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鉴于极化激元对介电环境异常敏感的特性, 本文中提出了双曲材料六方氮化硼(hBN)和石墨烯与相变材料二氧化钒(VO2)组成的异质结构, 用来研究hBN声子极化激元(PhPs)的主动可调谐性. 研究结果表明, 通过控制hBN/VO2异质结构中VO2相变可实现对hBN PhPs的主动调谐, 获得主动可调谐的自发发射(SE)率. 当在hBN/VO2异质结构中添加石墨烯时, 会在hBN双曲线带内耦合产生双曲等离子体-声子极化激元(HPPPs), 而在双曲线带外产生表面等离子体-声子极化激元(SPPPs), 通过控制VO2相态和调节石墨烯化学势亦可实现石墨烯/hBN/VO2异质结构的耦合色散及SE率的主动调谐. 该研究为使用诸如相变材料和石墨烯等功能材料调谐各向异性光学材料与光的相互作用机制提供了理论指导.
Active tunability of phonon dispersion and spontaneous emission (SE) are still open problems due to their exciting potential applications. In view of the fact that polaritons are very sensitive to the dielectric environment, in this study, with the help of the differences in optical property between the phase change material vanadium dioxide (VO2) during the phase transition from the insulating state to metallic state and the tunable surface plasmon polaritons (SPPs) in graphene, a heterostructure composed of hyperbolic material hexagonal boron nitride (hBN) and graphene and VO2 is proposed to investigate the active tunability of hBN phonon polaritons (PhPs). In order to illustrate the underlying physical mechanism of the above heterostructures, the dispersion distributions of the above heterostructures are calculated and represented by the imaginary part of the p-polarized Fresnel reflection coefficient of the heterostructure, meanwhile the dispersion relation of the hBN/VO2 heterostructure in hyperbolic region is verified by the quasi-static approximation method. Results indicate that the active tunability of hBN PhPs inside type-I and type-II hyperbolic bands can be achieved by controlling VO2 phase transition in hBN/VO2 heterostructure. The PhP dispersion change of the hBN/VO2 heterostructure is mainly caused by the change of the VO2 dielectric function when VO2 substrate changes from the insulating state into metallic state, which affects the total Fresnel reflection coefficient of the heterostructure, finally resulting in the PhP dispersion change of hBN/VO2 heterostructure. When graphene is introduced into the hBN/VO2 heterostructure, coupled hyperbolic plasmon-phonon polaritons (HPPPs) are obtained within type-I and type-II hyperbolic band of hBN, while the surface plasmon-phonon polaritons (SPPPs) are generated outside its hyperbolic bands. Moreover, comparative analysis of SE rates is presented for a quantum emitter positioned with the hBN/VO2 and graphene/hBN/VO2 heterostructure, revealing that the SE rates of these heterostructures can be modulated by the passive means including changing the hBN thickness and distance between the dipole emitter and the proposed heterostructure, and also by the active means including tuning VO2 phase states and graphene chemical potential without changing structural configurations. This study provides a theoretical guidance in realizing active tunability of both phonon dispersion and SE rate of the natural or artificial anisotropic optical materials by using functional materials including phase change materials and graphene. -
Keywords:
- anisotropic optical materials /
- phase change material /
- graphene /
- phonon polaritons /
- spontaneous emission rate
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图 1 (a) hBN/VO2异质结构示意图, t代表hBN的厚度; (b) VO2的折射系数n和消光系数k[15]; (c) hBN介电常数张量分量的实部
Fig. 1. (a) Schematic diagram of the hBN/VO2 heterostructure, t represents the hBN thickness; (b) the refractive index n and extinction coefficient k of VO2[15]; (c) real parts of the permittivity tensor components of hBN.
图 2 (a) hBN/VO2(I)和 (b) hBN/VO2(M)异质结构的PhPs色散分布, 其中白色圆圈代表利用(4)式计算得到的色散分支; hBN/VO2异质结构在 (c) kx/k0 = 20和 (d) kx/k0 = 30的PhPs色散曲线
Fig. 2. (a) Hybrid PhPs dispersion of hBN/VO2(I) and (b) hBN/VO2(M) heterostructures, the white circles represent the dispersion branches calculated by Eq. (4); Dispersion curves of hBN/VO2 heterostructures at (c) kx/k0 = 20 and (d) kx/k0 = 30.
图 3 (a)—(c)/(e)—(g) 石墨烯/hBN/VO2异质结构的耦合色散随石墨烯化学势μg的变化关系; (d) 石墨烯/hBN/VO2(I)异质结构在kx/k0 =20的色散曲线随石墨烯化学势μg的变化规律; (h) 石墨烯/hBN/VO2异质结构在kx/k0 = 20的色散曲线
Fig. 3. (a)–(c)/(e)–(g) Coupling dispersions of graphene/hBN/VO2 heterostructures as function of graphene chemical potentials μg; (d) dispersion curves of graphene/hBN/VO2(I) heterostructures at kx/k0 = 20 as function of graphene chemical potential μg; (h) dispersion curves of graphene/hBN/VO2 heterostructures at kx/k0 = 20.
图 4 hBN/VO2异质结构在 (a) I和 (b) II型双曲线带内的SE率随hBN厚度t的变化规律
Fig. 4. SE rates of hBN/VO2 heterostructures within (a) type-I and (b) type-II hyperbolic bands as function of hBN thickness t.
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[1] Poddubny A, Iorsh I, Belov P, Kivshar Y 2013 Nat. Photonics 7 948
Google Scholar
[2] Drachev V P, Podolskiy V A, Kildishev A V 2013 Opt. Express 21 15048
Google Scholar
[3] Wu X, McEleney C A, González-Jiménez M, Macêdo R 2019 Optica 6 1478
Google Scholar
[4] Zhou K, Lu L, Li B, Cheng Q 2021 J. Appl. Phys. 130 093102
Google Scholar
[5] Zhou C L, Zhang Y, Torbatian Z, Novko D, Antezza M 2022 Phys. Rev. Mater. 6 075201
Google Scholar
[6] 刘伟, 黄勇, 吴会海 2017 工程热物理学报 38 2665
Liu W, Huang Y, Wu H H 2017 J. Eng. Thermophys. 38 2665
[7] Jiang H, Choudhury S, Kudyshev Z A, Wang D 2019 Photonics Res. 7 815
Google Scholar
[8] Zhang Q, Hu G, Ma W, Li P, Krasnok A, Hillenbrand R, Alù A 2021 Nature 597 187
Google Scholar
[9] Dai S, Zhang J, Ma Q, Kittiwatanakul S, McLeod A, Chen, X 2019 Adv. Mater. 31 1900251
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[10] Fei Z, Rodin A, Andreev G O 2012 Nature 487 82
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[11] Ju L, Geng B, Horng J 2011 Nat. Nanotechnol. 6 630
Google Scholar
[12] Zhou K, Cheng Q, Lu L 2020 Appl. Opt. 59 595
Google Scholar
[13] 杨冲, 韩伟华, 陈俊东, 张晓迪, 郭仰岩 2020 微纳电子技术 57 341
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Yang C, Han W H, Chen J D, Zhang X D, Guo Y Y 2020 Micro-Nano Electron. Technol. 57 341
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[14] 罗明海, 徐马记, 黄其伟, 李派, 何云斌 2016 物理学报 65 047201
Google Scholar
Luo M H, Xu M J, Huang Q W, Li P, He Y B 2016 Acta Phys. Sin. 65 047201
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[15] Benkahoul M, Chaker M, Margot J 2011 Sol. Energy Mater. Sol. Cells. 95 3504
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[16] 赵海鹏, 章新源, 何云斌, 豆书亮, 李垚, 李孝峰, 詹耀辉 2021 光学学报 41 1523001
Zhao H P, Z X Y, He Y B, Dou S L, Li Y, Li X F, Zhan Y H 2021 Acta Opt. Sin. 41 1523001 (in Chinese)
[17] Soltani M, Chaker M, Haddad E 2004 Appl. Phys. Lett. 85 1958
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[18] Lee S, Hippalgaonkar K, Yang F 2017 Science 355 371
Google Scholar
[19] Tang K, Dong K, Li J 2021 Science 374 1504
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[20] 黄雅琴, 李毅, 李政鹏, 裴江恒, 田蓉, 刘进, 周建忠, 方宝英, 王晓华, 肖寒 2019 光学学报 39 0316001
Google Scholar
Huang Y Q, Li Y, Li Z P, Pei J H, Tian R, Liu J, Zhou J Z, Fang B Y, Wang X H, Xiao H 2019 Acta Optics Sinica 39 0316001
Google Scholar
[21] Mlyuka N, Niklasson G A, Granqvist C-G 2009 Sol. Energy Mater. Sol. Cells. 93 1685
Google Scholar
[22] Kumar A, Low T, Fung K H 2015 Nano Lett. 15 3172
Google Scholar
[23] Zhou K, Cheng Q, Lu L 2020 Opt. Express 28 1647
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[24] Zhou K, Cheng Q, Song J 2019 Opt. Lett. 44 3430
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Google Scholar
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Google Scholar
[27] Álvarez‐Pérez G, Folland T G, Errea I 2020 Adv. Mater. 32 1908176
Google Scholar
[28] Zhao B, Guizal B, Zhang Z M 2017 Phys. Rev. B 95 246437
Google Scholar
[29] Purcell E M, Torrey H C, Pound R V 1946 Phys. Rev. 69 37
Google Scholar
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Google Scholar
Zhao Y S, Song J F, Han W H, Li X M, Du G T, Gao D S 1999 Acta Optics Sinica. 19 452
Google Scholar
[31] Cortes C, Newman W, Molesky S 2012 J. Opt. 14 063001
Google Scholar
[32] Krishnamoorthy H N, Jacob Z, Narimanov E 2012 Science 336 205
Google Scholar
[33] Zhou K, Zhong X, Cheng Q, Wu X 2022 Opt. Mater. 131 112623
Google Scholar
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