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In this paper, the mode properties of graphene-coated asymmetric parallel dielectric nanowire waveguides are analyzed by the multipole expansion method. First, the surface plasmon modes supported by the waveguides are classified. Then, the influences of frequency, geometry parameters and graphene Fermi energy on the effective refractive index and propagation length of the seven low order modes are studied in detail. The seven low order modes can be divided into two categories: cos mode and sin mode. The cos mode includes modes 0, 2, 4 and 6, while sin mode includes modes 1, 3 and 5. The results show that the characteristics of the modes can be adjusted in a wide range by changing the frequency, geometrical parameters and the Fermi energy of graphene. When the frequency increases from 10 THz to 50 THz, the number of graphene surface plasmon modes increases and the effective refractive index of each mode increases monotonically. Moreover, with the increase of frequency, the propagation length of cos mode decreases monotonically, and the propagation length of sin mode shows the trend of first increasing and then decreasing. As the distance between the two dielectric nanowires increases, the mode properties of modes 0 and 1 change drastically, while the effective refractive indexes and propagation lengths of other modes vary very little. As the radius of one of the dielectric nanowires increases, the number of modes increases in the calculated range, while the effective refractive index and propagation length of each mode are less affected. In the process of increasing the Fermi energy of graphene from 0.3 eV to 0.7 eV, the effective refractive index and propagation length of each mode vary greatly. Moreover, the effective refractive index of each mode decreases monotonically, while the propagation length increases. It is also found that the compositions of the low order modes vary with the size of the two nanowires for this asymmetric structure. The comparison with the finite element method shows that the semi-analytical results based on multipole method are in good agreement with the numerical results from the finite element method. The present work may provide a theoretical basis for designing and fabricating the asymmetric parallel dielectric nanowires coated with graphene.
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Keywords:
- graphene /
- nanowires /
- waveguides /
- multipole method
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[1] Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109
[2] Bonaccorso F, Sun Z, Hasan T, Ferrari A C 2010 Nat. Photon. 4 611
[3] Vakil A, Engheta N 2011 Science 332 1291
[4] He X Y, Zhang X C, Zhang H, Xu M 2014 IEEE J. Sel. Top. Quant. 20 4500107
[5] Christensen J, Manjavacas A, Thongrattanasiri S, Kippens F H L, Abajo F J G 2012 ACS Nano 6 431
[6] Schedin F, Geim A K, Morozov S V, Hill E W, Blake P, Katsnelson M I, Novoselov K S 2007 Nat. Mater. 6 652
[7] Rodrigo D, Limaj O, Janner D, Etezadi D, Abajo F J G, Pruneri V, Altug H 2015 Science 349 165
[8] Lu Y, Goldsmith B R, Kybert N J, Johnson A T C 2010 Appl. Phys. Lett. 97 083107
[9] Huang Z R, Wang L L, Sun B, He M D, Liu J Q, Li H J, Zhai X 2014 J. Opt. 16 105004
[10] He S L, Zhang X Z, He Y G 2013 Opt. Express 21 30664
[11] Qin K, Xiao B G, Sun R L 2015 Micro Nano Lett. 10 558
[12] Xu W, Zhu Z H, Liu K, Zhang J F, Yuan X D, Lu Q S, Qin S Q 2015 Opt. Express 23 5147
[13] Liu P H, Zhang X Z, Ma Z H, Cai W, Wang L, Xu J J 2013 Opt. Express 21 32432
[14] Dai Y Y, Zhu X L, Mortensen N A, Zi J, Xiao S S 2015 J. Opt. 17 065002
[15] Gao Y X, Ren G B, Zhu B F, Wang J, Jian S S 2014 Opt. Lett. 39 5909
[16] Hajati M, Hajati Y 2016 J. Opt. Soc. Am. B 33 2560
[17] Gao Y X, Ren G B, Zhu B F, Liu H Q, Lian Y D, Jian S S 2014 Opt. Express 22 24322
[18] Yang J F, Yang J J, Deng W, Mao F C, Huang M 2015 Opt. Express 23 32289
[19] Liu J P, Zhai X, Wang L L, Li H J, Xie F, Lin Q, Xia S X 2016 Plasmonics 11 703
[20] Jiang J, Zhang D H, Zhang B L, Luo Y 2017 Opt. Lett. 42 2890
[21] Wijingaard W 1973 J. Opt. Soc. Am. 63 944
[22] Lo K M, McPhedran R C, Bassett I M, Milton G W 1994 J. Lightwave Technol. 12 396
[23] 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
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