Abstract

Coupling and hybridization of plasmon polaritons can commonly occur in graphene plasmonic nanostructures, providing new possibilities for developing many novel plasmonic optoelectronic devices. Here we have theoretically investigated the longitudinal plasmonic coupling between localized and delocalized surface plasmon polaritons in graphene nanoribbon arrays and monolayer structures in the mid-infrared region. It has been demonstrated that vertical plasmonic coupling can be actively controlled by either the geometric parameters or the Fermi energy in graphene, allowing for strong light–matter interaction. Thanks to the strong plasmon coupling, dual-band perfect absorption with A≈100% and large Rabi splitting exceeding 17.2 meV have been obtained in the absorption spectra of this hybrid system. More intriguingly, we found, by varying the distance between the graphene sheet and the metallic substrate, that periodic spectral nodes can emerge in absorption response of the hybrid mode, which was explained by the mechanism of longitudinal microcavity resonance in this coupled system. The controllable plasmonic coupling and ultrahigh dual-band absorption capability offered by this coupled structure open new avenues for designing tunable multi-channel graphene optoelectronic devices with high performance.

© 2019 Optical Society of America

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  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  20. Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14, 299–304 (2014).
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  25. J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
    [Crossref]
  26. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
    [Crossref]
  27. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
    [Crossref]
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    [Crossref]
  31. J. Nong, W. Wei, W. Wang, G. Lan, Z. Shang, J. Yi, and L. Tang, “Strong coherent coupling between graphene surface plasmons and anisotropic black phosphorus localized surface plasmons,” Opt. Express 26, 1633–1644 (2018).
    [Crossref]
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    [Crossref]
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    [Crossref]
  35. A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).
    [Crossref]
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    [Crossref]
  37. L. Novotny, “Strong coupling, energy splitting, and level crossings: a classical perspective,” Am. J. Phys. 78, 1199–1202 (2010).
    [Crossref]
  38. J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photon. 1, 347–353 (2014).
    [Crossref]
  39. J. Hu, Y. Qing, S. Yang, Y. Ren, X. Wu, W. Gao, and C. Wu, “Tailoring total absorption in a graphene monolayer covered subwavelength multilayer dielectric grating structure at near-infrared frequencies,” J. Opt. Soc. Am. B 34, 861–868 (2017).
    [Crossref]
  40. L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and G. H. Derrick, “Periodic models for thin optimal absorbers of electromagnetic radiation,” Phys. Rev. B 55, R16072 (1997).
    [Crossref]
  41. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. USA 107, 17491–17496 (2010).
    [Crossref]
  42. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
    [Crossref]
  43. V. M. Agranovich, M. Litinskaia, and D. G. Lidzey, “Cavity polaritons in microcavities containing disordered organic semiconductors,” Phys. Rev. B 67, 085311 (2003).
    [Crossref]
  44. A. Salomon, R. J. Gordon, Y. Prior, T. Seideman, and M. Sukharev, “Strong coupling between molecular excited states and surface plasmon modes of a slit array in a thin metal film,” Phys. Rev. Lett. 109, 073002 (2012).
    [Crossref]

2018 (1)

2017 (2)

2016 (5)

2015 (2)

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

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6, 8846 (2015).
[Crossref]

2014 (5)

B. Zhao and Z. M. Zhang, “Study of magnetic polaritons in deep gratings for thermal emission control,” J. Quant. Spectrosc. Radiat. Transfer 135, 81–89 (2014).
[Crossref]

F. J. G. de Abajo, “Graphene plasmonics: challenges and opportunities,” ACS Photon. 1, 135–152 (2014).
[Crossref]

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14, 299–304 (2014).
[Crossref]

J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photon. 1, 347–353 (2014).
[Crossref]

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, 085409 (2014).
[Crossref]

2013 (2)

H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103, 203112 (2013).
[Crossref]

P. I. Buslaev, I. V. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Plasmons in waveguide structures formed by two graphene layers,” JETP Lett. 97, 535–539 (2013).
[Crossref]

2012 (8)

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref]

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

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[Crossref]

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

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[Crossref]

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

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85, 081405 (2012).
[Crossref]

A. Salomon, R. J. Gordon, Y. Prior, T. Seideman, and M. Sukharev, “Strong coupling between molecular excited states and surface plasmon modes of a slit array in a thin metal film,” Phys. Rev. Lett. 109, 073002 (2012).
[Crossref]

2011 (6)

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

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[Crossref]

Y. Liu, R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, and X. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun. 2, 579 (2011).
[Crossref]

2010 (4)

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

L. Novotny, “Strong coupling, energy splitting, and level crossings: a classical perspective,” Am. J. Phys. 78, 1199–1202 (2010).
[Crossref]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. USA 107, 17491–17496 (2010).
[Crossref]

2009 (1)

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

2008 (3)

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308(2008).
[Crossref]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref]

2007 (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref]

2003 (2)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[Crossref]

V. M. Agranovich, M. Litinskaia, and D. G. Lidzey, “Cavity polaritons in microcavities containing disordered organic semiconductors,” Phys. Rev. B 67, 085311 (2003).
[Crossref]

1997 (1)

L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and G. H. Derrick, “Periodic models for thin optimal absorbers of electromagnetic radiation,” Phys. Rev. B 55, R16072 (1997).
[Crossref]

Agranovich, V. M.

V. M. Agranovich, M. Litinskaia, and D. G. Lidzey, “Cavity polaritons in microcavities containing disordered organic semiconductors,” Phys. Rev. B 67, 085311 (2003).
[Crossref]

Ajayan, P. M.

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14, 299–304 (2014).
[Crossref]

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, 085409 (2014).
[Crossref]

Alonso-González, P.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[Crossref]

Ansell, D.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6, 8846 (2015).
[Crossref]

Avouris, P.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref]

Badioli, M.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[Crossref]

Bai, J.

Y. Liu, R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, and X. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun. 2, 579 (2011).
[Crossref]

Basko, D. M.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Belov, P. A.

P. I. Buslaev, I. V. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Plasmons in waveguide structures formed by two graphene layers,” JETP Lett. 97, 535–539 (2013).
[Crossref]

Blake, P.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308(2008).
[Crossref]

Bonaccorso, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Booth, T. J.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308(2008).
[Crossref]

Botten, L. C.

L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and G. H. Derrick, “Periodic models for thin optimal absorbers of electromagnetic radiation,” Phys. Rev. B 55, R16072 (1997).
[Crossref]

Bozhevolnyi, S. I.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6, 8846 (2015).
[Crossref]

Britnell, L.

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[Crossref]

Buljan, H.

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

Buslaev, P. I.

P. I. Buslaev, I. V. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Plasmons in waveguide structures formed by two graphene layers,” JETP Lett. 97, 535–539 (2013).
[Crossref]

Camara, N.

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Nordlander, P.

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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, 192–200(2012).
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A. Salomon, R. J. Gordon, Y. Prior, T. Seideman, and M. Sukharev, “Strong coupling between molecular excited states and surface plasmon modes of a slit array in a thin metal film,” Phys. Rev. Lett. 109, 073002 (2012).
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K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
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P. I. Buslaev, I. V. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Plasmons in waveguide structures formed by two graphene layers,” JETP Lett. 97, 535–539 (2013).
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Shen, Y. R.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
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Shu, J.

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6, 7806–7813 (2012).
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R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308(2008).
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Sukharev, M.

A. Salomon, R. J. Gordon, Y. Prior, T. Seideman, and M. Sukharev, “Strong coupling between molecular excited states and surface plasmon modes of a slit array in a thin metal film,” Phys. Rev. Lett. 109, 073002 (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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Tian, J.

H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103, 203112 (2013).
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Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
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Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
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Wang, H.

B. Deng, Q. Guo, C. Li, H. Wang, X. Ling, D. B. Farmer, S.-J. Han, J. Kong, and F. Xia, “Coupling-enhanced broadband mid-infrared light absorption in graphene plasmonic nanostructures,” ACS Nano 10, 11172–11178 (2016).
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Wu, C.

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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
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B. Deng, Q. Guo, C. Li, H. Wang, X. Ling, D. B. Farmer, S.-J. Han, J. Kong, and F. Xia, “Coupling-enhanced broadband mid-infrared light absorption in graphene plasmonic nanostructures,” ACS Nano 10, 11172–11178 (2016).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
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Xia, S.-X.

Xie, B.

H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103, 203112 (2013).
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W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6, 7806–7813 (2012).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
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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, 085409 (2014).
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Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. USA 107, 17491–17496 (2010).
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Yuan, 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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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
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Zhang, S.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
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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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S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
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Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
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Zhang, Z. M.

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

B. Zhao and Z. M. Zhang, “Study of magnetic polaritons in deep gratings for thermal emission control,” J. Quant. Spectrosc. Radiat. Transfer 135, 81–89 (2014).
[Crossref]

Zhao, B.

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

B. Zhao and Z. M. Zhang, “Study of magnetic polaritons in deep gratings for thermal emission control,” J. Quant. Spectrosc. Radiat. Transfer 135, 81–89 (2014).
[Crossref]

Zhao, X.

Zhou, H.

Y. Liu, R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, and X. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun. 2, 579 (2011).
[Crossref]

Zhu, L.

Zhu, S.

Zhu, W.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref]

Zhu, X.

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14, 299–304 (2014).
[Crossref]

Zurutuza Elorza, A.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[Crossref]

ACS Nano (3)

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

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

B. Deng, Q. Guo, C. Li, H. Wang, X. Ling, D. B. Farmer, S.-J. Han, J. Kong, and F. Xia, “Coupling-enhanced broadband mid-infrared light absorption in graphene plasmonic nanostructures,” ACS Nano 10, 11172–11178 (2016).
[Crossref]

ACS Photon. (3)

F. J. G. de Abajo, “Graphene plasmonics: challenges and opportunities,” ACS Photon. 1, 135–152 (2014).
[Crossref]

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

J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photon. 1, 347–353 (2014).
[Crossref]

Am. J. Phys. (1)

L. Novotny, “Strong coupling, energy splitting, and level crossings: a classical perspective,” Am. J. Phys. 78, 1199–1202 (2010).
[Crossref]

Appl. Phys. Lett. (2)

H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103, 203112 (2013).
[Crossref]

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

J. Opt. Soc. Am. B (2)

J. Quant. Spectrosc. Radiat. Transfer (1)

B. Zhao and Z. M. Zhang, “Study of magnetic polaritons in deep gratings for thermal emission control,” J. Quant. Spectrosc. Radiat. Transfer 135, 81–89 (2014).
[Crossref]

JETP Lett. (1)

P. I. Buslaev, I. V. Iorsh, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Plasmons in waveguide structures formed by two graphene layers,” JETP Lett. 97, 535–539 (2013).
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Nano Lett. (2)

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14, 299–304 (2014).
[Crossref]

Nat. Commun. (3)

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[Crossref]

Y. Liu, R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, and X. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun. 2, 579 (2011).
[Crossref]

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6, 8846 (2015).
[Crossref]

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref]

Nat. Nanotechnol. (2)

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of the proposed graphene coupled structure. (a) Top view and (b) side view of this coupled system.

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Fig. 2.
Fig. 2. Absorption spectra as a function of the graphene nanoribbon width W for the different spacer thickness D of (a) 500 nm, (b) 250 nm, and (c) 100 nm between GNRA and graphene monolayer. Electric field | E | and magnetic field H z distributions at the points marked with numbers (1)–(4) in (a)–(c) are displayed in (d)–(e), (f)–(g), (h)–(i), and (j)–(k), respectively. White dashed lines in (b) and (c) indicate the resonance frequency of first- and second-order DSPP modes theoretically calculated by formula (6), and white solid lines in (d)–(k) outline the profile of the coupled graphene layers.

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Fig. 3.
Fig. 3. Absorption spectra of the system as a function of distance D between GNRA and graphene sheet at different graphene ribbon width W of (a) 90 nm, (b) 180 nm, (c) 210 nm, and (d) 300 nm, respectively.

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Fig. 4.
Fig. 4. (a) Absorption curves of the coupled structure at different W of 90 nm (orange dashed), 180 nm (blue dotted), 210 nm (red solid), and 300 nm (magenta dash-dot), in which D = 210     nm , and the other parameters are the same as those in Fig. 3. Magnetic field H z distributions at absorption peaks marked with numbers (1)–(4) in (a) and Fig. 3 are displayed in (b)–(f), respectively.

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Fig. 5.
Fig. 5. (a) Absorption spectra as a function of distance H between the graphene monolayer and the silver substrate. (b) Comparison of absorption spectra for the structure with (red solid) and without (black dashed) the silver substrate, in which H = 1250     nm , the other parameters of graphene being the same as those in Fig. 4(d). The magnetic field H z distributions at absorption (c) peak and (d) node at H = 1250     nm , 5050 nm marked with the white points of (1) and (2) in (a).

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Fig. 6.
Fig. 6. Absorption spectra as a function of the Fermi energy in graphene. (a) Fermi energy in graphene monolayer E f 2 is allowed to vary, while E f 1 is fixed at 0.6 eV. (b) Fermi energy in GNRA and graphene sheet is simultaneously changed with E F = E f 1 = E f 2 . (c) Absorption curves at the different Fermi energy E F of 0.55 eV (blue dashed), 0.6 (red solid), and 0.65 eV (black dotted) in (b). The geometric parameters of the structure are L = 600     nm , W = 210     nm , D = 120     nm , and H = 1250     nm , under TM-polarized vertical illumination.

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Equations (7)

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σ = e 2 E f π ℏ 2 i ( ω + i τ − 1 ) ,
Re ( β L ) = ℏ ω 2 / ( 2 α 0 E f c ) ,
ω L ∼ 2 π n α 0 E f c / ( ℏ W ) .
β ( ω ) ≈ π ℏ 2 ε 0 ( ε 1 + ε 2 ) e 2 E f ( 1 + i ω τ ) ω 2 ,
Re ( β ) = n ( 2 π / L ) + ε 1 k 0   sin   θ ,
ω D = 2 n e 2 E f L ℏ 2 ε 0 ( ε 1 + ε 2 ) .
ω ( E f ) = ω L + ω D ( E f ) 2 ± ω δ 2 + [ ω L − ω D ( E f ) ] 2 4 ,

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