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Surface plasmon polaritons (SPPs) are electromagnetic excitations propagating along the metal-dielectric interface. The SPPs excited by the metal micro/nano structures have the ability to manipulate the light on a subwavelength scale. The SPPs are of interest to researchers for its excellent subwavelength field confinement and local field enhancement. So far, the SPPs have found numerous applications in optical tweezers, biological sensors, and near-field holographic imaging, due to its subwavelength focusing. In order to achieve enhanced near field subwavelength focusing, we propose a metasurface structure in this paper, which is composed of rectangular nanoslit circular arrays and multilayer annular slits. The function of the inner ring arrays is to excite SPPs and the outer ring slits is to enhance focusing. The electric field expression of SPP is studied analytically and theoretically, and then the principle of rectangular nanoslit to excite SPP and the inner ring array structure to generate central focusing are explained. The parameters of the structure are optimized, and the focusing characteristics of the metasurface structure under different polarization light are studied by using the finite difference time domain method. Furthermore, we explain the principle of the external structure enhancing focusing by introducing the theory of Fresnel zone plate and depth modulation. The analytical expressions and simulations show that when the incident polarized light has a wavelength of 980 nm, the focal spot having a full width at half maximum of about 650 nm, and the distribution of the coupled field can be approximately expressed by the first kind Bessel function. Compared with the former single circular array structure, the composite structure proposed in this paper has a good effect of both enhancing the central focusing and inhibiting the outer field divergence, and the center focal spot intensity is doubled. In addition, the electric field excited by the arbitrary linearly polarized light is also discussed, the electric field satisfies the form of the polarization angle sinusoidal function multiplied by a Bessel function. The research results of our study have some applications in subwavelength light modulation, near-field imaging, optical tweezers, and subwavelength scale optical information processing and so on. -
Keywords:
- surface plasmon polaritons /
- subwavelength focusing /
- metasurface structure /
- Bessel optical field
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图 1 矩形纳米狭缝激发的SPPs场 (a) x方向线偏振光入射下x和y方向电场强度随L的变化; (b) x方向线偏振光入射激发的场; (c) y方向线偏振光入射激发的场
Figure 1. SPPs field excited by rectangular nanoslit: (a) Electric field intensity along the L curves in the x and y direction with the x-direction linearly polarized light incident; (b) electric field excited by the incident light in the x direction; (c) electric field excited by the incident light in the y direction.
图 2 左旋圆偏振光入射下, (a) 圆狭缝、(b) 螺旋线狭缝、(c) 旋转排列的矩形纳米狭缝阵列激发SPPs原理示意图; (d) 矩形纳米狭缝双圆环阵列结构示意图
Figure 2. Schematic diagram of excitation of SPPs by (a) circular slit, (b) spiral slit, (c) rotating rectangular nanoslit arrays under the incidence of left-handed circularly polarized light; (d) schematic diagram of double-ring rectangular nanoslit arrays.
图 3 复合聚焦结构示意图 (a) 二维俯视图; (b) 截面侧视图
Figure 3. Schematic diagram of compound focusing structure: (a) Two-dimensional top view; (b) sectional view.
图 4 中心电场随狭缝深度差值变化趋势
Figure 4. Variation of the center electric field with the difference of slit depth.
图 5 左旋圆偏振光入射结构仿真图 (a) 电场分布图; (b) 电场强度切面曲线图
Figure 5. Simulation diagram of left-hand circularly polarized light incident structure: (a) Electric field distribution diagram; (b) cross-section curve of electric field intensity.
图 6 不同偏振方向线偏振光激发的电场分布 (a)
$\psi = {0^\circ }$ ; (b)$\psi = +{45^\circ }$ ; (c)$\psi = {90^\circ }$ ; (d)$\psi = -{45^\circ }$ Figure 6. Electric field distribution excited by linearly polarized light in different polarization directions: (a)
$\psi = {0^\circ }$ ; (b)$\psi = +{45^\circ }$ ; (c)$\psi = {90^\circ }$ ; (d)$\psi = -{45^\circ }$ .
图 7 线偏振光入射结构仿真曲线 (a) 电场强度切面曲线; (b) 中心聚焦点强度随
$\psi $ 变化曲线Figure 7. Simulation curves of linearly polarized light incident structure: (a) Section curves of electric field intensity; (b) curve of the intensity of the central focal point changing with
$\psi $ .
图 8 简单结构和复合聚焦结构激发场强度曲线对比
Figure 8. Comparison of the excitation field intensity curves of the simple structure and the composite focusing structure.
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[1] Barnes W L, Dereux A, Ebbesen T W 2003 Nature 424 824
Google Scholar
[2] Fang N, Lee H, Sun C, Zhang X 2005 Science 308 534
Google Scholar
[3] Lieven V, Catrysse P B, Yu Z F, Fan S H 2009 Phys. Rev. Lett. 103 033902
Google Scholar
[4] Yin L, Vlasko-Vlasov V K, Pearson J, Hiller J M, Hua J, Welp U, Brown D E, Kimball C W 2005 Nano Lett. 5 1399
Google Scholar
[5] Shen Z, Hu Z J, Yuan G H, Min C J, Fang H, Yuan X C 2012 Opt. Lett. 37 4627
Google Scholar
[6] Wang J J, Duan G T, Liu G Q, Yue L, Chen Z X, Lei X, Cai W P 2016 J. Hazard. Mater. 303 94
Google Scholar
[7] Coluccio M L, Francardi M, Gentile F, Candeloro P, Ferrara L, Perozziello G, Fabrizio E D 2014 Sensors 14 6056
[8] Song W T, Fang Z Y, Huang S, Lin F, Zhu X 2010 Opt. Express 18 14762
Google Scholar
[9] Holmgaard T, Gosciniak J, Bozhevolnyi S I 2010 Opt. Express 18 23009
Google Scholar
[10] Raghunathan S B, Gan C H, Dijk T V, Kim B E, Schouten H F, Ubachs W, Lalanne P, Visser T D 2012 Opt. Express 20 15326
Google Scholar
[11] Song E Y, Lee Y L, Hong J, Lee K, Lee Y, Lee G Y, Kim H, Lee B 2016 Laser Photon. Rev. 10 299
[12] López-Tejeira F, Rodrigo S G, Martín-Moreno L, García-Vidal F J, Devaux E, Ebbesen T W, Krenn J R, Radko I P, Bozhevolnyi S I, González M U 2007 Nat. Phys. 3 324
Google Scholar
[13] Radko I P, Bozhevolnyi S I, Brucoli G, Martín-Moreno L, García-Vidal F J, Boltasseva A 2009 Opt. Express 17 7228
Google Scholar
[14] Li X W, Huang L L, Tan Q F, Bai B F, Jin G F 2011 Opt. Express 19 6541
Google Scholar
[15] Li L, Li T, Wang S, Zhu S, Zhang X 2011 Nano Lett. 11 4357
Google Scholar
[16] Tanemura T, Balram K C, Dany-Sebastien L G, Pierre W, White J S, Brongersma M L, Miller D A B 2011 Nano Lett. 11 2693
Google Scholar
[17] Lee S Y, Kim K, Lee G Y, Lee B 2015 Opt. Express 23 15598
Google Scholar
[18] Lee B, Park H, Kim K Y, Kim K, Lee S Y, Kim S J 2015 Optica 2 6
Google Scholar
[19] Wintz D, Genevet P, Ambrosio A, Woolf A, Capasso F 2015 Nano Lett. 15 3585
Google Scholar
[20] Kim H, Park J, Cho S W, Lee S Y, Kang M, Lee B 2010 Nano Lett. 10 529
Google Scholar
[21] Yang Y J, Thirunavukkarasu G, Babiker M, Yuan J 2017 Phys. Rev. Lett. 119 094802
Google Scholar
[22] Liu J L, Gao Y, Ran L L, Guo K, Lu Z W, Liu S T 2015 Appl. Phys. Lett. 106 013116
Google Scholar
[23] Chen C F, Ku C T, Tai Y H, Wei P K, Lin H N, Huang C B 2015 Nano Lett. 15 2746
Google Scholar
[24] Rui G H, Abeysinghe D C, Nelson R L, Zhan Q W 2013 Sci. Rep. 3 2237
Google Scholar
[25] Zhou H L, Dong J J, Zhou Y F, Zhang J H, Liu M, Zhang X L 2015 IEEE Photonics J. 7 1
[26] Ren H R, Li X P, Zhang Q M, Gu M 2016 Science 352 805
Google Scholar
[27] Garoli D, Ongarello T, Zilio P, Carli M, Romanato F 2015 Appl. Opt. 54 1161
Google Scholar
[28] Garoli D, Romanato F, Carli M, Zilio P, Giorgis V 2014 Opt. Express 22 26302
Google Scholar
[29] Hu C B, Xu J, Ding J 2017 J. Mod. Opt. 64 1
Google Scholar
[30] 王帅, 邓子岚, 王发强, 王晓雷, 李向平 2019 物理学报 68 077801
Google Scholar
Wang S, Deng Z L, Wang F Q, Wang X L, Li X P 2019 Acta Phys. Sin. 68 077801
Google Scholar
[31] Lin J, Mueller J P B, Wang Q, Yuan G H, Antoniou N, Yuan X C, Capasso F 2013 Science 340 331
Google Scholar
[32] Lee S Y, Kim S J, Kwon H, Lee B 2015 IEEE Photonics Technol. Lett. 27 705
Google Scholar
[33] Chen Y G, Li Z Y 2016 Plasmonics 11 1385
Google Scholar
[34] Li X, Zhang R R, Zhang Y Q, Ma L, He C W, Ren X R, Liu C X, Cheng C F 2018 New J. Phys. 20 063037
Google Scholar
[35] Wang S, Wang S, Zhang Y 2018 Opt. Express 26 5461
Google Scholar
[36] Wang J, Zhang J 2018 Opt. Express 26 14626
Google Scholar
[37] Jiang Q, Bao Y J, Lin F, Zhu X, Zhang S, Fang Z Y 2018 Adv. Funct. Mater. 28 1705503
[38] 祁云平, 周培阳, 张雪伟, 严春满, 王向贤 2018 物理学报 67 107104
Google Scholar
Qi Y P, Zhou P Y, Zhang X W, Yan C M, Wang X X 2018 Acta Phys. Sin. 67 107104
Google Scholar
[39] Maier S A 2007 Plasmonics: Fundamentals and Applications (Berlin: Springer Berlin) pp13−34
[40] Fu Y Q, Zhou W, Lim L E N, Du C L, Luo X G 2007 Appl. Phys. Lett. 91 061124
Google Scholar
[41] Shi H, Dong X, Lv Y, Du C 2009 Appl. Phys. B 95 345
Google Scholar
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