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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.
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Keywords:
- graphene /
- nanowires /
- waveguides /
- multipole method
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[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
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