Abstract

In this paper, a novel structure for a graphene-based directional coupler in the THz frequency region is presented. This new configuration consists of two graphene-based single-mode waveguides, placed side by side with some connection gaps between them to allow coupling. Two different types of directional couplers (single-gap and double-gap) are designed at the frequency of 50[THz]. The simulation results show that the designed single-gap coupler has the advantages of low insertion loss ($ \lt - 1.4\,\, {\rm dB} $), high directivity ($ \gt 15\,\, {\rm dB} $), high isolation ($ \lt - 19.4\,\, {\rm dB} $), wide bandwidth ($ \gt 25\% $), and small footprint (about 100[nm]) for high-coupling coefficients, while the double-gap coupler shows better directivity ($ \gt 30.17\,\, {\rm dB} $) and isolation ($ \lt - 41.5\,\, {\rm dB} $) for a low-coupling coupler, so it is superior to other structures reported in the literature. The propagation loss and dimensions of the coupler waveguides have been efficiently controlled to remain small by optimizing the imaginary and real parts of the effective mode index of the surface plasmon polariton mode. The full-wave simulations show that the presented approach gives very good results for designing graphene-based directional couplers with different coupling coefficients. These structures are analyzed and optimized by the commercial COMSOL Multiphysics electromagnetic solver.

© 2020 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  27. T. Zhang, X. Ke, X. Yin, L. Chen, and X. Li, “Graphene-assisted ultra-compact polarization splitter and rotator with an extended bandwidth,” Sci. Rep. 7, 12169 (2017).
    [Crossref]
  28. Y. Meng, F. Hu, Y. Shen, Y. Yang, Q. Xiao, X. Fu, and M. Gong, “Ultracompact graphene-assisted tunable waveguide couplers with high directivity and mode selectivity,” Sci. Rep. 8, 13362 (2018).
    [Crossref]
  29. J.-P. Liu, W.-L. Wang, F. Xie, X. Luo, X. Zhou, M. Lei, Y.-J. Yuan, M.-Q. Long, and L.-L. Wang, “Efficient directional coupling from multilayer-graphene-based long-range SPP waveguide to metal-based hybrid SPP waveguide in mid-infrared range,” Opt. Express 26, 29509–29520 (2018).
    [Crossref]
  30. M.-D. He, K.-J. Wang, L. Wang, J.-B. Li, J.-Q. Liu, Z.-R. Huang, L. Wang, L. Wang, W.-D. Hu, and X. Chen, “Graphene-based terahertz tunable plasmonic directional coupler,” Appl. Phys. Lett. 105, 081903 (2014).
    [Crossref]
  31. A. Auditore, C. de Angelis, A. Locatelli, and A. B. Aceves, “Tuning of surface plasmon polaritons beat length in graphene directional couplers,” Opt. Lett. 38, 4228–4231 (2013).
    [Crossref]
  32. W. Du, K. Li, D. Wu, K. Jiao, L. Jiao, L. Liu, F. Xia, W. Kong, L. Dong, and M. Yun, “Electrically controllable directional coupler based on tunable hybrid graphene nanoplasmonic waveguide,” Opt. Commun. 430, 450–455 (2019).
    [Crossref]
  33. T. Q. Tran and S. Kim, “Low-loss electrically controllable vertical directional couplers,” Curr. Opt. Photon. 1, 65–72 (2017).
    [Crossref]
  34. H. Li, L. Wang, Z. Huang, B. Sun, X. Zhai, and X. Li, “Mid-infrared, plasmonic switches and directional couplers induced by graphene sheets coupling system,” Europhys. Lett. 104, 37001 (2013).
    [Crossref]

2019 (6)

M. S. A. Naeini, M. Maddahali, and A. Bakhtafrouz, “Deriving a lumped element surface impedance model for periodic arrays of graphene micro-rings,” IEEE Trans. Nanotechnol. 18, 445–452 (2019).
[Crossref]

V. Dmitriev, S. L. M. da Silva, and W. Castro, “Ultrawideband graphene three-port circulator for THz region,” Opt. Express 27, 15982–15995 (2019).
[Crossref]

P. Karimi, M. Maddahali, A. Bakhtafrouz, and M. Shahabadi, “Design of a wideband terahertz absorber composed of graphene patches,” IET Optoelectronics 13, 235–239 (2019).
[Crossref]

K. Kanahashi, M. Ishihara, M. Hasegawa, H. Ohta, and T. Takenobu, “Giant power factors in p- and n-type large-area graphene films on a flexible plastic substrate,” npj 2D Mater. Appl. 3, 1–6 (2019).
[Crossref]

K. E. Kitko and Q. Zhang, “Graphene-based nanomaterials: from production to integration with modern tools in neuroscience,” Front. Syst. Neurosci. 13, 26 (2019).
[Crossref]

W. Du, K. Li, D. Wu, K. Jiao, L. Jiao, L. Liu, F. Xia, W. Kong, L. Dong, and M. Yun, “Electrically controllable directional coupler based on tunable hybrid graphene nanoplasmonic waveguide,” Opt. Commun. 430, 450–455 (2019).
[Crossref]

2018 (4)

Y. V. Bludov, M. Vasilevskiy, and N. Peres, “Magnetic field assisted transmission of THz waves through a graphene layer combined with a periodically perforated metallic film,” Phys. Rev. B 97, 045433 (2018).
[Crossref]

Y. Meng, F. Hu, Y. Shen, Y. Yang, Q. Xiao, X. Fu, and M. Gong, “Ultracompact graphene-assisted tunable waveguide couplers with high directivity and mode selectivity,” Sci. Rep. 8, 13362 (2018).
[Crossref]

J.-P. Liu, W.-L. Wang, F. Xie, X. Luo, X. Zhou, M. Lei, Y.-J. Yuan, M.-Q. Long, and L.-L. Wang, “Efficient directional coupling from multilayer-graphene-based long-range SPP waveguide to metal-based hybrid SPP waveguide in mid-infrared range,” Opt. Express 26, 29509–29520 (2018).
[Crossref]

V. Nikkhah, A. Bakhtafrouz, M. Maddahali, and S. K. Dezaki, “Three-port graphene-based electromagnetic circulator in the terahertz and infrared frequency ranges with a very low loss and wideband response,” J. Opt. Soc. Am. B 35, 1754–1763 (2018).
[Crossref]

2017 (3)

S.-J. Im, Y.-H. Han, K.-S. Ho, C.-S. Ri, Y.-H. Ko, and Q.-Q. Wang, “Nanoscale optical directional coupler,” Plasmonics 12, 1741–1747 (2017).
[Crossref]

T. Zhang, X. Ke, X. Yin, L. Chen, and X. Li, “Graphene-assisted ultra-compact polarization splitter and rotator with an extended bandwidth,” Sci. Rep. 7, 12169 (2017).
[Crossref]

T. Q. Tran and S. Kim, “Low-loss electrically controllable vertical directional couplers,” Curr. Opt. Photon. 1, 65–72 (2017).
[Crossref]

2016 (1)

2015 (1)

Y. Ying-Ying, L. Xu-You, S. Bo, and H. Kun-Peng, “Design and optimization of terahertz directional coupler based on hybrid-cladding hollow waveguide with low confinement loss,” Chin. Phys. B 24, 068702 (2015).
[Crossref]

2014 (2)

R. Yang, S. Wu, D. Wang, G. Xie, M. Cheng, G. Wang, W. Yang, P. Chen, D. Shi, and G. Zhang, “Fabrication of high-quality all-graphene devices with low contact resistances,” Nano Res. 7, 1449–1456 (2014).
[Crossref]

M.-D. He, K.-J. Wang, L. Wang, J.-B. Li, J.-Q. Liu, Z.-R. Huang, L. Wang, L. Wang, W.-D. Hu, and X. Chen, “Graphene-based terahertz tunable plasmonic directional coupler,” Appl. Phys. Lett. 105, 081903 (2014).
[Crossref]

2013 (4)

A. Auditore, C. de Angelis, A. Locatelli, and A. B. Aceves, “Tuning of surface plasmon polaritons beat length in graphene directional couplers,” Opt. Lett. 38, 4228–4231 (2013).
[Crossref]

W. B. Lu, W. Zhu, H. J. Xu, Z. H. Ni, Z. G. Dong, and T. J. Cui, “Flexible transformation plasmonics using graphene,” Opt. Express 21, 10475–10482 (2013).
[Crossref]

H. Li, L. Wang, Z. Huang, B. Sun, X. Zhai, and X. Li, “Mid-infrared, plasmonic switches and directional couplers induced by graphene sheets coupling system,” Europhys. Lett. 104, 37001 (2013).
[Crossref]

X. Luo, T. Qiu, W. Lu, and Z. Ni, “Plasmons in graphene: recent progress and applications,” Mater. Sci. Eng., R 74, 351–376 (2013).
[Crossref]

2012 (2)

D. R. Cooper, B. D’Anjou, N. Ghattamaneni, B. Harack, M. Hilke, A. Horth, N. Majlis, M. Massicotte, L. Vandsburger, E. Whiteway, and V. Yu, “Experimental review of graphene,” ISRN Condens. Matter Phys. 2012, 501686 (2012).

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100, 131111 (2012).
[Crossref]

2011 (2)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref]

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. Peres, and A. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011).
[Crossref]

2009 (1)

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

2007 (1)

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref]

2006 (2)

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface plasmon polaritons,” Opt. Commun. 259, 690–695 (2006).
[Crossref]

A. Boltasseva and S. I. Bozhevolnyi, “Directional couplers using long-range surface plasmon polariton waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1233–1241 (2006).
[Crossref]

Aceves, A. B.

Auditore, A.

Bakhtafrouz, A.

M. S. A. Naeini, M. Maddahali, and A. Bakhtafrouz, “Deriving a lumped element surface impedance model for periodic arrays of graphene micro-rings,” IEEE Trans. Nanotechnol. 18, 445–452 (2019).
[Crossref]

P. Karimi, M. Maddahali, A. Bakhtafrouz, and M. Shahabadi, “Design of a wideband terahertz absorber composed of graphene patches,” IET Optoelectronics 13, 235–239 (2019).
[Crossref]

V. Nikkhah, A. Bakhtafrouz, M. Maddahali, and S. K. Dezaki, “Three-port graphene-based electromagnetic circulator in the terahertz and infrared frequency ranges with a very low loss and wideband response,” J. Opt. Soc. Am. B 35, 1754–1763 (2018).
[Crossref]

P. K. Khoozani, M. Maddahali, M. Shahabadi, and A. Bakhtafrouz, “Analysis of magnetically biased graphene-based periodic structures using a transmission-line formulation,” J. Opt. Soc. Am. B 33, 2566–2576 (2016).
[Crossref]

Binzhen, Z.

W. Ying, Z. Binzhen, D. Junping, and S. Yujie, “Terahertz waveguide directional coupler with double” tian-shape,” in IEEE 9th International Conference on Communication Software and Networks (ICCSN) (IEEE, 2017), pp. 758–761.

Bludov, Y. V.

Y. V. Bludov, M. Vasilevskiy, and N. Peres, “Magnetic field assisted transmission of THz waves through a graphene layer combined with a periodically perforated metallic film,” Phys. Rev. B 97, 045433 (2018).
[Crossref]

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. Peres, and A. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011).
[Crossref]

Bo, S.

Y. Ying-Ying, L. Xu-You, S. Bo, and H. Kun-Peng, “Design and optimization of terahertz directional coupler based on hybrid-cladding hollow waveguide with low confinement loss,” Chin. Phys. B 24, 068702 (2015).
[Crossref]

Boltasseva, A.

A. Boltasseva and S. I. Bozhevolnyi, “Directional couplers using long-range surface plasmon polariton waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1233–1241 (2006).
[Crossref]

Bounaas, F.

A. Labbani, I. Moumeni, and F. Bounaas, “An ultra small optical switch design based on directional coupler in two-dimensional photonic crystals,” in International Conference on Communications and Electrical Engineering (ICCEE) (IEEE, 2018), pp. 1–4.

Bozhevolnyi, S. I.

A. Boltasseva and S. I. Bozhevolnyi, “Directional couplers using long-range surface plasmon polariton waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1233–1241 (2006).
[Crossref]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

Castro, W.

Chen, L.

T. Zhang, X. Ke, X. Yin, L. Chen, and X. Li, “Graphene-assisted ultra-compact polarization splitter and rotator with an extended bandwidth,” Sci. Rep. 7, 12169 (2017).
[Crossref]

Chen, P.

R. Yang, S. Wu, D. Wang, G. Xie, M. Cheng, G. Wang, W. Yang, P. Chen, D. Shi, and G. Zhang, “Fabrication of high-quality all-graphene devices with low contact resistances,” Nano Res. 7, 1449–1456 (2014).
[Crossref]

Chen, X.

M.-D. He, K.-J. Wang, L. Wang, J.-B. Li, J.-Q. Liu, Z.-R. Huang, L. Wang, L. Wang, W.-D. Hu, and X. Chen, “Graphene-based terahertz tunable plasmonic directional coupler,” Appl. Phys. Lett. 105, 081903 (2014).
[Crossref]

Cheng, M.

R. Yang, S. Wu, D. Wang, G. Xie, M. Cheng, G. Wang, W. Yang, P. Chen, D. Shi, and G. Zhang, “Fabrication of high-quality all-graphene devices with low contact resistances,” Nano Res. 7, 1449–1456 (2014).
[Crossref]

Cooper, D. R.

D. R. Cooper, B. D’Anjou, N. Ghattamaneni, B. Harack, M. Hilke, A. Horth, N. Majlis, M. Massicotte, L. Vandsburger, E. Whiteway, and V. Yu, “Experimental review of graphene,” ISRN Condens. Matter Phys. 2012, 501686 (2012).

Cui, T. J.

D’Anjou, B.

D. R. Cooper, B. D’Anjou, N. Ghattamaneni, B. Harack, M. Hilke, A. Horth, N. Majlis, M. Massicotte, L. Vandsburger, E. Whiteway, and V. Yu, “Experimental review of graphene,” ISRN Condens. Matter Phys. 2012, 501686 (2012).

da Silva, S. L. M.

de Angelis, C.

Dezaki, S. K.

Dmitriev, V.

Dong, L.

W. Du, K. Li, D. Wu, K. Jiao, L. Jiao, L. Liu, F. Xia, W. Kong, L. Dong, and M. Yun, “Electrically controllable directional coupler based on tunable hybrid graphene nanoplasmonic waveguide,” Opt. Commun. 430, 450–455 (2019).
[Crossref]

Dong, Z. G.

Du, W.

W. Du, K. Li, D. Wu, K. Jiao, L. Jiao, L. Liu, F. Xia, W. Kong, L. Dong, and M. Yun, “Electrically controllable directional coupler based on tunable hybrid graphene nanoplasmonic waveguide,” Opt. Commun. 430, 450–455 (2019).
[Crossref]

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref]

Ferreira, A.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. Peres, and A. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011).
[Crossref]

Forsberg, E.

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface plasmon polaritons,” Opt. Commun. 259, 690–695 (2006).
[Crossref]

Fu, X.

Y. Meng, F. Hu, Y. Shen, Y. Yang, Q. Xiao, X. Fu, and M. Gong, “Ultracompact graphene-assisted tunable waveguide couplers with high directivity and mode selectivity,” Sci. Rep. 8, 13362 (2018).
[Crossref]

Ghattamaneni, N.

D. R. Cooper, B. D’Anjou, N. Ghattamaneni, B. Harack, M. Hilke, A. Horth, N. Majlis, M. Massicotte, L. Vandsburger, E. Whiteway, and V. Yu, “Experimental review of graphene,” ISRN Condens. Matter Phys. 2012, 501686 (2012).

Gong, M.

Y. Meng, F. Hu, Y. Shen, Y. Yang, Q. Xiao, X. Fu, and M. Gong, “Ultracompact graphene-assisted tunable waveguide couplers with high directivity and mode selectivity,” Sci. Rep. 8, 13362 (2018).
[Crossref]

Han, Y.-H.

S.-J. Im, Y.-H. Han, K.-S. Ho, C.-S. Ri, Y.-H. Ko, and Q.-Q. Wang, “Nanoscale optical directional coupler,” Plasmonics 12, 1741–1747 (2017).
[Crossref]

Han, Z.

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface plasmon polaritons,” Opt. Commun. 259, 690–695 (2006).
[Crossref]

Harack, B.

D. R. Cooper, B. D’Anjou, N. Ghattamaneni, B. Harack, M. Hilke, A. Horth, N. Majlis, M. Massicotte, L. Vandsburger, E. Whiteway, and V. Yu, “Experimental review of graphene,” ISRN Condens. Matter Phys. 2012, 501686 (2012).

Hasegawa, M.

K. Kanahashi, M. Ishihara, M. Hasegawa, H. Ohta, and T. Takenobu, “Giant power factors in p- and n-type large-area graphene films on a flexible plastic substrate,” npj 2D Mater. Appl. 3, 1–6 (2019).
[Crossref]

He, M.-D.

M.-D. He, K.-J. Wang, L. Wang, J.-B. Li, J.-Q. Liu, Z.-R. Huang, L. Wang, L. Wang, W.-D. Hu, and X. Chen, “Graphene-based terahertz tunable plasmonic directional coupler,” Appl. Phys. Lett. 105, 081903 (2014).
[Crossref]

Hilke, M.

D. R. Cooper, B. D’Anjou, N. Ghattamaneni, B. Harack, M. Hilke, A. Horth, N. Majlis, M. Massicotte, L. Vandsburger, E. Whiteway, and V. Yu, “Experimental review of graphene,” ISRN Condens. Matter Phys. 2012, 501686 (2012).

Ho, K.-S.

S.-J. Im, Y.-H. Han, K.-S. Ho, C.-S. Ri, Y.-H. Ko, and Q.-Q. Wang, “Nanoscale optical directional coupler,” Plasmonics 12, 1741–1747 (2017).
[Crossref]

Horth, A.

D. R. Cooper, B. D’Anjou, N. Ghattamaneni, B. Harack, M. Hilke, A. Horth, N. Majlis, M. Massicotte, L. Vandsburger, E. Whiteway, and V. Yu, “Experimental review of graphene,” ISRN Condens. Matter Phys. 2012, 501686 (2012).

Hu, F.

Y. Meng, F. Hu, Y. Shen, Y. Yang, Q. Xiao, X. Fu, and M. Gong, “Ultracompact graphene-assisted tunable waveguide couplers with high directivity and mode selectivity,” Sci. Rep. 8, 13362 (2018).
[Crossref]

Hu, W.-D.

M.-D. He, K.-J. Wang, L. Wang, J.-B. Li, J.-Q. Liu, Z.-R. Huang, L. Wang, L. Wang, W.-D. Hu, and X. Chen, “Graphene-based terahertz tunable plasmonic directional coupler,” Appl. Phys. Lett. 105, 081903 (2014).
[Crossref]

Huang, Z.

H. Li, L. Wang, Z. Huang, B. Sun, X. Zhai, and X. Li, “Mid-infrared, plasmonic switches and directional couplers induced by graphene sheets coupling system,” Europhys. Lett. 104, 37001 (2013).
[Crossref]

Huang, Z.-R.

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D. R. Cooper, B. D’Anjou, N. Ghattamaneni, B. Harack, M. Hilke, A. Horth, N. Majlis, M. Massicotte, L. Vandsburger, E. Whiteway, and V. Yu, “Experimental review of graphene,” ISRN Condens. Matter Phys. 2012, 501686 (2012).

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Wang, Q.-Q.

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Wang, X.

X. Wang, P. Zhao, and T. Yang, “A THz cross-guide waveguide directional coupler with high directivity,” in 15th International Conference on Electronic Packaging Technology (IEEE, 2014), pp. 1329–1330.

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D. R. Cooper, B. D’Anjou, N. Ghattamaneni, B. Harack, M. Hilke, A. Horth, N. Majlis, M. Massicotte, L. Vandsburger, E. Whiteway, and V. Yu, “Experimental review of graphene,” ISRN Condens. Matter Phys. 2012, 501686 (2012).

Wu, D.

W. Du, K. Li, D. Wu, K. Jiao, L. Jiao, L. Liu, F. Xia, W. Kong, L. Dong, and M. Yun, “Electrically controllable directional coupler based on tunable hybrid graphene nanoplasmonic waveguide,” Opt. Commun. 430, 450–455 (2019).
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R. Yang, S. Wu, D. Wang, G. Xie, M. Cheng, G. Wang, W. Yang, P. Chen, D. Shi, and G. Zhang, “Fabrication of high-quality all-graphene devices with low contact resistances,” Nano Res. 7, 1449–1456 (2014).
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Y. Meng, F. Hu, Y. Shen, Y. Yang, Q. Xiao, X. Fu, and M. Gong, “Ultracompact graphene-assisted tunable waveguide couplers with high directivity and mode selectivity,” Sci. Rep. 8, 13362 (2018).
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Xu-You, L.

Y. Ying-Ying, L. Xu-You, S. Bo, and H. Kun-Peng, “Design and optimization of terahertz directional coupler based on hybrid-cladding hollow waveguide with low confinement loss,” Chin. Phys. B 24, 068702 (2015).
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R. Yang, S. Wu, D. Wang, G. Xie, M. Cheng, G. Wang, W. Yang, P. Chen, D. Shi, and G. Zhang, “Fabrication of high-quality all-graphene devices with low contact resistances,” Nano Res. 7, 1449–1456 (2014).
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X. Wang, P. Zhao, and T. Yang, “A THz cross-guide waveguide directional coupler with high directivity,” in 15th International Conference on Electronic Packaging Technology (IEEE, 2014), pp. 1329–1330.

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R. Yang, S. Wu, D. Wang, G. Xie, M. Cheng, G. Wang, W. Yang, P. Chen, D. Shi, and G. Zhang, “Fabrication of high-quality all-graphene devices with low contact resistances,” Nano Res. 7, 1449–1456 (2014).
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Y. Meng, F. Hu, Y. Shen, Y. Yang, Q. Xiao, X. Fu, and M. Gong, “Ultracompact graphene-assisted tunable waveguide couplers with high directivity and mode selectivity,” Sci. Rep. 8, 13362 (2018).
[Crossref]

Yin, X.

T. Zhang, X. Ke, X. Yin, L. Chen, and X. Li, “Graphene-assisted ultra-compact polarization splitter and rotator with an extended bandwidth,” Sci. Rep. 7, 12169 (2017).
[Crossref]

Ying, W.

W. Ying, Z. Binzhen, D. Junping, and S. Yujie, “Terahertz waveguide directional coupler with double” tian-shape,” in IEEE 9th International Conference on Communication Software and Networks (ICCSN) (IEEE, 2017), pp. 758–761.

Ying-Ying, Y.

Y. Ying-Ying, L. Xu-You, S. Bo, and H. Kun-Peng, “Design and optimization of terahertz directional coupler based on hybrid-cladding hollow waveguide with low confinement loss,” Chin. Phys. B 24, 068702 (2015).
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D. R. Cooper, B. D’Anjou, N. Ghattamaneni, B. Harack, M. Hilke, A. Horth, N. Majlis, M. Massicotte, L. Vandsburger, E. Whiteway, and V. Yu, “Experimental review of graphene,” ISRN Condens. Matter Phys. 2012, 501686 (2012).

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B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100, 131111 (2012).
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Yujie, S.

W. Ying, Z. Binzhen, D. Junping, and S. Yujie, “Terahertz waveguide directional coupler with double” tian-shape,” in IEEE 9th International Conference on Communication Software and Networks (ICCSN) (IEEE, 2017), pp. 758–761.

Yun, M.

W. Du, K. Li, D. Wu, K. Jiao, L. Jiao, L. Liu, F. Xia, W. Kong, L. Dong, and M. Yun, “Electrically controllable directional coupler based on tunable hybrid graphene nanoplasmonic waveguide,” Opt. Commun. 430, 450–455 (2019).
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H. Li, L. Wang, Z. Huang, B. Sun, X. Zhai, and X. Li, “Mid-infrared, plasmonic switches and directional couplers induced by graphene sheets coupling system,” Europhys. Lett. 104, 37001 (2013).
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R. Yang, S. Wu, D. Wang, G. Xie, M. Cheng, G. Wang, W. Yang, P. Chen, D. Shi, and G. Zhang, “Fabrication of high-quality all-graphene devices with low contact resistances,” Nano Res. 7, 1449–1456 (2014).
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L. Zhang, Q. Xiong, X. Li, and M. Zhang, “Transmission characteristics analysis of a directional coupler based on hybrid SNIMS plasmonic waveguide,” in International Conference on Mechatronics, Electronic, Industrial and Control Engineering (MEIC-14) (Atlantis, 2014).

Zhang, M.

L. Zhang, Q. Xiong, X. Li, and M. Zhang, “Transmission characteristics analysis of a directional coupler based on hybrid SNIMS plasmonic waveguide,” in International Conference on Mechatronics, Electronic, Industrial and Control Engineering (MEIC-14) (Atlantis, 2014).

Zhang, Q.

K. E. Kitko and Q. Zhang, “Graphene-based nanomaterials: from production to integration with modern tools in neuroscience,” Front. Syst. Neurosci. 13, 26 (2019).
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Zhang, T.

T. Zhang, X. Ke, X. Yin, L. Chen, and X. Li, “Graphene-assisted ultra-compact polarization splitter and rotator with an extended bandwidth,” Sci. Rep. 7, 12169 (2017).
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Zhang, X.

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100, 131111 (2012).
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Zhao, P.

X. Wang, P. Zhao, and T. Yang, “A THz cross-guide waveguide directional coupler with high directivity,” in 15th International Conference on Electronic Packaging Technology (IEEE, 2014), pp. 1329–1330.

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Zhu, W.

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S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
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Appl. Phys. Lett. (2)

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100, 131111 (2012).
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M.-D. He, K.-J. Wang, L. Wang, J.-B. Li, J.-Q. Liu, Z.-R. Huang, L. Wang, L. Wang, W.-D. Hu, and X. Chen, “Graphene-based terahertz tunable plasmonic directional coupler,” Appl. Phys. Lett. 105, 081903 (2014).
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Chin. Phys. B (1)

Y. Ying-Ying, L. Xu-You, S. Bo, and H. Kun-Peng, “Design and optimization of terahertz directional coupler based on hybrid-cladding hollow waveguide with low confinement loss,” Chin. Phys. B 24, 068702 (2015).
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Curr. Opt. Photon. (1)

Europhys. Lett. (1)

H. Li, L. Wang, Z. Huang, B. Sun, X. Zhai, and X. Li, “Mid-infrared, plasmonic switches and directional couplers induced by graphene sheets coupling system,” Europhys. Lett. 104, 37001 (2013).
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Front. Syst. Neurosci. (1)

K. E. Kitko and Q. Zhang, “Graphene-based nanomaterials: from production to integration with modern tools in neuroscience,” Front. Syst. Neurosci. 13, 26 (2019).
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IET Optoelectronics (1)

P. Karimi, M. Maddahali, A. Bakhtafrouz, and M. Shahabadi, “Design of a wideband terahertz absorber composed of graphene patches,” IET Optoelectronics 13, 235–239 (2019).
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Figures (16)

Fig. 1.
Fig. 1. Real and imaginary parts of the conductivity as a function of frequency for two values of chemical potential, and for $ {B_0} = 0 $, $ T = 300\,\, {\rm K}^{\circ } $, and $ \Gamma = \frac{1}{{2 \times 0.7638\,\, {\rm ps}}} $.
Fig. 2.
Fig. 2. FOM as a function of frequency for two values of chemical potential.
Fig. 3.
Fig. 3. Geometrical cross section of the proposed waveguide. $ {W_g} = 60[{\rm nm}],{t_g} = 0.1[{\rm nm}],{H_g} = 5[{\rm nm}] $; the metallic films are $ Ag $, and the dielectric between the two graphene strips and the substrate and the superstrate are $ {\rm SiO}_{2} $.
Fig. 4.
Fig. 4. Electric field distribution of the fundamental eigenmode ($ |E| $) at the cross section of proposed waveguide for $ {\mu _{{c_{\text{nonconductive}}}}} = 15[{\rm meV}] $, $ {\mu _{{c_{\text{conductive}}}}} = 2100[{\rm meV}] $, $ f = 50[{\rm THz}] $, $ {W_g} = 60[{\rm nm}] $, and $ T = 300\,\, {\rm K}^{ \circ } $.
Fig. 5.
Fig. 5. $ {\rm Re} \{ {n_{\text{eff}}}\} $ of the first three guided modes and the $ {\rm Im} \{ {n_{\text{eff}}}\} $ for the fundamental mode, as a function of $ {W_g} $ and for $ f = 50[{\rm THz}] $.
Fig. 6.
Fig. 6. Geometrical structure of the graphene-based coupler: (a) top view and (b) front view.
Fig. 7.
Fig. 7. Magnitude of electric field for total-coupling single-gap directional coupler ($ {d_g} = 178[{\rm nm}] $).
Fig. 8.
Fig. 8. Magnitude of electric field for half-power single-gap directional coupler ($ {d_g} = 102[{\rm nm}] $).
Fig. 9.
Fig. 9. Magnitude of electric field for $ - 6\,\, {\rm dB} $ single-gap directional coupler ($ {d_g} = 77[{\rm nm}] $).
Fig. 10.
Fig. 10. Magnitude of electric field for $ - 10\,\, {\rm dB} $ single-gap directional coupler ($ {d_g} = 55[{\rm nm}] $).
Fig. 11.
Fig. 11. Geometrical structure of the graphene-based double-gap directional coupler.
Fig. 12.
Fig. 12. Magnitude of electric field for total-coupling double-gap directional coupler ($ {d_g} = 93\,\, [{\rm nm}] $, $ d = 32\,\, [{\rm nm}] $).
Fig. 13.
Fig. 13. Magnitude of electric field for half-power double-gap directional coupler ($ {d_g} = 60[{\rm nm}] $, $ d = 15[{\rm nm}] $).
Fig. 14.
Fig. 14. Magnitude of electric field for $ - 6\,\, {\rm dB} $ double-gap directional coupler ($ {d_g} = 51[{\rm nm}] $, $ d = 30[{\rm nm}] $).
Fig. 15.
Fig. 15. Magnitude of electric field for $ - 10\,\, {\rm dB} $ double-gap directional coupler ($ {d_g} = 38[{\rm nm}] $, $ d = 48[{\rm nm}] $).
Fig. 16.
Fig. 16. Frequency response of scattering parameters for the (a) single-gap and (b) double-gap $ - 6\,\, {\rm dB} $ directional couplers.

Tables (3)

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Table 1. Length of the Coupling Gap for Six Important Coupling Factors in Single-Gap Directional Coupler

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Table 2. Length of the Coupling Gap for Six Important Coupling Factors in Double-Gap Directional Coupler

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Table 3. Bandwidth of Single-Gap and Double-Gap Couplers for Different Coupling Coefficients

Equations (4)

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σ ( ω , μ c ( E 0 ) , Γ , T , B 0 ) = x ^ x ^ σ xx + y ^ y ^ σ yy .
σ ( ω , μ c ( E 0 ) , Γ , T , B 0 ) = σ d I t ,
σ d = e 2 v F 2 | e B 0 | ( ω + i 2 Γ ) i π × n = 0 ( 1 Δ 2 M n M n + 1 ) × [ n F ( M n ) n F ( M n + 1 ) ] + [ n F ( M n + 1 ) n F ( M n ) ] ( M n + 1 M n ) 2 ( ω + 2 i Γ ) 2 × 1 M n + 1 M n + ( 1 + Δ 2 M n M n + 1 ) × [ n F ( M n ) n F ( M n + 1 ) ] + [ n F ( M n + 1 ) n F ( M n ) ] ( M n + 1 + M n ) 2 ( ω + 2 i Γ ) 2 × 1 M n + 1 + M n ,
[ S ] = [ 0 S 12 S 13 0 S 12 0 0 S 13 S 13 0 0 S 12 0 S 13 S 12 0 ] ,

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