect of different N, we plot the normalized reflection spectra of the designed terahertz metasurface. It can be noted from Fig. 5(c) that the reflection amplitudes rise gradually from 0.72 to 0.85 as N increases from 2 to 4. These examples clearly verify that the proposed terahertz metasurface can produce anomalous reflection with conveniently controlled directions by varying predesigned coding sequences without changing the geometric dimension parameters of the unit cells. The reflection efficiencies of the proposed anomalous reflectors are 51.84% (i.e. N=2), 62.41% (i.e. N=3), and 72.25% (i.e. N=4), respectively.
Fig. 5. Terahertz anomalous reflection. (a) coding patterns with coding sequence of “0 2 4 6 0 2 4 6 0 2 4 6 …”; (b) three-dimensional far-field scattering pattern when N=2, 3, 4; (c) normalized reflection amplitude when N=2, 3, 4. (Theoretical calculation results (θ1=22.02°, θ2=14.48°, θ3=and 10.81°), and simulation results (θ1=22°, θ2=14°, and θ3=10°))
3.3 Vortex beam generation
Furthermore, we demonstrate terahertz wave vortex beam generation feature of the proposed metasurface by simply arranging the coding unit cells. To generate a vortex beam on the metasurface, it is necessary to meet a spiral phase distribution, satisfying Δφ=2πl/(2n). For the case of l=1, we need use 3-bit coding metasurface to generate vortex beams and achieve across the 2π phase coverage. Figure 6(a) shows schematic diagram of the designed coding patterns with simply arranging the coding particles for vortex beam generation. Note that the eight coding unit cells have a 45° phase difference between adjacent unit cells. Figures 6(b) and 6(c) illustrate three-dimensional far-field diagrams of the vortex beam under normal incidence terahertz wave at 1.0THz, from which the effect of the generated vortex beam can be clearly found. Figures 7(a) and 7(b) show the simulated phase distribution and the two-dimensional electric field intensity distribution describing the vortex beam, respectively.
Fig. 6. Terahertz wave vortex beam generation, (a) designed terahertz metasurface with simply arranging the coding particles for vortex beam generation; (b) and (c) three-dimensional far-field scattering patterns of the vortex beam
Fig. 7. (a) and (b) are the phase and two-dimensional electric field intensity distributions of vortex beam
3.4 Angle controlled single-beam deflection
Interestingly, we verify that the dielectric coding metasurface can be utilized to carry out superposition and convolution operation which can reflect incidence terahertz wave to an angle-controlled direction. Here, the anomalous scattering angles of the convolution coding patterns structure can be calculated in the angular coordinate system as follows
We can clearly observe from Fig. 8(a) that the convolution operation is the addition of gradient coding sequence “0 2 4 6” along x-direction (N=2) and gradient coding sequence “0 2 4 6” along x-direction (N=3). The plotted three-dimensional scattering far-field patterns shows that the elevation angle of maximum radiation appears at α4=38° (see Fig. 8(c)), which is in accordance with the theoretical prediction of 38.68°. Similarly, from Fig. 8(b), we clearly see that the convolution operation is the subtraction of gradient coding sequence “0 2 4 6” along x-direction (N=2) and gradient coding sequence “0 2 4 6” along x-direction (N=3). The single beam scattering angle is about α5=8°, as displayed by three-dimensional scattering far-field patterns in Fig. 8(d). It can be seen from the figures that we can adjust the deflection angle of the single beam more flexibly.
Fig. 8. Coding patterns and three-dimensional scattering patterns with the functionality of a single-beam scattering to arbitrary direction. (a) and (b) Convolution operation of coding pattern with the gradient coding sequence “0 2 4 6 ….” under different (N=2, 3); (c) 3D far-field scattering patterns with a single beam of scattering angle α4=38° and (d) 3D far-field scattering patterns with a single beam of scattering angle α5 = 8°. (Theoretical calculation results (α4=38.68°, α5 = 7.18°), and simulation results (α4=38°, α5 = 8°)
3.5 Angle controlled multi-beam deflection
In addition, we investigate another important feature of the structured coding metasurface in angle controlled multi-beam deflection under normal incidence terahertz waves. Figures 9 a) and 9(b) show coding patterns of the gradient coding sequence “0 2 4 6 ….” along y-direction and x-direction at N=3, respectively. The coding patterns of the gradient coding sequence “0 2 4 6 ….” along y-direction at N=3 and a mixed gradient coding sequence, respectively (see Figs. 9(d) and 9(e)). Convolution operation of the coding patterns can be observed from Figs. 9(c) and 9(f). Under illumination by a normally incident terahertz wave, one can find that the 3D far-field scattering patterns of multiple beams can be scattered to arbitrary directions, as shown in Figs. 9(g) and 9(h). It can be clearly seen that the normal incidence terahertz wave is divided into two reflected beams with scattering angle of 14° when the terahertz wave illuminated on the coding patterns of the Fig. 9(c). If the terahertz wave illuminated on the coding patterns of the Fig. 9(f), the normal incidence terahertz wave is divided into four reflected beams with the same scattering angle of 14°. Since the gradient coding sequence “0 2 4 6 ….” along y-direction at N=3 can control the normal incidence terahertz wave to reflection beams with scattering angle of 14° (as depicted in Fig. 9), we can expect that different scattering angles are obtained by convolution with other gradient coding sequences.
Fig. 9. Coding patterns and three-dimensional scattering patterns with the functionality of multiple beams scattering to arbitrary direction. (a) and (b) Coding patterns of the gradient coding sequence “0 2 4 6 ….” along y-direction and x-direction at N=3, respectively; (d) and (e) Coding patterns of the gradient coding sequence “0 2 4 6 ….” along y-direction at N=3 and a mixed gradient coding sequence, respectively; (c) and (f) Convolution operation of coding patterns; (g) and (h) 3D far-field scattering patterns of multiple beams scattering to arbitrary directions.
3.6 Angle controlled vortex beam generation
Figures 10(a) and 10(f) show the designed metasurface coding patterns with simply arranging the coding particles for vortex beam generation. One can see that the coding patterns of the gradient coding sequence of the “0 2 4 6 ….” along x-direction for N=3 and N=4, respectively, makes the normal incidence terahertz wave reflect at oblique angles, as depicted in Figs. 10(b) and 10(g). We notice that the convolution operation of coding patterns from the addition and subtraction of the vortex beam generation coding sequence and the gradient coding sequence “0 2 4 6 ….” along x-direction for N=3 and N=4, as presented in Figs. 10(c) and 10(h), respectively. The structured convolution operation coding metasurfaces have been simulated to verify the theoretical predicted results by using the commercial software, CST Microwave Studio, as given in Figs. 10(d), 10(e), 10(i) and 10(j). We notice that the vortex beams scattering angles of the convolution operation coding metasurfaces are of θ2=14° and θ3=10°. Figures 11(a), 11(b), 11(c), and 11 (d) show the simulated phase distribution and the two-dimensional electric field intensity distribution of vortex beam scattering to arbitrary direction, respectively. It is easy to see from the figure that the vortex beam has a certain offset from the center point. It can be seen that the different deflection angles can be obtained by adding two coding sequences together convolution operation.
Fig. 10. Convolution operation of coding patterns and 3D far-field scattering patterns of vortex beam scattering to arbitrary direction; (a) and (f) Designed terahertz metasurface with simply arranging the coding particles for vortex beam generation; (b) and (g) Coding patterns of the gradient coding sequence “0 2 4 6 ….” along x-direction for N=3 and N=4, respectively; (c) and (h) Convolution operation of coding patterns; (d) and (e) 3D far-field scattering patterns of vortex beam scattering to arbitrary direction at N=3; (i) and (j) 3D far-field scattering patterns of vortex beam scattering to arbitrary direction at N=4.
Fig. 11. (a) and (b) are the phase and two-dimensional electric field intensity distributions of vortex beam scattering to arbitrary direction (N=3); (c) and (d) are the phase and two-dimensional electric field intensity distributions of vortex beam scattering to arbitrary direction (N=4).
3.7 Multi-vortex beam generation
To illustrate the function of generating multi-vortex beams, we convolve the gradient coding sequences of the vortex beam and the multi-beam, as displayed in Fig. 12. Figures 12(a) and 12(d) illustrate schematic diagram of the designed terahertz metasurface with simply arranging the gradient coding particles for vortex beam generation. Figures 12(b) and 12(e) displays the gradient coding sequence generated by multiple beams (‘0 4 0 4 0 4 0 4 …,’ and ‘0 2 4 6 0 2 4 6 0 2 4 6 …,’), respectively. Three-dimensional far-field scatter patterns of the convolution operation coding patterns generated by the vortex beam and the multi-beam as clearly illustrated in Figs. 12(c) and 12(f). It can be seen from the figure that two vortex beams (θ=22°, φ = 0°, 180°) and four vortex beams (θ=22°, φ=0°, 90°, 180°, 270°) have been successfully generated. The reflection directions of the vortex beams are at 22°, which are the same as the beam direction of the coding sequence generated by the multi-beam. Figures 13(a) and 13(b) show the two-dimensional electric field intensity distribution describing the multiple vortex beams, respectively. It is interesting to observe that the number and reflection direction of the multiple vortex beam generation exhibit to be controlled by the coding patterns of performing convolution operation.
Fig. 12. Convolution operation of coding patterns generated by the vortex beam and the multi-beam and their three-dimensional scattering patterns. (a) and (d) three-dimensional far-field scatter patterns of Vortex beam; (b) and (e) three-dimensional far-field scatter patterns of multi-beam generation; (c) and (f) 3D far-field scattering patterns of the convolution operation coding patterns generated by the vortex beam and the multi-beam.
Fig. 13. (a) and (b) are the two-dimensional electric field intensity distributions of the convolution operation shown in Figs. 12(c) and 12(f) coding patterns generated by the vortex beam and the multi-beam.
4. Conclusion
In summary, the studies on dielectric coding metasurfaces demonstrate that our proposed structure accomplish different functions for example beam splitting, anomalous reflection, vortex beam generation, angle controlled single-beam deflection, angle controlled multi-beam deflection, angle-controlled vortex beam generation and multi-vortex beam generation without changing the geometrical parameters. The coding particles consists of square dielectric silicon with two various sizes of square grooves located on a bottom metallic plate layer. Our coding metasurfaces are capable of powerful manipulation to terahertz waves with several different coding sequences. This study opens a new route to realize dynamic manipulations terahertz wavefront and provide potential applications in the future such as high-speed terahertz wireless communication and MIMO communication.
Funding
National Natural Science Foundation of China (61871355, 61831012); Zhejiang Key R & D Project of China (2021C03153); Fundamental Research Funds for the Provincial Universities of Zhejiang (2020YW20); Major Scientific Project of Zhejiang Laboratory (2019LC0AB03).
Disclosures
The authors declare no conflicts of interest.
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