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α相三氧化钼中各向异性双曲声子极化激元的耦合性质

钱黎明 孙梦然 郑改革

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α相三氧化钼中各向异性双曲声子极化激元的耦合性质

钱黎明, 孙梦然, 郑改革

Coupling interactions of anisotropic hyperbolic phonon polaritons in double layered orthorhombic molybdenum trioxide

Qian Li-Ming, Sun Meng-Ran, Zheng Gai-Ge
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  • 天然双曲声子极化激元材料-α相三氧化钼(α-MoO3)能够支持高度局域的表面声子极化激元(surface phonon polaritons, SPhPs), 达到在中红外波段对光与物质相互作用的过程进行揭示以及调节的目的. 我们理论上提出并研究了基于Kretschmann结构的单层和多层α-MoO3的面内各向异性表面声子极化激元(ASPhPs). 通过4×4传递矩阵法(TMM)快速准确地求解多层各向异性介质系统中的反射系数, 描述多层系统中激发的SPhPs及色散性质. 结果证实层间耦合可以通过多层膜的堆叠以及层厚来调制. 当入射角度大于全内反射角时, 满足SPhP激发的相位匹配条件. 在40°角范围内, SPhP谐振随着入射角度的增加迅速蓝移, 但是随后色散曲线不再随着入射角的增大而移动. 间隙层的增大会还会致使法布里-珀罗(FP)共振模式的激发. 层状异质结构中的ASPhPs是当今纳米光子技术的重要组成部分, 我们的研究有助于进一步优化和设计基于极化双曲材料的可控光电器件.
    The natural hyperbolic phonon polariton material-orthorhombic molybdenum trioxide (α-MoO3) has recently attracted much interest , due to the associated ultra-confinement of light and enhanced light-matter interactions. We theoretically propose and study the in-plane anisotropic phonon polaritons (APhPs) in the Kretschmann structure with monolayer and dual layers α-MoO3. The excitation of phonon polaritons and the corresponding dispersion properties in this multilayer system are studied by using a generalized 4×4 transfer matrix method (TMM). The frequency dispersions with geometrical parameters are also discussed in detail. The results confirm that the interlayer coupling can be modulated by stacking the multilayer films and regulating the thickness of each layer. More interestingly, when the distance between double α-MoO3 layers is much smaller than the propagation length of PhPs, a strong coupling phenomenon occurs, and the photon tunneling probability and intensity can be greatly improved. When the incident angle is greater than the total internal reflection angle, the phase matching condition for SPhP excitation can be satisfied. Within the 40° incident angle, the SPhP blue-shifts rapidly with the increase of incident angle. But then the dispersion curve no longer changes with increase of incidence angle. The enlargement of the interstitial layer can also lead the Fabry-Perot (FP) resonance mode to be excited. The APhP in layered heterostructure is an important part of today's nanophotonic technology, our study can help optimize and design tunable optoelectronic devices based on hyperbolic materials.
      通信作者: 郑改革, 002382@nuist.edu.cn
    • 基金项目: 江苏省自然科学基金(批准号: BK20191396)资助的课题.
      Corresponding author: Zheng Gai-Ge, 002382@nuist.edu.cn
    • Funds: Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20191396).
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    管福鑫, 董少华, 何琼, 肖诗逸, 孙树林, 周磊 2020 物理学报 69 157804Google Scholar

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    Zhu X P, Zhang S, Shi H M, Chen Z Q, Quan J, Xue S W, Zhang J, Duan H G 2019 Acta Phys. Sin. 68 247301Google Scholar

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    束方洲, 范仁浩, 王嘉楠, 彭茹雯, 王牧 2019 物理学报 68 147303Google Scholar

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    Dai S, Quan J, Hu G, Qiu C, Tao T, Li X, Alu A 2019 Nano Lett. 19 1009Google Scholar

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    Zheng Z, Xu N, Oscurato S L, Tamagnone M, Sun F, Jiang Y, Ke Y, Chen J, Huang W, Wilson W L, Ambrosio A, Deng S, Chen H 2019 Sci. Adv. 24 eaav8690

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    Larciprete M C, Dereshgi S A, Centini M, Aydin K 2022 Opt. Express 30 12788Google Scholar

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    Ni G, McLeod A S, Sun Z, Matson J R, Lo C F B, Rhodes D A, Ruta F L, Moore S L, Vitalone R A, Cusco R, Artús L, Xiong L, Dean C R, Hone A J, Millis J C, Fogler M M, Edgar J H, Caldwell J D, Basov D N 2021 Nano Lett. 21 5767Google Scholar

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    Ma W, Hu G, Hu D, Chen R, Sun T, Zhang X, Dai Q, Zeng Y, Alù A, Qiu C W, Li P 2021 Nature 596 362Google Scholar

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    Pavlidis G, Schwartz J J, Matson J, Folland T, Liu S, Edgar J H, Caldwell J D, Centrone A 2021 APL Mater. 9 091109Google Scholar

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    Gong Y, Zhao Y, Zhou Z, Li D, Mao H, Bao Q, Zhang Y, Wang G 2022 Adv. Opt. Mater. 10 2200038Google Scholar

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    Hajian H, Rukhlenko I D, Ercaglar V, Hanson G, Ozbay E 2022 Appl. Phys. Lett. 120 112204Google Scholar

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    Zhang Q, Ou Q, Hu G, Liu J, Dai Z, Fuhrer M S, Bao Q, Qiu C W 2021 Nano Lett. 21 3112Google Scholar

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    Passler N C, Paarmann A 2017 J. Opt. Soc. Am. B:Opt. Phys. 34 2128Google Scholar

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    Xia S, Zhai X, Wang L, Xiang Y, Wen S 2022 Phys. Rev. B 106 075401Google Scholar

  • 图 1  研究涉及的材料介电函数曲线 (a), (b) 对应通过(1)式—(4)式计算得到的介电函数的实部和虚部

    Fig. 1.  The dielectric function curves of the materials involved in the study: (a), (b) The real part and imaginary part of the dielectric function calculated by Eq. (1)–Eq.(4), respectively.

    图 2  (a) 单一α-MoO3层色散曲线的研究模型; (b)—(d) 计算得到的面内波矢量和光子能量函数的反射光谱. 亮线代表不同方向上SPhP的色散曲线

    Fig. 2.  (a) Model of the dispersion curve of a single α-MoO3 layer; (b)–(d) the calculated reflectance spectra as a function of in-plane wave vector and photon energy. Bright lines represent the dispersion curves of SPhP in different directions.

    图 3  由厚度为1 μm的α-MoO3组成的Kretschmann结构对应的反射谱线

    Fig. 3.  Reflection spectral corresponding to the Kretschmann structure composed of α-MoO3 with a thickness of 1 μm.

    图 4  双层α-MoO3耦合的多层膜模型

    Fig. 4.  Stacked film model of double-layer α-MoO3 for coupling research.

    图 5  计算得到的在不同t条件下反射率随入射角度的变化图谱 (a) t = 20 nm; (b) t = 100 nm; (c) t = 500 nm; (d) t = 1000 nm

    Fig. 5.  Calculated spectrum of reflectance variation with incident angle under different conditions: (a) t = 20 nm; (b) t = 100 nm; (c) t = 500 nm; (d) t = 1000 nm.

    图 6  (a)—(c) 频率为820 cm–1t = 100 nm, t = 500 nm和t = 1000 nm时数值计算得到的等频曲线; (d)—(f) 频率为900 cm–1t = 100 nm, t = 500 nm和t = 1000 nm时数值计算得到的等频曲线; (g)—(i) 频率为1000 cm–1t = 100 nm, t = 500 nm和t = 1000 nm时数值计算得到的等频曲线

    Fig. 6.  (a)–(c) The iso-frequency curves obtained by numerical calculation with t = 100 nm, t = 500 nm and t = 1000 nm at a frequency of 820 cm–1; (d)–(f) the iso-frequency curves obtained by numerical calculation at t = 100 nm, t = 500 nm and t = 1000 nm at a frequency of 900 cm–1; (g)–(i) the iso-frequency curves obtained by numerical calculation at 1000 cm–1 with t = 100 nm, t = 500 nm and t = 1000 nm.

    图 7  (a) 在Kretschmann结构中激发的 SPhP 反射谱线, t = 1000 nm, θ = 50°; (b) 多层界面处的|Ex|强度分布

    Fig. 7.  SPhP reflection spectral excited in the Kretschmann structure with t = 1000 nm and θ = 50°; (b) |Ex| intensity distribution within the multilayered structure.

    表 1  α-MoO3的介电函数的洛伦兹模型对应的参数

    Table 1.  The parameters corresponding to the Lorentzian model of the dielectric function of α-MoO3.

    主轴模式序数${{\varepsilon _x^\infty }} $ωTO/cm–1ωLO/cm–1γ/cm–1
    x15.86506.7534.349.1
    x2824.19636
    x3998.7999.20.35
    ${{\varepsilon _y^\infty }} $ωTO/cm–1ωLO/cm–1γ/cm–1
    y16.59544.6850.19.5
    ${{\varepsilon _z^\infty }}$ωTO/cm–1ωLO/cm–1γ/cm–1
    z14.474445081.5
    z2956.71006.91.5
    下载: 导出CSV
  • [1]

    管福鑫, 董少华, 何琼, 肖诗逸, 孙树林, 周磊 2020 物理学报 69 157804Google Scholar

    Guan F X, Dong S H, He Q, Xiao S Y, Sun S L, Zhou L 2020 Acta Phys. Sin. 69 157804Google Scholar

    [2]

    朱旭鹏, 张轼, 石惠民, 陈智全, 全军, 薛书文, 张军, 段辉高 2019 物理学报 68 247301Google Scholar

    Zhu X P, Zhang S, Shi H M, Chen Z Q, Quan J, Xue S W, Zhang J, Duan H G 2019 Acta Phys. Sin. 68 247301Google Scholar

    [3]

    束方洲, 范仁浩, 王嘉楠, 彭茹雯, 王牧 2019 物理学报 68 147303Google Scholar

    Shu F Z, Fan R H, Wang J N, Peng R W, Wang M 2019 Acta Phys. Sin. 68 147303Google Scholar

    [4]

    马赛群, 邓奥林, 吕博赛, 胡成, 史志文 2022 物理学报 71 127104Google Scholar

    Ma S Q, Deng A L, Lü B S, Hu C, Shi Z W 2022 Acta Phys. Sin. 71 127104Google Scholar

    [5]

    Jacob Z 2014 Nat. Mater. 13 1081Google Scholar

    [6]

    Chen M, Lin X, Dinh T H, Zheng Z, Shen J, Ma Q, Chen H, Jarillo-Herrero P, Dai S 2020 Nat. Mater. 19 1307Google Scholar

    [7]

    Wu X, Fu C J 2021 Int. J. Heat Mass Transfer 168 120908Google Scholar

    [8]

    Feng K, Streyer W, Zhong Y, Hoffman A J, Wasserman D 2015 Opt. Express 23 A1418Google Scholar

    [9]

    Passler N C, Ni X, Hu G, Matson J R, Carini G, Wolf M, Schubert M, Alu A, Caldwell J D, Thomas G Folland T G, Paarmann A 2022 Nature 602 595Google Scholar

    [10]

    Dai S, Quan J, Hu G, Qiu C, Tao T, Li X, Alu A 2019 Nano Lett. 19 1009Google Scholar

    [11]

    Zhao B, Zhang Z M 2017 Opt. Express 25 7791Google Scholar

    [12]

    Zheng Z, Xu N, Oscurato S L, Tamagnone M, Sun F, Jiang Y, Ke Y, Chen J, Huang W, Wilson W L, Ambrosio A, Deng S, Chen H 2019 Sci. Adv. 24 eaav8690

    [13]

    Larciprete M C, Dereshgi S A, Centini M, Aydin K 2022 Opt. Express 30 12788Google Scholar

    [14]

    Ni G, McLeod A S, Sun Z, Matson J R, Lo C F B, Rhodes D A, Ruta F L, Moore S L, Vitalone R A, Cusco R, Artús L, Xiong L, Dean C R, Hone A J, Millis J C, Fogler M M, Edgar J H, Caldwell J D, Basov D N 2021 Nano Lett. 21 5767Google Scholar

    [15]

    Ma W, Hu G, Hu D, Chen R, Sun T, Zhang X, Dai Q, Zeng Y, Alù A, Qiu C W, Li P 2021 Nature 596 362Google Scholar

    [16]

    Pavlidis G, Schwartz J J, Matson J, Folland T, Liu S, Edgar J H, Caldwell J D, Centrone A 2021 APL Mater. 9 091109Google Scholar

    [17]

    Chen M, Sanders S, Shen J, Li J, Harris E, Chen C, Ma Q, Edgar J H, Manjavacas A, Dai S 2022 Adv Opt. Mater. 10 2102723Google Scholar

    [18]

    Toyin O R, Ge W X, Gao L 2021 Chin. Phys. Lett. 38 016801Google Scholar

    [19]

    魏晨崴, 曹暾 2021 物理学报 70 048701Google Scholar

    Wei C W, Cao T 2021 Acta Phys. Sin. 70 048701Google Scholar

    [20]

    Chen M, Lin X, Dinh T, Zheng Z, Shen J, Ma Q, Chen H, Jarillo-Herrero P, Dai S 2020 Nat. Mater. 19 1372Google Scholar

    [21]

    Gong Y, Zhao Y, Zhou Z, Li D, Mao H, Bao Q, Zhang Y, Wang G 2022 Adv. Opt. Mater. 10 2200038Google Scholar

    [22]

    Hajian H, Rukhlenko I D, Ercaglar V, Hanson G, Ozbay E 2022 Appl. Phys. Lett. 120 112204Google Scholar

    [23]

    Zhang Q, Ou Q, Hu G, Liu J, Dai Z, Fuhrer M S, Bao Q, Qiu C W 2021 Nano Lett. 21 3112Google Scholar

    [24]

    Passler N C, Paarmann A 2017 J. Opt. Soc. Am. B:Opt. Phys. 34 2128Google Scholar

    [25]

    Wu X H, Fu C J, Zhang Z M 2020 J. Heat Transfer 142 072802Google Scholar

    [26]

    Passler N C, Jeannin M, Paarmann A 2020 Phys. Rev. B 101 165425Google Scholar

    [27]

    Li H H 1980 J. Phys. Chem. Ref. Data 9 161Google Scholar

    [28]

    Xia S, Zhai X, Wang L, Xiang Y, Wen S 2022 Phys. Rev. B 106 075401Google Scholar

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出版历程
  • 收稿日期:  2022-11-09
  • 修回日期:  2023-01-12
  • 上网日期:  2023-02-04
  • 刊出日期:  2023-04-05

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