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基于开口环阵列结构的表面晶格共振产生及二次谐波增强

张萌徕 覃赵福 陈卓

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基于开口环阵列结构的表面晶格共振产生及二次谐波增强

张萌徕, 覃赵福, 陈卓

Conditions for surface lattice resonances and enhancement of second harmonic generation based on split-ring resonators

Zhang Meng-Lai, Qin Zhao-Fu, Chen Zhuo
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  • 理论研究了二维周期排列的金开口环谐振器的磁共振模式与周期阵列的衍射模式发生强耦合所需满足的条件及其对二次谐波产生效率的影响. 通过控制阵列结构在xy方向的周期大小, 使得衍射模式只在其中一个方向产生, 当衍射模式的电场方向与入射光电场偏振方向一致时, 衍射模式才会与开口环谐振器的磁共振模式发生强耦合作用, 产生表面晶格共振进而实现近场场增强. 在此基础上, 进一步计算了金开口环谐振器阵列的二次谐波产生效率, 随着阵列周期逐渐增大, 即开口环谐振器的数密度减小, 二次谐波强度呈现先增加后降低的趋势, 当开口环谐振器数密度降为原来的1/4左右时, 二次谐波强度可以增强2倍以上. 本文的研究为金属超表面二次谐波产生效率的提高提供了一种新的可能途径.
    In this paper, we theoretically study the condition for the strong coupling between magnetic resonance mode of the two-dimensional periodically arranged gold split-ring resonators and the diffraction mode of the periodic array and its influence on the second harmonic generation efficiency. By controlling the size of the period of the array structure in the x-axis and y-axis, the diffraction mode is excited near the magnetic resonance provided by the gold split-ring resonator, solely in one of the directions. In both cases, the diffraction mode and the magnetic resonance coincide in the linear resonance spectrum, but by analyzing the electric field distribution at the position of the diffraction mode, it can be found that when ${a_x}$ is much larger than ${a_y}$, the electric field direction of the diffraction mode is perpendicular to the polarization direction of the incident light, and no strong coupling occurs. Therefore, the dilution effect is dominant, and the second harmonic intensity gradually decreases with the increase of the period. When ${a_y}$ is much larger than${a_x}$, the electric field direction of the diffraction mode is the same as the polarization direction of the incident light. At this time, the diffraction mode and the magnetic resonance mode are strongly coupled. As the period increases, the second harmonic intensity first increases and then decreases. The increase is due to the dominant mode coupling and the decrease is due to the dominant dilution effect. When the number density of split-ring resonators is reduced to about 1/4 of the original one, the second harmonic intensity can be increased by more than twice. From this, we find that the strong coupling between diffraction mode and magnetic resonance can occur when the electric field direction of the diffraction mode is consistent with the polarization direction of incident light, thus generating the surface lattice resonance to achieve near-field enhancement. In short, the rectangular periodic structure is used to distinguish the field enhancement effects in different directions, and the second harmonic enhancement can still be achieved when the number density of split-ring resonators is reduced, which relaxes the requirements for processing technology. This research provides a new possible way to improve the second harmonic generation efficiency based on metal metasurfaces.
      通信作者: 陈卓, zchen@nju.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11674168)资助的课题
      Corresponding author: Chen Zhuo, zchen@nju.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11674168)
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    Huttunen M J, Rasekh P, Boyd R W, Dolgaleva K 2018 Phys. Rev. A 97 053817Google Scholar

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    Michaeli L, Keren-Zur S, Avayu O, Suchowski H, Ellenbogen T 2017 Phys. Rev. Lett. 118 243904Google Scholar

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    Yu H K, Peng Y S, Yang Y, Li Z Y 2019 Npj Comput. Mater. 5 45Google Scholar

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    Zhou W, Dridi M, Suh J Y, Kim C H, Co D T, Wasielewski M R, Schatz G C, Odom T W 2013 Nat. Nanotechnol. 8 506Google Scholar

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    Czaplicki R, Kiviniemi A, Huttunen M J, Zang X R, Stolt T, Vartiainen I, Butet J, Kuittinen M, Martin O J F, Kauranen M 2018 Nano Lett. 18 7709Google Scholar

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    靳悦荣, 陈卓, 王振林 2013 中国科学: 物理学 力学 天文学 43 1022Google Scholar

    Jin Y R, Chen Z, Wang Z L 2013 Sci. Sin-Phys. Mech. Astron. 43 1022Google Scholar

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  • 图 1  (a) 处于均匀介质中的金开口环谐振器阵列结构示意图, x, y方向的周期分别为${a_x}$, ${a_y}$, 入射光垂直照射于阵列结构, 电场方向沿x轴; (b) SRRs单元结构图, 其中$l = 200\;{\rm{nm}}$, $w = 80\;{\rm{nm}}$, $d = 100\;{\rm{nm}}$, $h = 30\;{\rm{nm}}$

    Fig. 1.  (a) Schematic of SRRs array, the period of the x axis and y axis is ${a_x}$ and ${a_y}$, respectively, the incident light is perpendicular to the structure, and the electric field is along the x axis; (b) the unit cell of SRRs, where $l = 200\;{\rm{nm}}$, $w = 80\;{\rm{nm}}$, $d = 100\;{\rm{nm}}$, $h = 30\;{\rm{nm}}$.

    图 2  ${a_y} = 400\;{\rm{nm}}$固定不变, ${a_x} = 1200\;{\rm{nm}}$ (黑线)和${a_x} = 400\;{\rm{nm}}$ (红线)两种不同周期阵列结构的透射谱, 插图表示宽带透射谷(Dip1)位置x-y截面的磁场电流分布图

    Fig. 2.  The transmission spectrum of two different periods along the x axis, ${a_x} = 1200\;{\rm{nm}}$ (black line) and ${a_x} = 400 \;{\rm{nm}}$ (red line). The insert shows the distribution of magnetic field and current in x-y section at the position of Dip1.

    图 3  ${a_y} = 400\;{\rm{nm}}$, ${a_x} = 1200$—1550 nm (间隔50 nm) 时的 (a) 线性透射谱及(b) 透射谱中两透射谷随周期的变化; ${a_x} = 400\;{\rm{nm}}$, ${a_y} = 1200$—1500 nm (间隔50 nm)时的 (c) 线性透射谱及(d) 透射谱中两透射谷随周期的变化

    Fig. 3.  (a) Linear transmission spectrum and (b) the positions of two dips in transmission spectrum change with the period along the x axis, ${a_y} = 400\;{\rm{nm}}$, ${a_x} = 1200\!-\!1550 $ nm (interval 50 nm); (c) linear transmission spectrum and (d) the positions of two dips in transmission spectrum change with the period along the y axis, ${a_x} = 400\;{\rm{nm}}$, ${a_y} = 1200\!-\! 1500$ nm (50 nm interval).

    图 4  (a) ${a_x} = 1300\;{\rm{nm, }}\;$${a_y} = 400\;{\rm{nm}}$的SRRs阵列在激发波长为λ = 1900 nm时$x \text- z$截面的电场模值(左)与电场x (中)和y (右)分量的场分布图; (b) 周期${a_y} = 1300\;{\rm{nm, }}\;{a_x} = 400\;{\rm{nm}}$ 的SRRs阵列在激发波长λ = 1900 nm时$y \text- z$截面的电场模值(左)与电场x (中)和y (右)分量的场分布图

    Fig. 4.  Calculated total (left) and x (middle) component and y (right) component of electric field amplitude distribution in $x \text- z$cross-section at λ = 1900 nm for (a)${a_x} = 1300\;{\rm{nm, }}\;$${a_y} = 400\;{\rm{nm}}$and in $y \text- z$cross-section at λ = 1900 nm for (b)${a_y} = 1300\;{\rm{nm, }} \;{a_x} = 400\;{\rm{nm}}$.

    图 5  固定${a_x} = 400\;{\rm{nm}}$, 改变${a_y}$(蓝色实心圆)和固定${a_y} = 400\;{\rm{nm}}$, 改变${a_x}$(红色实心三角)时SRRs阵列的二次谐波强度变化

    Fig. 5.  The second harmonic intensity of the SRRs array at fixed ${a_x} = 400\;{\rm{nm}}$, variable ${a_y}$ (blue circles) and fixed ${a_y} = 400\;{\rm{nm}}$, variable ${a_x}$ (red triangles).

  • [1]

    Zayats A V, Smolyaninov I I, Maradudin A A 2005 Phys. Rep. 408 131Google Scholar

    [2]

    Stockman M I 2011 Opt. Express 19 22029Google Scholar

    [3]

    Piliarik M, Sipova H, Kvasnicka P, Galler N, Krenn J R, Homola J 2012 Opt. Express 20 672Google Scholar

    [4]

    Byun K M, Yoon S J, Kim D, Kim S J 2007 Opt. Lett. 32 1902Google Scholar

    [5]

    Clementi N C, Cooper C D, Barba L A 2019 Phys. Rev. E 100 063305Google Scholar

    [6]

    Chang C Y, Lin H T, Lai M S, Shieh T Y, Peng C C, Shih M H, Tung Y C 2018 Sci. Rep. 8 11812Google Scholar

    [7]

    Kim H M, Park J H, Lee S K 2019 Sci. Rep. 9 15605Google Scholar

    [8]

    Shen Y, Zhou J H, Liu T R, Tao Y T, Jiang R B, Liu M X, Xiao G H, Zhu J H, Zhou Z K, Wang X H, Jin C J, Wang J F 2013 Nat. Commun. 4 2381Google Scholar

    [9]

    Brolo A G 2012 Nat. Photonics 6 709Google Scholar

    [10]

    Wang T J, Chang H W, Chen J S, Chiang H P 2019 Sci. Rep. 9 10962Google Scholar

    [11]

    Lin K Q, Yi J, Zhong J H, Hu S, Liu B J, Liu J Y, Zong C, Lei Z C, Wang X, Aizpurua J, Esteban R, Ren B 2017 Nat. Commun. 8 14891Google Scholar

    [12]

    Boerigter C, Campana R, Morabito M, Linic S 2016 Nat. Commun. 7 10545Google Scholar

    [13]

    Davis T J, Gomez D E, Vernon K C 2010 Phys. Rev. B 82 205434Google Scholar

    [14]

    Carles R, Bayle M, Benzo P, Benassayag G, Bonafos C, Cacciato G, Privitera V 2015 Phys. Rev. B 92 174302Google Scholar

    [15]

    Grand J, de la Chapelle M L, Bijeon J L, Adam P M, Vial A, Royer P 2005 Phys. Rev. B 72 033407

    [16]

    Huttunen M J, Rasekh P, Boyd R W, Dolgaleva K 2018 Phys. Rev. A 97 053817Google Scholar

    [17]

    Michaeli L, Keren-Zur S, Avayu O, Suchowski H, Ellenbogen T 2017 Phys. Rev. Lett. 118 243904Google Scholar

    [18]

    Li Z, Xu C K, Liu W J, Li M, Chen X J 2018 Sci. Rep. 8 5626Google Scholar

    [19]

    Jin B Y, Argyropoulos C 2016 Sci. Rep. 6 28746Google Scholar

    [20]

    Kauranen M, Zayats A V 2012 Nat. Photonics 6 737Google Scholar

    [21]

    Li G, Zhang S, Zentgraf T 2017 Nat. Rev. Mater. 2 17010Google Scholar

    [22]

    Yu H K, Peng Y S, Yang Y, Li Z Y 2019 Npj Comput. Mater. 5 45Google Scholar

    [23]

    Thackray B D, Kravets V G, Schedin F, Anton G, Thomas P A, Grigorenko A N 2014 ACS Photonics 1 1116Google Scholar

    [24]

    Zhou W, Dridi M, Suh J Y, Kim C H, Co D T, Wasielewski M R, Schatz G C, Odom T W 2013 Nat. Nanotechnol. 8 506Google Scholar

    [25]

    Vakevainen A I, Moerland R J, Rekola H T, Eskelinen A P, Martikainen J P, Kim D H, Torma P 2014 Nano Lett. 14 1721Google Scholar

    [26]

    Vecchi G, Giannini V, Rivas J G 2009 Phys. Rev. Lett. 102 146807Google Scholar

    [27]

    Lozano G, Louwers D J, Rodríguez S R K, Murai S, Jansen O T A, Verschuuren M A, Gómez Rivas J 2013 Light-Sci. Appl. 2 e66

    [28]

    Czaplicki R, Kiviniemi A, Huttunen M J, Zang X R, Stolt T, Vartiainen I, Butet J, Kuittinen M, Martin O J F, Kauranen M 2018 Nano Lett. 18 7709Google Scholar

    [29]

    Ciracì C, Poutrina E, Scalora M, Smith D R 2012 Phys. Rev. B 85 201403Google Scholar

    [30]

    Tang C J, Zhan P, Cao Z S, Pan J, Chen Z, Wang Z L 2011 Phys. Rev. B 83 041402

    [31]

    Czaplicki R, Kiviniemi A, Laukkanen J, Lehtolahti J, Kuittinen M, Kauranen M 2016 Opt. Lett. 41 2684Google Scholar

    [32]

    靳悦荣, 陈卓, 王振林 2013 中国科学: 物理学 力学 天文学 43 1022Google Scholar

    Jin Y R, Chen Z, Wang Z L 2013 Sci. Sin-Phys. Mech. Astron. 43 1022Google Scholar

    [33]

    Klein M W, Enkrich C, Wegener M, Linden S 2006 Science 313 502Google Scholar

    [34]

    Linden S, Enkrich C, Wegener M, Zhou J, Koschny T, Soukoulis C M 2004 Science 306 1351Google Scholar

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出版历程
  • 收稿日期:  2020-08-30
  • 修回日期:  2020-10-28
  • 上网日期:  2021-02-21
  • 刊出日期:  2021-03-05

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