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A symmetrical wedge-to-wedge THz hybrid SPPs waveguide (WWTHSW) with low propagation loss is investigated. The WWTHSW consists of two identical dielectric wedge waveguides symmetrically placed on each side of a micro wedge-patterned thin metal film. The mode characteristics of the WWTHSW, such as the propagation length (Lp), the normalized effective mode area (A) and the figure of merit (FOM) are analyzed by using the finite element method (FEM). Firstly, the influences of the height of Si micro wedge waveguide (H) and the gap between two wedges (g) on Lp and A are studied. For the same g, A first decreases and then increases with the increase of H. A achieves a minimum at an H of ~40 μm. However, Lp monotonically increases as H increases. The change of Lp slows down when H is greater than 40 μm. At a fixed H, Lp slightly increases with the increase of g. But A achieves a minimum when g is ~50 nm. Secondly, the dependencies of the mode characteristics of the WWTHSW on Si wedge tip angle (α) and Ag wedge tip angle (θ) are analyzed. At a fixed α, θ has less effect on Lp and A. As α increases at a fixed θ, Lp increases monotonically but A decreases firstly and then increases. A reaches a minimum when α increases to ~100°. Then, the change of Lp and A with the thicknesses of Ag film (d) and Ag wedge (h) are demonstrated. At a fixed h, both Lp and A slightly decrease as d increases. For the same d, Lp and A decrease with the increase of h. A for h = 0 μm is distinctly larger than those for h = 2 μm and h = 5 μm. According to the above optimizations, the parameters of the WWTHSW are chosen as d = 100 nm, g = 50 nm, h = 2 μm, θ = 80°, α = 100°, H = 40 μm. Under the optimal parameters, Lp of ~51 mm is obtained when Am reaches ~λ2/10280. Compared with the previous hybrid THz plasmonic waveguide, Lp of the WWTHSW increases by 3 times, and A decreases by an order of magnitude. This result reveals that the WWTHSW enables low-loss propagation and ultra-deep-subwavelength mode confinement at THz frequencies. At last, the coupling property of the parallel WWTHSW is investigated. The coupling length of ~8958 μm is achieved without the crosstalk between two parallel waveguides. By comparison, the WWTHSW has more advantages in terms of transmission and coupling characteristics than the previous micro wedge waveguide structure and bow-tie waveguide structure. In summary, due to the excellent transmission and coupling characteristics, the WWTHSW has great potential in the fields of optical force in trapping, biomolecules transporting, and in high-density integrated circuits design.
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Keywords:
- hybrid plasmonic waveguide /
- surface plasmonpolaritons /
- transmission characteristics /
- coupling characteristics
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图 1 WWTHSW示意图 (a)三维图; (b)截面图
Figure 1. Schematic diagram of the proposed WWTHSW: (a) 3D diagram; (b) cross-section.
图 2 不同H和g时, WWTHSW的模式分析 (a) MC, (b) Lp, (c) A; 模场分布: (d) [H, g] = [10, 0.05] μm, (e) [H, g] = [40, 0.05] μm, (f) [H, g] = [90, 0.05] μm
Figure 2. Modes analysis of the WWTHSW with different H and g: (a) MC, (b) Lp, and (c) A;and normalized EM energy density distributions: (d) [H, g] = [10, 0.05] μm; (e) [H, g] = [40, 0.05] μm; (f) [H, g] = [90, 0.05] μm.
图 3 不同α和θ时, WWTHSW的模式分析 (a) Lp, (b) A; (c)模场分布随α的变化(θ = 80°); (d)模场分布随θ的变化(α = 100°)
Figure 3. Modes analysis of the WWTHSW with different α and θ, (a) Lp, (b) A; and normalized EM energy density distributions: (c) with different α at a fixed θ of 80°, (d) with different θ at a fixed α of 100°.
图 4 不同d和h时, WWTHSW的模式分析 (a) Lp、(b) A; (c)沿x方向的归一化能量密度
Figure 4. Modes analysis of the WWTHSW with different d and h, (a) Lp, (b) A, and (c) normalized EM energy density.
图 5 不同波导性能比较 (a) WWTHSW, HTMWSPPs和HTBTSPPs波导的截面图; (b) WWTHSW, HTMWSPPs和HTBTSPPs波导的A与Lp关系图; (c)品质因数
Figure 5. Performance comparison of the WWTHSW, HTMWSPPs and HTBTSPPs wavguide: (a) cross-section views; (b) the relationship between A and Lp; and (c) FOM with different parameters.
图 6 波导耦合特性分析 (a)平行波导三维结构示意图; (b)耦合长度随D的变化; (c)最大传输功率随D的变化
Figure 6. Coupling characteristic of waveguides: (a) schematic diagram parallel waveguides; (b) Lc versus the separation between the two waveguides; (c) the maximum transfer power (Pmax) as a function of distance D.
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[1] Andersen J, Solodukhov V 1978 IEEE T. Antenn. Propag. 26 598
Google Scholar
[2] Oulton R F, Sorger V J, Genov D A, Pile D F P, Zhang X J 2008 Nature Photon. 2 496
Google Scholar
[3] Li Qing, Pan D, Wei H, Xu H X 2018 Nano Lett. 18 2009
Google Scholar
[4] Bozhevolnyi S I, Volkov V S, Devaux, E, Laluet, J Y, Ebbesen, T W 2006 Nature 440 508
Google Scholar
[5] Zhu Z H, Garcia-Ortiz C E, Han Z H, Radko I P, Bozhevolnyi S I 2013 Appl. Phys. Lett. 103 061108
[6] Hassan K, Leroy F, Colas-Des-Francs G, Weeber, J C 2014 Opt. Lett. 39 697
Google Scholar
[7] Papaioannou S, Giannoulis G, Vyrsokinos K, Leroy F, Zacharatos F, Markey L, Weeber C J, Dereux A, Bozhevolnyi S, Prinzen A, Apostolopoulos D, Avramopoulos H, Pleros N 2015 IEEE Photon. Technol. Lett. 27 963
Google Scholar
[8] Hui F, Berini P 2016 J. Lightwave Technol. 34 2631
Google Scholar
[9] 涂鑫, 陈震旻, 付红岩 2019 物理学报 68 104210
Google Scholar
Tu X, Chen Z M, Fu H Y 2019 Acta Phys. Sin. 68 104210
Google Scholar
[10] Wang Y L, Li S L, Yan J Y, Li C, Jiang P, Wang L L, Yu L 2019 Nanophotonics 8 1271
Google Scholar
[11] Wang Y L, Li C, Duan G Y, Wang L L, Yu L 2019 Adv. Opt. Mater. 7 1801362
Google Scholar
[12] Mai W, Wang Y, Zhang Y, Cui L, Yu L 2017 Chin. Phys. Lett. 34 024204
Google Scholar
[13] Gosciniak J, Volkov V S, Bozhevolnyi S I, Markey L, Massenot S, Dereux A 2010 Opt. Express 18 5314
Google Scholar
[14] Berini P 2009 Adv. Opt. Photonic 1 484
Google Scholar
[15] Ma Y Q, Gerald F, Yuliya S, Wu Q 2014 Opt. Lett. 39 973
Google Scholar
[16] Pan M Y, Lin E H, Wang L, Wei P K 2014 Appl. Phys. A. 115 592
[17] Ma Y Q, Farrell G, Semenova Y, Wu Q 2015 J. Lightwave Technol. 33 3827
Google Scholar
[18] 贾智鑫, 段欣, 吕婷婷, 郭亚楠, 薛文瑞 2011 物理学报 60 057301
Google Scholar
Jia Z X, Du X, Lü T T, Guo Y N, Xue W R 2011 Acta Phys. Sin. 60 057301
Google Scholar
[19] Gong Q, Bian Y 2014 J. Lightwave Technol. 32 4504
Google Scholar
[20] Jacek G, Volkov V S, Bozhevolnyi S I, Markey L, Massenot S, Dereux A 2010 Optics Express 18 5314
[21] 彭滟, 施辰君, 朱亦鸣, 庄松林 2019 中国激光 46 0614002
Google Scholar
Peng Y, Shi C J, Zhu Y M, Zhuang S L 2019 Chin. J. Las. 46 0614002
Google Scholar
[22] 陈华, 汪力 2009 物理学报 58 4605
Google Scholar
Chen H, Wang L 2009 Acta Phys. Sin. 58 4605
Google Scholar
[23] Eldlio M, Ma Y Q, Maeda H, Cada M 2017 Infrared Phys. Technol. 80 93
Google Scholar
[24] Cao W, Song C Y, Lanier T E, Singh R, O’Hara J F, Dennis W M, Zhao Y P, Zhang W L 2013 Sci. Rep. 3 1766
Google Scholar
[25] Fitch M J, Osiander R 2004 J. Hopkins Apl. Technol. D. 25 348
[26] Berini P 2006 Opt. Express 14 13030
Google Scholar
[27] Moreno E, Rodrigo S G, Bozhevolnyi S I, Martín-Moreno L, García-Vidal F J 2008 Phys. Rev. Lett. 100 023901
Google Scholar
[28] Ma Y Q, Farrell G, Semenova Y, Chan H P, Zhang H Z, Wu Q 2013 Plasmonics 8 1259
Google Scholar
[29] Georgios V, Shanhui F 2008 Opt. Express 16 2129
Google Scholar
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