Abstract

Since graphene supports low loss plasmonic guided modes in the infrared range, we theoretically investigate the coupling of these modes in patterned sheets with nanocavities. We calculate cavity modes and (potentially critical) coupling in filter-type circuits, with resonances observed as multiple minima in the reflection spectrum. The origin and properties of the cavity modes are fully modeled by coupled mode theory, exploring for various positions of the cavity with respect to the access waveguide. A useful resonance frequency shift is examined by modifying the graphene doping (e.g., via voltage tuning). The deep subwavelength cavity modes reach quality factors up to 42 for ribbons of 30 nm width around 5 μm wavelength. These resonances provide opportunities for ultracompact optoelectronic circuits.

© 2014 Optical Society of America

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  4. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
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  7. P.-Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Opt. Mater. 24, OP281–OP304 (2012).
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    [CrossRef]
  13. J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
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  22. G. Pirruccio, L. Moreno, G. Lozano, and J. Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7, 4810–4817 (2013).
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  23. S. Fan, W. Suh, and J. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
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  25. K. Novoselov, A. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva, and A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
    [CrossRef]
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    [CrossRef]
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2014 (1)

P. Avouris and M. Freitag, “Graphene photonics, plasmonics, and optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 20, 6000112 (2014).
[CrossRef]

2013 (6)

J. Zhu, M. Chen, Q. He, L. Shao, S. Wei, and Z. Guo, “An overview of the engineered graphene nanostructures and nanocomposites,” RSC Adv. 3, 22790–22824 (2013).

Y. Yang, A. M. Asiri, Z. Tang, D. Du, and Y. Lin, “Graphene based materials for biomedical applications,” Mater. Today 16(10), 365–373 (2013).
[CrossRef]

G. Pirruccio, L. Moreno, G. Lozano, and J. Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7, 4810–4817 (2013).
[CrossRef]

H. Lizuka and S. Fan, “Deep subwavelength plasmonic waveguide switch in double graphene layer structure,” Appl. Phys. Lett. 103, 233107 (2013).
[CrossRef]

X. Zhu, W. Yan, N. A. Mortensen, and S. Xiao, “Bends and splitters in graphene nanoribbon waveguides,” Opt. Express 21, 3486–3491 (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).

2012 (6)

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

G. Jo, M. Choe, S. Lee, W. Park, Y. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology 23, 112001 (2012).
[CrossRef]

P.-Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Opt. Mater. 24, OP281–OP304 (2012).

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

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[CrossRef]

Q. Bao and K. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6, 3677–3694 (2012).
[CrossRef]

2011 (2)

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

D. Hecht, L. Hu, and G. Irvin, “Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures,” Adv. Mater. 23, 1482–1513 (2011).
[CrossRef]

2010 (4)

F. Bonaccorso, Z. Sun, and A. Ferrari, “Graphene photonics and optoelectronics,” Nature Photonics 4, 611–622 (2010).
[CrossRef]

D. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105, 265805 (2010).

V. Kravets, A. N. Grigorenko, R. Nair, P. Blake, S. Anissimova, K. Novoselov, and A. Geim, “Spectroscopic ellipsometry of graphene and an excitation-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[CrossRef]

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4, 795–808 (2010).
[CrossRef]

2009 (1)

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

2008 (2)

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

L. Falkovsky, “Optical properties of graphene,” J. Phys. 129, 012004 (2008).
[CrossRef]

2007 (1)

L. Falkovsky and A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281–284 (2007).
[CrossRef]

2004 (1)

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

2003 (1)

Alù, A.

P.-Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Opt. Mater. 24, OP281–OP304 (2012).

Anissimova, S.

V. Kravets, A. N. Grigorenko, R. Nair, P. Blake, S. Anissimova, K. Novoselov, and A. Geim, “Spectroscopic ellipsometry of graphene and an excitation-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[CrossRef]

Asiri, A. M.

Y. Yang, A. M. Asiri, Z. Tang, D. Du, and Y. Lin, “Graphene based materials for biomedical applications,” Mater. Today 16(10), 365–373 (2013).
[CrossRef]

Avouris, P.

P. Avouris and M. Freitag, “Graphene photonics, plasmonics, and optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 20, 6000112 (2014).
[CrossRef]

Bao, Q.

Q. Bao and K. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6, 3677–3694 (2012).
[CrossRef]

Basov, D. N.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

Blake, P.

V. Kravets, A. N. Grigorenko, R. Nair, P. Blake, S. Anissimova, K. Novoselov, and A. Geim, “Spectroscopic ellipsometry of graphene and an excitation-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[CrossRef]

Boltasseva, A.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4, 795–808 (2010).
[CrossRef]

Bonaccorso, F.

F. Bonaccorso, Z. Sun, and A. Ferrari, “Graphene photonics and optoelectronics,” Nature Photonics 4, 611–622 (2010).
[CrossRef]

Buljan, H.

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

Chen, M.

J. Zhu, M. Chen, Q. He, L. Shao, S. Wei, and Z. Guo, “An overview of the engineered graphene nanostructures and nanocomposites,” RSC Adv. 3, 22790–22824 (2013).

Chen, P.-Y.

P.-Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Opt. Mater. 24, OP281–OP304 (2012).

Choe, M.

G. Jo, M. Choe, S. Lee, W. Park, Y. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology 23, 112001 (2012).
[CrossRef]

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[CrossRef]

Cui, T. J.

de Abajo, F. J. G.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[CrossRef]

Dong, Z. G.

Du, D.

Y. Yang, A. M. Asiri, Z. Tang, D. Du, and Y. Lin, “Graphene based materials for biomedical applications,” Mater. Today 16(10), 365–373 (2013).
[CrossRef]

Dubonos, S.

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

Efetov, D.

D. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105, 265805 (2010).

Emani, N.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4, 795–808 (2010).
[CrossRef]

Engheta, N.

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

Falkovsky, L.

L. Falkovsky, “Optical properties of graphene,” J. Phys. 129, 012004 (2008).
[CrossRef]

L. Falkovsky and A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281–284 (2007).
[CrossRef]

Fan, S.

H. Lizuka and S. Fan, “Deep subwavelength plasmonic waveguide switch in double graphene layer structure,” Appl. Phys. Lett. 103, 233107 (2013).
[CrossRef]

S. Fan, W. Suh, and J. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
[CrossRef]

Ferrari, A.

F. Bonaccorso, Z. Sun, and A. Ferrari, “Graphene photonics and optoelectronics,” Nature Photonics 4, 611–622 (2010).
[CrossRef]

Firsov, A.

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

Freitag, M.

P. Avouris and M. Freitag, “Graphene photonics, plasmonics, and optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 20, 6000112 (2014).
[CrossRef]

Geim, A.

V. Kravets, A. N. Grigorenko, R. Nair, P. Blake, S. Anissimova, K. Novoselov, and A. Geim, “Spectroscopic ellipsometry of graphene and an excitation-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[CrossRef]

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

Grigorenko, A. N.

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

V. Kravets, A. N. Grigorenko, R. Nair, P. Blake, S. Anissimova, K. Novoselov, and A. Geim, “Spectroscopic ellipsometry of graphene and an excitation-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[CrossRef]

Grigorieva, I.

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

Guo, Z.

J. Zhu, M. Chen, Q. He, L. Shao, S. Wei, and Z. Guo, “An overview of the engineered graphene nanostructures and nanocomposites,” RSC Adv. 3, 22790–22824 (2013).

Hao, Z.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Inc., 1984).

He, Q.

J. Zhu, M. Chen, Q. He, L. Shao, S. Wei, and Z. Guo, “An overview of the engineered graphene nanostructures and nanocomposites,” RSC Adv. 3, 22790–22824 (2013).

Hecht, D.

D. Hecht, L. Hu, and G. Irvin, “Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures,” Adv. Mater. 23, 1482–1513 (2011).
[CrossRef]

Henriksen, E. A.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

Hu, L.

D. Hecht, L. Hu, and G. Irvin, “Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures,” Adv. Mater. 23, 1482–1513 (2011).
[CrossRef]

Irvin, G.

D. Hecht, L. Hu, and G. Irvin, “Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures,” Adv. Mater. 23, 1482–1513 (2011).
[CrossRef]

Ishii, S.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4, 795–808 (2010).
[CrossRef]

Jablan, M.

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

Jiang, D.

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

Jiang, Z.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

Jo, G.

G. Jo, M. Choe, S. Lee, W. Park, Y. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology 23, 112001 (2012).
[CrossRef]

Joannopoulos, J.

Kahng, Y.

G. Jo, M. Choe, S. Lee, W. Park, Y. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology 23, 112001 (2012).
[CrossRef]

Kim, P.

D. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105, 265805 (2010).

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

Koppens, F. H. L.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[CrossRef]

Kravets, V.

V. Kravets, A. N. Grigorenko, R. Nair, P. Blake, S. Anissimova, K. Novoselov, and A. Geim, “Spectroscopic ellipsometry of graphene and an excitation-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[CrossRef]

Lee, S.

G. Jo, M. Choe, S. Lee, W. Park, Y. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology 23, 112001 (2012).
[CrossRef]

Lee, T.

G. Jo, M. Choe, S. Lee, W. Park, Y. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology 23, 112001 (2012).
[CrossRef]

Li, Z. Q.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

Lin, Y.

Y. Yang, A. M. Asiri, Z. Tang, D. Du, and Y. Lin, “Graphene based materials for biomedical applications,” Mater. Today 16(10), 365–373 (2013).
[CrossRef]

Lizuka, H.

H. Lizuka and S. Fan, “Deep subwavelength plasmonic waveguide switch in double graphene layer structure,” Appl. Phys. Lett. 103, 233107 (2013).
[CrossRef]

Loh, K.

Q. Bao and K. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6, 3677–3694 (2012).
[CrossRef]

Lozano, G.

G. Pirruccio, L. Moreno, G. Lozano, and J. Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7, 4810–4817 (2013).
[CrossRef]

Lu, W. B.

Manjavacas, A.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[CrossRef]

Martin, M. C.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

Moreno, L.

G. Pirruccio, L. Moreno, G. Lozano, and J. Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7, 4810–4817 (2013).
[CrossRef]

Morozov, S.

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

Mortensen, N. A.

Naik, G.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4, 795–808 (2010).
[CrossRef]

Nair, R.

V. Kravets, A. N. Grigorenko, R. Nair, P. Blake, S. Anissimova, K. Novoselov, and A. Geim, “Spectroscopic ellipsometry of graphene and an excitation-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[CrossRef]

Ni, Z. H.

Novoselov, K.

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

V. Kravets, A. N. Grigorenko, R. Nair, P. Blake, S. Anissimova, K. Novoselov, and A. Geim, “Spectroscopic ellipsometry of graphene and an excitation-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[CrossRef]

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

Park, W.

G. Jo, M. Choe, S. Lee, W. Park, Y. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology 23, 112001 (2012).
[CrossRef]

Pirruccio, G.

G. Pirruccio, L. Moreno, G. Lozano, and J. Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7, 4810–4817 (2013).
[CrossRef]

Polini, M.

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

Rivas, J.

G. Pirruccio, L. Moreno, G. Lozano, and J. Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7, 4810–4817 (2013).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

Shalaev, V.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4, 795–808 (2010).
[CrossRef]

Shao, L.

J. Zhu, M. Chen, Q. He, L. Shao, S. Wei, and Z. Guo, “An overview of the engineered graphene nanostructures and nanocomposites,” RSC Adv. 3, 22790–22824 (2013).

Soljacic, M.

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

Soric, J.

P.-Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Opt. Mater. 24, OP281–OP304 (2012).

Stormer, H.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

Suh, W.

Sun, Z.

F. Bonaccorso, Z. Sun, and A. Ferrari, “Graphene photonics and optoelectronics,” Nature Photonics 4, 611–622 (2010).
[CrossRef]

Tang, Z.

Y. Yang, A. M. Asiri, Z. Tang, D. Du, and Y. Lin, “Graphene based materials for biomedical applications,” Mater. Today 16(10), 365–373 (2013).
[CrossRef]

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B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

Teng, J.

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

Thongrattanasiri, S.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[CrossRef]

Vakil, A.

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

Varlamov, A.

L. Falkovsky and A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281–284 (2007).
[CrossRef]

Wang, B.

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

Wei, S.

J. Zhu, M. Chen, Q. He, L. Shao, S. Wei, and Z. Guo, “An overview of the engineered graphene nanostructures and nanocomposites,” RSC Adv. 3, 22790–22824 (2013).

West, P.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4, 795–808 (2010).
[CrossRef]

Xiao, S.

Xu, H. J.

Yan, W.

Yang, Y.

Y. Yang, A. M. Asiri, Z. Tang, D. Du, and Y. Lin, “Graphene based materials for biomedical applications,” Mater. Today 16(10), 365–373 (2013).
[CrossRef]

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

Zhang, Y.

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

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J. Zhu, M. Chen, Q. He, L. Shao, S. Wei, and Z. Guo, “An overview of the engineered graphene nanostructures and nanocomposites,” RSC Adv. 3, 22790–22824 (2013).

Zhu, W.

Zhu, X.

ACS Nano (3)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[CrossRef]

Q. Bao and K. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6, 3677–3694 (2012).
[CrossRef]

G. Pirruccio, L. Moreno, G. Lozano, and J. Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7, 4810–4817 (2013).
[CrossRef]

Adv. Mater. (1)

D. Hecht, L. Hu, and G. Irvin, “Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures,” Adv. Mater. 23, 1482–1513 (2011).
[CrossRef]

Adv. Opt. Mater. (1)

P.-Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Opt. Mater. 24, OP281–OP304 (2012).

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).
[CrossRef]

H. Lizuka and S. Fan, “Deep subwavelength plasmonic waveguide switch in double graphene layer structure,” Appl. Phys. Lett. 103, 233107 (2013).
[CrossRef]

Eur. Phys. J. B (1)

L. Falkovsky and A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281–284 (2007).
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IEEE J. Sel. Top. Quantum Electron. (1)

P. Avouris and M. Freitag, “Graphene photonics, plasmonics, and optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 20, 6000112 (2014).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. (1)

L. Falkovsky, “Optical properties of graphene,” J. Phys. 129, 012004 (2008).
[CrossRef]

Laser Photonics Rev. (1)

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4, 795–808 (2010).
[CrossRef]

Mater. Today (1)

Y. Yang, A. M. Asiri, Z. Tang, D. Du, and Y. Lin, “Graphene based materials for biomedical applications,” Mater. Today 16(10), 365–373 (2013).
[CrossRef]

Nanotechnology (1)

G. Jo, M. Choe, S. Lee, W. Park, Y. Kahng, and T. Lee, “The application of graphene as electrodes in electrical and optical devices,” Nanotechnology 23, 112001 (2012).
[CrossRef]

Nat. Photonics (1)

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

Nat. Phys. (1)

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

Nature Photonics (1)

F. Bonaccorso, Z. Sun, and A. Ferrari, “Graphene photonics and optoelectronics,” Nature Photonics 4, 611–622 (2010).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (2)

V. Kravets, A. N. Grigorenko, R. Nair, P. Blake, S. Anissimova, K. Novoselov, and A. Geim, “Spectroscopic ellipsometry of graphene and an excitation-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[CrossRef]

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

Phys. Rev. Lett. (1)

D. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105, 265805 (2010).

RSC Adv. (1)

J. Zhu, M. Chen, Q. He, L. Shao, S. Wei, and Z. Guo, “An overview of the engineered graphene nanostructures and nanocomposites,” RSC Adv. 3, 22790–22824 (2013).

Science (2)

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

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

Other (2)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Inc., 1984).

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Figures (7)

Fig. 1.
Fig. 1.

Side view of the ribbon cavity.

Fig. 2.
Fig. 2.

(a) Normalized |Hz| field for EF=0.3eV at λ=7.95μm. The size of the cavity is L=75nm and the distance from the sheet is d=10nm. (b) Simulated reflection spectrum for different doping (EF). Theoretical points are shown for EF=0.3eV. Three orders of resonances are shown for each EF. (c) Table with fitted lifetimes and resonant frequency ω0, and the calculated absorption lifetime. The quality factors are computed from the fitted parameters as Q=ω0/ΔωFWHM.

Fig. 3.
Fig. 3.

Simulated reflection in function of the wavelength. (a) The resonances are modified with the scattering lifetime of the electrons in graphene. For the first-order minimum, critical coupling is obtained for τg=7.5×1013s (legend with τg in 1013s). EF=0.4eV, L=75nm, and d=10nm. (b) The resonances depend on the cavity–waveguide distance d. A critical coupling is observed for d=30nm. EF=0.3eV and L=75nm.

Fig. 4.
Fig. 4.

Dispersion of the plasmon propagating along a graphene sheet for different doping levels. The black vertical line represents the required real part of β for a resonance in a 75 nm long cavity. The horizontal lines indicate the resonance frequencies. The vertical gray line stands for the expected resonances in a 30 nm cavity.

Fig. 5.
Fig. 5.

Transversal view of the studied structure.

Fig. 6.
Fig. 6.

Map of the (a) simulated and (b) theoretical reflection of the system with a L=30nm length cavity varying the wavelength and its position (x2). The blue zones represent the reflection minima of the first-order cavity mode. (c) Theoretical map for a cavity length L=60nm. One observes the second-order minima for small wavelengths and the symmetric- and antisymmetric-type resonances for higher wavelengths. (d) Normalized |Hz| field of the cavity L=60nm, for two different resonances: the symmetric (up, with x2=57nm and λ=4.05μm) and antisymmetric (down, with x2=92nm and λ=3.53μm) mode, respectively.

Fig. 7.
Fig. 7.

Reflection as a function of the wavelength for different doping levels of the graphene ribbon cavity. One observes the tunability of the reflection dip with EF.

Equations (12)

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dadt=(jω01τ)a+2τcs+,
s=r0s++2τca,
ss+=r0(12τcj(ωω0)+1τ),
R=|ss+|2=|r0|2(ωω0)2+(1τc+1τa)2(ωω0)2+(1τc+1τa)2.
τa=1vgI(β),
2R{β(ω)}L+2φr=2mπ,
a1(x)=[cos(κx)a1(0)jsin(κx)a2(0)]ejβx,
a2(x)=[jsin(κx)a1(0)+cos(κx)a2(0)]ejβx,
(s1s2)=(S1SxSxS3)(s1+s2+),
Si=r0sin2(κL)1(r0cos(κL)ejβL)2e2jβ(L+xi),
Sx=cos(κL)ejβ(x1+L+x2)1r02cos(2κL)e2jβL1(r0cos(κL)ejβL)2,
R=|s1s1+|2=|S1+r0Sx21r0S3|2.

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