基于涂覆石墨烯的三根电介质纳米线的THz波导的模式特性分析

卫壮志; 薛文瑞; 彭艳玲; 程鑫; 李昌勇

doi:10.7498/aps.67.20180036

摘要

研究了一种基于涂覆石墨烯的三根电介质纳米线的THz波导，采用多极方法对这种波导所支持的5种低阶模的有效折射率的实部和传播长度进行了解析分析.结果表明，通过改变工作频率、中间纳米线半径、纳米线之间的间距以及石墨烯的费米能，可以有效地调节波导的模式特性.当工作频率从30 THz增加到40 THz时，这些模式的有效折射率的实部增大，传播长度减小，并且在变化的过程中会出现交叉现象.当中间纳米线的半径从25 nm增加到75 nm时，除了模式3和模式4基本不受影响，其他模式有效折射率的实部增大，传播长度变化各不相同.当纳米线之间的间距从10 nm增加到50 nm时，除了模式3和模式4基本不受影响，其他模式有效折射率的实部减小，传播长度增大，并且在变化的过程中会出现交叉现象.当石墨烯的费米能从0.4 eV增加到1.2 eV时，有效折射率的实部减小，传播长度增大.计算表明，多极法得到的结果与有限元方法得到的结果完全一致.本研究可以为基于涂覆石墨烯的电介质纳米线的THz波导的设计、制作和应用提供理论基础.

关键词:

石墨烯 /
纳米线 /
波导 /
多极方法

Abstract

In this paper, the real parts of the effective refractive indexes and the propagating lengths of five low-order modes of the terahertz waveguides based on three graphene-coated dielectric nanowires are analyzed by using the multipole method. The formation of these five lowest order modes can be attributed to the five combinations between the two lowest order modes supported when three nanowires exist alone. Therefore they are named Mode 1, Mode 2, Mode 3, Mode 4, and Mode 5 in sequence. The results show that the mode characteristics of the waveguide can be effectively tuned by changing the operating frequency, the radius of the intermediate nanowire, the gap distance between the nanowires and the Fermi energy of graphene. As the operating frequency increases from 30 THz to 40 THz, the real part of each of the effective refractive indexes increases and the propagation length decreases, and the crossover phenomenon occurs in the process of change. In addition, the real parts of the effective refractive indexes and the propagation lengths of Modes 3 and 4 are basically the same. When the radius of the middle nanowire increases from 25 nm to 75 nm, the real parts of the effective refractive indexes of Modes 1 and 2 increase, and the propagation length of Mode 1 decreases and then increases. Besides the real parts of the effective refractive indexes and the propagation lengths of Modes 3 and 4 are basically not affected by the change of radius, and the values of these two modes are basically the same. For Mode 5, the real part of the effective refractive index and propagation length slowly increase. When the spacing between the nanowires increases from 10 nm to 50 nm, Modes 3 and 4 are basically unaffected by the change of spacing, and the values of these two modes are basically the same. The real parts of the effective refractive indexes of the other modes decrease and the propagation lengths increase and eventually stabilize, and the crossover phenomenon occurs in the process of change. As the Fermi energy of graphene increases from 0.4 eV to 1.2 eV, the real part of the effective refractive index decreases and the propagation length increases. The calculation shows that the result obtained by the multipole method is exactly the same as that obtained by the finite element method. To date, no one has analyzed the terahertz waveguides based on three graphene-coated dielectric nanowires. This work can provide a theoretical basis for the design, fabrication and application of terahertz waveguide based on graphene-coated dielectric nanowires. Such waveguides have potential applications in the field of mode-division multiplexing.

Keywords:

作者及机构信息

1.
山西大学物理电子工程学院, 太原 030006;

2.
山西大学, 量子光学与光量子器件国家重点实验室, 激光光谱研究所, 太原 030006;

3.
山西大学, 极端光学协同创新中心, 太原 030006

通信作者: 薛文瑞, wrxue@sxu.edu.cn

基金项目: 国家自然科学基金（批准号：61378039，61575115）和国家基础科学人才培养基金（批准号：J1103210）资助的课题.

Authors and contacts

1.
College of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China;

2.
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China;

3.
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

Corresponding author: Xue Wen-Rui, wrxue@sxu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61378039, 61575115) and the National Basic Science Talents Training Fund of China (Grant No. J1103210).

参考文献

[1]	Siegel P H 2002 IEEE Trans. Microw. Theory 50 910
[2]	Wang S H, Ferguson B, Zhang C L, Zhang X C 2003 Acta Phys. Sin. 52 120 (in Chinese) [王少宏，B. Ferguson，张存林，张希成 2003 物理学报 52 120]
[3]	Chen Q, Tani M, Jiang Z P, Zhang X C 2001 J. Opt. Soc. Am. B 18 823
[4]	Han H, Park H, Cho M, Kim J 2002 Appl. Phys. Lett. 80 2634
[5]	Redo-Sanchez A, Zhang X C 2008 IEEE J. Sel. Top. Quant. 14 260
[6]	Gallot G, Jamison S P, McGowan R W, Grischkowsky D 2000 J. Opt. Soc. Am. B 17 851
[7]	Kawase K, Mizuno M, Sohma S, Takahashi T, Taniuchi T, Urata Y, Wada S, Tashiro H, Ito H 1999 Opt. Lett. 24 1065
[8]	Quema A, Takahashi H, Sakai M, Goto M, Ono S, Sarukura N, Shioda R, Yamada N 2003 Jpn. J. Appl. Phys. 42 L932
[9]	Chen L J, Chen H W, Kao T F, Lu J Y, Sun C K 2006 Opt. Lett. 31 308
[10]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197
[11]	Ju L, Geng B S, Horng J, Girit C, Martin M, Hao Z, Bechtel H A, Liang X G, Zettl A, Shen Y R, Wang F 2011 Nature Nanotechnol. 6 630
[12]	Wang J C, Song C, Hang J, Hu Z D, Zhang F 2017 Opt. Express 25 23880
[13]	Jablan M, Buljan H, Soljačić M 2009 Phys. Rev. B 80 245435
[14]	He X Y, Kim S 2013 J. Opt. Soc. Am. B 30 2461
[15]	Wang J C, Wang X S, Shao H Y, Hu Z D, Zheng G G, Zhang F 2017 Nanoscale Res. Lett. 12 9
[16]	Donnelly C, Tan D T H 2014 Opt. Express 22 22820
[17]	Christensen J, Manjavacas A, Thongrattanasiri S, Koppens F H L, Abajo F J G 2012 ACS Nano 6 431
[18]	Hajati M, Hajati Y 2016 Appl. Opt. 55 1878
[19]	Wang X S, Chen C, Pan L, Wang J C 2016 Sci. Rep. UK 6 32616
[20]	He S L, Zhang X Z, He Y R 2013 Opt. Express 21 30664
[21]	Gao Y X, Ren G B, Zhu B F, Wang J, Jian S S 2014 Opt. Lett. 39 5909
[22]	Yang J F, Yang J J, Deng W, Mao F C, Huang M 2015 Opt. Express 23 32289
[23]	Xing R, Jian S S 2016 IEEE Photon. Tech. L. 28 2779
[24]	Zhu B F, Ren G B, Yang Y, Gao Y X, Wu B L, Lian Y D, Wang J, Jian S S 2015 Plasmonics 10 839
[25]	Luo L W, Ophir N, Chen C P, Gabrielli L H, Poitras C B, Bergmen K, Lipson M 2014 Nat. Commun. 5 3069
[26]	Yang H B, Qiu M, Li Q 2016 Laser Photon. Rev. 10 278
[27]	Wu X R, Huang C R, Xu K, Shu C, Tsang H K 2017 J. Lightwave Technol. 35 3223
[28]	Nikitin A Y, Guinea F, García-Vidal F J, Martín-Moreno L 2011 Phys. Rev. B 84 195446
[29]	Wijngaard W 1973 J. Opt. Soc. Am. 63 944
[30]	Wijngaard W 1974 J. Opt. Soc. Am. 64 1136
[31]	Huang H S, Chang H C 1990 J. Lightwave Technol. 8 945
[32]	Lo K M, McPhedran R C, Bassett I M, Milton G W 1994 J. Lightwave Technol. 12 396
[33]	White T P, Kuhlmey B T, McPhedran R C, Maystre D, Renversez G, Sterke C M, Botten L C 2002 J. Opt. Soc. Am. B 19 2322
[34]	Kuhlmey B T, White T P, Renversez G, Maystre D, Botten L C, Sterke C M, McPhedran R C 2002 J. Opt. Soc. Am. B 19 2331

施引文献

[1]	Siegel P H 2002 IEEE Trans. Microw. Theory 50 910
[2]	Wang S H, Ferguson B, Zhang C L, Zhang X C 2003 Acta Phys. Sin. 52 120 (in Chinese) [王少宏，B. Ferguson，张存林，张希成 2003 物理学报 52 120]
[3]	Chen Q, Tani M, Jiang Z P, Zhang X C 2001 J. Opt. Soc. Am. B 18 823
[4]	Han H, Park H, Cho M, Kim J 2002 Appl. Phys. Lett. 80 2634
[5]	Redo-Sanchez A, Zhang X C 2008 IEEE J. Sel. Top. Quant. 14 260
[6]	Gallot G, Jamison S P, McGowan R W, Grischkowsky D 2000 J. Opt. Soc. Am. B 17 851
[7]	Kawase K, Mizuno M, Sohma S, Takahashi T, Taniuchi T, Urata Y, Wada S, Tashiro H, Ito H 1999 Opt. Lett. 24 1065
[8]	Quema A, Takahashi H, Sakai M, Goto M, Ono S, Sarukura N, Shioda R, Yamada N 2003 Jpn. J. Appl. Phys. 42 L932
[9]	Chen L J, Chen H W, Kao T F, Lu J Y, Sun C K 2006 Opt. Lett. 31 308
[10]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197
[11]	Ju L, Geng B S, Horng J, Girit C, Martin M, Hao Z, Bechtel H A, Liang X G, Zettl A, Shen Y R, Wang F 2011 Nature Nanotechnol. 6 630
[12]	Wang J C, Song C, Hang J, Hu Z D, Zhang F 2017 Opt. Express 25 23880
[13]	Jablan M, Buljan H, Soljačić M 2009 Phys. Rev. B 80 245435
[14]	He X Y, Kim S 2013 J. Opt. Soc. Am. B 30 2461
[15]	Wang J C, Wang X S, Shao H Y, Hu Z D, Zheng G G, Zhang F 2017 Nanoscale Res. Lett. 12 9
[16]	Donnelly C, Tan D T H 2014 Opt. Express 22 22820
[17]	Christensen J, Manjavacas A, Thongrattanasiri S, Koppens F H L, Abajo F J G 2012 ACS Nano 6 431
[18]	Hajati M, Hajati Y 2016 Appl. Opt. 55 1878
[19]	Wang X S, Chen C, Pan L, Wang J C 2016 Sci. Rep. UK 6 32616
[20]	He S L, Zhang X Z, He Y R 2013 Opt. Express 21 30664
[21]	Gao Y X, Ren G B, Zhu B F, Wang J, Jian S S 2014 Opt. Lett. 39 5909
[22]	Yang J F, Yang J J, Deng W, Mao F C, Huang M 2015 Opt. Express 23 32289
[23]	Xing R, Jian S S 2016 IEEE Photon. Tech. L. 28 2779
[24]	Zhu B F, Ren G B, Yang Y, Gao Y X, Wu B L, Lian Y D, Wang J, Jian S S 2015 Plasmonics 10 839
[25]	Luo L W, Ophir N, Chen C P, Gabrielli L H, Poitras C B, Bergmen K, Lipson M 2014 Nat. Commun. 5 3069
[26]	Yang H B, Qiu M, Li Q 2016 Laser Photon. Rev. 10 278
[27]	Wu X R, Huang C R, Xu K, Shu C, Tsang H K 2017 J. Lightwave Technol. 35 3223
[28]	Nikitin A Y, Guinea F, García-Vidal F J, Martín-Moreno L 2011 Phys. Rev. B 84 195446
[29]	Wijngaard W 1973 J. Opt. Soc. Am. 63 944
[30]	Wijngaard W 1974 J. Opt. Soc. Am. 64 1136
[31]	Huang H S, Chang H C 1990 J. Lightwave Technol. 8 945
[32]	Lo K M, McPhedran R C, Bassett I M, Milton G W 1994 J. Lightwave Technol. 12 396
[33]	White T P, Kuhlmey B T, McPhedran R C, Maystre D, Renversez G, Sterke C M, Botten L C 2002 J. Opt. Soc. Am. B 19 2322
[34]	Kuhlmey B T, White T P, Renversez G, Maystre D, Botten L C, Sterke C M, McPhedran R C 2002 J. Opt. Soc. Am. B 19 2331

计量

文章访问数: 4968
PDF下载量: 110
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板