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Mirrors can be seen everywhere in daily life and play an important role in modern optical systems. A traditional mirror, which is made of noble metals, usually has a zero electric field strength and maximal magnetic field strength at its surface induced by the out-of-phase of electric field and in-of-phase of magnetic field between the reflected field and incident field due to the boundary condition of perfect electric conductor. As the magnitude of local electric field determines the strength of the light-matter interaction, it is clear that this interaction is suppressed near the mirror surface. Magnetic mirror, which can enhance electric field on the surface, has been widely applied to strong light-matter interaction for biological sensing, material analysis, and imaging. However, the conventional smooth magnetic mirror with a plane surface is difficult to induce sufficient light-matter interaction when the matter has a complex geometrical shape. Here in this work, we propose a concept of magnetic mirror with a rough interface designed by an array of artificial surface plasmonic structures. The artificial surface plasmonic structure on a subwavelength scale is designed by periodically inserting spiral metallic strips into a dielectric cylinder to support the strong magnetic dipolar resonant mode. The magnetic dipolar resonance of the excited structure is induced by the displacement current circle. Therefore, the resonant frequency is related to the geometrical parameters of the helical structure closely. When we reduce the outer radius of the structure, the magnitude of the displacement current circle will change, resulting in blue-shift of the resonant frequency. At the same time, we also find that increasing the spiral degree of the structure will cause the magnetic dipolar resonance frequency to become red-shifted. Particularly, the same magnetic dipolar mode can be supported in a spiral structure of different size by tuning the spiral degree accordingly. In this context, we design a rough magnetic mirror constructed by the artificial surface plasmonic structures with various sizes, and demonstrate that the efficiency of rough magnetic mirror is in agreement with that of smooth magnetic mirror. The proposed rough magnetic mirror can provide the unique ability to enhance the interaction between light and complicated matter for the application of biological sensing and imaging in microwave and terahertz band.
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图 1 (a)人工表面等离激元结构示意图; (b)计算的由不同材料构成的人工表面等离激元结构的散射谱, 其中黑色曲线代表PEC, 蓝色曲线代表Ag, 红色曲线代表Cu; (c)图1(b)中的黑色实线对应的共振峰的近场模式Hz
Figure 1. (a) Schematic diagram of spoof surface plasmonic structure; (b)calculated scattering cross section spectrum of spoof surface plasmonic structure made of different materials, where the black curve represents PEC, the blue curve represents Ag and the red curve represents Cu; (c) near-field pattern
${H}_{ {z}}$ for the resonant peak in the black solid line of (b).
图 2 (a)不同外半径下, 磁偶极子共振频率与螺旋度的关系, 图中的虚线和4条实线的交点代表对应于相同共振频率的4种结构; (b)不同内半径下, 磁偶极子共振频率与螺旋度的关系; (c) 对于不同的a/d, 磁偶极子共振频率与螺旋度的关系
Figure 2. (a) The magnetic dipole resonance frequency as the function of spiral degree for different outside radii. The intersection of the horizontal dotted line and the four solid curves in the figure represent the four structures corresponding to the same resonance frequency; (b) the relationship between the resonance frequency of magnetic dipole and spiral degree at different inner radii; (c) for different a/d, the relationship between the resonance frequency of magnetic dipole and spiral degree.
图 3 具有 (a)理想PEC和(b)理想PMC边界壁的电场|E|的分布; (c)−(f)在图2中用“1” “2” “3”和“4”表示的4种结构的电场|E|的分布; (g)−(h) 对于(c)中的结构参数, 用不同材料制成的结构的透射谱和反射谱
Figure 3. Snapshots of the electric field |E| for boundary walls with (a) the ideal PEC and (b) the ideal PMC; (c)−(f) snapshots of the electric field |E| for four structures of Fig. 2 denoted by “1” “2” “3” and “4”; (g)−(h) for the structural parameters of (c), transmission and reflection spectrum of structures made of different materials.
图 4 (a), (b)不同大小的光滑磁镜的电场|E|的分布及其局部放大图; (c)与(a)和(b)相同, 只是用粗糙的磁镜代替光滑的磁镜
Figure 4. (a), (b) Snapshots of the electric field |E| for smooth magnetic mirror of different sizes and their enlarged views; (c) same as (a) and (b) except replacing smooth magnetic mirror by rough magnetic mirror.
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[1] Esfandyarpour M, Garnett E, Cui Y, McGehee M D, Brongersma1 M L 2014 Nature Nanotech. 9 542
Google Scholar
[2] Liu S, Sinclair M B, Mahony T S, Jun Y C, Campione S, Ginn J, Bender D A, Wendt J R, Ihlefeld J F, Clem P G, Wright J B, Brener I 2014 Optica 1 250
Google Scholar
[3] Valagiannopoulos C A, Tukiainen A, Aho T, Niemi T, Guina M, Tretyakov S A, Simovski C R 2015 Phys. Rev. B 91 115305
Google Scholar
[4] Moitra P, Slovick B A, Li W, Kravchencko I I, Briggs D P, Krishnamurthy S, Valentine J 2015 ACS Photon. 2 692
Google Scholar
[5] Zhou Y, He X T, Zhao F L, Dong J W 2016 Opt. Lett. 41 2209
Google Scholar
[6] Qin J, Zhao D, Luo S, Wang W, Lu J, Qiu M, Li Q 2017 Opt. Lett. 42 4478
Google Scholar
[7] Liu Y P, Dai Y Y, Feng Q C, Shan Y W, Du L, Xia Y Y, Lu G, Liu F, Du G Q, Tian C S, Wu S W, Shi L, Zi J 2017 Opt. Express 25 30754
Google Scholar
[8] Wang T T, Luo J, Gao L, Xu P, Lai Y 2014 Appl. Phys. Lett. 104 211904
Google Scholar
[9] 赵一, 曹祥玉, 高军, 姚旭, 马嘉俊, 李思佳, 杨欢欢 2013 物理学报 62 154204
Google Scholar
Zhao Y, Cao X Y, Gao J, Yao X, Ma J J, Li S J, Yang H H 2013 Acta Phys. Sin. 62 154204
Google Scholar
[10] 鲁磊, 屈绍波, 马华, 夏颂, 徐卓, 王甲富, 余斐 2013 物理学报 62 034206
Google Scholar
Lu L, Qu S B, Ma H, Xia S, Xu Z, Wang J F, Yu F 2013 Acta Phys. Sin. 62 034206
Google Scholar
[11] 郑月军, 高军, 曹祥玉, 李思佳, 杨欢欢, 李文强, 赵一, 刘红喜 2015 物理学报 64 024219
Google Scholar
Zheng Y J, Gao J, Cao X Y, Li S J, Yang H H, Li W Q, Zhao Y, Liu H X 2015 Acta Phys. Sin. 64 024219
Google Scholar
[12] 石泰峡, 董丽娟, 陈永强, 刘艳红, 刘丽想, 石云龙 2019 物理学报 68 214208
Google Scholar
Shi T X, Dong L J, Chen Y Q, Liu Y H, Liu L X, Shi Y L 2019 Acta Phys. Sin. 68 214208
Google Scholar
[13] Park J, Kang J H, Kim S J, Liu X G, Brongersma M L 2017 Nano Lett. 17 407
Google Scholar
[14] Choi S B, Park D J, Byun S J, Kyoung J, Hwang S W 2015 Adv. Opt. Mater. 3 1719
Google Scholar
[15] Schwanecke A S, Fedotov V A, Khardikov V V, Prosvirnin S L, Chen Y, Zheludev N I 2007 J. Opt. A: Pure Appl. Opt. 9 L1
Google Scholar
[16] Headland D, Nirantar S, Withayachumnankul W, GutrufP, Abbott D, Bhaskaran M, Fumeaux C, Sriram S 2015 Adv. Mater. 27 7137
Google Scholar
[17] Ma Z J, Hanham S M, Albella P, Ng B, Lu H T, Gong Y D, Maier S A, Hong M H 2016 ACS Photon. 3 1010
Google Scholar
[18] Lin L, Jiang Z H, Ma D, Yun S, Liu Z W, Werner D H, Mayer T S 2016 Appl. Phys. Lett. 108 171902
Google Scholar
[19] Liu W 2017 Phys. Rev. Lett. 119 123902
Google Scholar
[20] Liu W X, Sun Y, Lai Z Q, Chen H 2017 J. Opt. Soc. Am. B 34 1899
Google Scholar
[21] Pors A, Moreno E, Martin-Moreno L, Pendry J B, Garcia-Vidal F J 2012 Phys. Rev. Lett. 108 223905
Google Scholar
[22] Shen X P, Cui T J 2014 Laser Photon. Rev. 8 137
Google Scholar
[23] Gao Z, Gao F, Xu H, Zhang Y, Zhang B 2016 Opt. Lett. 41 2181
Google Scholar
[24] Li Z, Xu B, Liu L, Xu J, Chen C, Gu C, Zhou Y 2016 Sci. Rep. 6 27158
Google Scholar
[25] Huidobro P A, Shen X P, Cuerda J, Moreno E, Martin-Moreno L, Garcia-Vidal F J, Cui T J, Pendry J B 2014 Phys. Rev. X 4 021003
[26] Wu H W, Han Y Z, Chen H J, Zhou W, Li X C, Gao J, Sheng Z Q 2017 Opt. Lett. 42 4521
Google Scholar
[27] Rybin M V, Samusev K B, Sinev I S, Semouchkin G, Semouchkina E, Kivshar Y S, Limonov M F 2013 Opt. Express 21 30107
Google Scholar
[28] Liao Z, Fernández-Domínguez A I, Zhang J J, Maier S A, CuiT J, Luo Y 2016 ACS Photon. 3 1768
Google Scholar
[29] Gentile M J, Nunezsanchez S, Barnes W L 2014 Nano Lett. 14 2339
Google Scholar
[30] Feuillet-Palma C, Todorov Y, Vasanelli A 2013 Sci. Rep. 3 1361
Google Scholar
[31] Hatab N A, Hsueh C H, Gaddis A L, Retterer S T, Li J H, Eres G, Zhang Z, Gu B 2010 Nano Lett. 10 4952
Google Scholar
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