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提出一种宽带、高传输效率的双层超表面, 其单元结构是在介质层两边对称刻蚀结构参数相同的十字型金属贴片且将两层超表面沿y方向错位半个周期长度形成. 通过引入y方向的错位, 双层超表面的透射带宽得到大幅度提升. 同时, 采用等效电路理论分析了该双层超表面的带宽展宽机理. 在此基础上, 进一步结合Pancharatnam-Berry相位原理, 实现了宽带轨道角动量波束生成器. 实验和仿真结果表明, 在11—12.8 GHz的频率范围内, 器件能够将左旋圆极化波转换为携带轨道角动量的右旋圆极化波.
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关键词:
- 双层超表面 /
- 宽带 /
- Pancharatnam-Berry相位 /
- 轨道角动量
A broadband and high-efficieny bi-layer metasurface is proposed in this paper. The unit cell of the metasurface is formed by symmetrically etching two cross-type metal patches on both sides of a dielectric plate. Furthermore, the two metal patches have a displacement of half a period along the y-axis. By employing the displacement, the transmission bandwidth of the bi-layer metasurface is significantly expanded. In order to obtain a physical insight into bandwidth broadening, a π-type equivalent circuit that presents the electromagnetic coupling between within the bi-layer metasurfaces is successfully extracted to investigate the influence of electromagnetic coupling on transmission performance. The results show that by shifting the metal patches along the y-axis by half a period, the coupling impedance (Z12 or Z21) of bi-layer metasurface can be significantly modified, which further changes the electromagnetic coupling of the bi-layer metasurface. Correspondingly, the impedances Zp and Zs in the π-type circuit are changed to approximately meet the resonant condition of circuit in broadband, resulting in the bandwidth expansion of the proposed device. By using Pancharatnam-Berry phase theory, we redesign the proposed metasurface unit cell into a broadband orbital angular momentum generator. The simulation and measurement results verify that the bi-layer metasurface can convert a left-hand circularly polarized wave into a right-hand circularly polarized wave carrying orbital angular momentum in a frequency range between 11 GHz and 12.8 GHz, demonstrating the performance of device.[1] Allen L, Beijersbergen M W, Spreeuw R J, Woerdman J P 1992 Phys. Rev. A 45 8185
Google Scholar
[2] Babiker M, Power W L, Allen L 1994 Phys. Rev. Lett. 73 1239
Google Scholar
[3] Tennant A, Allen B 2012 Electron. Lett. 48 1365
Google Scholar
[4] Fahrbach F O, Simon P, Rohrbach A 2010 Nat. Photonics 4 780
Google Scholar
[5] Yao A M, Padgett M J 2011 Adv. Opt. Photonics 3 161
Google Scholar
[6] Duocastella M, Arnold C B 2012 Laser Photonics Rev. 6 607
Google Scholar
[7] Thide B, Then H, Sjoholm J, Palmer K, Bergman J, Carozzi T, Istomin Y N, Ibragimov N, Khamitova R 2007 Phys. Rev. Lett. 99 087701
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[8] Tamburini F, Mari E, Thide B, Barbieri C, Romanato F 2011 Appl. Phys. Lett. 99 204102
Google Scholar
[9] Mohammadi S M, Daldorff L K, Bergman J E, Karlsson R L, Thide B, Forozesh K, Carozzi T D, Isham B 2009 IEEE Trans. Antennas Propag. 58 565
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[10] Tamburini F, Mari E, Sponselli A, Thide B, Bianchini A, Romanato F 2012 New J. Phys. 14 033001
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[11] Yu N, Genevet P, Kats M A, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333
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[12] Kildishev A V, Boltasseva A, Shalaev V M 2013 Science 339 1232009
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[13] Momeni H A S M A, Behdad N 2016 IEEE Trans. Antennas Propag. 64 525
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[14] Wakatsuchi H, Kim S, Rushton J J, Sievenpiper D F 2013 Phys. Rev. Lett. 111 245501
Google Scholar
[15] West P R, Stewart J L, Kildishev A V, Shalaev V M, Shkunov V V, Strohkendl F, Zakharenkov Y A, Dodds R K, Byren R 2014 Opt. Express 22 26212
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[16] Ni X, Kildishev A V, Shalaev V M 2013 Nat. Commun. 4 1
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[17] Yu S, Li L, Shi G, Zhu C, Shi Y 2016 Appl. Phys. Lett. 108 241901
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[18] Achouri K, Lavigne G, Caloz C 2016 J. Appl. Phys. 120 235305
Google Scholar
[19] Chen M L N, Li J J, Sha W E I 2017 IEEE Trans. Antennas Propag. 65 396
Google Scholar
[20] Escuti M J, Kim J, Kudenov M W 2016 Opt. Photonics News 27 22
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[21] Olk A E, Powell D A 2019 Phys. Rev. Appl. 11 064007
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[22] Akram M R, Mehmood M Q, Bai X, Jin R, Premaratne M, Zhu W 2019 Adv. Opt. Mater. 7 1801628
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[23] Akram M R, Bai X, Jin R, Vandenbosch G A, Premaratne M, Zhu W 2019 IEEE Trans. Antennas Propag. 67 4650
Google Scholar
[24] Tang S, Cai T, Liang J G, Xiao Y, Zhang C W, Zhang Q, Hu Z, Jiang T 2019 Opt. Express 27 1816
Google Scholar
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图 1 超表面单元的物理模型 (a)上层结构俯视图; (b)下层结构仰视图; (c)侧视图
Fig. 1. Schematic of metasurface unit cell: (a) Top view; (b) bottom view; (c) side view of the unit cell.
图 2 超表面对线极化波的响应(txx和tyy为x极化波和y极化波的同极化传输系数的振幅, φxx 和φyy为同极化传输系数的相位)
Fig. 2. Amplitude and phase of co-polarized transmission coefficient, where txx and tyy are amplitudes of co-polarized transmission coefficients for x- and y-polarized incident waves, and φxx and φyy correspond to the phase of txx and tyy.
图 3 超表面对左旋圆极化波的响应(tL-L和tL-R为同极化和交叉极化传输系数, rL-L和rL-R为同极化和交叉极化反射系数)
Fig. 3. Response for left-hand circularly polarized incident wave, where tL-L and tL-R are co- and cross-polarized transmission coefficients, and rL-L and rL-R are co- and cross-polarized reflective coefficients.
图 4 (a) y极化波的透射系数; (b) x极化波的透射系数
Fig. 4. (a) Transmission coefficient for y-polarized wave; (b) transmission coefficient for x-polarized wave.
图 5 (a) 等效电路模型; (b) 由等效电路及CST仿真得到的y极化波的S参数
Fig. 5. (a) Equivalent circuit model; (b) transmission coefficients for y-polarized incident wave obtained from equivalent circuit (EC) modal and CST simulation.
图 6 等效电路模型中的阻抗元素 (a) Ly = 0 mm; (b) Ly = 7.5 mm
Fig. 6. Impedance elements of equivalent circuit for different Ly: (a) Ly = 0 mm; (b) Ly = 7.5 mm.
图 7 双层超表面的π型等效电路 (a) 精细结构; (b)总结构
Fig. 7. π-type equivalent circuit for bi-layer metasurface: (a) Fine structure; (b) overall framework.
图 8 不同Ly值的情况下, Zs和Zp随频率的变化关系 (a) Ly = 0 mm; (b) Ly = 7.5 mm.
Fig. 8. Zs and Zp function as frequency for different Ly: (a) Ly = 0 mm; (b) Ly = 7.5 mm.
图 9 产生OAM波束的超表面 (a) 整体结构排布; (b) 区域分布示意图
Fig. 9. Metasurface for generating OAM wave beam: (a) The whole structure; (b) phase distribution.
图 10 z = 100 mm处, 仿真得到的xoy平面内的电场及相位分布 (a), (b) 11 GHz处电场的振幅和相位; (c), (d) 11.9 GHz处电场的振幅和相位; (e), (f) 12.8 GHz处电场的振幅和相位
Fig. 10. Simulated amplitude and phase distributions of electromagnetic wave in xoy plane located at z = 100 mm: (a), (b) At 11 GHz; (c), (d) at 11 GHz; (e), (f) at 12.8 GHz.
图 11 加工的实物图 (a) 正面; (b) 背面
Fig. 11. Photos of fabricated samples: (a) Top view; (b) bottom view.
图 12 z = 100 mm处, 测试得到的xoy平面内的电场及相位分布 (a), (b) 11 GHz处电场的振幅和相位; (c), (d) 11.9 GHz处电场的振幅和相位; (e), (f) 12.8 GHz处电场的振幅和相位
Fig. 12. Measured amplitude and phase distributions of electromagnetic wave in xoy plane located at z = 100 mm: (a), (b) At 11 GHz; (c), (d) at 11 GHz; (e), (f) at 12.8 GHz.
表 1 与其他传输型超表面的性能对比(
${\lambda _0}$ 为中心频率对应的波长)Table 1. Comparison with other transmissive metasurface.
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[1] Allen L, Beijersbergen M W, Spreeuw R J, Woerdman J P 1992 Phys. Rev. A 45 8185
Google Scholar
[2] Babiker M, Power W L, Allen L 1994 Phys. Rev. Lett. 73 1239
Google Scholar
[3] Tennant A, Allen B 2012 Electron. Lett. 48 1365
Google Scholar
[4] Fahrbach F O, Simon P, Rohrbach A 2010 Nat. Photonics 4 780
Google Scholar
[5] Yao A M, Padgett M J 2011 Adv. Opt. Photonics 3 161
Google Scholar
[6] Duocastella M, Arnold C B 2012 Laser Photonics Rev. 6 607
Google Scholar
[7] Thide B, Then H, Sjoholm J, Palmer K, Bergman J, Carozzi T, Istomin Y N, Ibragimov N, Khamitova R 2007 Phys. Rev. Lett. 99 087701
Google Scholar
[8] Tamburini F, Mari E, Thide B, Barbieri C, Romanato F 2011 Appl. Phys. Lett. 99 204102
Google Scholar
[9] Mohammadi S M, Daldorff L K, Bergman J E, Karlsson R L, Thide B, Forozesh K, Carozzi T D, Isham B 2009 IEEE Trans. Antennas Propag. 58 565
Google Scholar
[10] Tamburini F, Mari E, Sponselli A, Thide B, Bianchini A, Romanato F 2012 New J. Phys. 14 033001
Google Scholar
[11] Yu N, Genevet P, Kats M A, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333
Google Scholar
[12] Kildishev A V, Boltasseva A, Shalaev V M 2013 Science 339 1232009
Google Scholar
[13] Momeni H A S M A, Behdad N 2016 IEEE Trans. Antennas Propag. 64 525
Google Scholar
[14] Wakatsuchi H, Kim S, Rushton J J, Sievenpiper D F 2013 Phys. Rev. Lett. 111 245501
Google Scholar
[15] West P R, Stewart J L, Kildishev A V, Shalaev V M, Shkunov V V, Strohkendl F, Zakharenkov Y A, Dodds R K, Byren R 2014 Opt. Express 22 26212
Google Scholar
[16] Ni X, Kildishev A V, Shalaev V M 2013 Nat. Commun. 4 1
Google Scholar
[17] Yu S, Li L, Shi G, Zhu C, Shi Y 2016 Appl. Phys. Lett. 108 241901
Google Scholar
[18] Achouri K, Lavigne G, Caloz C 2016 J. Appl. Phys. 120 235305
Google Scholar
[19] Chen M L N, Li J J, Sha W E I 2017 IEEE Trans. Antennas Propag. 65 396
Google Scholar
[20] Escuti M J, Kim J, Kudenov M W 2016 Opt. Photonics News 27 22
Google Scholar
[21] Olk A E, Powell D A 2019 Phys. Rev. Appl. 11 064007
Google Scholar
[22] Akram M R, Mehmood M Q, Bai X, Jin R, Premaratne M, Zhu W 2019 Adv. Opt. Mater. 7 1801628
Google Scholar
[23] Akram M R, Bai X, Jin R, Vandenbosch G A, Premaratne M, Zhu W 2019 IEEE Trans. Antennas Propag. 67 4650
Google Scholar
[24] Tang S, Cai T, Liang J G, Xiao Y, Zhang C W, Zhang Q, Hu Z, Jiang T 2019 Opt. Express 27 1816
Google Scholar
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