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Metasurfaces consist of arrays of artificial atoms arranged on a subwavelength scale, and have significant advantages in modulating the phase, amplitude, and polarization of optical field. Limited by the discrete sampling principle and the assumption of periodicity, the conventional forward design method suffers unavoidable design errors, which easily leads the device performance to degrade. In this paper, a freeform wavelength division multiplexing (WDM) metagrating with a large deflection angle and polarization-insensitive characteristics is inversely designed by using an adjoint multi-objective topology optimization method. The simulation results show that the topology-optimized WDM metagrating has superior polarization in sensitivity compared with the discrete regular structure, with a deflection angle of 70.8° at 510 nm, an absolute deflection efficiency of 48%, and a transmission efficiency of 98% for 852 nm incident light. On this basis, the absolute deflection efficiency can be optimized to more than 70% by using a random initial structure. The freeform WDM metagrating designed in this paper has the advantages of large deflection angle, high efficiency, and low spatial crosstalk, and has potential applications in optical communication, micro and nano-optical field modulation, and Rydberg atom-based microwave measurements.
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Keywords:
- freeform metasurface /
- inverse design /
- topology optimization /
- wavelength division multiplexing
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Google Scholar
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图 1 大角度波分复用超光栅示意图 (a) 器件示意图; (b) 单元示意图
Figure 1. Schematic diagram of large-angle wavelength-division multiplexing-based metagrating: (a) Overall schematic; (b) unit schematic.
图 2 波长为510和852 nm时, 具有不同单元尺寸和占空比的方形晶格上周期性TiO2圆柱的(a), (d)透射率和(b), (e)相位; (c), (f) 具有180 nm单元尺寸和600 nm高度的不同直径的周期性TiO2圆柱的透射率和相位
Figure 2. Calculation of (a), (d) the transmission and (b), (e) the phase of the periodic TiO2 cylinders on a square lattice with different unit size and duty cycles at λ = 510 nm and 852 nm; (c), (f) transmission and phase of the periodic TiO2 cylinders with 180 nm unit size and 600 nm height for different diameters.
图 3 (a) 超光栅结构的顶视图; (b) TM和(c) TE激励时, xoz平面的电场分布
Figure 3. (a) Top view of the metagrating; (b) electric field distribution in the xoz plane for TM and (c) TE excitation.
图 4 (a) 设计的超光栅在不同偏振方向下的传输效率与偏折效率; (b) TM和(c) TE平面波垂直入射时, 透射光强的远场分布
Figure 4. (a) Transmission efficiency and deflection efficiency of the designed metagrating with different polarization directions; far-field profiles of transmitted light intensity at normal incidence of (b) TM and (c) TE plane wave.
图 5 伴随方法示意图. 每次迭代都需要两次模拟(正向模拟和伴随模拟), 每个模拟激励源都以红色绘制
Figure 5. Adjoint method schematic. Two simulations (the forward and the adjoint simulation) are needed for every iteration. Sources for each simulation are drawn in red.
图 6 超光栅的拓扑优化过程: 绿光偏折效率与红光透过效率的演变, 以及拓扑形态的演变
Figure 6. Topology optimization process of metagratings: the evolution of green light deflection efficiency and red light transmission efficiency, and the evolution of topology shapes in different iterations.
图 7 (a) 拓扑优化后自由形状超光栅的顶视图; (b) TM和 (c) TE激励时xoz平面的电场分布
Figure 7. (a) Top view of the topology-optimized freeform metagrating; electric field distribution in the xoz plane for (b) TM and (c) TE excitation.
图 8 (a) 拓扑优化的超光栅在不同偏振方向下的传输效率与偏折效率; (b) TM和(c) TE平面波垂直入射时, 透射光强的远场分布
Figure 8. (a) Transmission efficiency and deflection efficiency of the topology-optimized metagrating with different polarization directions; far-field profiles of transmitted light intensity at normal incidence of (b) TM and (c) TE plane wave.
图 9 (a) 自由形状超光栅的优化演变过程; (b) 自由形状超光栅不同入射偏振的传输效率与偏折效率
Figure 9. (a) Evolution of freeform metagrating; (b) transmission efficiency and deflection efficiency of the freeform metagrating with different polarization directions
图 10 自由形状超表面的性能 (a)—(c) Py = 180 nm; (d) Py = 200 nm; (e) Py = 300 nm; (f) Py = 400 nm, 其中虚线表示正向设计的效率曲线
Figure 10. Performance of freeform metasurface: (a)–(c) Py = 180 nm; (d) Py = 200 nm; (e) Py = 300 nm; (f) Py = 400 nm, where the dashed lines indicate the efficiency curves of the forward design.
表 1 选取的不同直径TiO2圆柱的性能参数
Table 1. Performance parameters of selected TiO2 cylinders with different diameters.
圆柱直径 /nm 透过率 相位/(º) 510 nm 852 nm 510 nm 852 nm 64 0.989 0.988 45.0 22.6 106 0.968 0.981 163.4 69.4 130 0.970 0.964 285.2 112.7 
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[1] Yu N, Capasso F 2014 Nat. Mater. 13 139
Google Scholar
[2] Luo X 2019 Adv. Mater. 31 1804680
Google Scholar
[3] Yu Y F, Zhu A Y, Paniagua-Domínguez R, Fu Y H, Luk’yanchuk B, Kuznetsov A I 2015 Laser Photonics Rev. 9 412
Google Scholar
[4] Wang Y, Fan Q, Xu T 2021 Opto-Electron. Adv. 4 200008
Google Scholar
[5] Wang S, Wu P C, Su V C, Lai Y C, Chen M K, Kuo H Y, Chen B H, Chen Y H, Huang T T, Wang J H, Lin R M, Kuan C H, Li T, Wang Z, Zhu S, Tsai D P 2018 Nat. Nanotechnol. 13 227
Google Scholar
[6] Zheng G, Mühlenbernd H, Kenney M, Li G, Zentgraf T, Zhang S 2015 Nat. Nanotechnol. 10 308
Google Scholar
[7] Li X, Chen L, Li Y, Zhang X, Pu M, Zhao Z, Ma X, Wang Y, Hong M, Luo X 2016 Sci. Adv. 2 e1601102
Google Scholar
[8] Gao H, Fan X, Xiong W, Hong M 2021 Opto-Electron. Adv. 4 210030
Google Scholar
[9] Arbabi A, Horie Y, Bagheri M, Faraon A 2015 Nat. Nanotechnol. 10 937
Google Scholar
[10] Fan Q, Liu M, Zhang C, Zhu W, Wang Y, Lin P, Yan F, Chen L, Lezec H J, Lu Y, Agrawal A, Xu T 2020 Phys. Rev. Lett. 125 267402
Google Scholar
[11] Yue Z, Li J, Li J, Zheng C, Liu J, Wang G, Xu H, Chen M, Zhang Y, Zhang Y, Yao J 2022 Opto-Electron. Sci. 1 210014
Google Scholar
[12] Decker M, Staude I, Falkner M, Dominguez J, Neshev D N, Brener I, Pertsch T, Kivshar Y S 2015 Adv. Opt. Mater. 3 813
Google Scholar
[13] Shalaev M I, Sun J, Tsukernik A, Pandey A, Nikolskiy K, Litchinitser N M 2015 Nano Lett. 15 6261
Google Scholar
[14] Khorasaninejad M, Chen W T, Devlin R C, Oh J, Zhu A Y, Capasso F 2016 Science 352 1190
Google Scholar
[15] Lin D, Fan P, Hasman E, Brongersma M L 2014 Science 345 298
Google Scholar
[16] Xie X, Pu M, Jin J, Xu M, Guo Y, Li X, Gao P, Ma X, Luo X 2021 Phys. Rev. Lett. 126 183902
Google Scholar
[17] Lalanne P, Chavel P 2017 Laser Photonics Rev. 11 1600295
Google Scholar
[18] Khaidarov E, Hao H, Paniagua-Domínguez R, Yu Y F, Fu Y H, Valuckas V, Yap S L K, Toh Y T, Ng J S K, Kuznetsov A I 2017 Nano Lett. 17 6267
Google Scholar
[19] Paniagua-Domínguez R, Yu Y F, Khaidarov E, Choi S, Leong V, Bakker R M, Liang X, Fu Y H, Valuckas V, Krivitsky L A, Kuznetsov A I 2018 Nano Lett. 18 2124
Google Scholar
[20] Xu M, Pu M, Sang D, Zheng Y, Li X, Ma X, Guo Y, Zhang R, Luo X 2021 Opt. Express 29 10181
Google Scholar
[21] Xu M F, He Q, Pu M B, Zhang F, Li L, Sang D, Guo Y H, Zhang R Y, Li X, Ma X L, Luo X G 2022 Adv. Mater. 34 2108709
Google Scholar
[22] Pu M, Li X, Ma X, Wang Y, Zhao Z, Wang C, Hu C, Gao P, Huang C, Ren H, Li X, Qin F, Yang J, Gu M, Hong M, Luo X 2015 Sci. Adv. 1 e1500396
Google Scholar
[23] Molesky S, Lin Z, Piggott A Y, Jin W, Vuckovic J, Rodriguez A W 2018 Nat. Photonics 12 659
Google Scholar
[24] Elsawy M M R, Lanteri S, Duvigneau R, Fan J A, Genevet P 2020 Laser Photonics Rev. 14 1900445
Google Scholar
[25] Sell D, Yang J, Doshay S, Yang R, Fan J 2017 Nano Lett. 17 3752
Google Scholar
[26] Piggott A Y, Lu J, Lagoudakis K G, Petykiewicz J, Babinec T M, Vuckovic J 2015 Nat. Photonics 9 374
Google Scholar
[27] Shi Z, Zhu A Y, Li Z, Huang Y W, Chen W T, Qiu C W, Capasso F 2020 Sci. Adv. 6 eaba3367
Google Scholar
[28] Mansouree H K M, Arbabi E, Mcclung A, Faraon A, Arbabi A 2020 Optica 7 77
Google Scholar
[29] Zheng Y, Xu M, Pu M, Zhang F, Sang D, Guo Y, Li X, Ma X, Luo X 2022 Nanophotonics 11 2967
Google Scholar
[30] Chung Hand Miller O D 2020 Opt. Express 28 6945
Google Scholar
[31] Lalau-Keraly C M, Bhargava S, Miller O D, Yablonovitch E 2013 Opt. Express 21 21693
Google Scholar
[32] Luo X, Pu M, Zhang F, Xu M, Guo Y, Li X, Ma X 2022 J. Appl. Phys. 131 181101
Google Scholar
[33] 付云起, 林沂, 武博, 安强, 刘燚 2022 电波科学学报 37 279
Google Scholar
Fu Y Q, Lin Y, Wu B, An Q, Liu Y 2022 Chin. J. Radio Sci. 37 279
Google Scholar
[34] 林沂, 吴逢川, 毛瑞棋, 姚佳伟, 刘燚, 安强, 付云起 2022 71 170702
Google Scholar
Lin Y, Wu F C, Mao R Q, Yao J W, Liu Y, An Q, Fu Y Q 2022 Acta Phys. Sin. 71 170702
Google Scholar
[35] Yu N, Genevet P, Kats M A, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333
Google Scholar
[36] Mansouree M, McClung A, Samudrala S, Arbabi A 2021 ACS Photonics 8 455
Google Scholar
[37] Li L 1997 J. Opt. Soc. Am. A 14 2758
Google Scholar
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