Abstract

We theoretically study the mode energy of graphene plasmons and its fundamental role in determining the local field magnitudes. While neglecting the magnetic field energy of the mode, we derive a concise expression for the total mode energy, which is independent on the details of the mode field distributions and valid for both propagating and localized modes. We find that the mean square of the local electric fields of a graphene plasmonic mode scales linearly with the light absorption rate of the mode and the electron relaxation time of graphene. The possible strategies for improving the local field magnitudes of graphene plasmons are also discussed. Our theoretical analysis presented here may benefit the design of various graphene-based optical and optoelectronic devices for light-harvesting or energy conversion.

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

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References

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  3. B. Sharma, R. R. Frontiera, A.-I. Henry, E. Ringe, and R. P. Van Duyne, “SERS: Materials, applications, and the future,” Mater. Today 15(1-2), 16–25 (2012).
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  4. P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. (Palo Alto, Calif.) 1(1), 601–626 (2008).
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  5. E. Hutter and J. H. Fendler, “Exploitation of Localized Surface Plasmon Resonance,” Adv. Mater. 16(19), 1685–1706 (2004).
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  6. 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(8), 3370–3377 (2011).
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    [Crossref] [PubMed]
  22. A. Raman, W. Shin, and S. Fan, “Upper bound on the modal material loss rate in plasmonic and metamaterial systems,” Phys. Rev. Lett. 110(18), 183901 (2013).
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  23. M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
    [Crossref]
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    [Crossref] [PubMed]
  26. L. Tang, H. Shi, J. Yang, C. Du, F. Gao, J. Zhu, and J. Du, “Complete optical absorption in graphene by using nano-gratings to excite graphene surface plasmons,” Microelectron. Eng. 145, 58–61 (2015).
    [Crossref]
  27. 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]
  28. H. Lu, J. Zhao, and M. Gu, “Nanowires-assisted excitation and propagation of mid-infrared surface plasmon polaritons in graphene,” J. Appl. Phys. 120(16), 163106 (2016).
    [Crossref]
  29. H. S. Chu and C. How Gan, “Active plasmonic switching at mid-infrared wavelengths with graphene ribbon arrays,” Appl. Phys. Lett. 102(23), 231107 (2013).
    [Crossref]
  30. L. Tang, W. Wei, X. Wei, J. Nong, C. Du, and H. Shi, “Mechanism of propagating graphene plasmons excitation for tunable infrared photonic devices,” Opt. Express 26(3), 3709–3722 (2018).
    [Crossref] [PubMed]

2018 (1)

2017 (1)

2016 (6)

W. Liu, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Electrically Tunable Absorption Enhancement with Spectral and Polarization Selectivity through Graphene Plasmonic Light Trapping,” Nanomaterials (Basel) 6(9), 155 (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]

D. B. Farmer, P. Avouris, Y. Li, T. F. Heinz, and S.-J. Han, “Ultrasensitive Plasmonic Detection of Molecules with Graphene,” ACS Photonics 3(4), 553–557 (2016).
[Crossref]

I. Kaminer, Y. T. Katan, H. Buljan, Y. Shen, O. Ilic, J. J. López, L. J. Wong, J. D. Joannopoulos, and M. Soljačić, “Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene,” Nat. Commun. 7, s11880 (2016).
[Crossref] [PubMed]

H. Lu, J. Zhao, and M. Gu, “Nanowires-assisted excitation and propagation of mid-infrared surface plasmon polaritons in graphene,” J. Appl. Phys. 120(16), 163106 (2016).
[Crossref]

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

2015 (6)

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]

L. Tang, H. Shi, J. Yang, C. Du, F. Gao, J. Zhu, and J. Du, “Complete optical absorption in graphene by using nano-gratings to excite graphene surface plasmons,” Microelectron. Eng. 145, 58–61 (2015).
[Crossref]

T. J. Constant, S. M. Hornett, D. E. Chang, and E. Hendry, “All-optical generation of surface plasmons in graphene,” Nat. Phys. 12(2), 124–127 (2015).
[Crossref]

L. J. Wong, I. Kaminer, O. Ilic, J. D. Joannopoulos, and M. Soljačić, “Towards graphene plasmon-based free-electron infrared to X-ray sources,” Nat. Photonics 10(1), 46–52 (2015).
[Crossref]

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]

A. Marini, I. Silveiro, and F. J. García de Abajo, “Molecular Sensing with Tunable Graphene Plasmons,” ACS Photonics 2(7), 876–882 (2015).
[Crossref]

2014 (3)

F. J. García de Abajo, “Graphene Plasmonics: Challenges and Opportunities,” ACS Photonics 1(3), 135–152 (2014).
[Crossref]

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]

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
[Crossref] [PubMed]

2013 (2)

A. Raman, W. Shin, and S. Fan, “Upper bound on the modal material loss rate in plasmonic and metamaterial systems,” Phys. Rev. Lett. 110(18), 183901 (2013).
[Crossref] [PubMed]

H. S. Chu and C. How Gan, “Active plasmonic switching at mid-infrared wavelengths with graphene ribbon arrays,” Appl. Phys. Lett. 102(23), 231107 (2013).
[Crossref]

2012 (4)

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]

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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

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

B. Sharma, R. R. Frontiera, A.-I. Henry, E. Ringe, and R. P. Van Duyne, “SERS: Materials, applications, and the future,” Mater. Today 15(1-2), 16–25 (2012).
[Crossref]

2011 (1)

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(8), 3370–3377 (2011).
[Crossref] [PubMed]

2010 (1)

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[Crossref] [PubMed]

2009 (1)

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

2008 (1)

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. (Palo Alto, Calif.) 1(1), 601–626 (2008).
[Crossref] [PubMed]

2004 (1)

E. Hutter and J. H. Fendler, “Exploitation of Localized Surface Plasmon Resonance,” Adv. Mater. 16(19), 1685–1706 (2004).
[Crossref]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Altug, H.

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]

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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Avouris, P.

D. B. Farmer, P. Avouris, Y. Li, T. F. Heinz, and S.-J. Han, “Ultrasensitive Plasmonic Detection of Molecules with Graphene,” ACS Photonics 3(4), 553–557 (2016).
[Crossref]

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
[Crossref] [PubMed]

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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[Crossref] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Basov, D. N.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[Crossref] [PubMed]

Buljan, H.

I. Kaminer, Y. T. Katan, H. Buljan, Y. Shen, O. Ilic, J. J. López, L. J. Wong, J. D. Joannopoulos, and M. Soljačić, “Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene,” Nat. Commun. 7, s11880 (2016).
[Crossref] [PubMed]

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

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[Crossref] [PubMed]

Castro Neto, A. H.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Chang, D. E.

T. J. Constant, S. M. Hornett, D. E. Chang, and E. Hendry, “All-optical generation of surface plasmons in graphene,” Nat. Phys. 12(2), 124–127 (2015).
[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(8), 3370–3377 (2011).
[Crossref] [PubMed]

Chu, H. S.

H. S. Chu and C. How Gan, “Active plasmonic switching at mid-infrared wavelengths with graphene ribbon arrays,” Appl. Phys. Lett. 102(23), 231107 (2013).
[Crossref]

Constant, T. J.

T. J. Constant, S. M. Hornett, D. E. Chang, and E. Hendry, “All-optical generation of surface plasmons in graphene,” Nat. Phys. 12(2), 124–127 (2015).
[Crossref]

Dai, Q.

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]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Dieringer, J. A.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. (Palo Alto, Calif.) 1(1), 601–626 (2008).
[Crossref] [PubMed]

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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Du, C.

Du, J.

L. Tang, H. Shi, J. Yang, C. Du, F. Gao, J. Zhu, and J. Du, “Complete optical absorption in graphene by using nano-gratings to excite graphene surface plasmons,” Microelectron. Eng. 145, 58–61 (2015).
[Crossref]

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]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Etezadi, D.

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]

Fan, S.

A. Raman, W. Shin, and S. Fan, “Upper bound on the modal material loss rate in plasmonic and metamaterial systems,” Phys. Rev. Lett. 110(18), 183901 (2013).
[Crossref] [PubMed]

Farmer, D. B.

D. B. Farmer, P. Avouris, Y. Li, T. F. Heinz, and S.-J. Han, “Ultrasensitive Plasmonic Detection of Molecules with Graphene,” ACS Photonics 3(4), 553–557 (2016).
[Crossref]

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
[Crossref] [PubMed]

Fei, Z.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Fendler, J. H.

E. Hutter and J. H. Fendler, “Exploitation of Localized Surface Plasmon Resonance,” Adv. Mater. 16(19), 1685–1706 (2004).
[Crossref]

Fogler, M. M.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Frontiera, R. R.

B. Sharma, R. R. Frontiera, A.-I. Henry, E. Ringe, and R. P. Van Duyne, “SERS: Materials, applications, and the future,” Mater. Today 15(1-2), 16–25 (2012).
[Crossref]

Gan, X.

Gao, F.

L. Tang, H. Shi, J. Yang, C. Du, F. Gao, J. Zhu, and J. Du, “Complete optical absorption in graphene by using nano-gratings to excite graphene surface plasmons,” Microelectron. Eng. 145, 58–61 (2015).
[Crossref]

Gao, W.

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]

García de Abajo, F. J.

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]

A. Marini, I. Silveiro, and F. J. García de Abajo, “Molecular Sensing with Tunable Graphene Plasmons,” ACS Photonics 2(7), 876–882 (2015).
[Crossref]

F. J. García de Abajo, “Graphene Plasmonics: Challenges and Opportunities,” ACS Photonics 1(3), 135–152 (2014).
[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(8), 3370–3377 (2011).
[Crossref] [PubMed]

Goldflam, M. D.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

Grigorenko, A. N.

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

Gu, M.

H. Lu, J. Zhao, and M. Gu, “Nanowires-assisted excitation and propagation of mid-infrared surface plasmon polaritons in graphene,” J. Appl. Phys. 120(16), 163106 (2016).
[Crossref]

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]

Han, S.-J.

D. B. Farmer, P. Avouris, Y. Li, T. F. Heinz, and S.-J. Han, “Ultrasensitive Plasmonic Detection of Molecules with Graphene,” ACS Photonics 3(4), 553–557 (2016).
[Crossref]

Heinz, T. F.

D. B. Farmer, P. Avouris, Y. Li, T. F. Heinz, and S.-J. Han, “Ultrasensitive Plasmonic Detection of Molecules with Graphene,” ACS Photonics 3(4), 553–557 (2016).
[Crossref]

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
[Crossref] [PubMed]

Hendry, E.

T. J. Constant, S. M. Hornett, D. E. Chang, and E. Hendry, “All-optical generation of surface plasmons in graphene,” Nat. Phys. 12(2), 124–127 (2015).
[Crossref]

Henry, A.-I.

B. Sharma, R. R. Frontiera, A.-I. Henry, E. Ringe, and R. P. Van Duyne, “SERS: Materials, applications, and the future,” Mater. Today 15(1-2), 16–25 (2012).
[Crossref]

Hone, J.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

Hornett, S. M.

T. J. Constant, S. M. Hornett, D. E. Chang, and E. Hendry, “All-optical generation of surface plasmons in graphene,” Nat. Phys. 12(2), 124–127 (2015).
[Crossref]

Hossain, M. M.

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]

How Gan, C.

H. S. Chu and C. How Gan, “Active plasmonic switching at mid-infrared wavelengths with graphene ribbon arrays,” Appl. Phys. Lett. 102(23), 231107 (2013).
[Crossref]

Hu, D.

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]

Hu, H.

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]

Hutter, E.

E. Hutter and J. H. Fendler, “Exploitation of Localized Surface Plasmon Resonance,” Adv. Mater. 16(19), 1685–1706 (2004).
[Crossref]

Ilic, O.

I. Kaminer, Y. T. Katan, H. Buljan, Y. Shen, O. Ilic, J. J. López, L. J. Wong, J. D. Joannopoulos, and M. Soljačić, “Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene,” Nat. Commun. 7, s11880 (2016).
[Crossref] [PubMed]

L. J. Wong, I. Kaminer, O. Ilic, J. D. Joannopoulos, and M. Soljačić, “Towards graphene plasmon-based free-electron infrared to X-ray sources,” Nat. Photonics 10(1), 46–52 (2015).
[Crossref]

Jablan, M.

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

Janner, D.

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]

Joannopoulos, J. D.

I. Kaminer, Y. T. Katan, H. Buljan, Y. Shen, O. Ilic, J. J. López, L. J. Wong, J. D. Joannopoulos, and M. Soljačić, “Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene,” Nat. Commun. 7, s11880 (2016).
[Crossref] [PubMed]

L. J. Wong, I. Kaminer, O. Ilic, J. D. Joannopoulos, and M. Soljačić, “Towards graphene plasmon-based free-electron infrared to X-ray sources,” Nat. Photonics 10(1), 46–52 (2015).
[Crossref]

Jun, Y. C.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[Crossref] [PubMed]

Kaminer, I.

I. Kaminer, Y. T. Katan, H. Buljan, Y. Shen, O. Ilic, J. J. López, L. J. Wong, J. D. Joannopoulos, and M. Soljačić, “Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene,” Nat. Commun. 7, s11880 (2016).
[Crossref] [PubMed]

L. J. Wong, I. Kaminer, O. Ilic, J. D. Joannopoulos, and M. Soljačić, “Towards graphene plasmon-based free-electron infrared to X-ray sources,” Nat. Photonics 10(1), 46–52 (2015).
[Crossref]

Katan, Y. T.

I. Kaminer, Y. T. Katan, H. Buljan, Y. Shen, O. Ilic, J. J. López, L. J. Wong, J. D. Joannopoulos, and M. Soljačić, “Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene,” Nat. Commun. 7, s11880 (2016).
[Crossref] [PubMed]

Keilmann, F.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Koppens, F. H. L.

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(8), 3370–3377 (2011).
[Crossref] [PubMed]

Lau, C. 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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Li, Y.

D. B. Farmer, P. Avouris, Y. Li, T. F. Heinz, and S.-J. Han, “Ultrasensitive Plasmonic Detection of Molecules with Graphene,” ACS Photonics 3(4), 553–557 (2016).
[Crossref]

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
[Crossref] [PubMed]

Limaj, O.

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]

Liu, K.

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]

Liu, M. K.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

Liu, R.

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]

Liu, W.

W. Liu, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Electrically Tunable Absorption Enhancement with Spectral and Polarization Selectivity through Graphene Plasmonic Light Trapping,” Nanomaterials (Basel) 6(9), 155 (2016).
[Crossref] [PubMed]

Liu, X.

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]

López, J. J.

I. Kaminer, Y. T. Katan, H. Buljan, Y. Shen, O. Ilic, J. J. López, L. J. Wong, J. D. Joannopoulos, and M. Soljačić, “Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene,” Nat. Commun. 7, s11880 (2016).
[Crossref] [PubMed]

Lu, H.

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]

H. Lu, J. Zhao, and M. Gu, “Nanowires-assisted excitation and propagation of mid-infrared surface plasmon polaritons in graphene,” J. Appl. Phys. 120(16), 163106 (2016).
[Crossref]

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]

Mao, D.

Marini, A.

A. Marini, I. Silveiro, and F. J. García de Abajo, “Molecular Sensing with Tunable Graphene Plasmons,” ACS Photonics 2(7), 876–882 (2015).
[Crossref]

McLeod, A. S.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Meng, X.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
[Crossref] [PubMed]

Ni, G. X.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

Nong, J.

Novoselov, K. S.

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

Osgood, R. M.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
[Crossref] [PubMed]

Özyilmaz, B.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

Polini, M.

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

Pruneri, V.

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]

Qin, S.

W. Liu, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Electrically Tunable Absorption Enhancement with Spectral and Polarization Selectivity through Graphene Plasmonic Light Trapping,” Nanomaterials (Basel) 6(9), 155 (2016).
[Crossref] [PubMed]

Qiu, C.

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]

Raman, A.

A. Raman, W. Shin, and S. Fan, “Upper bound on the modal material loss rate in plasmonic and metamaterial systems,” Phys. Rev. Lett. 110(18), 183901 (2013).
[Crossref] [PubMed]

Reineck, P.

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]

Ringe, E.

B. Sharma, R. R. Frontiera, A.-I. Henry, E. Ringe, and R. P. Van Duyne, “SERS: Materials, applications, and the future,” Mater. Today 15(1-2), 16–25 (2012).
[Crossref]

Rodin, A. S.

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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Rodrigo, D.

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]

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[Crossref] [PubMed]

Shah, N. C.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. (Palo Alto, Calif.) 1(1), 601–626 (2008).
[Crossref] [PubMed]

Sharma, B.

B. Sharma, R. R. Frontiera, A.-I. Henry, E. Ringe, and R. P. Van Duyne, “SERS: Materials, applications, and the future,” Mater. Today 15(1-2), 16–25 (2012).
[Crossref]

Shen, Y.

I. Kaminer, Y. T. Katan, H. Buljan, Y. Shen, O. Ilic, J. J. López, L. J. Wong, J. D. Joannopoulos, and M. Soljačić, “Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene,” Nat. Commun. 7, s11880 (2016).
[Crossref] [PubMed]

Shi, H.

Shin, W.

A. Raman, W. Shin, and S. Fan, “Upper bound on the modal material loss rate in plasmonic and metamaterial systems,” Phys. Rev. Lett. 110(18), 183901 (2013).
[Crossref] [PubMed]

Shu, J.

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]

Silveiro, I.

A. Marini, I. Silveiro, and F. J. García de Abajo, “Molecular Sensing with Tunable Graphene Plasmons,” ACS Photonics 2(7), 876–882 (2015).
[Crossref]

Soljacic, M.

I. Kaminer, Y. T. Katan, H. Buljan, Y. Shen, O. Ilic, J. J. López, L. J. Wong, J. D. Joannopoulos, and M. Soljačić, “Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene,” Nat. Commun. 7, s11880 (2016).
[Crossref] [PubMed]

L. J. Wong, I. Kaminer, O. Ilic, J. D. Joannopoulos, and M. Soljačić, “Towards graphene plasmon-based free-electron infrared to X-ray sources,” Nat. Photonics 10(1), 46–52 (2015).
[Crossref]

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

Stiles, P. L.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. (Palo Alto, Calif.) 1(1), 601–626 (2008).
[Crossref] [PubMed]

Sun, Z.

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]

Tang, L.

Thiemens, 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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Van Duyne, R. P.

B. Sharma, R. R. Frontiera, A.-I. Henry, E. Ringe, and R. P. Van Duyne, “SERS: Materials, applications, and the future,” Mater. Today 15(1-2), 16–25 (2012).
[Crossref]

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. (Palo Alto, Calif.) 1(1), 601–626 (2008).
[Crossref] [PubMed]

Wagner, M.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

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. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref] [PubMed]

Wang, L.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

Wei, W.

Wei, X.

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[Crossref] [PubMed]

Wong, L. J.

I. Kaminer, Y. T. Katan, H. Buljan, Y. Shen, O. Ilic, J. J. López, L. J. Wong, J. D. Joannopoulos, and M. Soljačić, “Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene,” Nat. Commun. 7, s11880 (2016).
[Crossref] [PubMed]

L. J. Wong, I. Kaminer, O. Ilic, J. D. Joannopoulos, and M. Soljačić, “Towards graphene plasmon-based free-electron infrared to X-ray sources,” Nat. Photonics 10(1), 46–52 (2015).
[Crossref]

Xu, Q.

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]

Yan, H.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
[Crossref] [PubMed]

Yang, J.

L. Tang, H. Shi, J. Yang, C. Du, F. Gao, J. Zhu, and J. Du, “Complete optical absorption in graphene by using nano-gratings to excite graphene surface plasmons,” Microelectron. Eng. 145, 58–61 (2015).
[Crossref]

Yang, X.

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]

Yuan, X.

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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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W. Liu, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Electrically Tunable Absorption Enhancement with Spectral and Polarization Selectivity through Graphene Plasmonic Light Trapping,” Nanomaterials (Basel) 6(9), 155 (2016).
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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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Figures (4)

Fig. 1
Fig. 1 The power balance process of a graphene plasmonic mode. The power of the incident light (Pin) is either absorbed by the plasmonic mode with power of Pabs or reflected / transmitted with power of Pr/t, and Pabs should be equal to the loss power Ploss at the steady state.
Fig. 2
Fig. 2 Schematics of the configurations for the excitations of propagating graphene plasmons (a) and localized graphene plasmons (b). The absorption curves of the propagating plasmonic mode (c) and localized plasmonic mode (e), and the electric field patterns at the resonant centers (d) (f). In (d) and (f), (E) and (E)in represent the local and incident electric fields, respectively.
Fig. 3
Fig. 3 Total mode energy, absorption rates, electric and magnetic field energy versus electron relaxation time of graphene at resonant wavelengths 10 μm for propagating modes (a) and localized modes (b), and versus resonant wavelengths at electron relaxation time of 0.2 ps for propagating modes (c) and localized modes (d). The legend in (a) is also applicable to (b)-(d). The numerical energy are integrated in a period, and the incident power in a period is 1 W.
Fig. 4
Fig. 4 The |E|2mean / A and |E|2max / A versus graphene electron relaxation time τ for propagating graphene plasmonic modes (a) and localized graphene plasmonic modes (b). In the numerical calculations, other parameters are kept the same as in calculating Figs. 2(c) and 2(e), except the electron relaxation time varies now.

Equations (11)

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W total = W E + W H + W K , W E = W H + W K .
σ ( ω ) = i e 2 E f / π 2 ( ω + i τ 1 )
P loss = 2 W K / τ ,
W total = ( 1 + W H / W K ) P in A τ .
W total P in A τ .
W t o t a l = 2 W E = 2 i = 1 N { V i ε 0 ε i | Ε ( r ) | 2 d r / 4 } = | a | 2 i = 1 N ε 0 ε i β i / 2
| E | 2 mean = V | E ( r ) | 2 d r / V = | a | 2 / V ,
| E | max 2 = max { | E ( r ) | 2 } = | a | 2 f max 2 = f max 2 | E | mean 2 V
| E | 2 mean = C 1 W total / V , | E | 2 max = C 2 W total ,
| E | mean 2 = C 3 P i n A τ / V , | E | max 2 = C 4 P i n A τ
A = 4 γ 0 γ 1 / [ ( ω ω 0 ) 2 + ( γ 0 + γ 1 ) 2 ] ,

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