基于衬底的涂覆石墨烯层的三角形纳米线亚波长传输特性研究 
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1 引言
表面等离激元(Surface plasmons,SPs)[1-2]是一种沿金属-介质分界面传播的表面电磁波。由于可以突破衍射极限,SPs在亚波长光子器件领域有重要应用价值。近年来,作为亚波长光子器件的一个重要研究分支,表面等离激元纳米光波导[3]得到了广泛关注。早期基于贵金属材料的表面等离激元纳米光波导主要有金属线波导[4-7],金属缝隙波导[8],介质加载的等离激元波导[9],长程等离激元波导[10],金属沟槽/楔形等离激元波导[11],混合型波导[12-14]等。这类金属等离激元波导在近红外波段和可见光波段表现优异,但在中远红外波段模场约束性能相对较差[15]。此外,金属材料属性固定,缺乏可调节性。
近期研究表明,通过化学掺杂或加偏压,石墨烯在中远红外波段可以表现出类“金属”特性[16],进而可以激发表面等离激元。石墨烯表面等离激元因具备极强的场约束、巨大的场增强和性能可调的特性[17-18],引起学术界广泛关注。基于这些特性,研究人员提出诸多石墨烯等离激元器件,如石墨烯纳米带波导[19-20]、介质加载波导[21]、沟槽/楔形波导[22]、调制器[23-24]、天线[25]、开关[26]等。其中,作为纳米金属线的类似物,涂覆石墨烯层的纳米线波导[27-40]因结构简单、可解析计算、基模(TM0)无截止等特性引起了许多研究人员的关注。但是,涂覆石墨烯层的圆形纳米线等离激元模场约束性能相对较差,归一化模场面积约为1
基于尖端结构优良的光场聚焦效应,本文提出了一种由硅衬底和涂覆石墨烯层的三角形纳米线构成的混合波导。采用有限元方法对该混合波导中基模亚波长传输性能进行了详细研究。通过改变三角形纳米线与衬底间距、三角形纳米线顶角角度、顶角圆角半径以及石墨烯化学势等,发现该结构光场约束性能非常好,同时模式传输损耗也较低。相关研究结果在纳米光子学、可调谐光子器件等领域有潜在的应用价值。
2 理论模型
式中:σintra为电子带内跃迁对电导率的贡献;σinter为电子带间跃迁对电导率的贡献;τ为电子弛豫时间,τ=0.5 ps;T为温度,T=300 K;
在实验研究中,可通过加直流偏压来改变石墨烯中载流子浓度nc,进而改变石墨烯化学势μc,二者关系式为
在具体计算中,将石墨烯薄层等效为纳米线表面电流J=σgE,E为电场强度,并采用基于有限元方法的COMSOL软件计算模式复有效模式系数neff。传播常数β=k0neff,其中k0=2π/λ0,λ0为自由空间波长。模式传播距离定义为LP=λ0/[2πIm(neff)]。归一化模场面积定义为Aeff/A0,其中A0=
3 结果与讨论
图 2. μc=0.5 eV,f0=30 THz,R=10 nm时基模的归一化电场强度分布。 (a)当θ=π/6,Ggap=2 nm时;(b)当θ=π/2,Ggap=2 nm时;(c)当θ=π/6, Ggap=10 nm时;(d)当θ=π/2,Ggap=10 nm时; 归一化电场强度沿(e)x方向和(f)y方向的分布
Fig. 2. Normalized electric field intensity distributions of fundamental mode when μc=0.5 eV,f0=30 THz,and R=10 nm. (a) Under θ=π/6, Ggap=2 nm; (b) under θ=π/2, Ggap=2 nm;(c) under θ =π/6, Ggap=10 nm; (d) under θ=π/2, Ggap=10 nm; normalized electric field intensity distributions along (e) x and (f) y directions
图 3. μc=0.5 eV,f0=30 THz,R=10 nm,θ=π/2时模式特性随Ggap的变化。(a) Re(neff);(b)传播距离;(c)归一化模场面积
Fig. 3. Modal properties versus gap when μc=0.5 eV,f0=30 THz, R=10 nm, and θ=π/2. (a) Re(neff); (b) propagation length; (c) normalized mode area
本文采用三角形截面的纳米线是为了利用尖端效应来实现模场的深度亚波长约束。因此,进一步研究了三角形顶角大小对所提出波导传输性能的影响。如
图 4. μc=0.5 eV,f0=30 THz,Ggap=2 nm,R=10 nm时模式特性随θ的变化。(a) Re(neff);(b)传播距离;(c)归一化模场面积
Fig. 4. Modal properties versus θ when μc=0.5 eV,f0=30 THz, Ggap=2 nm, and R=10 nm. (a) Re(neff); (b) propagation length; (c) normalized mode area
此外,为了避免尖端处场分布的奇异性,对三角形的顶角进行了圆滑处理,形成一个圆角。因此,进一步研究了圆角半径R大小对模式特性的影响,如
图 5. μc=0.5 eV,f0=30 THz,Ggap=2 nm,θ=π/3时模式特性随R的变化。(a) Re(neff);(b)传播距离;(c)归一化模场面积
Fig. 5. Modal properties with respect to R when μc=0.5 eV,f0=30 THz,Ggap=2 nm,and θ=π/3. (a) Re(neff), (b) propagation length; (c) normalized mode area
相比金属材料,石墨烯化学势可以通过加偏压或者化学掺杂的方式进行调节[16],这为更好地调控模式传输特性提供了一种可行方法。如前文所述,本文中化学势取值范围为0.5~1.1 eV。
图 6. Ggap=2 nm,θ=π/3,R=10 nm时不同化学势下模式特性和频率的关系。(a) Re(neff);(b)传播距离;(c)归一化模场面积
Fig. 6. Modal properties versus frequency under different chemical potential values when Ggap=2 nm, θ=π/3,and R=10 nm. (a) Re(neff); (b) propagation length; (c) normalized mode area
最后,简要讨论一下所提出波导结构的实际加工以及传输特性对纳米线介电常数和形状的依赖性。现有研究表明,实验上可以相对容易地加工出涂覆石墨烯层的介质纳米线[51-52]。对于硅衬底,可采用等离子体增强化学气相沉积(Plasma enhanced chemical vapor deposition,PECVD)技术进行加工,且通过控制沉积速度和时间可实现对二氧化硅间隙层厚度的精确控制[53]。此外,本文中纳米线介电常数固定为2.25。前期研究表明,纳米线介电常数越小,波导性能越好[27,32],因此这类不再赘述。同时,研究发现,波导传输性能对纳米线形状有很大依赖性。因此,后续可探索纳米线形状对涂覆石墨烯层的纳米线波导传输性能的影响,这将进一步拓展相关领域的研究。
4 结论
提出一种基于硅衬底的涂覆石墨烯层的三角形纳米线等离激元结构,采用有限元方法详细研究了基模传输特性。结果表明:选择适当的低折射率间隙区域大小和三角形顶角角度,可较好展现该结构的模式传播特性;尖端圆角半径越小,模场在尖端处的聚焦效应越突出且模式传输损耗更低;增大石墨烯化学势可以大幅降低传输损耗。此外,研究发现,所提波导结构可在局部突破表面等离激元模式中传输损耗和模场面积之间的制约关系,即在实现模式损耗降低的同时减小模场面积。特别地,所提波导在保持模式传输损耗基本不变的前提下,进一步将模场面积压缩至10-6量级左右。该类石墨烯表面等离激元优异的亚波长传输特性使得其在可调谐纳米光子器件及光子集成领域具有潜在的应用价值。
[1] Gramotnev D K, Bozhevolnyi S I. Plasmonics beyond the diffraction limit[J]. Nature Photonics, 2010, 4(2): 83-91.
[2] 李盼. 表面等离激元纳米聚焦研究进展[J]. 物理学报, 2019, 68(14): 146201.
Li P. Research progress of plasmonic nanofocusing[J]. Acta Physica Sinica, 2019, 68(14): 146201.
[3] Fang Y, Sun M. Nanoplasmonic waveguides: towards applications in integrated nanophotonic circuits[J]. Light: Science & Applications, 2015, 4(6): e294.
[4] Wei H, Pan D, Zhang S, et al. Plasmon waveguiding in nanowires[J]. Chemical Reviews, 2018, 118(6): 2882-2926.
[6] Teng D, Cao Q, Li S, et al. Tapered dual elliptical plasmon waveguides as highly efficient terahertz connectors between approximate plate waveguides and two-wire waveguides[J]. Journal of the Optical Society of America A, 2014, 31(2): 268-273.
[7] 王文慧, 张孬. 银纳米线表面等离激元波导的能量损耗[J]. 物理学报, 2018, 67(24): 247302.
Wang W H, Zhang N. Energy loss of surface plasmon polaritons on Ag nanowire waveguide[J]. Acta Physica Sinica, 2018, 67(24): 247302.
[8] 陈奕霖, 许吉, 时楠楠, 等. 金属-介质-金属波导布拉格光栅的模式特性[J]. 光学学报, 2017, 37(11): 1123002.
[9] 邵晓珍, 张冠茂, 王琼, 等. 基于黄金分割比的长程介质加载表面等离子激元波导传输特性研究[J]. 激光与光电子学进展, 2016, 53(6): 061301.
[10] 张冠茂, 孙海丽, 李建明, 等. 一种对称混合长程表面等离子激元波导传输特性研究[J]. 激光与光电子学进展, 2013, 50(12): 121301.
[11] Yan M, Qiu M. Guided plasmon polariton at 2D metal corners[J]. Journal of the Optical Society of America B, 2007, 24(9): 2333-2342.
[12] 周沛, 卢启景, 吴根柱, 等. 基于半导体纳米线和金属脊的混合表面等离子体波导模式特性分析[J]. 光子学报, 2013, 42(12): 1460-1463.
[13] Bian Y S, Zheng Z, Zhao X, et al. Symmetric hybrid surface plasmon polariton waveguides for 3D photonic integration[J]. Optics Express, 2009, 17(23): 21320-21325.
[14] Dai D X, He S L. A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement[J]. Optics Express, 2009, 17(19): 16646-16653.
[15] Gao Y X, Shadrivov I V. Second harmonic generation in graphene-coated nanowires[J]. Optics Letters, 2016, 41(15): 3623-3626.
[17] 李勇, 张惠芳, 范天馨, 等. 双介质加载石墨烯表面等离子激元波导的理论分析[J]. 光学学报, 2016, 36(7): 0724001.
[18] 杨晓霞, 孔祥天, 戴庆. 石墨烯等离激元的光学性质及其应用前景[J]. 物理学报, 2015, 64(10): 106801.
Yang X X, Kong X T, Dai Q. Optical properties of graphene plasmons and their potential applications[J]. Acta Physica Sinica, 2015, 64(10): 106801.
[19] Lu H, Zhao J L, Gu M. Nanowires-assisted excitation and propagation of mid-infrared surface plasmon polaritons in graphene[J]. Journal of Applied Physics, 2016, 120(16): 163106.
[20] Lu H, Zeng C, Zhang Q M, et al. Graphene-based active slow surface plasmon polaritons[J]. Scientific Reports, 2015, 5: 8443.
[21] Xu W, Zhu Z H, Liu K, et al. Dielectric loaded graphene plasmon waveguide[J]. Optics Express, 2015, 23(4): 5147-5153.
[23] 李志全, 冯丹丹, 李欣, 等. 基于石墨烯表面等离激元的双支节结构光电调制器[J]. 光学学报, 2018, 38(1): 0124001.
[25] 谢亚楠, 刘志坤, 耿莉, 等. 石墨烯微波至太赫兹的特性及天线中的应用[J]. 光学学报, 2015, 35(s1): s116005.
[26] Cao T, Li Y, Tian L, et al. Fast switching “on/off” chiral surface plasmon polaritons in graphene-coated Ge2Sb2Te5 nanowire[J]. ACS Applied Nano Materials, 2018, 1(2): 759-767.
[29] Liu J P, Zhai X, Wang L L, et al. Analysis of mid-infrared surface plasmon modes in a graphene-based cylindrical hybrid waveguide[J]. Plasmonics, 2016, 11(3): 703-711.
[30] Liu J P, Zhai X, Xie F, et al. Analytical model of mid-infrared surface plasmon modes in a cylindrical long-range waveguide with double-layer graphene[J]. Journal of Lightwave Technology, 2017, 35(10): 1971-1979.
[31] Zhu B F, Ren G B. Yang, et al. Field enhancement and gradient force in the graphene-coated nanowire pairs[J]. Plasmonics, 2015, 10(4): 839-845.
[32] Teng D, Wang K, Li Z, et al. Graphene-coated nanowire dimers for deep subwavelength waveguiding in mid-infrared range[J]. Optics Express, 2019, 27(9): 12458-12469.
[33] 滕达, 王凯, 李哲, 等. 用于中红外波深度亚波长传输的石墨烯间隙等离激元波导[J]. 光学学报, 2020, 40(6): 0623002.
[34] Teng D, Wang K, Li Z, et al. Graphene-coated elliptical nanowires for low loss subwavelength terahertz transmission[J]. Applied Sciences, 2019, 9(11): 2351.
[35] Huang Y X, Zhang L, Yin H, et al. Graphene-coated nanowires with a drop-shaped cross section for 10 nm confinement and 1 mm propagation[J]. Optics Letters, 2017, 42(11): 2078-2081.
[36] Liang H, Zhang L, Zhang S, et al. Gate-programmable electro-optical addressing array of graphene-coated nanowires with sub-10 nm resolution[J]. ACS Photonics, 2016, 3(10): 1847-1853.
[37] 翟利, 薛文瑞, 杨荣草, 等. 涂覆石墨烯的电介质纳米并行线的传输特性[J]. 光学学报, 2015, 35(11): 1123002.
[38] 彭艳玲, 薛文瑞, 卫壮志, 等. 涂覆石墨烯的非对称并行电介质纳米线波导的模式特性分析[J]. 物理学报, 2018, 67(3): 038102.
Peng Y L, Xue W R, Wei Z Z, et al. Mode properties analysis of graphene-coated asymmetric parallel dielectric nanowire waveguides[J]. Acta Physica Sinica, 2018, 67(3): 038102.
[39] 卫壮志, 薛文瑞, 彭艳玲, 等. 涂覆石墨烯的三根电介质纳米线波导的模式特性[J]. 光学学报, 2019, 39(1): 0124001.
[40] Teng D, Wang K, Li Z. Graphene-coated nanowire waveguides and their applications[J]. Nanomaterials, 2020, 10(2): 229.
[41] Hajati M, Hajati Y. High-performance and low-loss plasmon waveguiding in graphene-coated nanowire with substrate[J]. Journal of the Optical Society of America B, 2016, 33(12): 2560-2565.
[42] Hajati M, Hajati Y. Plasmonic characteristics of two vertically coupled graphene-coated nanowires integrated with substrate[J]. Applied Optics, 2017, 56(4): 870-875.
[43] Wu D, Tian J P, Yang R C. Study of mode performances of graphene-coated nanowire integrated with triangle wedge substrate[J]. Journal of Nonlinear Optical Physics & Materials, 2018, 27(2): 1850013.
[44] Chandler-Horowitz D, Amirtharaj P M. High-accuracy, midinfrared (450 cm -1≤ω≤ 4000 cm -1) refractive index values of silicon[J]. Journal of Applied Physics, 2005, 97(12): 123526.
[45] Francescato Y, Giannini V, Maier S A. Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon[J]. New Journal of Physics, 2013, 15(6): 063020.
[46] Gan C H, Chu H S, Li E P. Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies[J]. Physical Review B, 2012, 85(12): 125431.
[47] Efetov D K, Kim P. Controlling electron-phonon interactions in graphene at ultrahigh carrier densities[J]. Physical Review Letters, 2010, 105(25): 256805.
[48] Jiang T, Huang D, Cheng J L, et al. Gate-tunable third-order nonlinear optical response of massless Dirac fermions in graphene[J]. Nature Photonics, 2018, 12(7): 430-436.
[49] Chen C F, Park C H, Boudouris B W, et al. Controlling inelastic light scattering quantum pathways in graphene[J]. Nature, 2011, 471(7340): 617-620.
[50] Oulton R F, Sorger V J, Genov D A, et al. A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation[J]. Nature Photonics, 2008, 2(8): 496-500.
[51] Cao T, Tian L, Liang H W, et al. Reconfigurable, graphene-coated, chalcogenide nanowires with a sub-10-nm enantioselective sorting capability[J]. Microsystems & Nanoengineering, 2018, 4: 7.
[53] Dai D, Liu L, Wosinski L, et al. Design and fabrication of ultra-small overlapped AWG demultiplexer based on α-Si nanowire waveguides[J]. Electronics Letters, 2006, 42(7): 400-402.
滕达, 马文帅, 杨研蝶, 郭晋康, 王凯. 基于衬底的涂覆石墨烯层的三角形纳米线亚波长传输特性研究[J]. 光学学报, 2020, 40(13): 1324002. Da Teng, Wenshuai Ma, Yandie Yang, Jinkang Guo, Kai Wang. Study on Subwavelength Transmission Properties of Triangular-Shaped Graphene-Coated Nanowires on Substrate[J]. Acta Optica Sinica, 2020, 40(13): 1324002.
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