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Abstract
Terahertz waves have attracted considerable attention in recent years because of their potential applications in different fields. The appearance of a digital metasurface simplifies the design of functional devices and manipulates the terahertz wave in a convenient way with a specific array of digital particles. Metal resonators are mostly used in traditional structures, and the ohmic loss of metal will affect the energy transmission efficiency. In our work, we propose a silicon medium metasurface by pre-designing different digital sequences for terahertz wave different control functions such as anomalous reflection, beam splitting, diffuse scattering and generation of vortex beam. The far-field scattering patterns and near-field distribution are obtained by numerical simulation, which are in accordance with the values predicted analytically. Our work provides an effective method to promote the diversification of the metasurface-based functional devices in the terahertz region.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Due to the special position of terahertz wave in electromagnetic spectrum, it has many unique characteristics and has extensive application prospect in many fields such as communication, imaging, biological detection, and so on [1–4]. However, terahertz wave manipulation becomes a key factor affecting these applications and has attracted considerable researchers’ attention [5–9]. In recent years, metasurfaces have been used in the fields of electromagnetic wave manipulation due to the ability of adjusting and controlling the phase, amplitude and polarization of incident electromagnetic wave flexibly [10–13]. In addition, compared with the wavelength of the working frequency, the metasurfaces have their extraordinary physical properties of negligible thickness, small physical space, easy intergration and less loss. Recently, coding metasurfaces have become a new design way for controlling the propagation of electromagnetic waves [14–20]. However, traditional coding metasurface needs a fixed phase difference, which requires many different geometric patterns or various sizes of metasurface structures. Furthermore, the top-layer patterns of these metasurfaces are made of metal, which will produce certain electromagnetic wave absorption loss. In addition, metal resonators are mostly used in traditional structures, and the ohmic loss of metal will affect the energy transmission efficiency. In order to solve this problem, silicon medium metasurfaces have become a good alternative tool for its negligible loss in terahertz region.
In this paper, we design a silicon medium metasurface for controlling the terahertz wave propagation. The particles are made of circular hollow silicon with various radius located on a metallic bottom plate. The manipulation of the terahertz wave, including anomalous reflection, beam splitting, radar cross section (RCS) reduction and generation of vortex beam are achieved by using our silicon medium metasurfaces with various pre-designing binary sequences of the optimized particles. The theoretical prediction results show excellent agreement with those of full-wave numerical simulations by using CST Microwave Studio. Compared with previous works [21], in this letter, the proposed silicon medium metasurface not only has perfect abnormal refraction and beam splitting, but also realize the generation of vortex beam. The maximum RCS reduction is more than -20 dB at 0.76THz. The presented silicon medium metasurface approach has potential applications in the design of terahertz switch, terahertz filter, terahertz radar and terahertz vortex beam generator.
2. Structure design
We proposed a silicon medium metasurface composed of a circular hollow silicon substrate and a bottom metal plate with a thickness of 0.2 μm, as shown in Fig. 1. The metasurface is composed of four different coding particles randomly. The radius of the circular air hole is r and the silicon substrate (ε=11.9) with a thickness of h = 90 μm. The circular air holes are arranged in a periodic square-array with a lattice constant P = 100 μm. The metasurface particles are designed by using the circular holes with different radius. The normal incidence terahertz wave is dispersed through the metasurface to form numerous reflection beams and diffuse around. Using the electromagnetic simulation software CST Microwave Studio, the excitation source is in the form of plane wave, and the particle boundary conditions and Floquent port are used for element simulation, the silicon medium metasurface particle is simulated in the frequency domain solver. The 2-bit silicon medium metasurface particles have four kinds of digital states with phases of 0°, 90°, 180° and 270°, as shown in Table 1, by careful selection of different radius of circular air hole. As shown in Table 1, the optimized parameters of the circular air holes are r = 5 μm, r = 22 μm, r = 29 μm and r = 41 μm, respectively. Under normal incidence of the terahertz wave, the reflection amplitudes of the four kinds of silicon medium metasurface particles are above 0.98, as shown in Fig. 2 (a). Figure 2 (b) describes the reflection phase of the four kinds of silicon medium metasurface particles with various radius. Changing the radius “r” of the circular air holes causes the resonance frequency point shift and generates a phase gradient between adjacent metasurface particles.
Fig. 2. (a) Reflection amplitude vs. frequency. (b) Reflection phase vs. frequency of the four kinds of silicon medium metasurface particles under the normal incidence of terahertz wave.
Table 1. Metasurface particles and phase response vs. size parameters.
3. Calculation results and discussion
Figures 3 (a) and 3(e) describe the schematic diagrams of silicon medium metasurfaces with the digital sequence “0000010110101111…” and “0001101100011011…”. The silicon medium metasurface is composed of 8 super particles arranged periodically along x-axis direction and each super particle consist of 3×3 the same size particles with a periodic distribution. According to the generalized Snell's law, the angle of the reflected terahertz wave beam can be calculated by
where ni (nr) is the refractive index of the incident (reflection) medium, θi (θr) is the incident (reflection) angle, and λ0 is the vacuum wavelength, dφ/dx is the phase gradient at the interface of the two media. After simplification, the elevation angle (θ) can be given by where Γ is the period of the phase gradient. Figs. 3(b) and 3(f) illustrate the simulated far-field distribution produced by the silicon medium metasurfaces. One can see that the metasurfaces with the digital sequence “0000010110101111…” and “0001101100011011…” make the incident wave reflect at oblique angles of 9.22° and 18.72°, which are in good agreement with elevation angles predicted by Eq. (2). It indicates that the y-polarization wave is deflected to the anomalous direction by the silicon medium metasurface. Figs. 3(c) and 3(g) depict the normalized reflected intensity amplitude of the silicon medium metasurface with predesigning “0000010110101111…” and “0001101100011011…” sequence under normal incidence of terahertz wave at 0.78 THz, respectively. It is obvious that the direction of the peak reflection intensities is close to the values predicted analytically. It further confirms that the silicon medium metasurface achieves perfect anomalous reflection. In order to verify anomalous reflection effect, we simulated the near-electric field distribution for the anomalous reflections with the predesigning “0000010110101111…” and “0001101100011011…” sequence under normal incidence of terahertz wave at 0.78 THz, as shown in Figs. 3(d) and 3(h), respectively. In the Figs. 3(c) and 3(g), one can see that the reflection angles are about 9.22° and 18.72° at 0.78 THz, respectively, which is consistent with the reflection angle calculated by Eq. (2). The anomalous reflection is close to 0.9.Fig. 3. Silicon medium metasurface for the predesigning squence (a) “0000010110101111…” and (e) “0001101100011011…”. (b) and (f) are three-dimensional far-field scattering patterns of the anomalous reflection with elevation angle of 9.22° and 18.72° at 0.78THz, respectively. (c) and (g) are the normalized reflected intensity amplitude of silicon medium digital metasurface with “0000010110101111…” and “0001101100011011…” predesigning sequence under normal incidence of terahertz wave at 0.78THz, respectively. (d) and (h) are near-electric field distribution for the anomalous reflections with “0000010110101111…” and “0001101100011011…” predesigning sequence under normal incidence of terahertz wave at 0.78THz, respectively.
For a periodic distribution digital sequence “00100010…” along y-axis direction, a normal incidence terahertz wave on the silicon medium metasurface is predominantly reflected in two directions and a direction determined by the incident terahertz frequencies of 0.78 THz and 0.6 THz, as shown in Figs. 4(a) and 4(b), respectively. In the case Γ = 3×2×100 μm, the elevation angle (θ=39.87°) can be calculated by the formula. Figure 4(c) depicts the normalized reflected intensity amplitude of the silicon medium metasurface in the Cartesian coordinate system (The insets is the far-field scattering pattern). The calculated elevation angle is good consistent with the simulation results as illustrated in Figs. 4(a) and 4(b). Similarly, the reflected wave beam in Fig. 4(d) is divided into four symmetrical beams evenly and the backscattering becomes very weak when the silicon medium metasurface with a chessboard arrangement of “0010…/1000…” is illuminated by a normally incident terahertz wave at 0.78 THz. Using the Eq. (2), the elevation angle of the reflected beam can be calculated as θ=65.10°. As the operating frequency moves to 0.6 THz, the reflected terahertz wave on the silicon medium metasurface is mainly vertical reflection, as shown in the Fig. 4(e). The normalized reflected intensity amplitude of silicon medium metasurface with chessboard arrangement is shown in Fig. 4(f).
Fig. 4. (a) and (b) are three-dimensional far-field scattering patterns of the silicon medium metasurface with the periodic distribution digital sequence “00100010…” along y-axis direction under normal incidence of terahertz wave at 0.78 THz and 0.6 THz, respectively. (c) Normalized reflected intensity amplitude of the silicon medium metasurface with the sequence “00100010…” periodically distributed along y-axis direction at 0.78 THz and 0.6 THz in the Cartesian coordinate system. (d) and (e) are three-dimensional far-field scattering patterns of the silicon medium metasurface with chessboard arrangement at 0.78 THz and 0.6 THz, respectively. (f) Normalized reflected intensity amplitude of silicon medium metasurface with chessboard arrangement at 0.78 THz and 0.6 THz in the Cartesian coordinate system.
Figures 5(a) and 5(b) show the simulated three-dimensional far-field distribution produced by the silicon medium metasurface under normal incidence terahertz wave. One can see that the proposed silicon medium metasurface makes the incident terahertz wave reflect at oblique angles, which are in good agreement with angles 9.21˚ and 18.72˚ predicted for the gradient phase change of Γ1=600 μm, Γ2=300√2 μm, Γ3=2400 μm and Γ4=1200$\surd 2$ μm by the generalized Snell’s law. The reflection terahertz wave efficiency of the silicon medium metasurface is 95% for the case chessboard arrangements of its particles. Here, the reflection efficiency is defined as the reflected terahertz wave power divided by the incident terahertz wave power.
Fig. 5. Three-dimensional far-field scattering patterns of the proposed silicon medium metasurface under normal incidence of y-polarized terahertz wave at 0.78 THz. (a) “0000000010101010…” periodically distributed along y-axis direction. (b) Chessboard arrangement of “0010…/1000…”.
To investigate the RCS properties of the silicon medium metasurface, we design two 1-bit and 2-bit digital metasurfaces which are composed of 24×24 particles by using the random digital sequence generated by MATLAB. In order to minimize coupling between different particles, each type is grouped into 3×3 sub-arrays of identical particles and then assembled into 8×8 arrays of the four particle types. We numerically calculate the effect of diffuse scattering of the silicon medium metasurface. The three-dimensional scattering patterns of the equal-size metal plane, 1-bit, and 2-bit silicon medium metasurface under normal incidence of y-polarized terahertz wave are shown in Figs. 6(a), 6(b) and 6(c). The bistatic RCS at frequency of 0.78 THz for different random digital metasurface demonstrate the ability of the designed silicon medium metasurface to strongly suppress bistatic RCS, as presented in Fig. 6(d). According to Fig. 6 (d), one sees that the RCS value of metal plate is about -25 dB, while that of 1-bit random coding metasurface is about -44 dB and that of 2-bit random coding metasurface is about -41 dB. It is obviously found that the RCS value of the dielectric-pattern implement is smaller than that of metallic counterpart. Figure 6(e) further confirm the performance of the designed silicon medium metasurface, which can provide the RCS reduction more than 10 dB at frequency range from 0.7 THz to 0.9 THz. The peak RCS reduction values is in excess of -21 dB at 0.76 THz. In addition, by using the silicon medium metasurface with a spiral phase distribution, one can see that the vortex wave beam can be generated. The silicon medium metasurface is divided into N equal segments, and the relationship between the phase difference Δφ, topological charge l and the number of segments N of the silicon medium metasurface is N·Δφ=2πl. It generates orbital angular momentum (OAM) beams with l = 1 and l = 2. In this paper, the silicon medium metasurfaces are divided into four equal segments and eight equal segments with phase shifts from 0 to 2π and 0 to 4π, respectively. As shown in Figs. 7(a) and 7(b), it is a schematic diagram of a metasurface generating vortex waves. In order to verify these results, the three-dimensional far-field of the normal incidence plane wave on the silicon medium metasurface of 2400×2400 μm2 is simulated, as shown in Figs. 7(c) and 7(d). It can be noted that wo kinds of terahertz vortex beams are generated.
Fig. 6. (a) Three-dimensional far-field scattering pattern of the identical size bare metal plate under normal incidence of terahertz wave at 0.78 THz. (b) Three-dimensional far-field scattering pattern of 1-bit random silicon medium metasurface at 0.78 THz. (c) Three-dimensional far-field scattering pattern of 2-bit random metasurface at 0.78 THz. (d) Bistatic RCS at 0.78 THz for different random silicon medium metasurface. (e) RCS of 1-bit and 2-bit random silicon medium metasurfaces and the same size bare metal plate at frequency ranging from 0.7 THz to 0.9 THz.
Fig. 7. (a) and (b) are schematic diagrams of vortex beam generation metasurface with l = 1 and l = 2. (c) and (d) are three-dimensional far-field scattering pattern of terahertz vortex beams with l = 1 and l = 2.
Our designed coding metasurfaces is also applicable to the fractional and convolution superposition theorem [22,23]. Figure 8 depicts three different coding patterns (a–c)and the corresponding scattering patterns (d–f), respectively. In this illustration, Fig. 8 (a) shows the coding pattern with gradient coding sequence “00011011…” periodically distributed along x-axis direction. Figure 8 (b) illustrates the coding pattern with gradient coding sequence “00100010…” periodically distributed along y-axis direction. Their convolution of the mixed coding patterns are shown in Fig. 8 (c). The calculated scattering patterns clearly show that the scattering pattern with a single beam have a certain reflected angle along the normal axis (Fig. 8 d). Noting that the normal incidence terahertz wave is reflected according to the two symmetric beams with a certain pitch angle and azimuth angle (sees in Fig. 8(e)). After conducted by a convolution operation, the coding metasurface operates with two beams scattering pattern according to the specific reflection angle (Fig. 8(f)).The designed coding metasurface not only realizes beam splitting, but also adjusts the reflection angle.
Fig. 8. Schematic illustration to the principle of scattering-pattern shift in analogy to the Fourier Transform. (a–c)Coding patterns with gradient coding sequence “00011011…” periodically distributed along x-axis direction, gradient coding sequence “00100010…” periodically distributed along y-axis direction, and their convolution (gradient coding sequence “00011011…/10110001…” periodic arrangement), respectively. (d–f) Three-dimensional far-field scattering patterns of the coding patterns in panels (a)-(c) under normal incidence of terahertz wave at 0.78 THz, respectively.
4. Conclusion
To sum up, we designed a silicon medium metasurface to realize anomalous reflection, beam splitting and diffuse scattering in terahertz region. By employing different predesigned arrangements of digital particles, the normal incidence terahertz wave is reflected to the desired angle. Compared with the identical size bare metal plate, the proposed silicon medium metasurface can reduce 21 dB RCS at frequency of 0.76 THz. The RCS reduction with more than 10 dB is obtained effectively in frequency range from 0.7 THz to 0.9 THz. The far-field scattering pattern confirms the proposed silicon medium metasurface can realize multi-function control of terahertz wave, which are beneficial to practical terahertz technology application.
Funding
National Natural Science Foundation of China (61831012, 61871355); Zhejiang Key R & D Project of China (2021C03153); Zhejiang Lab (2019LC0AB03).
Acknowledgment
This work was sponsored by the National Natural Science Foundation of China (Grant Nos. 61871355 and 61831012), Zhejiang Key R & D Project of China (No.2021C03153), and Zhejiang Lab (No.2019LC0AB03).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. T. Masayoshi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007). [CrossRef]
2. P. Radoslaw, K. Thomas, K. Norman, M. Daniel, K. Martin, S. Joerg, and K. Thomas, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas and Propagation Magazine 49(6), 24–39 (2007). [CrossRef]
3. P. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microwave Theory Tech. 52(10), 2438–2447 (2004). [CrossRef]
4. F. Zhou, Y. Bao, W. Cao, C. T. Stuart, J. Gu, W. Zhang, and C. Sun, “Hiding a realistic object using a broadband terahertz invisibility cloak,” Sci. Rep. 1(1), 78 (2011). [CrossRef]
5. L. Zhu, F. Meng, L. Dong, J. Fu, X. Ding, and Q. Wu, “Tunable transparency effect in a symmetry metamaterial based on subradiant magnetic resonance,” IEEE Trans. Magn. 50, 1–4 (2014). [CrossRef]
6. F. Antonio, Z. Dimitrios, C. Roberto, and B. Romeo, “Guided-mode resonant narrowband terahertz filtering by periodic metallic stripe and patch arrays on cyclo-olefn substrates,” Sci. Rep. 8(1), 15631 (2018). [CrossRef]
7. Y. Lin, H. Yao, X. Ju, Y. Chen, S. Zhong, and X. Wang, “Free-standing double-layer terahertz band-pass filters fabricated by femtosecond laser micro-machining,” Opt. Express 25(21), 25125–25134 (2017). [CrossRef]
8. P. Tang, J. Li, S. Zhong, Z. Zhai, B. Zhu, L. Du, Z. Li, and L. Zhu, “Giant dual-mode graphene-based terahertz modulator enabled by Fabry-Perot assisted multiple reflection,” Opt. Lett. 44(7), 1630–1633 (2019). [CrossRef]
9. B. Wang, “Quad-band terahertz metamaterial absorber based on the combining of the dipole and quadrupole resonances of two SRRs,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–7 (2017). [CrossRef]
10. X. Zhang, W. Jiang, H. Jiang, Q. Wang, H. Tian, L. Bai, J. Zhang, S. Sun, Y. Luo, C. Qiu, and T. Cui, “An optically driven digital metasurface for programming electromagnetic functions,” Nat. Electron. 3(3), 165–171 (2020). [CrossRef]
11. Z. Wang, J. Wu, X. Wan, L. Wu, Q. Xiao, Q. Cheng, and T. Cui, “Broadband and ultrathin Huygens metasurface with high transmittance,” J. Phys. D: Appl. Phys. 53(45), 455102 (2020). [CrossRef]
12. J. Li, S. Chen, H. Yang, J. Li, P. Yu, H. Cheng, C. Gu, H. Chen, and J. Tian, “Simultaneous control of light polarization and phase distributions using plasmonic metasurfaces,” Adv. Funct. Mater. 25(5), 704–710 (2015). [CrossRef]
13. A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Silicon medium metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015). [CrossRef]
14. T. Cui, M. Qi, X. Wan, J. Zhao, Q. Cheng, and X. Wan, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light: Sci. Appl. 3(10), e218 (2014). [CrossRef]
15. R. Wu, C. Shi, S. Liu, W. Wu, and T. Cui, “Addition theorem for digital coding metamaterials,” Adv. Opt. Mater. 6(5), 1701236 (2018). [CrossRef]
16. M. Akram, M. Mehmood, T. Tauqeer, A. Rana, I. Rukhlenko, and W. Zhu, “Highly efficient generation of bessel beams with polarization insensitive metasurfaces,” Opt. Express 27(7), 9467–9480 (2019). [CrossRef]
17. L. Chen, H. Ma, and H. Cui, “Wavefront manipulation based on mechanically reconfifigurable coding metasurface,” Appl. Phys. 124(4), 043101 (2018). [CrossRef]
18. K. Rouhi, H. Rajabalipanah, and A. Abdolali, “Real-time and broadband terahertz wave scattering manipulation via polarization insensitive conformal graphene-based coding metasurfaces,” Ann. Phys. 530(4), 1700310 (2018). [CrossRef]
19. T. Cui, S. Liu, and L. Zhang, “Information metamaterials and metasurfaces,” J. Mater. Chem. C 5(15), 3644–3668 (2017). [CrossRef]
20. H. Ma, Y. Liu, K. Luan, and T. Cui, “Multi-beam reflections with flexible control of polarizations by using anisotropic metasurfaces,” Sci. Rep. 6, 39390 (2016). [CrossRef]
21. Y. Saifullah, A. Waqas, G. Yang, and F. Xu, “Multi-bit dielectric coding metasurface for EM wave manipulation and anomalous reflection,” Opt. Express 28(2), 1139–1149 (2020). [CrossRef]
22. L. Wang, F. Lan, Y. Zhang, S. Liang, W. Liu, Z. Yang, L. Meng, Z. Shi, J. Yin, T. Song, H. Zeng, and P. Mazumder, “A fractional phase-coding strategy for terahertz beam patterning on digital metasurfaces,” Opt. Express 28(5), 6395–6407 (2020). [CrossRef]
23. S. Liu, T. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Gu, W. Tang, M. Qi, J. Han, W. Zhang, X. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016). [CrossRef]
