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利用超构表面优异的波前调控能力将片上光子集成电路对光场的操控拓展至自由空间是当前一项重要课题. 本文采用传输相位方法设计了一种基于波导模式激发的内嵌式超构表面, 其相位分布同时满足导模的基频以及二倍频的聚焦. 在此基础上, 将内嵌式材料限定为相变材料, 结合其在不同相态时的折射率差异, 通过仿真手段实现了两种相态下分别针对于基波和二次谐波的聚焦. 在基波(或二次谐波)实现高质量聚焦时, 焦点处二次谐波(或基波)的成分得到了很大程度上的抑制, 更有利于后续完全滤波. 进一步地, 通过在波导层底面嵌入与顶面完全相同的超构表面, 并横向错开半个周期, 最终将关于基波聚焦和二次谐波聚焦的器件效率提升为原先单阵列情形的2.2倍和3.7倍. 本文的研究为导波驱动(或激发)超构表面的线性及非线性多功能复合调控提供了一种新的可能途径.It is an important project to use metasurfaces to extend the manipulation of light field by on-chip photonic integrated circuits to the free-space. In this paper, a waveguide mode-driven embedded metasurface is designed by using the propagation phase method. The phase distribution of the metasurface satisfies the focusing of both the fundamental wave and second harmonic wave. On this basis, a phase-change material is chosen to be embedded in waveguide. Combined with its refractive index difference in different phase states, the fundamental wave and second harmonic wave are focused in two phase states, respectively, through the simulation method. When the fundamental wave (or second harmonic wave) achieves high-quality focusing, the components of the second harmonic wave (or fundamental wave) at the focus are suppressed to a large extent, which is more conducive to the subsequent complete filtering. Furthermore, the efficiency at the fundamental wave and second harmonic wave are increased by 2.2 and 3.7 times by embedding another metasurface at the bottom of the waveguide layer which is exactly the same as that at the top but staggers half a period laterally. This study provides a new alternative approach for the linear and nonlinear multifunctional control of guided wave mode-driven metasurfaces.
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Keywords:
- waveguide /
- focus /
- second harmonics /
- metasurfaces
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图 1 (a) 导波驱动相变材料超构表面的线性与非线性多功能聚焦示意图; (b) 单个周期块结构的示意图, 图中标注了波导及超构基元(金色方块)的相关参数; (c) 波导驱动超构表面的聚焦原理, 其中伪彩图展示了未嵌入相变材料时硅波导xz截面的电场y分量分布, 符合TE基模的特性
Fig. 1. (a) Schematic of the fundamental wave and second-harmonic focusing based on guided mode-driven phase-change materials metasurfaces; (b) schematic of a single periodic block structure, in which the parameters of the waveguide and the metasurface element (golden square) are annotated; (c) focusing principle of guided wave-driven metasurfaces, in which the pseudo-color diagram shows the distribution of the y component of the electric field on the xz cross-section of silicon waveguide without embedded phase-change materials, which conforms to the characteristics of TE fundamental mode.
图 2 对于不同的超构基元, 通过仿真得到的xz截面上的基波(第二列)和二次谐波(第三列)聚焦效应. 聚焦现象的展示采用归一化的电场强度模值表示, 下同. (a)−(c) 金开口环谐振器; (d)−(f) 长方体块状介质; (g)−(i) 嵌入式长方体块状介质. 图中FW表示基波, SH表示二次谐波, 下同
Fig. 2. Simulated focusing of the fundamental wave (second column) and second harmonic (third column) on xz cross-section for different metasurface element. The pseudo-color diagram shows the distribution of the normalized electric field intensity modulus values (the same below). (a)−(c) Gold split-ring resonator; (d)−(f) cuboid block dielectric; (g)−(i) embedded cuboid block dielectric. FW, fundamental wave; SH, second harmonics, the same below.
图 3 相变材料处于相态A (第一行)与相态B (第二行)时, 通过仿真得到的xz截面上的基波(第一列)和二次谐波(第二列)聚焦效应. 不同相态下基波(二次谐波)的聚焦使用了相同标度. 黑色点线圆圈出了目标聚焦斑所在的位置
Fig. 3. Simulated focusing of the fundamental wave (first column) and second harmonic (second column) on xz cross-section when phase-change material is in phase state A (first row) and state B (second row). Focusing of the fundamental wave (second harmonic) in different phase states are on the same scale is used to. The black dotted circles mark the locations of the target focal spot.
图 4 对于二维平板波导模型, 相变材料处于相态A (第一行)与相态B (第二行)时, 通过仿真得到的xz截面上的基波(第一列)和二次谐波(第二列)聚焦效应. 不同相态下基波(二次谐波)的聚焦使用了相同标度. 黑色点线圆圈出了目标聚焦斑所在的位置
Fig. 4. For the two-dimensional flat waveguide model, simulated focusing of the fundamental wave (first column) and second harmonic (second column) on xz cross-section when phase-change material is in phase state A (first row) and state B (second row). Focusing of the fundamental wave (second harmonic) in different phase states are on the same scale is used to. The black dottted circles mark the locations of the target focal spot.
图 5 (a) 导波驱动的双层相变材料超构表面示意图; (b) 不同相态下焦点处归一化的基波和二次谐波电场模值随偏移距离d变化的曲线, 上、下图中的灰色水平虚线分别标记出单层相变材料超构表面在相态A下焦点处的基波电场模值以及相态B下焦点处的二次谐波电场模值, 蓝色虚线标记了偏移量为半个周期的情形; (c) 相变材料处于相态A时, 不同偏移量d所对应的基波聚焦结果; (d) 相变材料处于相态B时, 不同偏移量d所对应的二次谐波聚焦结果; 图(c)和图(d)中图片外框的颜色与图(b)中箭头颜色一致, 分别代表d的不同取值. 黑色点线圆圈出了高质量聚焦斑所在的位置
Fig. 5. (a) Schematic of the bi-layer phase-change material metasurface driven by guide mode. (b) The normalized amplitude of the electric field of the fundamental wave and second harmonic at the focal point versus the offset distance d under different phase states. The gray horizontal dashed lines mark the value of the electric field amplitude of the fundamental wave under phase state A, and the electric field amplitude of the second harmonic under phase state B, respectively, for the monolayer phase-change material metasurface. The dotted blue line marks the case where the offset is equal to half of the period. (c) Focusing of the fundamental wave with respect to different offsets when phase-change material is in phase state A. (d) Focusing of the second harmonic with respect to different offsets when phase-change material is in phase state B. Colors of the outer frame of the pictures in panel (c) and panel (d) are consistent with the colors of the arrows in panel (b), which correspond to different values of d. The black dotted circles mark the location of the high quality focal spot.
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[1] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
Google Scholar
[2] Yu N, Capasso F 2014 Nat. Mater. 13 139
Google Scholar
[3] Meinzer N, Barnes W L, Hooper I R 2014 Nat. Photonics 8 889
Google Scholar
[4] Jahani S, Jacob Z 2016 Nat. Nanotechnol. 11 23
Google Scholar
[5] Kuznetsov A I, Miroshnichenko A E, Brongersma M L, Kivshar Y S, Luk′yanchuk B 2016 Science 354 aag2472
Google Scholar
[6] Genevet P, Capasso F, Aieta F, Khorasaninejad M, Devlin R 2017 Optica 4 139
Google Scholar
[7] Kamali S M, Arbabi E, Arbabi A, Faraon A 2018 Nanophotonics 7 1041
Google Scholar
[8] Schurig D, Mock J J, Justice B J, Cummer S A, Pendry J B, Starr A F, Smith D R 2006 Science 314 977
Google Scholar
[9] Shalaev V M 2007 Nat. Photonics 1 41
Google Scholar
[10] Yu N, Genevet P, Kats M A, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333
Google Scholar
[11] Chen X, Huang L, Muhlenbernd H, Li G, Bai B, Tan Q, Jin G, Qiu C W, Zhang S, Zentgraf T 2012 Nat. Commun. 3 1198
Google Scholar
[12] Khorasaninejad M, Chen W T, Oh J, Capasso F 2016 Nano Lett. 16 3732
Google Scholar
[13] Khorasaninejad M, Zhu A Y, Roques-Carmes C, Chen W T, Oh J, Mishra I, Devlin R C, Capasso F 2016 Nano Lett. 16 7229
Google Scholar
[14] 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
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[15] Chen W T, Khorasaninejad M, Zhu A Y, Oh J, Devlin R C, Zaidi A, Capasso F 2017 Light Sci. Appl. 6 e16259
Google Scholar
[16] Wang Z, Dong S H, Luo W J, Jia M, Liang Z Z, He Q, Sun S L, Zhou L 2018 Appl. Phys. Lett. 112 191901
Google Scholar
[17] Akram M R, Mehmood M Q, Tauqeer T, Rana A S, Rukhlenko I D, Zhu W 2019 Opt. Express 27 9467
Google Scholar
[18] Li T Y, Li X Y, Yan S H, Xu X H, Wang S M, Yao B L, Wang Z L, Zhu S N 2021 Phys. Rev. Appl. 15 014059
Google Scholar
[19] Sun C, Wade M T, Lee Y, Orcutt J S, Alloatti L, Georgas M S, Waterman A S, Shainline J M, Avizienis R R, Lin S, Moss B R, Kumar R, Pavanello F, Atabaki A H, Cook H M, Ou A J, Leu J C, Chen Y H, Asanovic K, Ram R J, Popovic M A, Stojanovic V M 2015 Nature 528 534
Google Scholar
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Google Scholar
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Google Scholar
[22] Guo X, Ding Y, Chen X, Duan Y, Ni X 2020 Sci. Adv. 6 eabb4142
Google Scholar
[23] Ha Y, Guo Y, Pu M, Zhang F, Li X, Ma X, Xu M, Luo X 2020 Opt. Express 28 7943
Google Scholar
[24] Ha Y L, Guo Y H, Pu M B, Li X, Ma X L, Zhang Z J, Luo X G 2021 Adv. Theory Simul. 4 2000239
Google Scholar
[25] Kauranen M, Zayats A V 2012 Nat. Photonics 6 737
Google Scholar
[26] Butet J, Brevet P F, Martin O J 2015 ACS Nano 9 10545
Google Scholar
[27] 邓俊鸿, 李贵新 2017 物理学报 66 147803
Google Scholar
Deng J H, Li G X 2017 Acta Phys. Sin. 66 147803
Google Scholar
[28] Krasnok A, Tymchenko M, Alu A 2018 Mater. Today 21 8
Google Scholar
[29] Li G, Chen S, Pholchai N, Reineke B, Wong P W, Pun E Y, Cheah K W, Zentgraf T, Zhang S 2015 Nat. Mater. 14 607
Google Scholar
[30] Kivshar Y 2018 Natl. Sci. Rev. 5 144
Google Scholar
[31] Kang L, Cui Y, Lan S, Rodrigues S P, Brongersma M L, Cai W 2014 Nat. Commun. 5 4680
Google Scholar
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Google Scholar
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Google Scholar
[34] Tsai W Y, Chung T L, Hsiao H H, Chen J W, Lin R J, Wu P C, Sun G, Wang C M, Misawa H, Tsai D P 2019 Adv. Mater. 31 e1806479
Google Scholar
[35] Ciracì C, Poutrina E, Scalora M, Smith D R 2012 Phys. Rev. B 86 115451
Google Scholar
[36] Ciracì C, Poutrina E, Scalora M, Smith D R 2012 Phys. Rev. B 85 201403
Google Scholar
[37] Ruiz de Galarreta C, Sinev I, Alexeev A M, Trofimov P, Ladutenko K, Garcia-Cuevas Carrillo S, Gemo E, Baldycheva A, Bertolotti J, David Wright C 2020 Optica 7 476
Google Scholar
[38] 严巍, 王纪永, 曲俞睿, 李强, 仇旻 2020 物理学报 69 154202
Google Scholar
Yan W, Wang J Y, Qu Y R, Li Q, Qiu M 2020 Acta Phys. Sin. 69 154202
Google Scholar
[39] Feldmann J, Stegmaier M, Gruhler N, Rios C, Bhaskaran H, Wright C D, Pernice W H P 2017 Nat. Commun. 8 1256
Google Scholar
[40] Ríos C, Stegmaier M, Hosseini P, Wang D, Scherer T, Wright C D, Bhaskaran H, Pernice W H P 2015 Nat. Photonics 9 725
Google Scholar
[41] de Galarreta C R, Alexeev A M, Au Y Y, Lopez-Garcia M, Klemm M, Cryan M, Bertolotti J, Wright C D 2018 Adv. Funct. Mater. 28 1704993
Google Scholar
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