Abstract

Graphene-based surface plasmon waveguides (SPWs) show high confinement well beyond the diffraction limit at terahertz frequencies. By combining a graphene SPW and nonlinear material, we propose a novel graphene/AlGaAs SPW structure for terahertz wave difference frequency generation (DFG) under near-infrared pumps. The composite waveguide, which supports single-mode operation at terahertz frequencies and guides two pumps by a high-index-contrast AlGaAs/AlOx structure, can confine terahertz waves tightly and realize good mode field overlap of three waves. The phase-matching condition is satisfied via artificial birefringence in an AlGaAs/AlOx waveguide together with the tunability of graphene, and the phase-matching terahertz wave frequency varies from 4 to 7 THz when the Fermi energy level of graphene changes from 0.848 to 2.456 eV. Based on the coupled-mode theory, we investigate the power-normalized conversion efficiency for the tunable terahertz wave DFG process by using the finite difference method under continuous wave pumps, where the tunable bandwidth can reach 2 THz with considerable conversion efficiency. To exploit the high peak powers of pulses, we also discuss optical pulse evolutions for pulse-pumped terahertz wave DFG processes.

© 2018 Chinese Laser Press

Full Article  |  PDF Article
OSA Recommended Articles
AlxGa1-xAs nested waveguide heterostructures for continuously phase-matched terahertz difference frequency generation

C. M. Staus, T. F. Kuech, and L. McCaughan
Opt. Express 18(3) 2332-2338 (2010)

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
    [Crossref]
  3. S. Liu, Z. Li, Y. Ge, H. Wang, R. Yue, X. Jiang, J. Li, Q. Wen, and H. Zhang, “Graphene/phosphorene nano-heterojunction: facile synthesis, nonlinear optics, and ultrafast photonics applications with enhanced performance,” Photon. Res. 5, 662–668 (2017).
    [Crossref]
  4. Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
    [Crossref]
  5. Y. Wu, B. C. Yao, A. Q. Zhang, X. L. Cao, Z. G. Wang, Y. J. Rao, Y. Gong, W. Zhang, Y. F. Chen, and K. S. Chiang, “Graphene-based D-shaped fiber multicore mode interferometer for chemical gas sensing,” Opt. Lett. 39, 6030–6033 (2014).
    [Crossref]
  6. M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12, 1482–1485 (2012).
    [Crossref]
  7. L. Luo, K. Wang, C. Ge, K. Guo, F. Shen, Z. Yin, and Z. Guo, “Actively controllable terahertz switches with graphene-based nongroove gratings,” Photon. Res. 5, 604–611 (2017).
    [Crossref]
  8. T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4, 297–301 (2010).
    [Crossref]
  9. H. Zhou, T. Gu, J. F. Mcmillan, N. Petrone, A. V. D. Zande, J. C. Hone, M. Yu, G. Lo, D. L. Kwong, and G. Feng, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105, 091111 (2014).
    [Crossref]
  10. L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12, 3711–3715 (2012).
    [Crossref]
  11. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
    [Crossref]
  12. H. Lu, X. Gan, D. Mao, and J. Zhao, “Graphene-supported manipulation of surface plasmon polaritons in metallic nanowaveguides,” Photon. Res. 5, 162–167 (2017).
    [Crossref]
  13. M. Jablan, M. Soljačić, and H. Buljan, “Plasmons in graphene: fundamental properties and potential applications,” Proc. IEEE 101, 1689–1704 (2013).
    [Crossref]
  14. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
    [Crossref]
  15. C. Zhao, D. Mao, J. Zhao, L. Han, L. Fang, X. Gan, and Y. Wang, “Graphene-assisted all-fiber phase shifter and switching,” Optica 2, 468–471 (2015).
    [Crossref]
  16. F. Xie, H. J. Li, J. P. Liu, L. L. Wang, S. X. Xia, X. Zhai, X. Luo, and X. J. Shang, “Graphene-based long-range SPP hybrid waveguide with ultra-long propagation length in mid-infrared range,” Opt. Express 24, 5376–5386 (2016).
    [Crossref]
  17. L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, and Y. R. Shen, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
    [Crossref]
  18. C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101, 111609 (2012).
    [Crossref]
  19. T. J. Constant, S. M. Hornett, D. E. Chang, and E. Hendry, “All-optical generation of surface plasmons in graphene,” Nat. Phys. 12, 124–127 (2016).
    [Crossref]
  20. X. He and S. Kim, “Graphene-supported tunable waveguide structure in the terahertz regime,” J. Opt. Soc. Am. B 30, 2461–2468 (2013).
    [Crossref]
  21. X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32, 4199–4203 (2014).
    [Crossref]
  22. W. Xu, Z. H. Zhu, K. Liu, J. F. Zhang, X. D. Yuan, Q. S. Lu, and S. Q. Qin, “Dielectric loaded graphene plasmon waveguide,” Opt. Express 23, 5147–5153 (2015).
    [Crossref]
  23. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
    [Crossref]
  24. A. Barh, B. M. A. Rahman, B. P. Pal, G. P. Agrawal, and R. K. Varshney, “Plastic fiber design for THz generation through wavelength translation,” Opt. Lett. 40, 2107–2110 (2015).
    [Crossref]
  25. Y. Sun, G. Qiao, and G. Sun, “Direct generation of graphene plasmonic polaritons at THz frequencies via four wave mixing in the hybrid graphene sheets waveguides,” Opt. Express 22, 27880–27891 (2014).
    [Crossref]
  26. Y. Takushima, S. Shin, and Y. C. Chung, “Design of a LiNbO3 ribbon waveguide for efficient difference-frequency generation of terahertz wave in the collinear configuration,” Opt. Express 15, 14783–14792 (2007).
    [Crossref]
  27. Y. Huang, T. Wang, Y. Lin, C. Lee, M. Chuang, Y. Lin, and F. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express 19, 24577–24582 (2011).
    [Crossref]
  28. Y. H. Avetisyan, “Terahertz-wave surface-emitted difference-frequency generation without quasi-phase-matching technique,” Opt. Lett. 35, 2508–2510 (2010).
    [Crossref]
  29. C. M. Staus, T. F. Kuech, and L. McCaughan, “AlxGa1−xAs nested waveguide heterostructures for continuously phase-matched terahertz difference frequency generation,” Opt. Express 18, 2332–2338 (2010).
    [Crossref]
  30. T. Chen, J. Sun, L. Li, and J. Tang, “Proposal for efficient terahertz-wave difference frequency generation in an AlGaAs photonic crystal waveguide,” J. Lightwave Technol. 30, 2156–2162 (2012).
    [Crossref]
  31. Z. Ruan, G. Veronis, K. L. Vodopyanov, M. M. Fejer, and S. Fan, “Enhancement of optics-to-THz conversion efficiency by metallic slot waveguides,” Opt. Express 17, 13502–13515 (2009).
    [Crossref]
  32. Y. Ge, J. Cao, Z. Shen, Y. Zheng, X. Chen, and W. Wan, “Terahertz wave generation by plasmonic-enhanced difference-frequency generation,” J. Opt. Soc. Am. B 31, 1533–1538 (2014).
    [Crossref]
  33. S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, “Influence of scattering and two-photon absorption on the optical loss in GaAs–A2O3 nonlinear waveguides measured using femtosecond pulses,” IEEE J. Quantum. Electron. 39, 478–486 (2003).
    [Crossref]
  34. J. Ota, W. Narita, I. Ohta, T. Matsushita, and T. Kondo, “Fabrication of periodically-inverted AlGaAs waveguides for quasi-phase-matched wavelength conversion at 1.55 μm,” Jpn. J. Appl. Phys. 48, 04C110 (2009).
    [Crossref]
  35. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
  36. M. Pu, L. Ottaviano, E. Semenova, and K. Yvind, “Efficient frequency comb generation in AlGaAs-on-insulator,” Optica 3, 823–826 (2016).
    [Crossref]
  37. T. W. Kim, T. Matsushita, and T. Kondo, “Phase-matched second-harmonic generation in thin rectangular high-index-contrast AlGaAs waveguides,” Appl. Phys. Express 4, 082201 (2011).
    [Crossref]
  38. Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15, 8271–8276 (2015).
    [Crossref]
  39. C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9, 511–514 (2015).
    [Crossref]
  40. J. Wang, J. Sun, and Q. Sun, “Proposal for all-optical format conversion based on a periodically poled lithium niobate loop mirror,” Opt. Lett. 32, 1477–1479 (2007).
    [Crossref]
  41. P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5, 5855–5863 (2011).
    [Crossref]
  42. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
    [Crossref]
  43. F. H. L. Koppens, D. E. Chang, and F. J. G. D. Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
    [Crossref]
  44. G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).
  45. L. Ottaviano, M. Pu, E. Semenova, and K. Yvind, “Low-loss high-confinement waveguides and microring resonators in AlGaAs-on-insulator,” Opt. Lett. 41, 3996–3999 (2016).
    [Crossref]
  46. Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
    [Crossref]
  47. K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
    [Crossref]

2017 (3)

2016 (4)

2015 (5)

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15, 8271–8276 (2015).
[Crossref]

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9, 511–514 (2015).
[Crossref]

W. Xu, Z. H. Zhu, K. Liu, J. F. Zhang, X. D. Yuan, Q. S. Lu, and S. Q. Qin, “Dielectric loaded graphene plasmon waveguide,” Opt. Express 23, 5147–5153 (2015).
[Crossref]

A. Barh, B. M. A. Rahman, B. P. Pal, G. P. Agrawal, and R. K. Varshney, “Plastic fiber design for THz generation through wavelength translation,” Opt. Lett. 40, 2107–2110 (2015).
[Crossref]

C. Zhao, D. Mao, J. Zhao, L. Han, L. Fang, X. Gan, and Y. Wang, “Graphene-assisted all-fiber phase shifter and switching,” Optica 2, 468–471 (2015).
[Crossref]

2014 (5)

2013 (2)

M. Jablan, M. Soljačić, and H. Buljan, “Plasmons in graphene: fundamental properties and potential applications,” Proc. IEEE 101, 1689–1704 (2013).
[Crossref]

X. He and S. Kim, “Graphene-supported tunable waveguide structure in the terahertz regime,” J. Opt. Soc. Am. B 30, 2461–2468 (2013).
[Crossref]

2012 (7)

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12, 3711–3715 (2012).
[Crossref]

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

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12, 1482–1485 (2012).
[Crossref]

T. Chen, J. Sun, L. Li, and J. Tang, “Proposal for efficient terahertz-wave difference frequency generation in an AlGaAs photonic crystal waveguide,” J. Lightwave Technol. 30, 2156–2162 (2012).
[Crossref]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101, 111609 (2012).
[Crossref]

2011 (8)

T. W. Kim, T. Matsushita, and T. Kondo, “Phase-matched second-harmonic generation in thin rectangular high-index-contrast AlGaAs waveguides,” Appl. Phys. Express 4, 082201 (2011).
[Crossref]

Y. Huang, T. Wang, Y. Lin, C. Lee, M. Chuang, Y. Lin, and F. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express 19, 24577–24582 (2011).
[Crossref]

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5, 5855–5863 (2011).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref]

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

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[Crossref]

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

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

2010 (4)

T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4, 297–301 (2010).
[Crossref]

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

C. M. Staus, T. F. Kuech, and L. McCaughan, “AlxGa1−xAs nested waveguide heterostructures for continuously phase-matched terahertz difference frequency generation,” Opt. Express 18, 2332–2338 (2010).
[Crossref]

Y. H. Avetisyan, “Terahertz-wave surface-emitted difference-frequency generation without quasi-phase-matching technique,” Opt. Lett. 35, 2508–2510 (2010).
[Crossref]

2009 (2)

Z. Ruan, G. Veronis, K. L. Vodopyanov, M. M. Fejer, and S. Fan, “Enhancement of optics-to-THz conversion efficiency by metallic slot waveguides,” Opt. Express 17, 13502–13515 (2009).
[Crossref]

J. Ota, W. Narita, I. Ohta, T. Matsushita, and T. Kondo, “Fabrication of periodically-inverted AlGaAs waveguides for quasi-phase-matched wavelength conversion at 1.55 μm,” Jpn. J. Appl. Phys. 48, 04C110 (2009).
[Crossref]

2008 (1)

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[Crossref]

2007 (3)

2003 (1)

S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, “Influence of scattering and two-photon absorption on the optical loss in GaAs–A2O3 nonlinear waveguides measured using femtosecond pulses,” IEEE J. Quantum. Electron. 39, 478–486 (2003).
[Crossref]

Abajo, F. J. G. D.

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

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

Agrawal, G. P.

Alù, A.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5, 5855–5863 (2011).
[Crossref]

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, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Avetisyan, Y. H.

Avouris, P.

T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4, 297–301 (2010).
[Crossref]

Bao, Q.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[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, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Barh, A.

Basko, D. M.

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

Bechtel, H. A.

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

Berger, V.

S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, “Influence of scattering and two-photon absorption on the optical loss in GaAs–A2O3 nonlinear waveguides measured using femtosecond pulses,” IEEE J. Quantum. Electron. 39, 478–486 (2003).
[Crossref]

Bolotin, K.

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[Crossref]

Bonaccorso, F.

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

Buljan, H.

M. Jablan, M. Soljačić, and H. Buljan, “Plasmons in graphene: fundamental properties and potential applications,” Proc. IEEE 101, 1689–1704 (2013).
[Crossref]

Calligaro, M.

S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, “Influence of scattering and two-photon absorption on the optical loss in GaAs–A2O3 nonlinear waveguides measured using femtosecond pulses,” IEEE J. Quantum. Electron. 39, 478–486 (2003).
[Crossref]

Cao, J.

Cao, X. L.

Cardenas, J.

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9, 511–514 (2015).
[Crossref]

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, 124–127 (2016).
[Crossref]

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

Chen, L.

X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32, 4199–4203 (2014).
[Crossref]

Chen, P. Y.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5, 5855–5863 (2011).
[Crossref]

Chen, T.

Chen, X.

Chen, Y. F.

Chiang, K. S.

Chuang, M.

Chung, Y. C.

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]

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, 124–127 (2016).
[Crossref]

Dai, S.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15, 8271–8276 (2015).
[Crossref]

De Rossi, A.

S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, “Influence of scattering and two-photon absorption on the optical loss in GaAs–A2O3 nonlinear waveguides measured using femtosecond pulses,” IEEE J. Quantum. Electron. 39, 478–486 (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, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Ebrahimzadeh, M.

S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, “Influence of scattering and two-photon absorption on the optical loss in GaAs–A2O3 nonlinear waveguides measured using femtosecond pulses,” IEEE J. Quantum. Electron. 39, 478–486 (2003).
[Crossref]

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]

Fan, S.

Fang, L.

Fei, Z.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15, 8271–8276 (2015).
[Crossref]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Fejer, M. M.

Feng, G.

H. Zhou, T. Gu, J. F. Mcmillan, N. Petrone, A. V. D. Zande, J. C. Hone, M. Yu, G. Lo, D. L. Kwong, and G. Feng, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105, 091111 (2014).
[Crossref]

Ferrari, A. C.

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

Fudenberg, G.

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[Crossref]

Gan, C. H.

C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101, 111609 (2012).
[Crossref]

Gan, X.

Ge, C.

Ge, Y.

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.

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

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref]

Gintz, G.

S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, “Influence of scattering and two-photon absorption on the optical loss in GaAs–A2O3 nonlinear waveguides measured using femtosecond pulses,” IEEE J. Quantum. Electron. 39, 478–486 (2003).
[Crossref]

Girit, C.

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

Goldflam, M. D.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15, 8271–8276 (2015).
[Crossref]

Gong, Y.

Grigorenko, A. N.

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

Gu, T.

H. Zhou, T. Gu, J. F. Mcmillan, N. Petrone, A. V. D. Zande, J. C. Hone, M. Yu, G. Lo, D. L. Kwong, and G. Feng, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105, 091111 (2014).
[Crossref]

Guo, K.

Guo, Z.

Han, L.

Hao, Z.

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

Hasan, T.

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

He, X.

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, 124–127 (2016).
[Crossref]

Hone, J.

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[Crossref]

Hone, J. C.

H. Zhou, T. Gu, J. F. Mcmillan, N. Petrone, A. V. D. Zande, J. C. Hone, M. Yu, G. Lo, D. L. Kwong, and G. Feng, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105, 091111 (2014).
[Crossref]

Hong, W.

X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32, 4199–4203 (2014).
[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, 124–127 (2016).
[Crossref]

Horng, J.

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

Huang, Y.

Jablan, M.

M. Jablan, M. Soljačić, and H. Buljan, “Plasmons in graphene: fundamental properties and potential applications,” Proc. IEEE 101, 1689–1704 (2013).
[Crossref]

Janssen, G. C. A. M.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15, 8271–8276 (2015).
[Crossref]

Jiang, X.

Jiang, Z.

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[Crossref]

Jin, Z.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12, 3711–3715 (2012).
[Crossref]

Ju, L.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref]

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

Kaneko, R.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12, 3711–3715 (2012).
[Crossref]

Kawayama, I.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12, 3711–3715 (2012).
[Crossref]

Kim, K.

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]

Kim, P.

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[Crossref]

Kim, S.

Kim, T. W.

T. W. Kim, T. Matsushita, and T. Kondo, “Phase-matched second-harmonic generation in thin rectangular high-index-contrast AlGaAs waveguides,” Appl. Phys. Express 4, 082201 (2011).
[Crossref]

Klima, M.

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[Crossref]

Kondo, T.

T. W. Kim, T. Matsushita, and T. Kondo, “Phase-matched second-harmonic generation in thin rectangular high-index-contrast AlGaAs waveguides,” Appl. Phys. Express 4, 082201 (2011).
[Crossref]

J. Ota, W. Narita, I. Ohta, T. Matsushita, and T. Kondo, “Fabrication of periodically-inverted AlGaAs waveguides for quasi-phase-matched wavelength conversion at 1.55 μm,” Jpn. J. Appl. Phys. 48, 04C110 (2009).
[Crossref]

Koppens, F. H. L.

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

Kuech, T. F.

Kwong, D. L.

H. Zhou, T. Gu, J. F. Mcmillan, N. Petrone, A. V. D. Zande, J. C. Hone, M. Yu, G. Lo, D. L. Kwong, and G. Feng, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105, 091111 (2014).
[Crossref]

Lee, C.

Lee, Y. H. D.

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9, 511–514 (2015).
[Crossref]

Li, H. J.

Li, J.

Li, L.

Li, X.

X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32, 4199–4203 (2014).
[Crossref]

Li, Z.

Liang, X.

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

Lim, C. H. Y. X.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[Crossref]

Lin, F.

Lin, Y.

Lipson, M.

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9, 511–514 (2015).
[Crossref]

Liu, J. P.

Liu, K.

Liu, M.

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12, 1482–1485 (2012).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref]

Liu, M. K.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15, 8271–8276 (2015).
[Crossref]

Liu, S.

Lo, G.

H. Zhou, T. Gu, J. F. Mcmillan, N. Petrone, A. V. D. Zande, J. C. Hone, M. Yu, G. Lo, D. L. Kwong, and G. Feng, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105, 091111 (2014).
[Crossref]

Loh, K. P.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[Crossref]

Lu, H.

Lu, Q. S.

Luo, L.

Luo, X.

Mao, D.

Martin, M.

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

Matsushita, T.

T. W. Kim, T. Matsushita, and T. Kondo, “Phase-matched second-harmonic generation in thin rectangular high-index-contrast AlGaAs waveguides,” Appl. Phys. Express 4, 082201 (2011).
[Crossref]

J. Ota, W. Narita, I. Ohta, T. Matsushita, and T. Kondo, “Fabrication of periodically-inverted AlGaAs waveguides for quasi-phase-matched wavelength conversion at 1.55 μm,” Jpn. J. Appl. Phys. 48, 04C110 (2009).
[Crossref]

McCaughan, L.

Mcleod, A. S.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15, 8271–8276 (2015).
[Crossref]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Mcmillan, J. F.

H. Zhou, T. Gu, J. F. Mcmillan, N. Petrone, A. V. D. Zande, J. C. Hone, M. Yu, G. Lo, D. L. Kwong, and G. Feng, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105, 091111 (2014).
[Crossref]

Moutzouris, K.

S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, “Influence of scattering and two-photon absorption on the optical loss in GaAs–A2O3 nonlinear waveguides measured using femtosecond pulses,” IEEE J. Quantum. Electron. 39, 478–486 (2003).
[Crossref]

Mueller, T.

T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4, 297–301 (2010).
[Crossref]

Nanot, S.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12, 3711–3715 (2012).
[Crossref]

Narita, W.

J. Ota, W. Narita, I. Ohta, T. Matsushita, and T. Kondo, “Fabrication of periodically-inverted AlGaAs waveguides for quasi-phase-matched wavelength conversion at 1.55 μm,” Jpn. J. Appl. Phys. 48, 04C110 (2009).
[Crossref]

Ni, Z.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[Crossref]

Novoselov, K. S.

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

Ohta, I.

J. Ota, W. Narita, I. Ohta, T. Matsushita, and T. Kondo, “Fabrication of periodically-inverted AlGaAs waveguides for quasi-phase-matched wavelength conversion at 1.55 μm,” Jpn. J. Appl. Phys. 48, 04C110 (2009).
[Crossref]

Ortiz, V.

S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, “Influence of scattering and two-photon absorption on the optical loss in GaAs–A2O3 nonlinear waveguides measured using femtosecond pulses,” IEEE J. Quantum. Electron. 39, 478–486 (2003).
[Crossref]

Ota, J.

J. Ota, W. Narita, I. Ohta, T. Matsushita, and T. Kondo, “Fabrication of periodically-inverted AlGaAs waveguides for quasi-phase-matched wavelength conversion at 1.55 μm,” Jpn. J. Appl. Phys. 48, 04C110 (2009).
[Crossref]

Ottaviano, L.

Pal, B. P.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Petrone, N.

H. Zhou, T. Gu, J. F. Mcmillan, N. Petrone, A. V. D. Zande, J. C. Hone, M. Yu, G. Lo, D. L. Kwong, and G. Feng, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105, 091111 (2014).
[Crossref]

Phare, C. T.

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9, 511–514 (2015).
[Crossref]

Polini, M.

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

Popa, D.

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

Post, K. W.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15, 8271–8276 (2015).
[Crossref]

Privitera, G.

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

Pu, M.

Qiao, G.

Qin, S. Q.

Rahman, B. M. A.

Rao, S.

S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, “Influence of scattering and two-photon absorption on the optical loss in GaAs–A2O3 nonlinear waveguides measured using femtosecond pulses,” IEEE J. Quantum. Electron. 39, 478–486 (2003).
[Crossref]

Rao, Y. J.

Ren, L.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12, 3711–3715 (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, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Ruan, Z.

Schwab, M. G.

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]

Semenova, E.

Shang, X. J.

Shen, F.

Shen, Y. R.

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

Shen, Z.

Shin, S.

Sikes, K.

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[Crossref]

Soljacic, M.

M. Jablan, M. Soljačić, and H. Buljan, “Plasmons in graphene: fundamental properties and potential applications,” Proc. IEEE 101, 1689–1704 (2013).
[Crossref]

Staus, C. M.

Stormer, H.

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[Crossref]

Sun, G.

Sun, J.

Sun, Q.

Sun, Y.

Sun, Z.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12, 3711–3715 (2012).
[Crossref]

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

Takushima, Y.

Tang, D. Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[Crossref]

Tang, J.

Thiemens, M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Tonouchi, M.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12, 3711–3715 (2012).
[Crossref]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

Torrisi, F.

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

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref]

Vakil, A.

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

Varshney, R. K.

Veronis, G.

Vodopyanov, K. L.

Wagner, M.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15, 8271–8276 (2015).
[Crossref]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Wan, W.

Wang, B.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[Crossref]

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref]

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

Wang, H.

Wang, J.

Wang, K.

Wang, L. L.

Wang, T.

Wang, Y.

C. Zhao, D. Mao, J. Zhao, L. Han, L. Fang, X. Gan, and Y. Wang, “Graphene-assisted all-fiber phase shifter and switching,” Optica 2, 468–471 (2015).
[Crossref]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[Crossref]

Wang, Z. G.

Wen, Q.

Wu, J. S.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15, 8271–8276 (2015).
[Crossref]

Wu, Y.

Xia, F.

T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4, 297–301 (2010).
[Crossref]

Xia, S. X.

Xie, F.

Xu, W.

Yan, Z.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12, 3711–3715 (2012).
[Crossref]

Yao, B. C.

Yao, J.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12, 3711–3715 (2012).
[Crossref]

Yin, X.

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12, 1482–1485 (2012).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref]

Yin, Z.

Yu, M.

H. Zhou, T. Gu, J. F. Mcmillan, N. Petrone, A. V. D. Zande, J. C. Hone, M. Yu, G. Lo, D. L. Kwong, and G. Feng, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105, 091111 (2014).
[Crossref]

Yuan, X. D.

Yue, R.

Yvind, K.

Zande, A. V. D.

H. Zhou, T. Gu, J. F. Mcmillan, N. Petrone, A. V. D. Zande, J. C. Hone, M. Yu, G. Lo, D. L. Kwong, and G. Feng, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105, 091111 (2014).
[Crossref]

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref]

Zettl, A.

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

Zhai, X.

Zhang, A. Q.

Zhang, H.

Zhang, J. F.

Zhang, L. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Zhang, Q.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12, 3711–3715 (2012).
[Crossref]

Zhang, T.

X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32, 4199–4203 (2014).
[Crossref]

Zhang, W.

Zhang, X.

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12, 1482–1485 (2012).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref]

Zhao, C.

Zhao, J.

Zhao, Z.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Zheng, Y.

Zhou, H.

H. Zhou, T. Gu, J. F. Mcmillan, N. Petrone, A. V. D. Zande, J. C. Hone, M. Yu, G. Lo, D. L. Kwong, and G. Feng, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105, 091111 (2014).
[Crossref]

Zhou, X.

X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32, 4199–4203 (2014).
[Crossref]

Zhu, S.

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15, 8271–8276 (2015).
[Crossref]

Zhu, Z. H.

ACS Nano (2)

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

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5, 5855–5863 (2011).
[Crossref]

Appl. Phys. Express (1)

T. W. Kim, T. Matsushita, and T. Kondo, “Phase-matched second-harmonic generation in thin rectangular high-index-contrast AlGaAs waveguides,” Appl. Phys. Express 4, 082201 (2011).
[Crossref]

Appl. Phys. Lett. (2)

C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101, 111609 (2012).
[Crossref]

H. Zhou, T. Gu, J. F. Mcmillan, N. Petrone, A. V. D. Zande, J. C. Hone, M. Yu, G. Lo, D. L. Kwong, and G. Feng, “Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 105, 091111 (2014).
[Crossref]

IEEE J. Quantum. Electron. (1)

S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, “Influence of scattering and two-photon absorption on the optical loss in GaAs–A2O3 nonlinear waveguides measured using femtosecond pulses,” IEEE J. Quantum. Electron. 39, 478–486 (2003).
[Crossref]

J. Lightwave Technol. (2)

X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32, 4199–4203 (2014).
[Crossref]

T. Chen, J. Sun, L. Li, and J. Tang, “Proposal for efficient terahertz-wave difference frequency generation in an AlGaAs photonic crystal waveguide,” J. Lightwave Technol. 30, 2156–2162 (2012).
[Crossref]

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

Jpn. J. Appl. Phys. (1)

J. Ota, W. Narita, I. Ohta, T. Matsushita, and T. Kondo, “Fabrication of periodically-inverted AlGaAs waveguides for quasi-phase-matched wavelength conversion at 1.55 μm,” Jpn. J. Appl. Phys. 48, 04C110 (2009).
[Crossref]

Nano Lett. (4)

Z. Fei, M. D. Goldflam, J. S. Wu, S. Dai, M. Wagner, A. S. Mcleod, M. K. Liu, K. W. Post, S. Zhu, and G. C. A. M. Janssen, “Edge and surface plasmons in graphene nanoribbons,” Nano Lett. 15, 8271–8276 (2015).
[Crossref]

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, and M. Tonouchi, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12, 3711–3715 (2012).
[Crossref]

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

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12, 1482–1485 (2012).
[Crossref]

Nat. Nanotechnol. (1)

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

Nat. Photonics (5)

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[Crossref]

T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4, 297–301 (2010).
[Crossref]

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

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9, 511–514 (2015).
[Crossref]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

Nat. Phys. (1)

T. J. Constant, S. M. Hornett, D. E. Chang, and E. Hendry, “All-optical generation of surface plasmons in graphene,” Nat. Phys. 12, 124–127 (2016).
[Crossref]

Nature (3)

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]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, and G. Dominguez, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref]

Opt. Express (7)

Y. Takushima, S. Shin, and Y. C. Chung, “Design of a LiNbO3 ribbon waveguide for efficient difference-frequency generation of terahertz wave in the collinear configuration,” Opt. Express 15, 14783–14792 (2007).
[Crossref]

Z. Ruan, G. Veronis, K. L. Vodopyanov, M. M. Fejer, and S. Fan, “Enhancement of optics-to-THz conversion efficiency by metallic slot waveguides,” Opt. Express 17, 13502–13515 (2009).
[Crossref]

C. M. Staus, T. F. Kuech, and L. McCaughan, “AlxGa1−xAs nested waveguide heterostructures for continuously phase-matched terahertz difference frequency generation,” Opt. Express 18, 2332–2338 (2010).
[Crossref]

Y. Sun, G. Qiao, and G. Sun, “Direct generation of graphene plasmonic polaritons at THz frequencies via four wave mixing in the hybrid graphene sheets waveguides,” Opt. Express 22, 27880–27891 (2014).
[Crossref]

W. Xu, Z. H. Zhu, K. Liu, J. F. Zhang, X. D. Yuan, Q. S. Lu, and S. Q. Qin, “Dielectric loaded graphene plasmon waveguide,” Opt. Express 23, 5147–5153 (2015).
[Crossref]

F. Xie, H. J. Li, J. P. Liu, L. L. Wang, S. X. Xia, X. Zhai, X. Luo, and X. J. Shang, “Graphene-based long-range SPP hybrid waveguide with ultra-long propagation length in mid-infrared range,” Opt. Express 24, 5376–5386 (2016).
[Crossref]

Y. Huang, T. Wang, Y. Lin, C. Lee, M. Chuang, Y. Lin, and F. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express 19, 24577–24582 (2011).
[Crossref]

Opt. Lett. (5)

Optica (2)

Photon. Res. (3)

Proc. IEEE (1)

M. Jablan, M. Soljačić, and H. Buljan, “Plasmons in graphene: fundamental properties and potential applications,” Proc. IEEE 101, 1689–1704 (2013).
[Crossref]

Science (1)

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

Solid State Commun. (1)

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
[Crossref]

Other (2)

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1. Schematic of the graphene/AlGaAs surface plasmon waveguide.
Fig. 2.
Fig. 2. (a) Real and (b) imaginary refractive index of graphene versus the Fermi energy level for 2, 4, 6, and 8 THz, respectively.
Fig. 3.
Fig. 3. Electric field profiles of (a) TM single mode at 6 THz, (b) TE fundamental mode at pump wavelength λp=1.53  μm, and (c) TM fundamental mode at signal wavelength λs=1.5783  μm. (d) Effective interaction area Aeff as a function of THz wave frequency.
Fig. 4.
Fig. 4. (a) Phase mismatch Δk as a function of Fermi energy level for 5.8, 5.9, 6.0, and 6.1 THz generation. (b) Phase-matching THz frequency as a function of Fermi energy level.
Fig. 5.
Fig. 5. (a) Contour image of power-normalized conversion efficiency versus waveguide length for different THz wave frequencies. (b) THz wave power versus THz frequency for waveguide length 500 μm and 2500 μm with Pp=100  W and Ps=1  W.
Fig. 6.
Fig. 6. Optical pulse evolutions along the waveguide with 30 ps pulse input pump with peak power 100 W and 1 W CW input signal: (a) pump wave power, (b) signal wave power, and (c) THz wave power.

Tables (1)

Tables Icon

Table 1. Effective Refractive Index and Fermi Energy Level EF for Phase-Matching THz Frequency

Equations (5)

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

Apx+βp1Apt+12αpAp=iωpκAsAiexp(iΔkx),Asx+βs1Ast+12αsAs=iωsκAi*Apexp(iΔkx),Aix+βi1Ait+12αiAi=iωiκAs*Apexp(iΔkx),
κ=deff2μ0/(cnpnsniAeff),
Aeff=|ep|2dydz|es|2dydz|ei|2dydz|epeseidydz|2,
δg=ie2kBTπ2(ω+iτ1){EFkBT+2ln[exp(EFkBT)+1]}+ie24πln[2|EF|(ω+iτ1)2|EF|+(ω+iτ1)],
npns=ωiωp(nins).

Metrics