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In this paper, we study the second harmonic generation (SHG) from the stero-stacked meta-molecules consisting of two vertically stacked split ring resonators (SRRs) that resonate at the fundamental wavelength. When pumped by the linearly polarized incident wave with the electric field direction along one of the SRRs’ arms, the meta-molecules emit the SHG that can have two non-zero orthogonal electric field components, provided that the top SRR and the bottom SRR are not arranged in mutually parallel or anti-parallel manner. Due to the strong coupling between the two SRRs, the plasmonic properties of the stero-stacked meta-molecules could be tuned by varying the twist angle between the two SRRs. In this process, we demonstrate that the amplitudes of the two orthogonal SHG field components, and the phase difference between these two components can be varied with changing the twist angle between two SRRs. Based on the concept of the light polarization, different polarization states can be achieved by changing the differences in phase and amplitude between the orthogonal field components. Therefore, the twist angle dependent amplitudes of and phase difference between two orthogonal SHG field components can be used to manipulate the polarization states of the emitted SHG. For the stero-stacked meta-molecules with a fixed twist angle of 60°, elliptically, near-circularly andnear-linearly polarized SHG emission can be obtained at different fundamental wavelengths. In addition, for the fundamental wave with a fixed wavelength of 1500 nm, the stero-stacked meta-molecules with different twist angles are demonstrated to be able to emit SHG with elliptical andnear-linear polarization states.
[1] Wan P B,Wen X M, Sun C Z, Bevita K C, Zhang H, Sun X M, Chen X D 2015 Small 11 5409
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[3] Ren X H, Li Z J, Huang Z Y, Sang D, Qiao H, Qi X, Li J Q, Zhong J X, Zhang H 2017 Adv. Funct. Mater. 27 1606834
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[4] Lu L, Liang Z M, Wu L M, Chen Y X, Song Y F, Dhanabalan S C, Ponraj J S, Dong B Q, Xiang Y J, Xing F, Fan D Y, Zhang H 2018 Laser Photonics Rev. 12 1700221
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[22] Zhou J F, Koschny T, Soukoulis C M 2007 Opt. Express 15 17881
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 (a)由两个金属SRR上下堆叠组成的超构分子结构示意图; (b)上下两个SRR相对开口朝向夹角为φ = 90°时超构分子的吸收谱; (c)与吸收谱中两个吸收峰对应的波长wl1和wl2处SRR表面的磁场垂直分量Hz分布图
Figure 1. (a) Schematic diagram of SRR-based meta-molecule; (b) absorption spectrum of the meta-molecule consisting of two SRRs with a twist angle φ = 90°; (c) distributions of magnetic field component Hz on the surface of the SRRs at wavelengths corresponding to two absorption peaks wl1 and wl2.
图 2 双层相对角度改变时, (a)吸收谱和(b) SHG强度的变化, 黑色划线代表每条线左右峰值的连线
Figure 2. (a) Absorption spectrum and (b) the SHG intensity with the relative angle of the two layers changing. The black dash line represents the line connecting the left and right peaks of each line.
图 3 双层相对角度为30°—150°时的远场SHG强度 (a)、SHG辐射的y和x分量的振幅比Ey/Ex (b)和相位差δ (c)随着波长的变化; 双层相对角度为60°时的远场SHG强度 (d)、SHG辐射的y和x分量的振幅比Ey/Ex (e)和相位差δ (f)随着波长的变化; 其中阴影区域表示SHG效率较大的一段波长区域
Figure 3. When the relative angle of the two layers changes from 30° to 150°, (a) SHG intensity, (b) amplitude ratio of SHG in the y and x directions and (c) the phase difference of SHG in the y and x directions as a function of wavelength; when the relative angle of the two layers is 60°, (d) SHG intensity, (e) amplitude ratio of SHG in the y and x directions and (f) the phase difference of SHG in the y and x directions as a function of wavelength. The shaded area indicates a wavelength region where the SHG efficiency is relatively large.
图 4 双层相对角度为60°、不同波长的基波入射时, 远场SHG偏振态的变化
Figure 4. Polarization of the far-field SHG changes when the relative angle of the two layers is 60°, and the the fundamental wave of different wavelengths is incident.
图 5 基波波长为1500 nm入射时, 不同相对角度的结构的远场SHG偏振态的变化
Figure 5. When the incidentwavelengthis 1500 nm, the polarization of the far-field SHG changes with the relative angle of the two layers
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[1] Wan P B,Wen X M, Sun C Z, Bevita K C, Zhang H, Sun X M, Chen X D 2015 Small 11 5409
Google Scholar
[2] Wang T, Guo Y L, Wan P B, Zhang H, Chen X D, Sun X M 2016 Small 12 3748
Google Scholar
[3] Ren X H, Li Z J, Huang Z Y, Sang D, Qiao H, Qi X, Li J Q, Zhong J X, Zhang H 2017 Adv. Funct. Mater. 27 1606834
Google Scholar
[4] Lu L, Liang Z M, Wu L M, Chen Y X, Song Y F, Dhanabalan S C, Ponraj J S, Dong B Q, Xiang Y J, Xing F, Fan D Y, Zhang H 2018 Laser Photonics Rev. 12 1700221
Google Scholar
[5] Mu H R, Wang Z T, Yuan J, Xiao S, Chen C Y, Chen Y, Chen Y, Song J C, Wang Y S, Xue Y Z, Zhang H, Bao Q L 2015 ACS Photon. 2 832
Google Scholar
[6] 殷玉龙, 孙晓兵, 宋茂新, 陈卫, 陈斐楠 2019 物理学报 68 024203
Google Scholar
Yin Y L, Sun X B, Song M X, Chen W, Chen F N 2019 Acta Phys. Sin. 68 024203
Google Scholar
[7] 林贤, 金钻明, 李炬赓, 郭飞云, 庄乃锋, 陈建中, 戴晔, 阎晓娜, 马国宏 2018 物理学报 67 237801
Google Scholar
Lin X, Jin Z M, Li J G, Guo F Y, Zhuang N F, Chen J Z, Dai Y, Yan X N, Ma G H 2018 Acta Phys. Sin. 67 237801
Google Scholar
[8] Nicholls L H, Rodríguez-Fortuño F J, Nasir M E, Córdova-Castro R M, Olivier N, Wurtz G A, Zayats A V 2017 Nat. Photon. 11 628
Google Scholar
[9] Norrman A, Blomstedt K, Setala T, Friberg A T 2017 Phys. Rev. Lett. 119 040401
Google Scholar
[10] Laudari A, Mazza A R, Daykin A, Khanra S, Ghosh K, Cummings F, Muller T, Miceli P F, Guha S 2018 Phys. Rev. Appl. 10 014011
Google Scholar
[11] Xiong X, Xue Z H, Meng C, Jiang S C, Hu Y H, Peng R W, Wang M 2013 Phys. Rev. B 88 115105
Google Scholar
[12] Wu P C, Tsai W Y, Chen W T, Huang Y W, Chen T Y, Chen J W, Liao C Y, Chu C H, Sun G, Tsai D P 2017 Nano Lett. 17 445
Google Scholar
[13] Liu H, Genov D A, Wu D M, Liu Y M, Liu Z W, Sun C, Zhu S N, Zhang X 2007 Phys. Rev. B 76 073101
Google Scholar
[14] Li Z Y, Kim M H, Wang C, Han Z H, Shrestha S, Overvig A C, Lu M, Stein A, Agarwal A M, Loncar M, Yu N F 2017 Nat. Nanotechnol. 12 675
Google Scholar
[15] Gao X, Singh L, Yang W 2017 Sci. Rep. 7 6817
Google Scholar
[16] Alam M Z, Schulz S A, Upham J, Leon I D, Boyd R W 2018 Nat. Photon. 12 79
Google Scholar
[17] Semmlinger M, Tseng M L, Yang J, Zhang M, Zhang C, Tsai W Y, Tsai D P, Nordlander P, Halas N J 2018 Nano Lett. 18 5738
Google Scholar
[18] Woerner M, Somma C, Reimann K, Elsaesser T, Liu P Q, Yang Y M, Reno J L, Brener I 2019 Phys. Rev. Lett. 122 107402
Google Scholar
[19] Liu N, Giessen H 2010 Angewandte Chemie International Edition 49 9838
Google Scholar
[20] Brettin A, Abolmaali F, Blanchette K F, McGinnis C L, Nesmelov Y E, Limberopoulos N I, Walker D E, Anisimov I, Urbas A M, Poffo L, Maslov A V, Astratov V N 2019 Appl. Phys. Lett. 114 131101
Google Scholar
[21] Wen Y Z, Zhou J 2017 Phys. Rev. Lett. 118 167401
Google Scholar
[22] Zhou J F, Koschny T, Soukoulis C M 2007 Opt. Express 15 17881
Google Scholar
[23] Segal N, Keren-Zur S, Hendler N, Ellenbogen T 2015 Nat. Photon. 9 180
Google Scholar
[24] Johnson P B, Christy R W 1972 Phys. Rev. B 6 4370
Google Scholar
[25] Liu N, Liu H, Zhu S N, Giessen H 2009 Nat. Photon. 3 157
Google Scholar
[26] Ciracì C, Poutrina E, Scalora M, Smith D R 2012 Phys. Rev. B 85 201403
Google Scholar
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