Abstract

The anisotropic plasmons properties of black phosphorus allow for realizing direction-dependent plasmonics devices. Here, we theoretically investigated the hybridization between graphene surface plasmons (GSP) and anisotropic black phosphorus localized surface plasmons (BPLSP) in the strong coupling regime. By dynamically adjusting the Fermi level of graphene, we show that the strong coherent GSP-BPLSP coupling can be achieved in both armchair and zigzag directions, which is attributed to the anisotropic black phosphorus with different in-plane effective electron masses along the two crystal axes. The strong coupling is quantitatively described by calculating the dispersion of the hybrid modes using a coupled oscillator model. Mode splitting energy of 26.5 meV and 19 meV are determined for the GSP-BPLSP hybridization along armchair and zigzag direction, respectively. We also find that the coupling strength can be strongly affected by the distance between graphene sheet and black phosphorus nanoribbons. Our work may provide the building blocks to construct future highly compact anisotropic plasmonics devices based on two-dimensional materials at infrared and terahertz frequencies.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  5. T. Low and P. Avouris, “Graphene Plasmonics for Terahertz to Mid-Infrared Applications,” ACS Nano 8(2), 1086–1101 (2014).
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  6. L. Tang, J. Du, C. Du, P. Zhu, and H. Shi, “Scaling phenomenon of graphene surface plasmon modes in grating-spacer-graphene hybrid systems,” Opt. Express 22(17), 20214–20222 (2014).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  23. S. Kim, M. S. Jang, V. W. Brar, Y. Tolstova, K. W. Mauser, and H. A. Atwater, “Electronically tunable extraordinary optical transmission in graphene plasmonic ribbons coupled to subwavelength metallic slit arrays,” Nat. Commun. 7, 12323 (2016).
    [Crossref] [PubMed]
  24. B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
    [Crossref]
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    [Crossref] [PubMed]
  26. R. Yu, R. Alaee, F. Lederer, and C. Rockstuhl, “Manipulating the interaction between localized and delocalized surface plasmon-polaritons in graphene,” Phys. Rev. B 90(8), 085409 (2014).
    [Crossref]
  27. H. Lu, Y. Gong, D. Mao, X. Gan, and J. Zhao, “Strong plasmonic confinement and optical force in phosphorene pairs,” Opt. Express 25(5), 5255–5263 (2017).
    [Crossref] [PubMed]
  28. X. Wang and S. Lan, “Optical properties of black phosphorus,” Adv. Opt. Photonics 8(4), 618 (2016).
    [Crossref]
  29. N. Mao, J. Tang, L. Xie, J. Wu, B. Han, J. Lin, S. Deng, W. Ji, H. Xu, K. Liu, L. Tong, and J. Zhang, “Optical Anisotropy of Black Phosphorus in the Visible Regime,” J. Am. Chem. Soc. 138(1), 300–305 (2016).
    [Crossref] [PubMed]
  30. X. Ling, S. Huang, E. H. Hasdeo, L. Liang, W. M. Parkin, Y. Tatsumi, A. R. Nugraha, A. A. Puretzky, P. M. Das, B. G. Sumpter, D. B. Geohegan, J. Kong, R. Saito, M. Drndic, V. Meunier, and M. S. Dresselhaus, “Anisotropic Electron-Photon and Electron-Phonon Interactions in Black Phosphorus,” Nano Lett. 16(4), 2260–2267 (2016).
    [Crossref] [PubMed]
  31. M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
    [Crossref] [PubMed]
  32. L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
    [Crossref] [PubMed]
  33. Y. Deng, Z. Luo, N. J. Conrad, H. Liu, Y. Gong, S. Najmaei, P. M. Ajayan, J. Lou, X. Xu, and P. D. Ye, “Black Phosphorus-Monolayer MoS2 van der Waals Heterojunction P-N Diode,” ACS Nano 8(8), 8292–8299 (2014).
    [Crossref] [PubMed]
  34. M. Buscema, D. J. Groenendijk, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Photovoltaic effect in few-layer black phosphorus PN junctions defined by local electrostatic gating,” Nat. Commun. 5, 4651 (2014).
    [Crossref] [PubMed]
  35. M. Huang, M. Wang, C. Chen, Z. Ma, X. Li, J. Han, and Y. Wu, “Broadband black-phosphorus photodetectors with high responsivity,” Adv. Mater. 28(18), 3481–3485 (2016).
    [Crossref] [PubMed]
  36. J. Wang and Y. Jiang, “Infrared absorber based on sandwiched two-dimensional black phosphorus metamaterials,” Opt. Express 25(5), 5206–5216 (2017).
    [Crossref] [PubMed]
  37. Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016).
    [Crossref] [PubMed]
  38. X. Ni, L. Wang, J. Zhu, X. Chen, and W. Lu, “Surface plasmons in a nanostructured black phosphorus flake,” Opt. Lett. 42(13), 2659–2662 (2017).
    [Crossref] [PubMed]
  39. F. Xiong, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Strong anisotropic perfect absorption in monolayer black phosphorous and its application as tunable polarizer,” J. Opt. 19(7), 075002 (2017).
    [Crossref]
  40. D. Correas-Serrano, J. S. Gomez-Diaz, A. A. Melcon, and A. Alù, “Black phosphorus plasmonics: anisotropic elliptical propagation and nonlocality-induced canalization,” J. Opt. 18(10), 104006 (2016).
    [Crossref]
  41. Z. W. Bao, H. W. Wu, and Y. Zhou, “Edge plasmons in monolayer black phosphorus,” Appl. Phys. Lett. 109(24), 241902 (2016).
    [Crossref]
  42. K. T. Lam and J. Guo, “Plasmonics in strained monolayer black phosphorus,” J. Appl. Phys. 117(11), 113105 (2015).
    [Crossref]
  43. T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
    [Crossref] [PubMed]
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    [Crossref]
  45. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
    [Crossref]
  46. W. Wang, P. Vasa, R. Pomraenke, R. Vogelgesang, A. De Sio, E. Sommer, M. Maiuri, C. Manzoni, G. Cerullo, and C. Lienau, “Interplay between strong coupling and radiative damping of excitons and surface plasmon polaritons in hybrid nanostructures,” ACS Nano 8(1), 1056–1064 (2014).
    [Crossref] [PubMed]
  47. W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
    [Crossref] [PubMed]
  48. P. Vasa, W. Wang, R. Pomraenke, M. Maiuri, C. Manzoni, G. Cerullo, and C. Lienau, “Optical stark effects in j-aggregate-metal hybrid nanostructures exhibiting a strong exciton-surface-plasmon-polariton interaction,” Phys. Rev. Lett. 114(3), 036802 (2015).
    [Crossref] [PubMed]

2017 (9)

F. Monticone and A. Alù, “Metamaterial, plasmonic and nanophotonic devices,” Rep. Prog. Phys. 80(3), 036401 (2017).
[Crossref] [PubMed]

H. Lu, X. Gan, D. Mao, and J. Zhao, “Graphene-supported manipulation of surface plasmon polaritons in metallic nanowaveguides,” Photon. Res. 5(3), 162 (2017).
[Crossref]

Q. Guo, F. Guinea, B. Deng, I. Sarpkaya, C. Li, C. Chen, X. Ling, J. Kong, and F. Xia, “Electrothermal Control of Graphene Plasmon-Phonon Polaritons,” Adv. Mater. 29(31), 1700566 (2017).
[Crossref] [PubMed]

S. Qu, H. Liu, L. Dong, L. Wu, C. Ma, and S. Wang, “Graphene-Hexagonal Boron Nitride Heterostructure as a Tunable Phonon–Plasmon Coupling System,” Crystals 7(2), 49 (2017).
[Crossref]

H. Lu, Y. Gong, D. Mao, X. Gan, and J. Zhao, “Strong plasmonic confinement and optical force in phosphorene pairs,” Opt. Express 25(5), 5255–5263 (2017).
[Crossref] [PubMed]

J. Wang and Y. Jiang, “Infrared absorber based on sandwiched two-dimensional black phosphorus metamaterials,” Opt. Express 25(5), 5206–5216 (2017).
[Crossref] [PubMed]

X. Ni, L. Wang, J. Zhu, X. Chen, and W. Lu, “Surface plasmons in a nanostructured black phosphorus flake,” Opt. Lett. 42(13), 2659–2662 (2017).
[Crossref] [PubMed]

F. Xiong, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Strong anisotropic perfect absorption in monolayer black phosphorous and its application as tunable polarizer,” J. Opt. 19(7), 075002 (2017).
[Crossref]

D. A. Prishchenko, V. G. Mazurenko, M. I. Katsnelson, and A. N. Rudenko, “Coulomb interactions and screening effects in few-layer black phosphorus: a tight-binding consideration beyond the long-wavelength limit,” 2D Materials 4(2), 025064 (2017).
[Crossref]

2016 (11)

D. Correas-Serrano, J. S. Gomez-Diaz, A. A. Melcon, and A. Alù, “Black phosphorus plasmonics: anisotropic elliptical propagation and nonlocality-induced canalization,” J. Opt. 18(10), 104006 (2016).
[Crossref]

Z. W. Bao, H. W. Wu, and Y. Zhou, “Edge plasmons in monolayer black phosphorus,” Appl. Phys. Lett. 109(24), 241902 (2016).
[Crossref]

Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016).
[Crossref] [PubMed]

M. Huang, M. Wang, C. Chen, Z. Ma, X. Li, J. Han, and Y. Wu, “Broadband black-phosphorus photodetectors with high responsivity,” Adv. Mater. 28(18), 3481–3485 (2016).
[Crossref] [PubMed]

S. Kim, M. S. Jang, V. W. Brar, Y. Tolstova, K. W. Mauser, and H. A. Atwater, “Electronically tunable extraordinary optical transmission in graphene plasmonic ribbons coupled to subwavelength metallic slit arrays,” Nat. Commun. 7, 12323 (2016).
[Crossref] [PubMed]

X. Wang and S. Lan, “Optical properties of black phosphorus,” Adv. Opt. Photonics 8(4), 618 (2016).
[Crossref]

N. Mao, J. Tang, L. Xie, J. Wu, B. Han, J. Lin, S. Deng, W. Ji, H. Xu, K. Liu, L. Tong, and J. Zhang, “Optical Anisotropy of Black Phosphorus in the Visible Regime,” J. Am. Chem. Soc. 138(1), 300–305 (2016).
[Crossref] [PubMed]

X. Ling, S. Huang, E. H. Hasdeo, L. Liang, W. M. Parkin, Y. Tatsumi, A. R. Nugraha, A. A. Puretzky, P. M. Das, B. G. Sumpter, D. B. Geohegan, J. Kong, R. Saito, M. Drndic, V. Meunier, and M. S. Dresselhaus, “Anisotropic Electron-Photon and Electron-Phonon Interactions in Black Phosphorus,” Nano Lett. 16(4), 2260–2267 (2016).
[Crossref] [PubMed]

H. Hu, X. Yang, F. Zhai, D. Hu, R. Liu, K. Liu, Z. Sun, and Q. Dai, “Far-field nanoscale infrared spectroscopy of vibrational fingerprints of molecules with graphene plasmons,” Nat. Commun. 7, 12334 (2016).
[Crossref] [PubMed]

R. J. Koch, S. Fryska, M. Ostler, M. Endlich, F. Speck, T. Hänsel, J. A. Schaefer, and T. Seyller, “Robust Phonon-Plasmon Coupling in Quasifreestanding Graphene on Silicon Carbide,” Phys. Rev. Lett. 116(10), 106802 (2016).
[Crossref] [PubMed]

T. Guo and C. Argyropoulos, “Broadband polarizers based on graphene metasurfaces,” Opt. Lett. 41(23), 5592–5595 (2016).
[Crossref] [PubMed]

2015 (8)

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015).
[Crossref] [PubMed]

B. Zhao and Z. M. Zhang, “Strong plasmonic coupling between graphene ribbon array and metal gratings,” ACS Photonics 2(11), 1611–1618 (2015).
[Crossref]

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

I. D. Barcelos, A. R. Cadore, L. C. Campos, A. Malachias, K. Watanabe, T. Taniguchi, F. C. Maia, R. Freitas, and C. Deneke, “Graphene/h-BN plasmon-phonon coupling and plasmon delocalization observed by infrared nano-spectroscopy,” Nanoscale 7(27), 11620–11625 (2015).
[Crossref] [PubMed]

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref] [PubMed]

K. T. Lam and J. Guo, “Plasmonics in strained monolayer black phosphorus,” J. Appl. Phys. 117(11), 113105 (2015).
[Crossref]

P. Vasa, W. Wang, R. Pomraenke, M. Maiuri, C. Manzoni, G. Cerullo, and C. Lienau, “Optical stark effects in j-aggregate-metal hybrid nanostructures exhibiting a strong exciton-surface-plasmon-polariton interaction,” Phys. Rev. Lett. 114(3), 036802 (2015).
[Crossref] [PubMed]

2014 (9)

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref] [PubMed]

W. Wang, P. Vasa, R. Pomraenke, R. Vogelgesang, A. De Sio, E. Sommer, M. Maiuri, C. Manzoni, G. Cerullo, and C. Lienau, “Interplay between strong coupling and radiative damping of excitons and surface plasmon polaritons in hybrid nanostructures,” ACS Nano 8(1), 1056–1064 (2014).
[Crossref] [PubMed]

R. Yu, R. Alaee, F. Lederer, and C. Rockstuhl, “Manipulating the interaction between localized and delocalized surface plasmon-polaritons in graphene,” Phys. Rev. B 90(8), 085409 (2014).
[Crossref]

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
[Crossref] [PubMed]

L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
[Crossref] [PubMed]

Y. Deng, Z. Luo, N. J. Conrad, H. Liu, Y. Gong, S. Najmaei, P. M. Ajayan, J. Lou, X. Xu, and P. D. Ye, “Black Phosphorus-Monolayer MoS2 van der Waals Heterojunction P-N Diode,” ACS Nano 8(8), 8292–8299 (2014).
[Crossref] [PubMed]

M. Buscema, D. J. Groenendijk, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Photovoltaic effect in few-layer black phosphorus PN junctions defined by local electrostatic gating,” Nat. Commun. 5, 4651 (2014).
[Crossref] [PubMed]

T. Low and P. Avouris, “Graphene Plasmonics for Terahertz to Mid-Infrared Applications,” ACS Nano 8(2), 1086–1101 (2014).
[Crossref] [PubMed]

L. Tang, J. Du, C. Du, P. Zhu, and H. Shi, “Scaling phenomenon of graphene surface plasmon modes in grating-spacer-graphene hybrid systems,” Opt. Express 22(17), 20214–20222 (2014).
[Crossref] [PubMed]

2013 (1)

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

2012 (6)

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete Optical Absorption in Periodically Patterned Graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
[Crossref] [PubMed]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

2011 (2)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

M. Jablan, M. Soljačić, and H. Buljan, “Unconventional plasmon-phonon coupling in graphene,” Phys. Rev. B 83(16), 161409 (2011).
[Crossref]

2010 (1)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

2009 (1)

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Ajayan, P. M.

Y. Deng, Z. Luo, N. J. Conrad, H. Liu, Y. Gong, S. Najmaei, P. M. Ajayan, J. Lou, X. Xu, and P. D. Ye, “Black Phosphorus-Monolayer MoS2 van der Waals Heterojunction P-N Diode,” ACS Nano 8(8), 8292–8299 (2014).
[Crossref] [PubMed]

Alaee, R.

R. Yu, R. Alaee, F. Lederer, and C. Rockstuhl, “Manipulating the interaction between localized and delocalized surface plasmon-polaritons in graphene,” Phys. Rev. B 90(8), 085409 (2014).
[Crossref]

Alonso-González, P.

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P. Vasa, W. Wang, R. Pomraenke, M. Maiuri, C. Manzoni, G. Cerullo, and C. Lienau, “Optical stark effects in j-aggregate-metal hybrid nanostructures exhibiting a strong exciton-surface-plasmon-polariton interaction,” Phys. Rev. Lett. 114(3), 036802 (2015).
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Mao, N.

N. Mao, J. Tang, L. Xie, J. Wu, B. Han, J. Lin, S. Deng, W. Ji, H. Xu, K. Liu, L. Tong, and J. Zhang, “Optical Anisotropy of Black Phosphorus in the Visible Regime,” J. Am. Chem. Soc. 138(1), 300–305 (2016).
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S. Kim, M. S. Jang, V. W. Brar, Y. Tolstova, K. W. Mauser, and H. A. Atwater, “Electronically tunable extraordinary optical transmission in graphene plasmonic ribbons coupled to subwavelength metallic slit arrays,” Nat. Commun. 7, 12323 (2016).
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D. A. Prishchenko, V. G. Mazurenko, M. I. Katsnelson, and A. N. Rudenko, “Coulomb interactions and screening effects in few-layer black phosphorus: a tight-binding consideration beyond the long-wavelength limit,” 2D Materials 4(2), 025064 (2017).
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K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
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L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
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H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
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L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
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Zhang, Z. M.

B. Zhao and Z. M. Zhang, “Strong plasmonic coupling between graphene ribbon array and metal gratings,” ACS Photonics 2(11), 1611–1618 (2015).
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Zhao, B.

B. Zhao and Z. M. Zhang, “Strong plasmonic coupling between graphene ribbon array and metal gratings,” ACS Photonics 2(11), 1611–1618 (2015).
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Zhao, J.

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Z. W. Bao, H. W. Wu, and Y. Zhou, “Edge plasmons in monolayer black phosphorus,” Appl. Phys. Lett. 109(24), 241902 (2016).
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Zhu, J.

Zhu, P.

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Zhu, W.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
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Zhu, Z.

F. Xiong, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Strong anisotropic perfect absorption in monolayer black phosphorous and its application as tunable polarizer,” J. Opt. 19(7), 075002 (2017).
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B. Zhao and Z. M. Zhang, “Strong plasmonic coupling between graphene ribbon array and metal gratings,” ACS Photonics 2(11), 1611–1618 (2015).
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M. Huang, M. Wang, C. Chen, Z. Ma, X. Li, J. Han, and Y. Wu, “Broadband black-phosphorus photodetectors with high responsivity,” Adv. Mater. 28(18), 3481–3485 (2016).
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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(13), 131111 (2012).
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K. T. Lam and J. Guo, “Plasmonics in strained monolayer black phosphorus,” J. Appl. Phys. 117(11), 113105 (2015).
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F. Xiong, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Strong anisotropic perfect absorption in monolayer black phosphorous and its application as tunable polarizer,” J. Opt. 19(7), 075002 (2017).
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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of monolayer BP, where x and y axes are along the armchair (AC) and zigzag (ZZ) directions, respectively. (b) Schematic of the hybrid system consisting of continuous graphene sheet and patterned BP nanoribbons along armchair (x-) direction. The other hybrid system with BP nanoribbons along zigzag (y-) direction is not shown here. The inset shows the cross section of the structure.
Fig. 2
Fig. 2 Absorption spectra of the BP nanoribbons without graphene along (a) x- and (b) y-direction, respectively. The insets are the corresponding electric field mode profile |Ex| of the BPLSP plasmons resonant peaks. Absorption spectra of BP nanoribbons with graphene along (c) x- and (d) y-direction, respectively. (e) and (f) are the corresponding electric field mode profile of the resonant peaks in (c) and (d). (g) and (h) are the energy diagrams corresponding to the cases in (c) and (d). The parameters used for fitting are θb = π/2 rad, θd = π/2 rad, γb = 1.02 THz, γd = 0.42 THz. For x-direction cb = 0.44, cd = 0.34, while for y-direction cb = 0.31, cd = 0.2.
Fig. 3
Fig. 3 Numerical absorption spectra mapping of hybrid modes as Ef varied from 0.05 eV to 1 eV with BP nanoribbons along (a) x- and (b) y-direction. Analytical dispersion relations of the GSP, BPLSP, and hybrid modes, and the comparison between the analytical and numerical hybrid dispersion relations for BP nanoribbon along (c) x- and (d) y-direction.
Fig. 4
Fig. 4 (a), (d) and (g) are the extracted absorption spectra of the hybrid modes from 3(a) at Fermi energy of 0.2 eV, 0.45 eV and 0.8eV, respectively. (b), (e), (h) shown their corresponding electric field |Ex| patterns. (c), (f), (i) are the energy diagrams corresponding to the cases in (a), (d), (g), respectively.
Fig. 5
Fig. 5 Numerical absorption spectra mapping of hybrid modes as Fermi energy is varied from 0.05 eV to 1 eV when d is (a) 100 nm, (b) 60 nm, and (c) 20 nm for x-direction. (d) Comparison of the derived mode splitting energy of the hybrid system with BP nanoribbons along x- and y-direction as d increases from 20 nm to 120 nm.

Equations (8)

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σ(ω)= e 2 E f π 2 i ω+i τ 1 ,
σ jj (ω)= i D j π(ω+iη/) , D j =π e 2 n m j ,
m x = 2 2 γ 2 Δ + η c , m y = 2 2 ν c .
a(ω)= c b γ b exp(i θ b ) (f f b )+i γ b + c d γ d exp(i θ d ) (f f d )+i γ d .
σ jj ε 0 ω = ( ε 2 + ε 3 ) iq .
f BPLSPj = D j 2 π 2 ε 0 ( ε 2 + ε 3 )Pξ .
f GSP = e π E f 2 ε 0 ( ε 1 + ε 2 )P
f ± = f GSP + f BPLSPj 2 ± ( f GSP f BPLSPj ) 2 + Ω j 2 2 ,

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