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极性电介质支持的表面声子极化激元(surface phonon polaritons, SPhP)在红外波段增强光与物质相互作用过程中引起了广泛的关注, 然而存在光场操控有限、调制波段限定在剩余射线带区域的问题. 提出了一种由双轴范德瓦耳斯材料(α-MoO3)和外尔半金属组成的异质结构, 用来研究各向异性SPhP的主动可调谐性. 在横磁波入射条件下, 通过4×4传递矩阵法准确地求解异质系统中的反射系数以及场分布, 描述各向异性SPhP的色散性质. 研究结果表明: 模式杂化和色散操控可以通过方位角度及α-MoO3的厚度大小实现. 更重要的是外尔半金属中费米能级的大小能够启用动态色散曲线调节, 而费米能级依赖于外界温度的变化. 因此研究有助于进一步优化和设计基于范德瓦耳斯材料的可控光电器件, 在红外热辐射和生物传感等方面具有较好的应用前景.Surface phonon polaritons (SPhP) as an alternative constituent for mid-infrared (MIR) nanophotonic applications have attracted extensive attention and they maybe solve the intrinsic loss problem of plasmonics. SPhP arise in polar dielectrics due to IR-active phonon resonances, leading to negative permittivity within the Reststrahlen band. Although SPhP have great potential in enhancing the interaction between light and matter in the infrared region, it is still limited to enhance optical fields and fixed resonance band because of the existing Reststrahlen band. Moreover, active manipulating of phonon polaritons in MIR range remains elusive. The significant research progress of natural van der Waals (vdW) crystal and heterostructures have been made, which are characterized by an anisotropic polaritonic response, leading to elliptical, hyperbolic, or biaxial polaritonic dispersions. Among these structures, SPhP with hyperbolicity in α-MoO3 are of particular interest, due to not only the strong field confinement, low losses, and long lifetimes, but also the natural in-plane anisotropic dispersion. A heterostructure composed of a biaxial vdW material (α-MoO3) and a Weyl semimetal (WSM) is proposed to study the active tunability of anisotropic SPhP. The control of polaritons can show more degrees of freedom, which has not yet been addressed. Under the incident condition of transverse magnetic incident wave, the reflection coefficient and field distribution in the heterogeneous system are accurately solved by the 4×4 transfer matrix method, and the dispersion properties of anisotropic SPhP are described in detail. Variation of dispersion spectrum with azimuthal angle and α-MoO3 thickness is presented. The research results indicate that mode hybridization and dispersion manipulation can be realized by controlling the azimuth angle and the thickness of α-MoO3. More importantly, the Fermi level of WSM enable the adjustment of dynamic dispersion curve, which depends on the change of external temperature. Isofrequency curves of hybridized SPhP at different Fermi levels are also demonstrated. By chemically changing the Femi level of α-MoO3, the topology of polariton isofrequency surfaces transforms from open shape to closed shape as a result of polariton hybridization. Therefore, our research is helpful in further optimizing and designing active optoelectronic devices based on vdW materials, which have good application prospects in infrared heat radiation and biosensing.
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Keywords:
- Weyl semimetals /
- surface phonon polaritons /
- anisotropy /
- dispersion relation
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图 1 (a) α-MoO3/WSM异质结模型示意图; (b) WSM介电常数张量分量
Fig. 1. (a) Schematic diagram of α-MoO3/WSM heterostructure mode; (b) different parts of permittivity tensor components of WSM.
图 2 不同传播角条件下的色散图谱(α-MoO3的厚度固定在d = 50 nm) (a) φ = 0°; (b) φ = 45°; (c) φ = 90° . k0和kx分别代表真空中和x方向的波矢
Fig. 2. Dispersion spectra under different propagation angle conditions (Thickness of α-MoO3 is fixed at d = 50 nm): (a) φ = 0°; (b) φ = 45°; (c) φ = 90° . k0 and kx represent wave vectors in the vacuum and x direction, respectively
图 3 色散图谱随方位角和α-MoO3厚度的变化 (a) 50 nm; (b) 500 nm; (c) 1000 nm; (d) 2000 nm
Fig. 3. Variation of dispersion spectra with azimuthal angle and α-MoO3 thickness: (a) 50 nm; (b) 500 nm; (c) 1000 nm; (d) 2000 nm.
图 5 不同费米能级下色散图谱随方位角和频率的变化 (a) EF = 0.2 eV; (b) EF = 0.3 eV; (c) EF = 0. 35 eV; (d) EF = 0.4 eV
Fig. 5. Variation of dispersion spectra with azimuthal angle and frequency with different Femi levels: (a) EF = 0.2 eV; (b) EF = 0.3 eV; (c) EF = 0. 35 eV; (d) EF = 0.4 eV.
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[1] 段嘉华, 陈佳宁 2019 68 110701
Google Scholar
Duan J H, Chen J N 2019 Acta Phys. Sin. 68 110701
Google Scholar
[2] 郑嘉璐, 戴志高, 胡光维, 欧清东, 张津瑞, 甘雪涛, 仇成伟, 鲍桥梁 2021 中国光学 14 812
Google Scholar
Zheng J L, Dai Z G, Hu G W, Ou Q D, Zhang J R, Gan X T, Qiu C W, Bao Q L 2021 Chin. Opt. 14 812
Google Scholar
[3] 徐琨淇, 胡成, 沈沛约, 马赛群, 周先亮, 梁齐, 史志文 2023 72 027102
Google Scholar
Xu K Q, Hu C, Shen P Y, Ma S Q, Zhou X L, Liang Q, Shi Z W 2023 Acta Phys. Sin. 72 027102
Google Scholar
[4] Hu G W, Ou Q D, Si G Y, Wu Y J, Wu J, Dai Z G, Krasnok A, Mazor Y, Zhang Q, Bao Q L, Qiu C W, Alù A 2020 Nature 582 209
Google Scholar
[5] Chaudhary K, Tamagnone M, Rezaee M, Bediako D K, Ambrosio A, Kim P, Capasso F 2019 Sci. Adv. 5 eaau7171
Google Scholar
[6] Álvarez-Pérez G, González-Morán A, Capote-Robayna N, Voronin K V, Duan J H, Volkov V S, Alonso-González P, Nikitin A Y 2022 ACS Photonics 9 383
Google Scholar
[7] Duan J, Álvarez-Pérez G, Voronin K V, Prieto I, Taboada-Gutiérrez J, Volkov V S, Martín-Sánchez J, Nikitin A Y, Alonso-González P 2021 Sci. Adv. 7 eabf2690
Google Scholar
[8] Hajian H, Rukhlenko I D, Hanson G W, Low T, Butun B, Ozbay E 2020 Nanophotonics 9 3909
Google Scholar
[9] Lee I H, He M Z, Zhang X, Luo Y J, Liu S, Edgar J H, Wang K, Avouris P, Low T, Caldwell J D, Oh S H 2020 Nat. Commun. 11 3649
Google Scholar
[10] Menabde S G, Jahng J, Boroviks S, Ahn J, Heiden J T, Hwang D K, Lee E S, Mortensen N A, Jang M S 2022 Adv. Optical Mater. 10 2201492
Google Scholar
[11] Erçağlar V, Hajian H, Rukhlenko I D, Ozbay E 2022 Appl. Phys. Lett. 121 182201
Google Scholar
[12] Schwartz J J, Le Son T, Krylyuk S, Richter C A, Davydov A V, Centrone A 2021 Nanophotonics 10 1517
Google Scholar
[13] Larciprete M C, Dereshgi S A, Centini M, Aydin K 2022 Opt. Express 30 12788
Google Scholar
[14] Gong Y, Zhao Y, Zhou Z, Li D, Mao H, Bao Q, Zhang Y, Wang G 2022 Adv. Opt. Mater. 10 2200038
Google Scholar
[15] Zheng Z, Chen J, Wang Y, Wang X, Chen X, Liu P, Xu J, Xie W, Chen H, Deng S, Xu N 2018 Adv. Mater. 30 1705318
Google Scholar
[16] Zhang Q, Zhen Z, Yang Y F, Gan G W, Jariwala D, Cui X D 2019 Opt. Express 27 18585
Google Scholar
[17] Huang W, Sun F, Zheng Z, Folland T G, Chen X, Liao H, Xu N, Caldwell J D, Chen H, Deng S 2021 Adv. Sci. 8 2004872
Google Scholar
[18] Hu G, Shen J, Qiu C W, Alù A, Dai S 2020 Adv. Optical Mater. 8 1901393
Google Scholar
[19] Dai S, Zhang J, MaQ, Kittiwatanakul S, McLeod A, Chen X, Corder S N G, Watanabe K, Taniguchi T, Lu J, Dai Q, Jarillo-Herrero P, Liu M, Basov D N 2019 Adv. Mater. 31 1900251
Google Scholar
[20] Passler N C, Heßler A, Wuttig M, Taubner T, Paarmann A 2020 Adv. Optical Mater. 8 1901056
Google Scholar
[21] Zhang Q, Ou Q, Hu G, Liu J, Dai Z, Fuhrer M S, Bao Q, Qiu C W 2021 Nano Lett. 21 3112
Google Scholar
[22] Hofmann J, Das S S 2016 Phys. Rev. B 93 241402
Google Scholar
[23] Zhao B, Guo C, Garcia C A C, Narang P, Fan S 2020 Nano Lett. 20 1923
Google Scholar
[24] Kotov O V, Lozovik Y E 2018 Phys. Rev. B 98 195446
Google Scholar
[25] Tamaya T, Kato T, Tsuchikawa K, Konabe S, Kawabata S 2019 J. Phys. Condens. Matter 31 305001
Google Scholar
[26] Schubert M 1996 Phys. Rev. B 53 4265
Google Scholar
[27] Wu X H, Fu C J, Zhang Z M 2019 Int. J. Heat Mass Tran. 135 1207
Google Scholar
[28] Hajian H, Ghobadi A, Dereshgi S A, Butun B, Ozbay E 2017 J. Opt. Soc. Am. B 34 D29
Google Scholar
[29] Fandan R, Pedrós J, Schiefele J, Boscá A, Martínez J, Calle F 2018 J. Phys. D: Appl. Phys. 51 204004
Google Scholar
[30] Wang Y, Khandekar C, Gao X, Li T, Jiao D, Jacob Z 2021 Opt. Mater. Express 11 3880
Google Scholar
[31] Wu J, Wu B Y, Wang Z M, Wu X H 2022 Int. J. Therm. Sci. 181 107788
Google Scholar
[32] Ashby P E C, Carbotte J P 2014 Phys. Rev. B 89 245121
Google Scholar
[33] Wu X H 2020 J. Heat Transfer 142 072802
Google Scholar
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