-
古斯-汉欣（GH）位移作为一种特殊的光学现象，在高灵敏传感、光开关及纳米光子器件等领域具有广泛应用前景。本文构建了一种黑磷烯-硅介质交替堆叠的层状结构，采用转移矩阵法研究了光电导率、偏振模式、周期层数以及外加电压对该结构在近红外波段的反射特性与GH位移的影响。研究表明，黑磷烯的引入使横磁（TM）波在布儒斯特角处的反射相位由阶跃突变转变为连续变化，从而产生高达40倍波长的GH位移；横电（TE）波在掠入射条件下亦可实现数倍波长的GH位移；通过增加周期层数和施加外电压可有效增强GH位移并调节其角度响应。该结构对末端介质折射率变化表现出高达105 λ/RIU量级灵敏度，在近红外可调谐光电器件与高灵敏度光学传感器方面展现出良好的应用潜力。As a unique optical phenomenon, the Goos–Hänchen (GH) shift has attracted considerable interest due to its broad potential in high-sensitivity sensing, optical switching, and nanoscale photonic devices. In this work, a multilayer heterostructure constructed by alternating layers of black phosphorene (BP) and silicon (Si) is designed, and its GH shifts are systematically investigated, aiming to achieve large-amplitude, electrically tunable GH shifts in the near-infrared region. Furthermore, we elaborate on the underlying phase-modulation mechanisms and the sensing performance of the proposed structure. Based on the transfer matrix method and the optical conductivity of BP calculated via the Kubo formalism, we comprehensively examine the cooperative effects of polarized modes, structural periodicity, incident optical energy, and external voltage on the evolution of the reflection phase and the consequent GH displacement. The results indicate that the incorporation of BP, through the introduction of complex surface conductivity, substantially modifies the phase response of transverse magnetic (TM) waves near the conventional Brewster angle, converting the original π-phase jump into a continuous and differentiable phase transition. This effect enables a GH shift as large as 40λ even in a single-period structure. Although transverse electric (TE) waves do not exhibit Brewster-angle behavior, several-wavelength-scale GH shifts can still be achieved under near-grazing incidence due to Fabry–Pérot interference. Further analysis reveals that increasing the number of (BP–Si) periods steepens the slope of the reflection phase, thereby enhancing the GH shift of the TM wave from 40λ to 128λ in a fourperiod structure at the incident optical energy of 1.52 eV. In addition, the application of an external voltage modulates the energy bandgap and optical conductivity of BP, providing dual control over the magnitude and angular position of the GH shift. For example, under an external voltage of 0.5 eV, the maximum GH shift of the TM wave in a single-period structure at an incident optical energy of 1.4 eV increases from 184λ to 586λ. The structure also exhibits an ultrahigh refractive index sensitivity exceeding 105λ/RIU toward variations in the refractive index of the terminal medium, with further enhancement under electrical bias. These findings reveal the mechanism through which two-dimensional materials induce phase continuity and enhanced GH shifts, while demonstrating the strong potential of BP–Si multilayers for the development of tunable near-infrared photonic components and high-sensitivity optical sensing platforms.
-
Keywords:
- Black phosphorene /
- Goos-Hänchen shift /
- Transfer matrix /
- Optical sensing
-
[1] . Goos F, Hänchen H 1947 Ann. Phys. (Berlin) 436 333
[2] . Artmann K 1948 Ann. Phys. (Berlin) 437 87
[3] . Wu F, Wu J J, Guo Z W, Jiang H T, Sun Y, Li Y H, Ren J, Ren J, Chen H 2019 Phys. Rev. Appl. 12 014028
[4] . Wu F, Luo M, Wu J J, Fan C F, Qi X, Jian Y R, Liu D J, Xiao S Y, Chen G Y, Jiang H T, Sun Y, Chen H 2021 Phys. Rev A 104 023518
[5] . Mao M Y, Zhang T, Li F Y, Ma Y, Zhang H F 2021 IEEE J. Quantum Electron. 57 1
[6] . Broe J, Keller O 2002 J. Opt. Soc. Am. A 19 1212
[7] . Yasumoto K, Ōishi Y 1983 Appl. Phys. 54 2170
[8] . Horowitz B R, Tamir T 1971 J. Opt. Soc. Am. 61 586
[9] . McGuirk M, Carniglia C K 1977 J. Opt. Soc. Am. 67 103
[10] . Sakata T, Togo H, Shimokawa F 2000 Appl. Phys. Lett. 76 2841
[11] . Yu T Y, Li H G, Cao Z Q, Wang Y, Sheng Q S, He Y 2008 Opt. Lett. 33 1001
[12] . Wang X P, Yin C, Sun J J, Li H G, Wang Y, Ran M W, Cao Z Q 2013 Opt. Express 21 13380
[13] . Chen F, Hao J, Li H G, Cao Z Q 2011 Acta Phys. Sin. 60 074223（in Chinese）[陈凡，郝军，李红根，曹庄琪 2011 60 074233]
[14] . Wild W J, Giles C L 1982 Phys. Rev. A 25 2099
[15] . Wang C, Wang Z P, Zhang Z H 2008 Acta Photon. Sin. 37 2321（in Chinese）[王成，王政平，张振辉 2008光子学报37 2321]
[16] . Bonnet C, Chauvat D, Emile O, Bretenaker F, Le Floch A, Dutriaux L 2001 Opt. Lett. 26 666
[17] . Cheng M, Fu P, Weng M H, Chen X Y, Zeng X H, Feng S Y, Chen R 2015 J. Phys. D: Appl. Phys. 48 285105
[18] . Wei M G, Long Y, Wu F, Liu C G, Zhang B L 2025 Sci. Bull. 70 882
[19] . Sharma B K, Ahn J H 2013 Solid-State Electron. 89 177
[20] . Xia F N, Mueller T, Lin Y M, Valdes-Garcia A, Avouris P 2009 Nat. Nanotechnol. 4 839
[21] . Schedin F, Geim A K, Morozov S V, Hill E W, Blake P, Katsnelson M I, Novoselov K S 2007 Nat. Mater. 6 652
[22] . Jahani D, Akhavan O, Hayat A, Shah M 2023 J. Opt. Soc. Am. A 40 21
[23] . Han L, Hu Z M, Pan J X, Huang T Y, Luo D P 2020 Sensors 20 3605
[24] . Farmani A, Mir A, Sharifpour Z 2018 Appl. Surf. Sci. 453 358
[25] . Ye Y Y, Zhang X Y, Jiang L Y 2023 Coatings 13 1763
[26] . Shu Y T, Song Y F, Tang P, Liu S Q, Luo Z M 2023 Opt. Commun. 530 129174
[27] . Li Y B, Song H Y, Zhang Y Q, Zhou S, Fu S F, Zhang Q, Wang X Z 2023 Opt. Laser Technol. 159 108968
[28] . Xue T, Li Y B, Song H Y, Wang X G, Zhang Q, Fu S F, Zhou S, Wang X Z 2023 Chinese Phys. B 33 014207
[29] . Wu J H, Song H Y, Li Y B, Hao S P, Zhang Q, Zhou S, Fu S F, Wang X Z 2024 Eur. Phys. J. Plus 139 897
[30] . Xia F N, Wang H, Xiao D, Dubey M, Ramasubramaniam A 2014 Nat. Photonics 8 899
[31] . Qiao J S, Kong X H, Hu Z X, Yang F, Ji W 2014 Nat. Commun. 5 4475
[32] . Liu H, Neal A T, Zhu Z, Luo Z, Xu X F, Tománek D, Ye P D 2014 ACS Nano 8 4033
[33] . Tran V, Soklaski R, Liang Y, Yang L 2014 Phys. Rev. B 89 235319
[34] . Peng X H, Wei Q, Copple A 2014 Phys. Rev. B 90 085402
[35] . Rodin A S, Carvalho A, Castro Neto A H 2014 Phys. Rev. Lett. 112 176801
[36] . Le P T T, Yarmohammadi M 2019 J. Magn. Magn. Mater. 491 165629
[37] . Zhou X Y, Lou W K, Zhai F, Chang K 2015 Phys. Rev. B 92 165405
[38] . Green M A 2008 Sol. Energy Mater. Sol. Cells 92 1305
[39] . Yang C H, Wang G X, Zhang C, Ao Z M 2017 J. Appl. Phys. 122 133109
[40] . Yang C H, Zhang J Y, Wang G X, Zhang C 2018 Phys. Rev. B 97 245408
[41] . Bai W Q, Yang J T, Yang C H, Cheng Y Y 2024 Acta Phys. Sin. 73 137803（in Chinese）[柏文庆，杨江涛，杨翠红，陈云云 2024 73 137803]
[42] . Wang L G, Chen H, Zhu S Y 2005 Opt. lett. 30 2936
计量
- 文章访问数: 20
- PDF下载量: 0
- 被引次数: 0
下载:
