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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
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
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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
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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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
Figure 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)
Figure 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)
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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.
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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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