Abstract

The mechanism of propagating graphene plasmons excitation using a nano-grating and a Fabry-Pérot cavity as the optical coupling components is studied. It is demonstrated that the system could be well described within the temporal coupled mode theory using two phenomenological parameters, namely, the intrinsic loss rate and the coupling rate of a graphene plasmonic mode, and their analytical expressions are derived. It is found that the intrinsic loss rate is solely determined by the electron relaxation time of graphene, while independent of the field distributions of the modes. Such result originates from the negligible magnetic field energy of the graphene plasmonic mode. The coupling rate is governed by the optical coupling components parameters, and varies periodically with the Fabry-Pérot cavity length. By modulating the two rates, quality factors and absorption rates can be adjusted. Furthermore, it is revealed that low refractive index of the Fabry-Pérot cavity material is vital to the enlargement of tunable band, and the underlying physics is discussed. Such plasmon excitation configuration is insensitive to light incident angle and could serve as a platform for many tunable infrared photonic device, such as surface-enhanced infrared absorption spectroscopies, infrared detectors and modulators.

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

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    [Crossref] [PubMed]
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  25. R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express 20(27), 28017–28024 (2012).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  31. H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
    [Crossref] [PubMed]
  32. Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active Tunable Absorption Enhancement with Graphene Nanodisk Arrays,” Nano Lett. 14(1), 299–304 (2014).
    [Crossref] [PubMed]
  33. H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
    [Crossref]
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    [Crossref] [PubMed]
  35. 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]
  36. 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]
  37. N. M. R. Peres, Y. V. Bludov, A. Ferreira, and M. I. Vasilevskiy, “Exact solution for square-wave grating covered with graphene: surface plasmon-polaritons in the terahertz range,” J. Phys.- Condes. Matter 25(12), 12 (2013).
    [Crossref]
  38. L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
    [Crossref]
  39. M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the Ideal Plasmonic Nanoshell: The Effects of Surface Scattering and Alternatives to Gold and Silver,” J. Phys. Chem. C 113(8), 3041–3045 (2009).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]

2017 (2)

T. Wu, Y. Luo, and L. Wei, “Mid-infrared sensing of molecular vibrational modes with tunable graphene plasmons,” Opt. Lett. 42(11), 2066–2069 (2017).
[Crossref] [PubMed]

M. B. Lundeberg, Y. Gao, A. Woessner, C. Tan, P. Alonso-González, K. Watanabe, T. Taniguchi, J. Hone, R. Hillenbrand, and F. H. Koppens, “Thermoelectric detection and imaging of propagating graphene plasmons,” Nat. Mater. 16(2), 204–207 (2017).
[Crossref] [PubMed]

2016 (3)

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 (2016).
[Crossref]

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]

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 (2016).
[Crossref]

2015 (3)

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

B. G. Xiao, R. L. Sun, J. L. He, K. Qin, S. Kong, J. Chen, and W. Xiumin, “A Terahertz Modulator Based on Graphene Plasmonic Waveguide,” IEEE Photonics Technol. Lett. 27(20), 2190–2192 (2015).
[Crossref]

2014 (5)

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active Tunable Absorption Enhancement with Graphene Nanodisk Arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref] [PubMed]

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

D. Spirito, D. Coquillat, S. L. De Bonis, A. Lombardo, M. Bruna, A. C. Ferrari, V. Pellegrini, A. Tredicucci, W. Knap, and M. S. Vitiello, “High performance bilayer-graphene terahertz detectors,” Appl. Phys. Lett. 104(6), 061111 (2014).
[Crossref]

X. Cai, A. B. Sushkov, R. J. Suess, M. M. Jadidi, G. S. Jenkins, L. O. Nyakiti, R. L. Myers-Ward, S. Li, J. Yan, D. K. Gaskill, T. E. Murphy, H. D. Drew, and M. S. Fuhrer, “Sensitive room-temperature terahertz detection via the photothermoelectric effect in graphene,” Nat. Nanotechnol. 9(10), 814–819 (2014).
[Crossref] [PubMed]

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

2013 (6)

F. Liu and E. Cubukcu, “Tunable omnidirectional strong light-matter interactions mediated by graphene surface plasmons,” Phys. Rev. B 88(11), 115439 (2013).
[Crossref]

A. Andryieuski and A. V. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21(7), 9144–9155 (2013).
[Crossref] [PubMed]

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

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(8), 3698–3702 (2013).
[Crossref] [PubMed]

N. M. R. Peres, Y. V. Bludov, A. Ferreira, and M. I. Vasilevskiy, “Exact solution for square-wave grating covered with graphene: surface plasmon-polaritons in the terahertz range,” J. Phys.- Condes. Matter 25(12), 12 (2013).
[Crossref]

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]

2012 (10)

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]

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express 20(27), 28017–28024 (2012).
[Crossref] [PubMed]

S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

A. Ferreira and N. M. R. Peres, “Complete light absorption in graphene-metamaterial corrugated structures,” Phys. Rev. B 86(20), 205401 (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(8), 081405 (2012).
[Crossref]

L. Vicarelli, M. S. Vitiello, D. Coquillat, A. Lombardo, A. C. Ferrari, W. Knap, M. Polini, V. Pellegrini, and A. Tredicucci, “Graphene field-effect transistors as room-temperature terahertz detectors,” Nat. Mater. 11(10), 865–871 (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]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref] [PubMed]

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

2011 (2)

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene Plasmonics: A Platform for Strong Light-Matter Interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

2010 (1)

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

2009 (3)

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

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the Ideal Plasmonic Nanoshell: The Effects of Surface Scattering and Alternatives to Gold and Silver,” J. Phys. Chem. C 113(8), 3041–3045 (2009).
[Crossref]

2007 (4)

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75(20), 205418 (2007).
[Crossref]

A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, “Quasiparticle dynamics in graphene,” Nat. Phys. 3(1), 36–40 (2007).
[Crossref]

2005 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Ajayan, P. M.

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active Tunable Absorption Enhancement with Graphene Nanodisk Arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref] [PubMed]

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(8), 3698–3702 (2013).
[Crossref] [PubMed]

Alaee, R.

Alonso-González, P.

M. B. Lundeberg, Y. Gao, A. Woessner, C. Tan, P. Alonso-González, K. Watanabe, T. Taniguchi, J. Hone, R. Hillenbrand, and F. H. Koppens, “Thermoelectric detection and imaging of propagating graphene plasmons,” Nat. Mater. 16(2), 204–207 (2017).
[Crossref] [PubMed]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[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]

Andryieuski, A.

Arnold, M. D.

M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the Ideal Plasmonic Nanoshell: The Effects of Surface Scattering and Alternatives to Gold and Silver,” J. Phys. Chem. C 113(8), 3041–3045 (2009).
[Crossref]

Avouris, P.

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

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

Badioli, M.

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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(8), 081405 (2012).
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X. Cai, A. B. Sushkov, R. J. Suess, M. M. Jadidi, G. S. Jenkins, L. O. Nyakiti, R. L. Myers-Ward, S. Li, J. Yan, D. K. Gaskill, T. E. Murphy, H. D. Drew, and M. S. Fuhrer, “Sensitive room-temperature terahertz detection via the photothermoelectric effect in graphene,” Nat. Nanotechnol. 9(10), 814–819 (2014).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
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[Crossref] [PubMed]

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

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(8), 081405 (2012).
[Crossref]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
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Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active Tunable Absorption Enhancement with Graphene Nanodisk Arrays,” Nano Lett. 14(1), 299–304 (2014).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
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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 (2016).
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M. B. Lundeberg, Y. Gao, A. Woessner, C. Tan, P. Alonso-González, K. Watanabe, T. Taniguchi, J. Hone, R. Hillenbrand, and F. H. Koppens, “Thermoelectric detection and imaging of propagating graphene plasmons,” Nat. Mater. 16(2), 204–207 (2017).
[Crossref] [PubMed]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 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(8), 3698–3702 (2013).
[Crossref] [PubMed]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of Plasmonic Waves in Graphene by Guided-Mode Resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

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.

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 (2016).
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M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref] [PubMed]

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D. Spirito, D. Coquillat, S. L. De Bonis, A. Lombardo, M. Bruna, A. C. Ferrari, V. Pellegrini, A. Tredicucci, W. Knap, and M. S. Vitiello, “High performance bilayer-graphene terahertz detectors,” Appl. Phys. Lett. 104(6), 061111 (2014).
[Crossref]

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X. Cai, A. B. Sushkov, R. J. Suess, M. M. Jadidi, G. S. Jenkins, L. O. Nyakiti, R. L. Myers-Ward, S. Li, J. Yan, D. K. Gaskill, T. E. Murphy, H. D. Drew, and M. S. Fuhrer, “Sensitive room-temperature terahertz detection via the photothermoelectric effect in graphene,” Nat. Nanotechnol. 9(10), 814–819 (2014).
[Crossref] [PubMed]

Sun, R. L.

B. G. Xiao, R. L. Sun, J. L. He, K. Qin, S. Kong, J. Chen, and W. Xiumin, “A Terahertz Modulator Based on Graphene Plasmonic Waveguide,” IEEE Photonics Technol. Lett. 27(20), 2190–2192 (2015).
[Crossref]

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]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Sushkov, A. B.

X. Cai, A. B. Sushkov, R. J. Suess, M. M. Jadidi, G. S. Jenkins, L. O. Nyakiti, R. L. Myers-Ward, S. Li, J. Yan, D. K. Gaskill, T. E. Murphy, H. D. Drew, and M. S. Fuhrer, “Sensitive room-temperature terahertz detection via the photothermoelectric effect in graphene,” Nat. Nanotechnol. 9(10), 814–819 (2014).
[Crossref] [PubMed]

Tan, C.

M. B. Lundeberg, Y. Gao, A. Woessner, C. Tan, P. Alonso-González, K. Watanabe, T. Taniguchi, J. Hone, R. Hillenbrand, and F. H. Koppens, “Thermoelectric detection and imaging of propagating graphene plasmons,” Nat. Mater. 16(2), 204–207 (2017).
[Crossref] [PubMed]

Tang, L.

Taniguchi, T.

M. B. Lundeberg, Y. Gao, A. Woessner, C. Tan, P. Alonso-González, K. Watanabe, T. Taniguchi, J. Hone, R. Hillenbrand, and F. H. Koppens, “Thermoelectric detection and imaging of propagating graphene plasmons,” Nat. Mater. 16(2), 204–207 (2017).
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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).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
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S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
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D. Spirito, D. Coquillat, S. L. De Bonis, A. Lombardo, M. Bruna, A. C. Ferrari, V. Pellegrini, A. Tredicucci, W. Knap, and M. S. Vitiello, “High performance bilayer-graphene terahertz detectors,” Appl. Phys. Lett. 104(6), 061111 (2014).
[Crossref]

L. Vicarelli, M. S. Vitiello, D. Coquillat, A. Lombardo, A. C. Ferrari, W. Knap, M. Polini, V. Pellegrini, and A. Tredicucci, “Graphene field-effect transistors as room-temperature terahertz detectors,” Nat. Mater. 11(10), 865–871 (2012).
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Tulevski, G.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (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(8), 3698–3702 (2013).
[Crossref] [PubMed]

Vasilevskiy, M. I.

N. M. R. Peres, Y. V. Bludov, A. Ferreira, and M. I. Vasilevskiy, “Exact solution for square-wave grating covered with graphene: surface plasmon-polaritons in the terahertz range,” J. Phys.- Condes. Matter 25(12), 12 (2013).
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Vicarelli, L.

L. Vicarelli, M. S. Vitiello, D. Coquillat, A. Lombardo, A. C. Ferrari, W. Knap, M. Polini, V. Pellegrini, and A. Tredicucci, “Graphene field-effect transistors as room-temperature terahertz detectors,” Nat. Mater. 11(10), 865–871 (2012).
[Crossref] [PubMed]

Vitiello, M. S.

D. Spirito, D. Coquillat, S. L. De Bonis, A. Lombardo, M. Bruna, A. C. Ferrari, V. Pellegrini, A. Tredicucci, W. Knap, and M. S. Vitiello, “High performance bilayer-graphene terahertz detectors,” Appl. Phys. Lett. 104(6), 061111 (2014).
[Crossref]

L. Vicarelli, M. S. Vitiello, D. Coquillat, A. Lombardo, A. C. Ferrari, W. Knap, M. Polini, V. Pellegrini, and A. Tredicucci, “Graphene field-effect transistors as room-temperature terahertz detectors,” Nat. Mater. 11(10), 865–871 (2012).
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Wagner, 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).
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Wang, F.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Wang, Y.

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active Tunable Absorption Enhancement with Graphene Nanodisk Arrays,” Nano Lett. 14(1), 299–304 (2014).
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Watanabe, K.

M. B. Lundeberg, Y. Gao, A. Woessner, C. Tan, P. Alonso-González, K. Watanabe, T. Taniguchi, J. Hone, R. Hillenbrand, and F. H. Koppens, “Thermoelectric detection and imaging of propagating graphene plasmons,” Nat. Mater. 16(2), 204–207 (2017).
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Wei, L.

Woessner, A.

M. B. Lundeberg, Y. Gao, A. Woessner, C. Tan, P. Alonso-González, K. Watanabe, T. Taniguchi, J. Hone, R. Hillenbrand, and F. H. Koppens, “Thermoelectric detection and imaging of propagating graphene plasmons,” Nat. Mater. 16(2), 204–207 (2017).
[Crossref] [PubMed]

Wong, L. J.

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 (2016).
[Crossref]

Wu, T.

Wu, Y.

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

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
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Xia, F.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
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B. G. Xiao, R. L. Sun, J. L. He, K. Qin, S. Kong, J. Chen, and W. Xiumin, “A Terahertz Modulator Based on Graphene Plasmonic Waveguide,” IEEE Photonics Technol. Lett. 27(20), 2190–2192 (2015).
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Xiumin, W.

B. G. Xiao, R. L. Sun, J. L. He, K. Qin, S. Kong, J. Chen, and W. Xiumin, “A Terahertz Modulator Based on Graphene Plasmonic Waveguide,” IEEE Photonics Technol. Lett. 27(20), 2190–2192 (2015).
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Xu, Q.

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(8), 3698–3702 (2013).
[Crossref] [PubMed]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of Plasmonic Waves in Graphene by Guided-Mode Resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Yan, H.

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

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

Yan, J.

X. Cai, A. B. Sushkov, R. J. Suess, M. M. Jadidi, G. S. Jenkins, L. O. Nyakiti, R. L. Myers-Ward, S. Li, J. Yan, D. K. Gaskill, T. E. Murphy, H. D. Drew, and M. S. Fuhrer, “Sensitive room-temperature terahertz detection via the photothermoelectric effect in graphene,” Nat. Nanotechnol. 9(10), 814–819 (2014).
[Crossref] [PubMed]

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).
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Zettl, A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Zhai, F.

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).
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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).
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Zhang, Q.

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(8), 3698–3702 (2013).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
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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).
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Zhu, P.

Zhu, W.

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

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
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Zhu, X.

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active Tunable Absorption Enhancement with Graphene Nanodisk Arrays,” Nano Lett. 14(1), 299–304 (2014).
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ACS Nano (1)

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).
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ACS Photonics (2)

F. J. García de Abajo, “Graphene Plasmonics: Challenges and Opportunities,” ACS Photonics 1(3), 135–152 (2014).
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A. Marini, I. Silveiro, and F. J. García de Abajo, “Molecular Sensing with Tunable Graphene Plasmons,” ACS Photonics 2(7), 876–882 (2015).
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Appl. Phys. Lett. (1)

D. Spirito, D. Coquillat, S. L. De Bonis, A. Lombardo, M. Bruna, A. C. Ferrari, V. Pellegrini, A. Tredicucci, W. Knap, and M. S. Vitiello, “High performance bilayer-graphene terahertz detectors,” Appl. Phys. Lett. 104(6), 061111 (2014).
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IEEE Photonics Technol. Lett. (1)

B. G. Xiao, R. L. Sun, J. L. He, K. Qin, S. Kong, J. Chen, and W. Xiumin, “A Terahertz Modulator Based on Graphene Plasmonic Waveguide,” IEEE Photonics Technol. Lett. 27(20), 2190–2192 (2015).
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Nano Lett. (3)

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active Tunable Absorption Enhancement with Graphene Nanodisk Arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref] [PubMed]

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(8), 3698–3702 (2013).
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Nat. Commun. (1)

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).
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L. Vicarelli, M. S. Vitiello, D. Coquillat, A. Lombardo, A. C. Ferrari, W. Knap, M. Polini, V. Pellegrini, and A. Tredicucci, “Graphene field-effect transistors as room-temperature terahertz detectors,” Nat. Mater. 11(10), 865–871 (2012).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
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H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
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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 (2016).
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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).
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Figures (7)

Fig. 1
Fig. 1 (a) Schematic of the propagating graphene plasmon excitation configuration. (b) The absorption curves of the excitation configuration. Inset is the electric field distribution of the graphene plasmonic mode in a grating period.
Fig. 2
Fig. 2 (a) The evolution of absorption spectra with graphene electron relaxation time. (b) Three extracted absorption spectra from the position marked by white dashed lines in (a). (c) The extracted absorption peaks from (a), and the analytical results.
Fig. 3
Fig. 3 (a) The evolution of absorption spectra with spacer thickness. (b) Three extracted absorption spectra from the position marked in white dashed lines in (a). (c) The extracted absorption peaks of every spectrum in (a), and the analytical results calculated by Eq. (1) and (4).
Fig. 4
Fig. 4 Two absorption spectra with peak absorption rates of 100% but different bandwidths. The relaxation times, spacer thicknesses for the broad and narrow spectrum are 0.35 ps, 0.85 μm and 1 ps, 1.2 μm, respectively.
Fig. 5
Fig. 5 The evolution of absorption spectra with Fermi energy as the refractive index of spacer layer is 4.2 (a) and 1.5 (b). (c) and (d) are extracted spectra and absorption peaks from (a) and (b), respectively. In (c) and (d), the analytical absorption peaks versus resonant wavelength are also shown, which is calculated using Eq. (1), (3) and (4) by setting γ0 = 1.25 THz and α = 0.4 THz.
Fig. 6
Fig. 6 (a) The evolution of absorption spectra with the incident angle of light. (b) The extracted absorption peaks from (a) and the analytical results.
Fig. 7
Fig. 7 Schematic of the transfer matrix method calculation of the light intensity.

Equations (16)

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A = 4 γ 0 γ 1 ( ω ω a ) 2 + ( γ 0 + γ 1 ) 2 .
σ ( ω ) = 2 e 2 π 2 k B T ln [ 2 cos h ( E f 2 k B T ) ] i ω + i τ 1 .
γ 0 = 1 / ( 2 τ ) .
γ 1 ( h ) = 4 α 1 + [ n 2 cos θ 1 n 1 cos θ 2 c o t ( 2 π n 2 λ a h cos θ 2 ) ] 2
Q = ω a / 2 γ 0 ,
Q ω a W s t o r e d P l o s s ,
γ 0 = P l o s s 2 W s t o r e d ,
W E = W H + W K
P l o s s = 2 τ W K .
γ 0 = P l o s s 2 W s t o r e d = 2 τ W K 2 ( W E + W H + W K ) = 1 τ W K 2 ( 1 + β ) W K = 1 2 ( 1 + β ) τ ,
γ 0 = 1 2 τ .
[ 1 r ] = 1 t 12 [ 1 r 12 r 12 1 ] [ 0 e i δ e i δ 0 ] 1 t 23 [ 1 r 23 r 23 1 ] [ t 0 ] ,
r = r 12 e i 2 δ 1 r 12 e i 2 δ .
N = | 1 + r | 2 = 2 [ 1 cos ( 2 δ ) ] 1 2 r 12 ( 1 r 12 ) 2 [ 1 + cos ( 2 δ ) ] .
N = | 1 + r | 2 = 4 1 [ n 2 cos θ 1 n 1 cos θ 2 cot δ ] 2 .
γ 1 = 4 α 1 [ n 2 cos θ 1 n 1 cos θ 2 cot ( 2 π n 2 h cos θ 2 λ ) ] 2 .

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