Abstract

Surface plasmons in graphene have many promising properties, such as high confinement, low losses, and gate-tunability. However, it is also the high confinement that makes them difficult to excite due to their large momentum mismatch with free-space mid-infrared light. We propose to use shaped graphene nano-vacancies to compensate for the momentum mismatch, revealing its high flexibility in graphene plasmon (GP) excitation and manipulation. We first examine the electromagnetic standing waves generated with a pair of straight vacancies, in order to verify the excitation of GPs and to illustrate their tunability with gate voltage. Plasmonic lenses are then designed to achieve the super-focusing of mid-infrared light and to generate plasmonic vortices in graphene. A0.0125λ0 hotspot is generated, far below the optical diffraction limit, hence revealing the capability of light control at deep-subwavelength scale.

© 2014 Optical Society of America

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    [CrossRef]
  4. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
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  5. 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]
  6. M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
  7. J. N. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. 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).
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  11. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
    [CrossRef]
  12. L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
    [CrossRef]
  13. H. G. Yan, T. Low, W. J. Zhu, Y. Q. Wu, M. Freitag, X. S. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
    [CrossRef]
  14. 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(R) (2012).
    [CrossRef]
  15. B. Wang, X. Zhang, F. J. Garcia-Vidal, X. C. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109, 073901 (2012).
    [CrossRef]
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    [CrossRef]
  21. Q. Wang, J. Bu, P. S. Tan, G. H. Yuan, J. H. Teng, H. Wang, and X. C. Yuan, “Subwavelength-sized plasmonic structures for wide-field optical microscopic imaging with super-resolution,” Plasmonics 7, 427–433 (2012).
    [CrossRef]
  22. L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).
  23. L. P. Du, G. H. Yuan, D. Y. Tang, and X. C. Yuan, “Tightly focused radially polarized beam for propagating surface plasmon-assisted gap-mode Raman spectroscopy,” Plasmonics 6, 651–657 (2011).
    [CrossRef]
  24. H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10, 529–536 (2010).
    [CrossRef]

2013

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

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).
[CrossRef]

X. L. Zhu, W. Yan, P. U. Jepsen, O. Hansen, N. A. Mortensen, and S. S. Xiao, “Experimental observation of plasmons in a graphene monolayer resting on a two-dimensional subwavelength silicon grating,” Appl. Phys. Lett. 102, 131101 (2013).
[CrossRef]

L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).

2012

Q. Wang, J. Bu, P. S. Tan, G. H. Yuan, J. H. Teng, H. Wang, and X. C. Yuan, “Subwavelength-sized plasmonic structures for wide-field optical microscopic imaging with super-resolution,” Plasmonics 7, 427–433 (2012).
[CrossRef]

W. L. Gao, J. Shu, C. Y. Qiu, and Q. F. 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(R) (2012).
[CrossRef]

B. Wang, X. Zhang, F. J. Garcia-Vidal, X. C. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109, 073901 (2012).
[CrossRef]

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337, 549–552 (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]

J. N. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. 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).

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

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

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

2011

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

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

L. P. Du, G. H. Yuan, D. Y. Tang, and X. C. Yuan, “Tightly focused radially polarized beam for propagating surface plasmon-assisted gap-mode Raman spectroscopy,” Plasmonics 6, 651–657 (2011).
[CrossRef]

2010

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10, 529–536 (2010).
[CrossRef]

V. V. Popov, T. Y. Bagaeva, T. Otsuji, and V. Ryzhii, “Oblique terahertz plasmons in graphene nanoribbon arrays,” Phys. Rev. B 81, 073404 (2010).
[CrossRef]

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

2009

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

2007

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

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef]

Ajayan, P. M.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).
[CrossRef]

Alonso-Gonzalez, P.

J. N. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. 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).

Andreev, G. O.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Anissimova, S.

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

Aubry, A.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337, 549–552 (2012).
[CrossRef]

Avouris, P.

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

Badioli, M.

J. N. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. 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).

Bagaeva, T. Y.

V. V. Popov, T. Y. Bagaeva, T. Otsuji, and V. Ryzhii, “Oblique terahertz plasmons in graphene nanoribbon arrays,” Phys. Rev. B 81, 073404 (2010).
[CrossRef]

Bao, Q. L.

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

Bao, W.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef]

Basov, D. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Bechtel, H. A.

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

Blake, P.

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

Bu, J.

Q. Wang, J. Bu, P. S. Tan, G. H. Yuan, J. H. Teng, H. Wang, and X. C. Yuan, “Subwavelength-sized plasmonic structures for wide-field optical microscopic imaging with super-resolution,” Plasmonics 7, 427–433 (2012).
[CrossRef]

Buljan, H.

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

Camara, N.

J. N. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. 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).

Centeno, A.

J. N. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. 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).

Chen, J. N.

J. N. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. 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).

Cho, S. W.

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10, 529–536 (2010).
[CrossRef]

Colombo, L.

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]

de Abajo, F. J. G.

J. N. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. 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).

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef]

Dominguez, G.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Du, L.

L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).

Du, L. P.

L. P. Du, G. H. Yuan, D. Y. Tang, and X. C. Yuan, “Tightly focused radially polarized beam for propagating surface plasmon-assisted gap-mode Raman spectroscopy,” Plasmonics 6, 651–657 (2011).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef]

Elorza, A. Z.

J. N. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. 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).

Engheta, N.

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

Fal’ko, V. I.

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]

Fang, H.

L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).

Fei, Z.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Fogler, M. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).

Freitag, M.

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

Gao, W.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).
[CrossRef]

Gao, W. L.

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

Garcia-Vidal, F. J.

B. Wang, X. Zhang, F. J. Garcia-Vidal, X. C. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109, 073901 (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(R) (2012).
[CrossRef]

Geim, A. K.

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

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

Gellert, P. R.

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]

Geng, B. S.

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

Girit, C.

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

Godignon, P.

J. N. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. 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).

Grigorenko, A. N.

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

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

Guinea, F.

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

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W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).
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M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).

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L. P. Du, G. H. Yuan, D. Y. Tang, and X. C. Yuan, “Tightly focused radially polarized beam for propagating surface plasmon-assisted gap-mode Raman spectroscopy,” Plasmonics 6, 651–657 (2011).
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J. N. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. 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).

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W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).
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B. Wang, X. Zhang, F. J. Garcia-Vidal, X. C. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109, 073901 (2012).
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Q. Wang, J. Bu, P. S. Tan, G. H. Yuan, J. H. Teng, H. Wang, and X. C. Yuan, “Subwavelength-sized plasmonic structures for wide-field optical microscopic imaging with super-resolution,” Plasmonics 7, 427–433 (2012).
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X. L. Zhu, W. Yan, P. U. Jepsen, O. Hansen, N. A. Mortensen, and S. S. Xiao, “Experimental observation of plasmons in a graphene monolayer resting on a two-dimensional subwavelength silicon grating,” Appl. Phys. Lett. 102, 131101 (2013).
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W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).
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W. L. Gao, J. Shu, C. Y. Qiu, and Q. F. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6, 7806–7813 (2012).
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L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).

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Q. Wang, J. Bu, P. S. Tan, G. H. Yuan, J. H. Teng, H. Wang, and X. C. Yuan, “Subwavelength-sized plasmonic structures for wide-field optical microscopic imaging with super-resolution,” Plasmonics 7, 427–433 (2012).
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L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).

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Q. Wang, J. Bu, P. S. Tan, G. H. Yuan, J. H. Teng, H. Wang, and X. C. Yuan, “Subwavelength-sized plasmonic structures for wide-field optical microscopic imaging with super-resolution,” Plasmonics 7, 427–433 (2012).
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L. P. Du, G. H. Yuan, D. Y. Tang, and X. C. Yuan, “Tightly focused radially polarized beam for propagating surface plasmon-assisted gap-mode Raman spectroscopy,” Plasmonics 6, 651–657 (2011).
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L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. 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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W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).
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B. Wang, X. Zhang, F. J. Garcia-Vidal, X. C. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109, 073901 (2012).
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H. G. Yan, T. Low, W. J. Zhu, Y. Q. Wu, M. Freitag, X. S. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
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Nat. Photonics

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of SP generation in graphene with a single straight graphene vacancy.

Fig. 2.
Fig. 2.

Verification of SP generation in graphene by a pair of straight graphene vacancies. (a) Schematic diagram of the excitation configuration. (b) Snapshot of Ez component during calculation, clearly showing an electromagnetic standing wave and the strong confinement of the electric field near graphene. (c) Cross-section distribution of real (Ez) 5 nm above graphene from (b). The pitch (i.e., the SP wavelength) of the standing wave is 284 nm, in line well with the value predicted from theory (290 nm). (d) Obtained dispersion relation from a wavelength sweep (circles), according excellently with the dispersion curve (solid line) calculated with Eq. (1).

Fig. 3.
Fig. 3.

Gate-tuning of GPs. (a) Dispersion curves at various Fermi energies obtained with Eq. (1). The inset plots the relationship between plasmon wavelength and Fermi energy at a fixed incident wavelength of 8 μm, showing linearity between them. The FDTD data are derived from (b). (b) Series of SP standing waves between the two vacancies at various Fermi energies as shown in Fig. 2(a).

Fig. 4.
Fig. 4.

Super-focusing of mid-infrared light via GPs by using a spiral-shaped graphene vacancy together with a circularly polarized incident beam. (a) Excitation scheme. (b) Specification of the designed spiral vacancy. (c) FDTD simulation result, showing the amplitude of Ez component 5 nm above graphene. A hotspot is generated at the geometric center. (d) Cross-section distribution along the white dashed line in (c) as compared with the analytical one obtained with Eq. (3). The size of hotspot is measured to be 101 nm, 0.0125λ0 in terms of incident wavelength. The inset shows the dependence of hotspot size on the Fermi energy of graphene.

Fig. 5.
Fig. 5.

Generation of plasmonic vortices at graphene. (a) Amplitude distribution of Ez component 5 nm above graphene obtained with FDTD, when the topological charge of vacancy is 5 together with a right-handed circular polarization. (b) Normalized Ez distribution from Eq. (3) assuming l=5 and m=1. (c) Snapshot of the real part of the Ez component during calculation, showing the evolution of the plasmonic vortex. (d) Cross-section comparison between (a) and (b), which presents a good agreement.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

q=ε0(ε1+ε2)22iωσ(ω,q),
σ(ω)=e2Efπ2iω+iτ1.
Ez02πexp(imφ)exp(ilφ)exp[ikSP(xcosφ+ysinφ)]dφ=2πJ(m+l)(kSPr)exp[i(m+l)(φ+π/2)],

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