搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

球形双曲色散超材料腔的多重窄带回音廊模式及透明显示应用

李艳 任思萌 褚博 燕汝江 于群星 孙辉 邵立 钟发成

引用本文:
Citation:

球形双曲色散超材料腔的多重窄带回音廊模式及透明显示应用

李艳, 任思萌, 褚博, 燕汝江, 于群星, 孙辉, 邵立, 钟发成

Multiple narrowband whispering-gallery model and transparent display applications of spherical hyperbolic dispersive metamaterial cavity

Li Yan, Ren Si-Meng, Chu Bo, Yan Ru-Jiang, Yu Qun-Xing, Sun Hui, Shao Li, Zhong Fa-Cheng
PDF
HTML
导出引用
  • 本文提出并设计了一种用于提高彩色透明显示性能的球形双曲色散超材料(HMM)腔. 该腔由介质/银层交替包裹银核组成, 具有深度亚波长性质, 并支持和银层数目相同的同阶回音廊模式. 这些模式能够将电磁波能量高度局域在不同介质壳层内, 从而降低欧姆损耗, 减小共振线宽. 针对5层银/介质交替包裹形成的HMM腔, 详细分析了结构参数对回音廊模式的调谐作用. 发现仅改变最外层介质或银层厚度, 几乎不影响TM1,2和TM1,3模式的共振位置, 但对TM1,1模式的共振位置及3个模式的强度产生明显调谐. 通过优化HMM腔, 在红绿蓝波段实现三重窄带共振, 且在三重共振位置均具有偶极辐射特点, 能够将散射光限制在和入射光夹角为–45°—+45°范围内. 该HMM腔不仅支持红绿蓝三重窄带共振, 并具有宽的散射角, 可应用于实现高透明度、高亮度和宽视角的全彩透明显示.
    A novel spherical hyperbolic metamaterial (HMM) cavity for enhancing color-transparent display is designed in this work. This HMM cavity consists of a silver core wrapped alternatively by several dielectric layers and silver layers. According to the effective medium theory and Mie scattering theory, we demonstrate that such an HMM cavity supports multiple whispering-gallery modes with deep subwavelength characteristics. The number of whispering-gallery modes with the same angular momentum is equal to the number of silver layers within the HMM cavity. Furthermore, we demonstrate that these excited whispering-gallery modes are capable of strongly confining the electric fields within the different dielectric shell layers, thus reducing Ohmic losses and narrowing resonance linewidths. In addition, we systematically investigate how the structure parameters affect whispering-gallery modes for an HMM cavity with 5 alternative dielectric layers and silver layers. Interestingly, by increasing the thickness of outermost dielectric layer and silver layer, the resonance wavelength of TM1,2 mode and TM1,3 mode remain nearly unchanged. However, the TM1,1 mode experiences a significant blueshift, and the intensity of the TM1,1, TM1,2 and TM1,3 mode can be substantially tuned. Consequently, through structural optimization, the HMM cavity can support triple narrowband resonances in the red, green, and blue spectral regions. Finally, we show that the HMM cavity exhibits dipole radiation characteristics at the three resonance wavelengths, effectively confining light within an angular range from –45° to +45° relative to the incident light direction, and confirming the scattered light viewed from a wide angle. These features make the HMM cavity suitable for achieving high transparency, brightness, and wide viewing angles in full-color transparent displays.
      通信作者: 李艳, yanli@zua.edu.cn ; 钟发成, zhongfacheng@163.com
    • 基金项目: 河南省高等学校重点研究项目计划基础专项(批准号: 23ZX018)、国家自然科学基金 (批准号: 11704344)和河南省高等学校研究项目(批准号: 22A140030)资助的课题.
      Corresponding author: Li Yan, yanli@zua.edu.cn ; Zhong Fa-Cheng, zhongfacheng@163.com
    • Funds: Project supported by the Key Research Projects of Colleges and Universities of Henan Province, China (Grant No. 23ZX018), the National Natural Science Foundation of China (Grant No. 11704344), and the Research Projects of Colleges and Universities of Henan Province, China (Grant No. 22A140030).
    [1]

    Hsu C W, Zhen B, Qiu W J, Shapira O, DeLacy B G, Joannopoulos J D, Soljačić M 2014 Nat. Commun. 5 3152Google Scholar

    [2]

    Hedili M K, Freeman M O, Urey H 2012 Proc. SPIE. 8428 84280XGoogle Scholar

    [3]

    Görrn P, Sander M, Meyer J, Kroger M, Becker E, Johannes H, Kowalsky W, Riedl T 2006 Adv. Mater. 18 738Google Scholar

    [4]

    Hedili M K, Freeman M O, Urey H 2013 Appl. Opt. 52 1117Google Scholar

    [5]

    Goldenberg J F, McKechnie T S 1985 Opt. Soc. Am. A 2 2337Google Scholar

    [6]

    Hedili M K, Freeman M O, Urey H 2013 Opt. Express 21 24636Google Scholar

    [7]

    Hong K, Yeom J, Jang C, Hong Jisoo, Lee B 2014 Opt. Lett. 39 127Google Scholar

    [8]

    Soomro S R, Urey H 2016 Opt. Express 24 24232Google Scholar

    [9]

    Kravets V G, Schedin F, Grigorenko A N 2008 Phys. Rev. Lett. 101 087403Google Scholar

    [10]

    王振林 2009 物理学进展 3 287Google Scholar

    Wang Z L 2009 Phys. Pro. 3 287Google Scholar

    [11]

    Smith D R, Schurig D 2003 Phys. Lett. 90 077405Google Scholar

    [12]

    Yang X D, Yao J, Rho J, Yin X B, Zhang X 2012 Nat. Photon. 6 450Google Scholar

    [13]

    Saito K, Tatsuma T 2015 Nanoscale 7 20365Google Scholar

    [14]

    Ye Y Y, Chen T P, Zhen J Y, Xu C, Zhang J, Li H K 2018 Nanoscale 10 2438Google Scholar

    [15]

    Soomro S R, Urey H 2017 Appl. Opt. 56 6108Google Scholar

    [16]

    Shin S, Boyeon H, Zhao Z J, Jeon S H, Jung J Y, Lee J H, Ju B K, Jeonget J H 2018 Sci. Rep. 8 2463Google Scholar

    [17]

    Chu B, Li Y, Qin Y H, Hu T Z, Zhong F C, Zeng F G, Ding P, Shao L, Du Y X, Tian S, Chen Z 2023 Nanotechnology 34 325301Google Scholar

    [18]

    Barnes W L, Alain D, Ebbesen T W 2003 Nature 424 824Google Scholar

    [19]

    Sun J B, Shalaev M I, Litchinitser N M 2015 Nat. Commun. 6 7201Google Scholar

    [20]

    Wan M J, Gu P, Liu W Y, Chen Z, Wang Z L 2017 Appl. Phys. Lett. 110 031103Google Scholar

    [21]

    李艳, 钟发成, 褚博, 邵立, 王俊俏, 万明杰, 杨鹏, 王妍妍, 丁佩, 曾凡光, 于占军, 许坤, 杜银霄, 霍海波, 陈卓, 王振林 2021 中国科学: 物理学 力学 天文学 51 104211Google Scholar

    Li Y, Zhong F C, Chu B, Shao L, Wang J Q, Wan M J, Yang P, Wang Y Y, Ding P, Zeng F G, Yu Z J, Xu K, Du Y X, Huo H B, Chen Z, Wang Z L 2021 Sci. Sin. Phys. Mech. As. 51 104211Google Scholar

    [22]

    Gu P, Chen J, Chen S Y, Yang C, Zhang Z X, Du W, Yan Z D, Tang C J, Chen Z 2021 Photonics Res. 9 829Google Scholar

    [23]

    Gu P, Guo Y H, Chen J, Zhang Z X, Yan Z D, Liu F X, Tang C J, Du W, Chen Z 2021 Nanomaterials 11 2301Google Scholar

    [24]

    Bohren C F, Huffman D R 1983 Absorption and Scattering of Light by Small Particls Optics (New York: Wiley) p475

    [25]

    Johnson P B, Christy R W 1972 Phys. Rev. B 6 4370Google Scholar

    [26]

    Wu C, Salandrino A, Ni X, Zhang X 2014 Phys. Rev. X 4 021015Google Scholar

    [27]

    Knight M W, Halas N J 2008 New J. Phys. 10 105006Google Scholar

    [28]

    Fan X, Zheng W, Singh D J 2014 Light Sci. Appl. 3 179Google Scholar

    [29]

    Prodan E, Radloff C, Halas N J, Nordlander P 2003 Science 302 419Google Scholar

  • 图 1  (a) 由介质和银交替包裹银核组成的球形HMM腔结构示意图; (b) 由有效介质理论在f = 0.5 ×1015 Hz处计算该HMM腔的等频面 (黑色曲线), 蓝色圆代表光在空气中的等频面; (c) 4对银 (Rin = d = 5 nm)/介质层 (s = 4 nm) 交替包裹形成的HMM腔, 在角动量数n = 3的八极子共振 (波长λ = 600 nm, 频率f = 0.5 ×1015 Hz) 处的电场强度分布图

    Fig. 1.  (a) A schematic of the HMM cavity formed by alternately wrapping a silver core with dielectric and silver layers; (b) the hyperbolic isofrequency contour (black line) of the cavity in the momentum space calculated with the effective medium approximation at a frequency of f = 0.5×1015 Hz, the blue line represents the corresponding isofrequency contour of air; (c) electric field intensity enhancement distributions of the HMM cavity formed by 4 pairs of silver (Rin = d = 5 nm) and dielectric (s = 4 nm, nd = 1.45) layers at octupolar resonant wavelength λ = 600 nm with the angular momentum n = 3.

    图 4  固定HMM腔中Rin = 5 nm, s1 = 4 nm, d1 = 5 nm, 介质折射率n1 = 1.8, n2 = 1.45情况下 (a) 同时固定s2 = 9 nm, 银壳层厚度d2从0 nm到10 nm时, HMM腔的散射效率谱; (b) 同时固定d2=8 nm, 介质层厚度s2从5 nm到15 nm时, HMM腔的散射效率谱

    Fig. 4.  (a) The scattering efficiency spectra as a function of the wavelength and the thinkness of the third silver layer (d2 ) for the HMM cavities with fixed Rin = 5 nm, s1 = 4 nm, d1 = 5 nm, d2 = 8 nm, s2 = 9 nm and n2 = 1.45; (b) the scattering efficiency spectra as a function of the wavelength and the thickness of the second dielectric layer (s2 ) for the HMM cavities with fixed Rin = 5 nm, s1 = 4 nm, d1 = 5 nm, d2 = 8 nm, n1 = 1.8, and n2 = 1.45.

    图 2  (a) 由8层银(Rin = d = 5 nm)和介质层(s = 4 nm, nb = 1.5) 交替包裹组成的HMM腔的散射谱, 这里展示了偶极和四极电分量的贡献(a1, a2), 为了更清楚地显示电四极子的贡献, 将其散射效率值扩大了50倍, 右上方插图是通过Comsol软件模拟(蓝色三角)和米氏散射理论计算(蓝色实线)的总散射效率谱; (b) 结构在TM1,1模式共振波长λ = 1266 nm处的电场强度分布图; (c) 结构在TM1,2模式共振波长λ = 768 nm处的电场强度分布图; (d) 结构在TM2,1模式共振波长λ = 791 nm处的电场强度分布图; (e) 结构在TM2,2模式共振波长λ = 531 nm处的电场强度分布图

    Fig. 2.  (a) The scattering efficiency spectra (the contributions from the first two electric terms (a1, a2), respectively) of the HMM cavity (inset) formed by eight layers of silver (Rin = d = 5 nm) and dielectric (s = 4 nm). For clarity, the contribution from a2 is magnified 50 times. Top inset shows the total scattering efficiency spectra simulated based on Comsol software (blue triangle) and calculated based on Mie scattering theory (blue line), respectively. (b)—(e) Electric field intensity enhancement distributions of the two dipolar resonances (b) TM1,1 and (c) TM1,2, and two quadrupolar resonances (d) TM2,1 and (e) TM2,2, respectively.

    图 3  (a) 5层银(Rin = d1 = d2 = 5 nm)/介质层(s1 = s2 = 4 nm, n1 = 1.8, n2 = 1.45)交替包裹组成的球形HMM腔的散射谱, 插图为HMM腔的结构示意图; (b) 改变HMM腔中银核尺寸Rin的散射效率谱; (c) 改变HMM腔中银层厚度(保持Rin = 5 nm, d1 = d2)的散射效率谱; (d) 改变HMM腔中介质层厚度s1 = s2的散射效率谱; (e) 分别改变HMM腔中第2层银层厚度d1和第1层介质层厚度s1的散射效率谱; (f) 分别改变HMM腔中第3层银层厚度d2和第2层介质层厚度s2的散射效率谱

    Fig. 3.  (a) The scattering efficiency spectrum of the HMM cavity (inset) formed by five layers of silver (Rin = d1 = d2 = 5 nm) and dielectric (s1 = s2 = 4 nm, n1 = 1.8, n2 = 1.45); (b)–(d) the scattering efficiency spectra of HMM cavities same as the structure used in (a), but with different core radii (b), different thinknesses of the silver layers (c) and different thinknesses of the dielectric layers (d); (e), (f) the scattering efficiency spectra of HMM cavities same as the structure used in (a), but with different thinknesses of the second silver layer (d1) and first dielectric layers (s1) (e) and different thinknesses of third silver layer (d2) and second dielectric layers (s2) (f).

    图 5  (a) 5层银 (Rin = d1 = 5 nm, d2 = 10 nm) /介质层 (s1 = 4 nm, s2 = 9 nm, n1 = 1.8, n2 = 1.45) 交替包裹形成的球形HMM腔的散射效率谱, 黑色三角形代表用Comsol软件模拟的结果, 黑色实线为基于米氏散射理论求解析计算的结果; (b) 基于HMM腔波长选择性散射的透明显示器示意图; (c)—(e) HMM腔在偶极共振波长 (c) λ ≈ 425 nm (TM1,3), (d) λ ≈ 544 nm (TM1,2), (e) λ ≈ 680 nm (TM1,3)的二维散射角分布图. 其中红色和黑色曲线分别为散射平面处于和ϕ = 0和ϕ = π/2的情况

    Fig. 5.  (a) The total scattering efficiency spectra based on Comsol software (black triangle) and Mie scattering theory (black line) for the HMM cavity formed by five layers of silver (Rin = d1 = 5 nm, d2 = 10 nm) and dielectric (s1 = 4 nm. s2 = 9 nm, n1 = 1.8, n2 = 1.45); (b) a schematic for a transparent display based on HMM cavities with wavelength-selective scattering; (c)–(e) the 2D scattering angle distribution of the structure at wavelengths of (c) λ ≈ 425 nm (TM1,3), (d) λ ≈ 544 nm (TM1,2), and (e) λ ≈ 680 nm (TM1,3) at dipole resonance. Red and black curves correspond to the case of scattering plane at ϕ = 0 and ϕ = π/2, respectively.

  • [1]

    Hsu C W, Zhen B, Qiu W J, Shapira O, DeLacy B G, Joannopoulos J D, Soljačić M 2014 Nat. Commun. 5 3152Google Scholar

    [2]

    Hedili M K, Freeman M O, Urey H 2012 Proc. SPIE. 8428 84280XGoogle Scholar

    [3]

    Görrn P, Sander M, Meyer J, Kroger M, Becker E, Johannes H, Kowalsky W, Riedl T 2006 Adv. Mater. 18 738Google Scholar

    [4]

    Hedili M K, Freeman M O, Urey H 2013 Appl. Opt. 52 1117Google Scholar

    [5]

    Goldenberg J F, McKechnie T S 1985 Opt. Soc. Am. A 2 2337Google Scholar

    [6]

    Hedili M K, Freeman M O, Urey H 2013 Opt. Express 21 24636Google Scholar

    [7]

    Hong K, Yeom J, Jang C, Hong Jisoo, Lee B 2014 Opt. Lett. 39 127Google Scholar

    [8]

    Soomro S R, Urey H 2016 Opt. Express 24 24232Google Scholar

    [9]

    Kravets V G, Schedin F, Grigorenko A N 2008 Phys. Rev. Lett. 101 087403Google Scholar

    [10]

    王振林 2009 物理学进展 3 287Google Scholar

    Wang Z L 2009 Phys. Pro. 3 287Google Scholar

    [11]

    Smith D R, Schurig D 2003 Phys. Lett. 90 077405Google Scholar

    [12]

    Yang X D, Yao J, Rho J, Yin X B, Zhang X 2012 Nat. Photon. 6 450Google Scholar

    [13]

    Saito K, Tatsuma T 2015 Nanoscale 7 20365Google Scholar

    [14]

    Ye Y Y, Chen T P, Zhen J Y, Xu C, Zhang J, Li H K 2018 Nanoscale 10 2438Google Scholar

    [15]

    Soomro S R, Urey H 2017 Appl. Opt. 56 6108Google Scholar

    [16]

    Shin S, Boyeon H, Zhao Z J, Jeon S H, Jung J Y, Lee J H, Ju B K, Jeonget J H 2018 Sci. Rep. 8 2463Google Scholar

    [17]

    Chu B, Li Y, Qin Y H, Hu T Z, Zhong F C, Zeng F G, Ding P, Shao L, Du Y X, Tian S, Chen Z 2023 Nanotechnology 34 325301Google Scholar

    [18]

    Barnes W L, Alain D, Ebbesen T W 2003 Nature 424 824Google Scholar

    [19]

    Sun J B, Shalaev M I, Litchinitser N M 2015 Nat. Commun. 6 7201Google Scholar

    [20]

    Wan M J, Gu P, Liu W Y, Chen Z, Wang Z L 2017 Appl. Phys. Lett. 110 031103Google Scholar

    [21]

    李艳, 钟发成, 褚博, 邵立, 王俊俏, 万明杰, 杨鹏, 王妍妍, 丁佩, 曾凡光, 于占军, 许坤, 杜银霄, 霍海波, 陈卓, 王振林 2021 中国科学: 物理学 力学 天文学 51 104211Google Scholar

    Li Y, Zhong F C, Chu B, Shao L, Wang J Q, Wan M J, Yang P, Wang Y Y, Ding P, Zeng F G, Yu Z J, Xu K, Du Y X, Huo H B, Chen Z, Wang Z L 2021 Sci. Sin. Phys. Mech. As. 51 104211Google Scholar

    [22]

    Gu P, Chen J, Chen S Y, Yang C, Zhang Z X, Du W, Yan Z D, Tang C J, Chen Z 2021 Photonics Res. 9 829Google Scholar

    [23]

    Gu P, Guo Y H, Chen J, Zhang Z X, Yan Z D, Liu F X, Tang C J, Du W, Chen Z 2021 Nanomaterials 11 2301Google Scholar

    [24]

    Bohren C F, Huffman D R 1983 Absorption and Scattering of Light by Small Particls Optics (New York: Wiley) p475

    [25]

    Johnson P B, Christy R W 1972 Phys. Rev. B 6 4370Google Scholar

    [26]

    Wu C, Salandrino A, Ni X, Zhang X 2014 Phys. Rev. X 4 021015Google Scholar

    [27]

    Knight M W, Halas N J 2008 New J. Phys. 10 105006Google Scholar

    [28]

    Fan X, Zheng W, Singh D J 2014 Light Sci. Appl. 3 179Google Scholar

    [29]

    Prodan E, Radloff C, Halas N J, Nordlander P 2003 Science 302 419Google Scholar

  • [1] 吕宇曦, 王晨, 段添期, 赵彤, 常朋发, 王安帮. 级联声光器件与回音壁模式微腔实现非对称传输. 物理学报, 2024, 73(1): 014101. doi: 10.7498/aps.73.20230653
    [2] 蒋乐昕, 谢振龙, 郭泽虹, 丘伊宁, 陈溢杭. 基于准正则模式的全电介质超材料宽带反射器机理. 物理学报, 2023, 72(20): 204205. doi: 10.7498/aps.72.20230915
    [3] 吴丰, 郭志伟, 吴家驹, 江海涛, 杜桂强. 含双曲超构材料的复合周期结构的带隙调控及应用. 物理学报, 2020, 69(15): 154205. doi: 10.7498/aps.69.20200084
    [4] 王梦宇, 孟令俊, 杨煜, 钟汇凯, 吴涛, 刘彬, 张磊, 伏燕军, 王克逸. 扁长型微瓶腔中的回音壁模式选择及Fano谐振. 物理学报, 2020, 69(23): 234203. doi: 10.7498/aps.69.20200817
    [5] 陈华俊, 方贤文, 陈昌兆, 李洋. 基于双回音壁模式腔光力学系统的光学传播特性和超高分辨率光学质量传感. 物理学报, 2016, 65(19): 194205. doi: 10.7498/aps.65.194205
    [6] 龚健, 张利伟, 陈亮, 乔文涛, 汪舰. 石墨烯基双曲色散特异材料的负折射与体等离子体性质. 物理学报, 2015, 64(6): 067301. doi: 10.7498/aps.64.067301
    [7] 刘李辉, 吕炜煜, 杨超, 麦灿基, 陈德鹏. 部分相干双曲余弦厄米高斯光束在非Kolmogorov大气湍流中的传输特性. 物理学报, 2015, 64(3): 034208. doi: 10.7498/aps.64.034208
    [8] 李丹, 张宝龙, 郭海成. 垂直向列型彩色滤光膜硅覆液晶微显示器的三维光学建模. 物理学报, 2015, 64(14): 140701. doi: 10.7498/aps.64.140701
    [9] 沈晓鹏, 崔铁军, 叶建祥. 基于超材料的微波双波段吸收器. 物理学报, 2012, 61(5): 058101. doi: 10.7498/aps.61.058101
    [10] 张宝龙, 李丹, 戴凤智, 杨世凤, 郭海成. 彩色滤光膜硅覆液晶微显示器的三维光学建模. 物理学报, 2012, 61(4): 040701. doi: 10.7498/aps.61.040701
    [11] 王斌, 杜朝海, 刘濮鲲, 耿志辉, 徐寿喜. W波段边廊模回旋管准光模式变换器的研究与设计. 物理学报, 2010, 59(4): 2512-2518. doi: 10.7498/aps.59.2512
    [12] 李晋红, 杨爱林, 吕百达. 部分相干厄米-双曲正弦-高斯光束通过湍流大气传输的平均光强分布演化和角扩展. 物理学报, 2009, 58(1): 674-683. doi: 10.7498/aps.58.674
    [13] 张远宪, 普小云, 祝昆, 韩德昱, 江楠. 回音壁模式光纤激光器的阈值特性研究. 物理学报, 2009, 58(5): 3179-3184. doi: 10.7498/aps.58.3179
    [14] 普小云, 白然, 向文丽, 杜飞, 江楠. 消逝波激励的双波段光纤回音壁模式激光辐射. 物理学报, 2009, 58(6): 3923-3928. doi: 10.7498/aps.58.3923
    [15] 姚军财, 申 静, 王剑华. 阴极射线管显示器亮度范围内对人眼视觉特性的实验研究. 物理学报, 2008, 57(7): 4034-4041. doi: 10.7498/aps.57.4034
    [16] 杨 睿, 於文华, 鲍 洋, 张远宪, 普小云. 消逝场耦合圆柱形微腔中回音壁模式结构的实验研究. 物理学报, 2008, 57(10): 6412-6418. doi: 10.7498/aps.57.6412
    [17] 马燕萍, 尚学府, 顾智企, 李振华, 王 淼, 徐亚伯. 单壁碳纳米管在场发射显示器中的应用研究. 物理学报, 2007, 56(11): 6701-6704. doi: 10.7498/aps.56.6701
    [18] 林志贤, 郭太良, 胡利勤, 姚 亮, 王晶晶, 杨春建, 张永爱, 郑可炉. 四角状氧化锌纳米材料的场致发射平板显示器. 物理学报, 2006, 55(10): 5531-5534. doi: 10.7498/aps.55.5531
    [19] 王喜庆, 吕百达. 厄米-双曲正弦-高斯光束的M2因子. 物理学报, 2002, 51(2): 247-252. doi: 10.7498/aps.51.247
    [20] 郭建新, 郭海成. 高性能双稳态向列相液晶显示器. 物理学报, 2000, 49(10): 1995-2000. doi: 10.7498/aps.49.1995
计量
  • 文章访问数:  2268
  • PDF下载量:  38
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-08-18
  • 修回日期:  2023-10-01
  • 上网日期:  2023-11-24
  • 刊出日期:  2024-01-20

/

返回文章
返回