Abstract

The scattering matrix theory has been developed to calculate the third-order nonlinear effect in sphere-graphene-slab structures. By designing structural parameters, we have demonstrated that the incident electromagnetic wave can be well confined in the graphene in these structures due to the formation of a bound state in the continuum (BIC) of radiation modes. Based on such a bound state, third-harmonic (TH) generation and four-wave mixing (FWM) have been studied. It is found that the efficiency of TH generation in monolayer graphene can be enhanced about 7 orders of magnitude. It is interesting that we can design structure parameters to make all beams (the pump beam, probe beam, and generated FWM signal) be BICs at the same time. In such a case, the efficiency of FWM in monolayer graphene can be enhanced about 9 orders of magnitude. Both the TH and FWM signals are sensitive to the wavelength, and possess high Q factors, which exhibit very good monochromaticity. By taking suitable BICs, the selective generation of TH and FWM signals for S- and P-polarized waves can also be realized, which is beneficial for the design of optical devices.

© 2017 Chinese Laser Press

Full Article  |  PDF Article
OSA Recommended Articles
Improved generation of correlated photon pairs from monolayer WS2 based on bound states in the continuum

Tiecheng Wang, Zhixin Li, and Xiangdong Zhang
Photon. Res. 7(3) 341-350 (2019)

Strong terahertz magneto-optical phenomena based on quasi-bound states in the continuum and Fano resonances

G. Y. Chen, W. X. Zhang, and X. D. Zhang
Opt. Express 27(12) 16449-16460 (2019)

References

  • View by:
  • |
  • |
  • |

  1. E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
    [Crossref]
  2. R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11, 5159–5164 (2011).
    [Crossref]
  3. H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37, 1856–1858 (2012).
    [Crossref]
  4. X. Yao and A. Belyanin, “Giant optical nonlinearity of graphene in a strong magnetic field,” Phys. Rev. Lett. 108, 255503 (2012).
    [Crossref]
  5. M. Tokman, X. Yao, and A. Belyanin, “Generation of entangled photons in graphene in a strong magnetic field,” Phys. Rev. Lett. 110, 077404 (2013).
    [Crossref]
  6. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
    [Crossref]
  7. W. B. Cho, J. W. Kim, H. W. Lee, S. Bae, B. H. Hong, S. Y. Choi, I. H. Baek, K. Kim, D.-I. Yeom, and F. Rotermund, “High-quality, large-area monolayer graphene for efficient bulk laser mode-locking near 1:25  μm,” Opt. Lett. 36, 4089–4091 (2011).
    [Crossref]
  8. D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. Ferrari, “Sub 200  fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
    [Crossref]
  9. Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96, 051122 (2010).
    [Crossref]
  10. W. Tan, C. Su, R. Knize, G. Xie, L. Li, and D. Tang, “Mode locking of ceramic Nd: yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96, 031106 (2010).
    [Crossref]
  11. J.-L. Xu, X.-L. Li, Y.-Z. Wu, X.-P. Hao, J.-L. He, and K.-J. Yang, “Graphene saturable absorber mirror for ultra-fast-pulse solid-state laser,” Opt. Lett. 36, 1948–1950 (2011).
    [Crossref]
  12. J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
    [Crossref]
  13. M. Feng, H. Zhan, and Y. Chen, “Nonlinear optical and optical limiting properties of graphene families,” Appl. Phys. Lett. 96, 033107 (2010).
    [Crossref]
  14. H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11, 2622–2627 (2011).
    [Crossref]
  15. H. Harutyunyan, R. Beams, and L. Novotny, “Controllable optical negative refraction and phase conjugation in graphite thin films,” Nat. Phys. 9, 423–425 (2013).
    [Crossref]
  16. S. M. Rao, A. Lyons, T. Roger, M. Clerici, N. I. Zheludev, and D. Faccio, “Geometries for the coherent control of four-wave mixing in graphene multilayers,” Sci. Rep. 5, 15399 (2015).
    [Crossref]
  17. J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third order optical nonlinearity of graphene,” New J. Phys. 16, 053014 (2014).
    [Crossref]
  18. S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
    [Crossref]
  19. N. Kumar, J. Kumar, C. Gerstenkorn, R. Wang, H.-Y. Chiu, A. L. Smirl, and H. Zhao, “Third harmonic generation in graphene and few-layer graphite films,” Phys. Rev. B 87, 121406 (2013).
    [Crossref]
  20. S. A. Mikhailov, “Quantum theory of third-harmonic generation in graphene,” Phys. Rev. B 90, 241301 (2014).
    [Crossref]
  21. S. A. Mikhailov, “Quantum theory of third-harmonic generation in graphene,” Phys. Rev. B (erratum) 91, 039904 (2014).
    [Crossref]
  22. J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature,” Phys. Rev. B 91, 235320 (2016).
    [Crossref]
  23. J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature,” Phys. Rev. B (erratum) 93, 039904 (2016).
    [Crossref]
  24. A. V. Gorbach and E. Ivanov, “Perturbation theory for graphene-integrated waveguide: cubic nonlinearity and third-harmonic generation,” Phys. Rev. A 94, 013811 (2016).
    [Crossref]
  25. D. B. S. Soh, R. Hamerly, and H. Mabuchi, “Comprehensive analysis of the optical Kerr coefficient of graphene,” Phys. Rev. A 94, 023845 (2016).
    [Crossref]
  26. Y. F. Song, L. Li, H. Zhang, D. Y. Shen, D. Y. Tang, and K. P. Loh, “Vector multi-soliton operation and interaction in a graphene mode-locked fiber laser,” Opt. Express 21, 10010–10018 (2013).
    [Crossref]
  27. Z.-C. Luo, M. Liu, Z.-N. Guo, X.-F. Jiang, A.-P. Luo, C.-J. Zhao, X.-F. Yu, W.-C. Xu, and H. Zhang, “Microfiber-based few layer black phosphorus saturable absorber for ultra-fast fiber laser,” Opt. Express 23, 20030–20039 (2015).
    [Crossref]
  28. M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Third-harmonic generation in one-dimensional photonic crystal with graphene-based defect,” Phys. Rev. B 89, 165139 (2014).
    [Crossref]
  29. J. Niu, M. Luo, and Q. H. Liu, “Enhancement of graphene’s third-harmonic generation with localized surface plasmon resonance under optical/electro-optic Kerr effects,” J. Opt. Soc. Am. B 33, 615–621 (2016).
    [Crossref]
  30. A. V. Gorbach, “Nonlinear graphene plasmonics: amplitude equation for surface plasmons,” Phys. Rev. A 87, 013830 (2013).
    [Crossref]
  31. G. T. Adamashvili and D. J. Kaup, “Optical surface breather in graphene,” Phys. Rev. A 95, 053801 (2017).
    [Crossref]
  32. D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound states in the continuum in photonics,” Phys. Rev. Lett. 100, 183902 (2008).
    [Crossref]
  33. E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum in photonic waveguides inspired by defects,” Phys. Rev. B 78, 075105 (2008).
    [Crossref]
  34. Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
    [Crossref]
  35. M. I. Molina, A. E. Miroshnichenko, and Y. S. Kivshar, “Surface bound states in the continuum,” Phys. Rev. Lett. 108, 070401 (2012).
    [Crossref]
  36. J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
    [Crossref]
  37. C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
    [Crossref]
  38. C. W. Hsu, B. Zhen, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2, e84 (2013).
    [Crossref]
  39. F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112, 213903 (2014).
    [Crossref]
  40. Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Analytical perspective for bound states in the continuum in photonic crystal slabs,” Phys. Rev. Lett. 113, 037401 (2014).
    [Crossref]
  41. B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
    [Crossref]
  42. M. G. Silveirinha, “Trapping light in open plasmonic nanostructures,” Phys. Rev. A 89, 023813 (2014).
    [Crossref]
  43. M. Zhang and X. D. Zhang, “Ultrasensitive optical absorption in graphene based on bound states in the continuum,” Sci. Rep. 5, 8266 (2015).
    [Crossref]
  44. E. N. Bulgakov and A. F. Sadreev, “Light trapping above the light cone in a one-dimensional array of dielectric spheres,” Phys. Rev. A 92, 023816 (2015).
    [Crossref]
  45. E. N. Bulgakov and A. F. Sadreev, “Transfer of spin angular momentum of an incident wave into orbital angular momentum of the bound states in the continuum in an array of dielectric spheres,” Phys. Rev. A 94, 033856 (2016).
    [Crossref]
  46. J. Li, J. Ren, and X. D. Zhang, “Three-dimensional vector wave bound states in a continuum,” J. Opt. Soc. Am. B 34, 559–565 (2017).
    [Crossref]
  47. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
    [Crossref]
  48. G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
    [Crossref]
  49. P. A. D. Gonçalves, E. J. C. Dias, Yu. V. Bludov, and N. M. R. Peres, “Modeling the excitation of graphene plasmons in periodic grids of graphene ribbons: an analytical approach,” Phys. Rev. B 94, 195421 (2016).
    [Crossref]
  50. K. Ziegler, “Robust transport properties in graphene,” Phys. Rev. Lett. 97, 266802 (2006).
    [Crossref]
  51. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and Hall conductivity in graphene,” Phys. Rev. B 75, 165407 (2007).
    [Crossref]
  52. T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
    [Crossref]
  53. S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
    [Crossref]
  54. K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
    [Crossref]
  55. S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
    [Crossref]
  56. J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
    [Crossref]
  57. A. Marini, J. D. Cox, and F. J. García de Abajo, “Theory of graphene saturable absorption,” Phys. Rev. B 95, 125408 (2017).
    [Crossref]
  58. A. Auditore, C. De Angelis, A. Locatelli, S. Boscolo, M. Midrio, M. Romagnoli, A. D. Capobianco, and G. Nalesso, “Graphene sustained nonlinear modes in dielectric waveguides,” Opt. Lett. 38, 631–633 (2013).
    [Crossref]
  59. A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99, 121107 (2011).
    [Crossref]
  60. N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
    [Crossref]
  61. H. Nasari and M. S. Abrishamian, “Electrically tunable, plasmon resonance enhanced terahertz third harmonic generation via graphene,” RSC Adv. 6, 50190–50200 (2016).
    [Crossref]
  62. H. Nasari and M. S. Abrishamian, “Nonlinear terahertz frequency conversion via graphene microribbon array,” Nanotechnology 27, 305202 (2016).
    [Crossref]
  63. E. D. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).
  64. S. Adachi, “GaAs, AlAs, and AlxGa1−xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
    [Crossref]
  65. A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20, 024701 (2017).
    [Crossref]

2017 (4)

G. T. Adamashvili and D. J. Kaup, “Optical surface breather in graphene,” Phys. Rev. A 95, 053801 (2017).
[Crossref]

A. Marini, J. D. Cox, and F. J. García de Abajo, “Theory of graphene saturable absorption,” Phys. Rev. B 95, 125408 (2017).
[Crossref]

A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20, 024701 (2017).
[Crossref]

J. Li, J. Ren, and X. D. Zhang, “Three-dimensional vector wave bound states in a continuum,” J. Opt. Soc. Am. B 34, 559–565 (2017).
[Crossref]

2016 (9)

J. Niu, M. Luo, and Q. H. Liu, “Enhancement of graphene’s third-harmonic generation with localized surface plasmon resonance under optical/electro-optic Kerr effects,” J. Opt. Soc. Am. B 33, 615–621 (2016).
[Crossref]

H. Nasari and M. S. Abrishamian, “Electrically tunable, plasmon resonance enhanced terahertz third harmonic generation via graphene,” RSC Adv. 6, 50190–50200 (2016).
[Crossref]

H. Nasari and M. S. Abrishamian, “Nonlinear terahertz frequency conversion via graphene microribbon array,” Nanotechnology 27, 305202 (2016).
[Crossref]

P. A. D. Gonçalves, E. J. C. Dias, Yu. V. Bludov, and N. M. R. Peres, “Modeling the excitation of graphene plasmons in periodic grids of graphene ribbons: an analytical approach,” Phys. Rev. B 94, 195421 (2016).
[Crossref]

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature,” Phys. Rev. B 91, 235320 (2016).
[Crossref]

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature,” Phys. Rev. B (erratum) 93, 039904 (2016).
[Crossref]

A. V. Gorbach and E. Ivanov, “Perturbation theory for graphene-integrated waveguide: cubic nonlinearity and third-harmonic generation,” Phys. Rev. A 94, 013811 (2016).
[Crossref]

D. B. S. Soh, R. Hamerly, and H. Mabuchi, “Comprehensive analysis of the optical Kerr coefficient of graphene,” Phys. Rev. A 94, 023845 (2016).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Transfer of spin angular momentum of an incident wave into orbital angular momentum of the bound states in the continuum in an array of dielectric spheres,” Phys. Rev. A 94, 033856 (2016).
[Crossref]

2015 (4)

M. Zhang and X. D. Zhang, “Ultrasensitive optical absorption in graphene based on bound states in the continuum,” Sci. Rep. 5, 8266 (2015).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Light trapping above the light cone in a one-dimensional array of dielectric spheres,” Phys. Rev. A 92, 023816 (2015).
[Crossref]

S. M. Rao, A. Lyons, T. Roger, M. Clerici, N. I. Zheludev, and D. Faccio, “Geometries for the coherent control of four-wave mixing in graphene multilayers,” Sci. Rep. 5, 15399 (2015).
[Crossref]

Z.-C. Luo, M. Liu, Z.-N. Guo, X.-F. Jiang, A.-P. Luo, C.-J. Zhao, X.-F. Yu, W.-C. Xu, and H. Zhang, “Microfiber-based few layer black phosphorus saturable absorber for ultra-fast fiber laser,” Opt. Express 23, 20030–20039 (2015).
[Crossref]

2014 (8)

M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Third-harmonic generation in one-dimensional photonic crystal with graphene-based defect,” Phys. Rev. B 89, 165139 (2014).
[Crossref]

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third order optical nonlinearity of graphene,” New J. Phys. 16, 053014 (2014).
[Crossref]

S. A. Mikhailov, “Quantum theory of third-harmonic generation in graphene,” Phys. Rev. B 90, 241301 (2014).
[Crossref]

S. A. Mikhailov, “Quantum theory of third-harmonic generation in graphene,” Phys. Rev. B (erratum) 91, 039904 (2014).
[Crossref]

F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112, 213903 (2014).
[Crossref]

Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Analytical perspective for bound states in the continuum in photonic crystal slabs,” Phys. Rev. Lett. 113, 037401 (2014).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

M. G. Silveirinha, “Trapping light in open plasmonic nanostructures,” Phys. Rev. A 89, 023813 (2014).
[Crossref]

2013 (9)

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

C. W. Hsu, B. Zhen, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2, e84 (2013).
[Crossref]

A. V. Gorbach, “Nonlinear graphene plasmonics: amplitude equation for surface plasmons,” Phys. Rev. A 87, 013830 (2013).
[Crossref]

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

N. Kumar, J. Kumar, C. Gerstenkorn, R. Wang, H.-Y. Chiu, A. L. Smirl, and H. Zhao, “Third harmonic generation in graphene and few-layer graphite films,” Phys. Rev. B 87, 121406 (2013).
[Crossref]

H. Harutyunyan, R. Beams, and L. Novotny, “Controllable optical negative refraction and phase conjugation in graphite thin films,” Nat. Phys. 9, 423–425 (2013).
[Crossref]

M. Tokman, X. Yao, and A. Belyanin, “Generation of entangled photons in graphene in a strong magnetic field,” Phys. Rev. Lett. 110, 077404 (2013).
[Crossref]

A. Auditore, C. De Angelis, A. Locatelli, S. Boscolo, M. Midrio, M. Romagnoli, A. D. Capobianco, and G. Nalesso, “Graphene sustained nonlinear modes in dielectric waveguides,” Opt. Lett. 38, 631–633 (2013).
[Crossref]

Y. F. Song, L. Li, H. Zhang, D. Y. Shen, D. Y. Tang, and K. P. Loh, “Vector multi-soliton operation and interaction in a graphene mode-locked fiber laser,” Opt. Express 21, 10010–10018 (2013).
[Crossref]

2012 (5)

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37, 1856–1858 (2012).
[Crossref]

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

M. I. Molina, A. E. Miroshnichenko, and Y. S. Kivshar, “Surface bound states in the continuum,” Phys. Rev. Lett. 108, 070401 (2012).
[Crossref]

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
[Crossref]

X. Yao and A. Belyanin, “Giant optical nonlinearity of graphene in a strong magnetic field,” Phys. Rev. Lett. 108, 255503 (2012).
[Crossref]

2011 (7)

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11, 2622–2627 (2011).
[Crossref]

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99, 121107 (2011).
[Crossref]

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11, 5159–5164 (2011).
[Crossref]

J.-L. Xu, X.-L. Li, Y.-Z. Wu, X.-P. Hao, J.-L. He, and K.-J. Yang, “Graphene saturable absorber mirror for ultra-fast-pulse solid-state laser,” Opt. Lett. 36, 1948–1950 (2011).
[Crossref]

W. B. Cho, J. W. Kim, H. W. Lee, S. Bae, B. H. Hong, S. Y. Choi, I. H. Baek, K. Kim, D.-I. Yeom, and F. Rotermund, “High-quality, large-area monolayer graphene for efficient bulk laser mode-locking near 1:25  μm,” Opt. Lett. 36, 4089–4091 (2011).
[Crossref]

2010 (5)

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref]

M. Feng, H. Zhan, and Y. Chen, “Nonlinear optical and optical limiting properties of graphene families,” Appl. Phys. Lett. 96, 033107 (2010).
[Crossref]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. Ferrari, “Sub 200  fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[Crossref]

Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

W. Tan, C. Su, R. Knize, G. Xie, L. Li, and D. Tang, “Mode locking of ceramic Nd: yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96, 031106 (2010).
[Crossref]

2009 (2)

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

2008 (5)

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
[Crossref]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref]

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound states in the continuum in photonics,” Phys. Rev. Lett. 100, 183902 (2008).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum in photonic waveguides inspired by defects,” Phys. Rev. B 78, 075105 (2008).
[Crossref]

2007 (3)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and Hall conductivity in graphene,” Phys. Rev. B 75, 165407 (2007).
[Crossref]

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref]

2006 (1)

K. Ziegler, “Robust transport properties in graphene,” Phys. Rev. Lett. 97, 266802 (2006).
[Crossref]

1998 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[Crossref]

1985 (1)

S. Adachi, “GaAs, AlAs, and AlxGa1−xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
[Crossref]

Abrishamian, M. S.

H. Nasari and M. S. Abrishamian, “Electrically tunable, plasmon resonance enhanced terahertz third harmonic generation via graphene,” RSC Adv. 6, 50190–50200 (2016).
[Crossref]

H. Nasari and M. S. Abrishamian, “Nonlinear terahertz frequency conversion via graphene microribbon array,” Nanotechnology 27, 305202 (2016).
[Crossref]

Adachi, S.

S. Adachi, “GaAs, AlAs, and AlxGa1−xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
[Crossref]

Adamashvili, G. T.

G. T. Adamashvili and D. J. Kaup, “Optical surface breather in graphene,” Phys. Rev. A 95, 053801 (2017).
[Crossref]

Alù, A.

F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112, 213903 (2014).
[Crossref]

Aryshev, A.

A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20, 024701 (2017).
[Crossref]

Auditore, A.

Bae, M. K.

Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

Bae, S.

Baek, I. H.

Bai, X.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11, 5159–5164 (2011).
[Crossref]

Bao, Q.

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37, 1856–1858 (2012).
[Crossref]

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Beams, R.

H. Harutyunyan, R. Beams, and L. Novotny, “Controllable optical negative refraction and phase conjugation in graphite thin films,” Nat. Phys. 9, 423–425 (2013).
[Crossref]

Bechtel, H. A.

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Belyanin, A.

M. Tokman, X. Yao, and A. Belyanin, “Generation of entangled photons in graphene in a strong magnetic field,” Phys. Rev. Lett. 110, 077404 (2013).
[Crossref]

X. Yao and A. Belyanin, “Giant optical nonlinearity of graphene in a strong magnetic field,” Phys. Rev. Lett. 108, 255503 (2012).
[Crossref]

Bian, F.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11, 5159–5164 (2011).
[Crossref]

Blau, W. J.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Bludov, Yu. V.

P. A. D. Gonçalves, E. J. C. Dias, Yu. V. Bludov, and N. M. R. Peres, “Modeling the excitation of graphene plasmons in periodic grids of graphene ribbons: an analytical approach,” Phys. Rev. B 94, 195421 (2016).
[Crossref]

Borisov, A. G.

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound states in the continuum in photonics,” Phys. Rev. Lett. 100, 183902 (2008).
[Crossref]

Boscolo, S.

Bulgakov, E. N.

E. N. Bulgakov and A. F. Sadreev, “Transfer of spin angular momentum of an incident wave into orbital angular momentum of the bound states in the continuum in an array of dielectric spheres,” Phys. Rev. A 94, 033856 (2016).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Light trapping above the light cone in a one-dimensional array of dielectric spheres,” Phys. Rev. A 92, 023816 (2015).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum in photonic waveguides inspired by defects,” Phys. Rev. B 78, 075105 (2008).
[Crossref]

Capobianco, A. D.

Carbotte, J. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and Hall conductivity in graphene,” Phys. Rev. B 75, 165407 (2007).
[Crossref]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

Chen, C.

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Chen, W.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11, 2622–2627 (2011).
[Crossref]

Chen, Y.

M. Feng, H. Zhan, and Y. Chen, “Nonlinear optical and optical limiting properties of graphene families,” Appl. Phys. Lett. 96, 033107 (2010).
[Crossref]

Cheng, J. L.

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature,” Phys. Rev. B 91, 235320 (2016).
[Crossref]

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature,” Phys. Rev. B (erratum) 93, 039904 (2016).
[Crossref]

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third order optical nonlinearity of graphene,” New J. Phys. 16, 053014 (2014).
[Crossref]

Chiu, H.-Y.

N. Kumar, J. Kumar, C. Gerstenkorn, R. Wang, H.-Y. Chiu, A. L. Smirl, and H. Zhao, “Third harmonic generation in graphene and few-layer graphite films,” Phys. Rev. B 87, 121406 (2013).
[Crossref]

Cho, W. B.

Choi, S. Y.

Chua, S. L.

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

C. W. Hsu, B. Zhen, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2, e84 (2013).
[Crossref]

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
[Crossref]

Clerici, M.

S. M. Rao, A. Lyons, T. Roger, M. Clerici, N. I. Zheludev, and D. Faccio, “Geometries for the coherent control of four-wave mixing in graphene multilayers,” Sci. Rep. 5, 15399 (2015).
[Crossref]

Coleman, J. N.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Cox, J. D.

A. Marini, J. D. Cox, and F. J. García de Abajo, “Theory of graphene saturable absorption,” Phys. Rev. B 95, 125408 (2017).
[Crossref]

Crommie, M. F.

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

D’Orazio, A.

M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Third-harmonic generation in one-dimensional photonic crystal with graphene-based defect,” Phys. Rev. B 89, 165139 (2014).
[Crossref]

Dadap, J. I.

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

De Angelis, C.

de Ceglia, D.

M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Third-harmonic generation in one-dimensional photonic crystal with graphene-based defect,” Phys. Rev. B 89, 165139 (2014).
[Crossref]

Dias, E. J. C.

P. A. D. Gonçalves, E. J. C. Dias, Yu. V. Bludov, and N. M. R. Peres, “Modeling the excitation of graphene plasmons in periodic grids of graphene ribbons: an analytical approach,” Phys. Rev. B 94, 195421 (2016).
[Crossref]

Dreisow, F.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Faccio, D.

S. M. Rao, A. Lyons, T. Roger, M. Clerici, N. I. Zheludev, and D. Faccio, “Geometries for the coherent control of four-wave mixing in graphene multilayers,” Sci. Rep. 5, 15399 (2015).
[Crossref]

Feng, M.

M. Feng, H. Zhan, and Y. Chen, “Nonlinear optical and optical limiting properties of graphene families,” Appl. Phys. Lett. 96, 033107 (2010).
[Crossref]

Feng, X.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11, 2622–2627 (2011).
[Crossref]

Ferrari, A.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. Ferrari, “Sub 200  fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[Crossref]

Fuse, K.

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99, 121107 (2011).
[Crossref]

García de Abajo, F. J.

A. Marini, J. D. Cox, and F. J. García de Abajo, “Theory of graphene saturable absorption,” Phys. Rev. B 95, 125408 (2017).
[Crossref]

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

Geim, A. K.

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

Geng, B.

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Gerstenkorn, C.

N. Kumar, J. Kumar, C. Gerstenkorn, R. Wang, H.-Y. Chiu, A. L. Smirl, and H. Zhao, “Third harmonic generation in graphene and few-layer graphite films,” Phys. Rev. B 87, 121406 (2013).
[Crossref]

Ghosh, G.

E. D. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).

Girit, C.

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Godbout, N.

Gonçalves, P. A. D.

P. A. D. Gonçalves, E. J. C. Dias, Yu. V. Bludov, and N. M. R. Peres, “Modeling the excitation of graphene plasmons in periodic grids of graphene ribbons: an analytical approach,” Phys. Rev. B 94, 195421 (2016).
[Crossref]

Gorbach, A. V.

A. V. Gorbach and E. Ivanov, “Perturbation theory for graphene-integrated waveguide: cubic nonlinearity and third-harmonic generation,” Phys. Rev. A 94, 013811 (2016).
[Crossref]

A. V. Gorbach, “Nonlinear graphene plasmonics: amplitude equation for surface plasmons,” Phys. Rev. A 87, 013830 (2013).
[Crossref]

Grande, M.

M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Third-harmonic generation in one-dimensional photonic crystal with graphene-based defect,” Phys. Rev. B 89, 165139 (2014).
[Crossref]

Guo, Z.-N.

Gusynin, V. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and Hall conductivity in graphene,” Phys. Rev. B 75, 165407 (2007).
[Crossref]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

Hale, P. J.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref]

Hamerly, R.

D. B. S. Soh, R. Hamerly, and H. Mabuchi, “Comprehensive analysis of the optical Kerr coefficient of graphene,” Phys. Rev. A 94, 023845 (2016).
[Crossref]

Han, W. S.

Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

Hanson, G. W.

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
[Crossref]

Hao, X.-P.

Hao, Z.

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Harutyunyan, H.

H. Harutyunyan, R. Beams, and L. Novotny, “Controllable optical negative refraction and phase conjugation in graphite thin films,” Nat. Phys. 9, 423–425 (2013).
[Crossref]

Hasan, T.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. Ferrari, “Sub 200  fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[Crossref]

He, J.-L.

Heinrich, M.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Heinz, T. F.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref]

Hendry, E.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref]

Hernandez, Y.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Honda, Y.

A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20, 024701 (2017).
[Crossref]

Hone, J.

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

Hong, B. H.

Hong, S.-Y.

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

Horng, J.

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Hsu, C. W.

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

C. W. Hsu, B. Zhen, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2, e84 (2013).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Huang, H.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11, 2622–2627 (2011).
[Crossref]

Ivanov, E.

A. V. Gorbach and E. Ivanov, “Perturbation theory for graphene-integrated waveguide: cubic nonlinearity and third-harmonic generation,” Phys. Rev. A 94, 013811 (2016).
[Crossref]

Jang, S. Y.

Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

Ji, W.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11, 2622–2627 (2011).
[Crossref]

Jiang, X.-F.

Joannopoulos, J. D.

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

C. W. Hsu, B. Zhen, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2, e84 (2013).
[Crossref]

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
[Crossref]

Johnson, S. G.

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

C. W. Hsu, B. Zhen, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2, e84 (2013).
[Crossref]

Karataev, P.

A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20, 024701 (2017).
[Crossref]

Kaup, D. J.

G. T. Adamashvili and D. J. Kaup, “Optical surface breather in graphene,” Phys. Rev. A 95, 053801 (2017).
[Crossref]

Kim, J. W.

Kim, K.

Kivshar, Y. S.

M. I. Molina, A. E. Miroshnichenko, and Y. S. Kivshar, “Surface bound states in the continuum,” Phys. Rev. Lett. 108, 070401 (2012).
[Crossref]

Knize, R.

W. Tan, C. Su, R. Knize, G. Xie, L. Li, and D. Tang, “Mode locking of ceramic Nd: yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96, 031106 (2010).
[Crossref]

Kockaert, P.

Koppens, F. H. L.

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

Kumar, J.

N. Kumar, J. Kumar, C. Gerstenkorn, R. Wang, H.-Y. Chiu, A. L. Smirl, and H. Zhao, “Third harmonic generation in graphene and few-layer graphite films,” Phys. Rev. B 87, 121406 (2013).
[Crossref]

Kumar, N.

N. Kumar, J. Kumar, C. Gerstenkorn, R. Wang, H.-Y. Chiu, A. L. Smirl, and H. Zhao, “Third harmonic generation in graphene and few-layer graphite films,” Phys. Rev. B 87, 121406 (2013).
[Crossref]

Lee, H. W.

Lee, J.

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
[Crossref]

Lekomtsev, K.

A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20, 024701 (2017).
[Crossref]

Li, J.

Li, L.

Y. F. Song, L. Li, H. Zhang, D. Y. Shen, D. Y. Tang, and K. P. Loh, “Vector multi-soliton operation and interaction in a graphene mode-locked fiber laser,” Opt. Express 21, 10010–10018 (2013).
[Crossref]

W. Tan, C. Su, R. Knize, G. Xie, L. Li, and D. Tang, “Mode locking of ceramic Nd: yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96, 031106 (2010).
[Crossref]

Li, X.-L.

Li, Z.

Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Analytical perspective for bound states in the continuum in photonic crystal slabs,” Phys. Rev. Lett. 113, 037401 (2014).
[Crossref]

Liang, Y.

Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Analytical perspective for bound states in the continuum in photonic crystal slabs,” Phys. Rev. Lett. 113, 037401 (2014).
[Crossref]

Liu, M.

Liu, Q. H.

Locatelli, A.

Loh, K. P.

Y. F. Song, L. Li, H. Zhang, D. Y. Shen, D. Y. Tang, and K. P. Loh, “Vector multi-soliton operation and interaction in a graphene mode-locked fiber laser,” Opt. Express 21, 10010–10018 (2013).
[Crossref]

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Lotya, M.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Lu, L.

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

Lu, X.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11, 5159–5164 (2011).
[Crossref]

Lui, C. H.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref]

Luo, A.-P.

Luo, M.

Luo, Z.-C.

Lyons, A.

S. M. Rao, A. Lyons, T. Roger, M. Clerici, N. I. Zheludev, and D. Faccio, “Geometries for the coherent control of four-wave mixing in graphene multilayers,” Sci. Rep. 5, 15399 (2015).
[Crossref]

Mabuchi, H.

D. B. S. Soh, R. Hamerly, and H. Mabuchi, “Comprehensive analysis of the optical Kerr coefficient of graphene,” Phys. Rev. A 94, 023845 (2016).
[Crossref]

Mak, K. F.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref]

Marini, A.

A. Marini, J. D. Cox, and F. J. García de Abajo, “Theory of graphene saturable absorption,” Phys. Rev. B 95, 125408 (2017).
[Crossref]

Marinica, D. C.

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound states in the continuum in photonics,” Phys. Rev. Lett. 100, 183902 (2008).
[Crossref]

Martin, M.

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Martinez, A.

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99, 121107 (2011).
[Crossref]

Massar, S.

Midrio, M.

Mikhailov, S. A.

S. A. Mikhailov, “Quantum theory of third-harmonic generation in graphene,” Phys. Rev. B 90, 241301 (2014).
[Crossref]

S. A. Mikhailov, “Quantum theory of third-harmonic generation in graphene,” Phys. Rev. B (erratum) 91, 039904 (2014).
[Crossref]

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref]

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref]

Miroshnichenko, A. E.

M. I. Molina, A. E. Miroshnichenko, and Y. S. Kivshar, “Surface bound states in the continuum,” Phys. Rev. Lett. 108, 070401 (2012).
[Crossref]

Misewich, J. A.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref]

Modinos, A.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[Crossref]

Moger, J.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref]

Molina, M. I.

M. I. Molina, A. E. Miroshnichenko, and Y. S. Kivshar, “Surface bound states in the continuum,” Phys. Rev. Lett. 108, 070401 (2012).
[Crossref]

Monticone, F.

F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112, 213903 (2014).
[Crossref]

Nalesso, G.

Nasari, H.

H. Nasari and M. S. Abrishamian, “Electrically tunable, plasmon resonance enhanced terahertz third harmonic generation via graphene,” RSC Adv. 6, 50190–50200 (2016).
[Crossref]

H. Nasari and M. S. Abrishamian, “Nonlinear terahertz frequency conversion via graphene microribbon array,” Nanotechnology 27, 305202 (2016).
[Crossref]

Naumenko, G.

A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20, 024701 (2017).
[Crossref]

Ni, Z.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Niu, J.

Noda, S.

Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Analytical perspective for bound states in the continuum in photonic crystal slabs,” Phys. Rev. Lett. 113, 037401 (2014).
[Crossref]

Nolte, S.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Novotny, L.

H. Harutyunyan, R. Beams, and L. Novotny, “Controllable optical negative refraction and phase conjugation in graphite thin films,” Nat. Phys. 9, 423–425 (2013).
[Crossref]

Osgood, R. M.

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

Palik, E. D.

E. D. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).

Peleg, O.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Peng, C.

Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Analytical perspective for bound states in the continuum in photonic crystal slabs,” Phys. Rev. Lett. 113, 037401 (2014).
[Crossref]

Peres, N. M. R.

P. A. D. Gonçalves, E. J. C. Dias, Yu. V. Bludov, and N. M. R. Peres, “Modeling the excitation of graphene plasmons in periodic grids of graphene ribbons: an analytical approach,” Phys. Rev. B 94, 195421 (2016).
[Crossref]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

Petrone, N.

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

Ping, L. K.

Plotnik, Y.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Popa, D.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. Ferrari, “Sub 200  fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[Crossref]

Potylitsyn, A.

A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20, 024701 (2017).
[Crossref]

Qiu, W.

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
[Crossref]

Rao, S. M.

S. M. Rao, A. Lyons, T. Roger, M. Clerici, N. I. Zheludev, and D. Faccio, “Geometries for the coherent control of four-wave mixing in graphene multilayers,” Sci. Rep. 5, 15399 (2015).
[Crossref]

Ren, J.

Roger, T.

S. M. Rao, A. Lyons, T. Roger, M. Clerici, N. I. Zheludev, and D. Faccio, “Geometries for the coherent control of four-wave mixing in graphene multilayers,” Sci. Rep. 5, 15399 (2015).
[Crossref]

Romagnoli, M.

Rotermund, F.

Sadreev, A. F.

E. N. Bulgakov and A. F. Sadreev, “Transfer of spin angular momentum of an incident wave into orbital angular momentum of the bound states in the continuum in an array of dielectric spheres,” Phys. Rev. A 94, 033856 (2016).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Light trapping above the light cone in a one-dimensional array of dielectric spheres,” Phys. Rev. A 92, 023816 (2015).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum in photonic waveguides inspired by defects,” Phys. Rev. B 78, 075105 (2008).
[Crossref]

Savchenko, A. K.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref]

Scalora, M.

M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Third-harmonic generation in one-dimensional photonic crystal with graphene-based defect,” Phys. Rev. B 89, 165139 (2014).
[Crossref]

Segev, M.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Sfeir, M. Y.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref]

Shabanov, S. V.

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound states in the continuum in photonics,” Phys. Rev. Lett. 100, 183902 (2008).
[Crossref]

Shapira, O.

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
[Crossref]

Sharapov, S. G.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and Hall conductivity in graphene,” Phys. Rev. B 75, 165407 (2007).
[Crossref]

Shen, D. Y.

Shen, Y. R.

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Shen, Z. X.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Shevelev, M.

A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20, 024701 (2017).
[Crossref]

Silveirinha, M. G.

M. G. Silveirinha, “Trapping light in open plasmonic nanostructures,” Phys. Rev. A 89, 023813 (2014).
[Crossref]

Sipe, J. E.

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature,” Phys. Rev. B 91, 235320 (2016).
[Crossref]

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature,” Phys. Rev. B (erratum) 93, 039904 (2016).
[Crossref]

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third order optical nonlinearity of graphene,” New J. Phys. 16, 053014 (2014).
[Crossref]

Smirl, A. L.

N. Kumar, J. Kumar, C. Gerstenkorn, R. Wang, H.-Y. Chiu, A. L. Smirl, and H. Zhao, “Third harmonic generation in graphene and few-layer graphite films,” Phys. Rev. B 87, 121406 (2013).
[Crossref]

Soh, D. B. S.

D. B. S. Soh, R. Hamerly, and H. Mabuchi, “Comprehensive analysis of the optical Kerr coefficient of graphene,” Phys. Rev. A 94, 023845 (2016).
[Crossref]

Soljacic, M.

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

C. W. Hsu, B. Zhen, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2, e84 (2013).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
[Crossref]

Song, Y. F.

Song, Y. W.

Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

Stauber, T.

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

Stefanou, N.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[Crossref]

Stone, A. D.

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

Su, C.

W. Tan, C. Su, R. Knize, G. Xie, L. Li, and D. Tang, “Mode locking of ceramic Nd: yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96, 031106 (2010).
[Crossref]

Sukhikh, L.

A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20, 024701 (2017).
[Crossref]

Sun, Z.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. Ferrari, “Sub 200  fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[Crossref]

Szameit, A.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

Tan, W.

W. Tan, C. Su, R. Knize, G. Xie, L. Li, and D. Tang, “Mode locking of ceramic Nd: yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96, 031106 (2010).
[Crossref]

Tang, D.

W. Tan, C. Su, R. Knize, G. Xie, L. Li, and D. Tang, “Mode locking of ceramic Nd: yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96, 031106 (2010).
[Crossref]

Tang, D. Y.

Y. F. Song, L. Li, H. Zhang, D. Y. Shen, D. Y. Tang, and K. P. Loh, “Vector multi-soliton operation and interaction in a graphene mode-locked fiber laser,” Opt. Express 21, 10010–10018 (2013).
[Crossref]

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Terunuma, N.

A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20, 024701 (2017).
[Crossref]

Thongrattanasiri, S.

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

Tokman, M.

M. Tokman, X. Yao, and A. Belyanin, “Generation of entangled photons in graphene in a strong magnetic field,” Phys. Rev. Lett. 110, 077404 (2013).
[Crossref]

Torrisi, F.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. Ferrari, “Sub 200  fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[Crossref]

Urakawa, J.

A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20, 024701 (2017).
[Crossref]

Vermeulen, N.

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature,” Phys. Rev. B (erratum) 93, 039904 (2016).
[Crossref]

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature,” Phys. Rev. B 91, 235320 (2016).
[Crossref]

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third order optical nonlinearity of graphene,” New J. Phys. 16, 053014 (2014).
[Crossref]

Vincenti, M. A.

M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Third-harmonic generation in one-dimensional photonic crystal with graphene-based defect,” Phys. Rev. B 89, 165139 (2014).
[Crossref]

Virally, S.

Wang, E.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11, 5159–5164 (2011).
[Crossref]

Wang, F.

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. Ferrari, “Sub 200  fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[Crossref]

Wang, J.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Wang, Q.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11, 2622–2627 (2011).
[Crossref]

Wang, R.

N. Kumar, J. Kumar, C. Gerstenkorn, R. Wang, H.-Y. Chiu, A. L. Smirl, and H. Zhao, “Third harmonic generation in graphene and few-layer graphite films,” Phys. Rev. B 87, 121406 (2013).
[Crossref]

Wang, W.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11, 5159–5164 (2011).
[Crossref]

Wang, Y.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Wee, A. T.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11, 2622–2627 (2011).
[Crossref]

Wu, R.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11, 5159–5164 (2011).
[Crossref]

Wu, Y.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref]

Wu, Y.-Z.

Xie, G.

W. Tan, C. Su, R. Knize, G. Xie, L. Li, and D. Tang, “Mode locking of ceramic Nd: yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96, 031106 (2010).
[Crossref]

Xu, J.-L.

Xu, W.-C.

Yamashita, S.

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99, 121107 (2011).
[Crossref]

Yan, S.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11, 5159–5164 (2011).
[Crossref]

Yan, Y.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Yang, H.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11, 2622–2627 (2011).
[Crossref]

Yang, K.-J.

Yang, Y.

Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Analytical perspective for bound states in the continuum in photonic crystal slabs,” Phys. Rev. Lett. 113, 037401 (2014).
[Crossref]

Yannopapas, V.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[Crossref]

Yao, X.

M. Tokman, X. Yao, and A. Belyanin, “Generation of entangled photons in graphene in a strong magnetic field,” Phys. Rev. Lett. 110, 077404 (2013).
[Crossref]

X. Yao and A. Belyanin, “Giant optical nonlinearity of graphene in a strong magnetic field,” Phys. Rev. Lett. 108, 255503 (2012).
[Crossref]

Yeh, P.-C.

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

Yeom, D.-I.

Yu, X.-F.

Zettl, A.

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Zhan, H.

M. Feng, H. Zhan, and Y. Chen, “Nonlinear optical and optical limiting properties of graphene families,” Appl. Phys. Lett. 96, 033107 (2010).
[Crossref]

Zhang, H.

Zhang, M.

M. Zhang and X. D. Zhang, “Ultrasensitive optical absorption in graphene based on bound states in the continuum,” Sci. Rep. 5, 8266 (2015).
[Crossref]

Zhang, X. D.

J. Li, J. Ren, and X. D. Zhang, “Three-dimensional vector wave bound states in a continuum,” J. Opt. Soc. Am. B 34, 559–565 (2017).
[Crossref]

M. Zhang and X. D. Zhang, “Ultrasensitive optical absorption in graphene based on bound states in the continuum,” Sci. Rep. 5, 8266 (2015).
[Crossref]

Zhang, Y.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11, 5159–5164 (2011).
[Crossref]

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Zhao, C.-J.

Zhao, H.

N. Kumar, J. Kumar, C. Gerstenkorn, R. Wang, H.-Y. Chiu, A. L. Smirl, and H. Zhao, “Third harmonic generation in graphene and few-layer graphite films,” Phys. Rev. B 87, 121406 (2013).
[Crossref]

Zhao, J.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11, 5159–5164 (2011).
[Crossref]

Zheludev, N. I.

S. M. Rao, A. Lyons, T. Roger, M. Clerici, N. I. Zheludev, and D. Faccio, “Geometries for the coherent control of four-wave mixing in graphene multilayers,” Sci. Rep. 5, 15399 (2015).
[Crossref]

Zhen, B.

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

C. W. Hsu, B. Zhen, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2, e84 (2013).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
[Crossref]

Ziegler, K.

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref]

K. Ziegler, “Robust transport properties in graphene,” Phys. Rev. Lett. 97, 266802 (2006).
[Crossref]

Adv. Funct. Mater. (1)

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Adv. Mater. (1)

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Appl. Phys. Lett. (5)

M. Feng, H. Zhan, and Y. Chen, “Nonlinear optical and optical limiting properties of graphene families,” Appl. Phys. Lett. 96, 033107 (2010).
[Crossref]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. Ferrari, “Sub 200  fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97, 203106 (2010).
[Crossref]

Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

W. Tan, C. Su, R. Knize, G. Xie, L. Li, and D. Tang, “Mode locking of ceramic Nd: yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96, 031106 (2010).
[Crossref]

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99, 121107 (2011).
[Crossref]

Comput. Phys. Commun. (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[Crossref]

J. Appl. Phys. (2)

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
[Crossref]

S. Adachi, “GaAs, AlAs, and AlxGa1−xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
[Crossref]

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

J. Phys. Condens. Matter (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

Light Sci. Appl. (1)

C. W. Hsu, B. Zhen, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2, e84 (2013).
[Crossref]

Nano Lett. (2)

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11, 5159–5164 (2011).
[Crossref]

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11, 2622–2627 (2011).
[Crossref]

Nanotechnology (1)

H. Nasari and M. S. Abrishamian, “Nonlinear terahertz frequency conversion via graphene microribbon array,” Nanotechnology 27, 305202 (2016).
[Crossref]

Nat. Phys. (1)

H. Harutyunyan, R. Beams, and L. Novotny, “Controllable optical negative refraction and phase conjugation in graphite thin films,” Nat. Phys. 9, 423–425 (2013).
[Crossref]

Nature (1)

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

New J. Phys. (1)

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third order optical nonlinearity of graphene,” New J. Phys. 16, 053014 (2014).
[Crossref]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (7)

M. G. Silveirinha, “Trapping light in open plasmonic nanostructures,” Phys. Rev. A 89, 023813 (2014).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Light trapping above the light cone in a one-dimensional array of dielectric spheres,” Phys. Rev. A 92, 023816 (2015).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Transfer of spin angular momentum of an incident wave into orbital angular momentum of the bound states in the continuum in an array of dielectric spheres,” Phys. Rev. A 94, 033856 (2016).
[Crossref]

A. V. Gorbach and E. Ivanov, “Perturbation theory for graphene-integrated waveguide: cubic nonlinearity and third-harmonic generation,” Phys. Rev. A 94, 013811 (2016).
[Crossref]

D. B. S. Soh, R. Hamerly, and H. Mabuchi, “Comprehensive analysis of the optical Kerr coefficient of graphene,” Phys. Rev. A 94, 023845 (2016).
[Crossref]

A. V. Gorbach, “Nonlinear graphene plasmonics: amplitude equation for surface plasmons,” Phys. Rev. A 87, 013830 (2013).
[Crossref]

G. T. Adamashvili and D. J. Kaup, “Optical surface breather in graphene,” Phys. Rev. A 95, 053801 (2017).
[Crossref]

Phys. Rev. Accel. Beams (1)

A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20, 024701 (2017).
[Crossref]

Phys. Rev. B (10)

P. A. D. Gonçalves, E. J. C. Dias, Yu. V. Bludov, and N. M. R. Peres, “Modeling the excitation of graphene plasmons in periodic grids of graphene ribbons: an analytical approach,” Phys. Rev. B 94, 195421 (2016).
[Crossref]

J. Horng, C. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

A. Marini, J. D. Cox, and F. J. García de Abajo, “Theory of graphene saturable absorption,” Phys. Rev. B 95, 125408 (2017).
[Crossref]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and Hall conductivity in graphene,” Phys. Rev. B 75, 165407 (2007).
[Crossref]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum in photonic waveguides inspired by defects,” Phys. Rev. B 78, 075105 (2008).
[Crossref]

M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Third-harmonic generation in one-dimensional photonic crystal with graphene-based defect,” Phys. Rev. B 89, 165139 (2014).
[Crossref]

N. Kumar, J. Kumar, C. Gerstenkorn, R. Wang, H.-Y. Chiu, A. L. Smirl, and H. Zhao, “Third harmonic generation in graphene and few-layer graphite films,” Phys. Rev. B 87, 121406 (2013).
[Crossref]

S. A. Mikhailov, “Quantum theory of third-harmonic generation in graphene,” Phys. Rev. B 90, 241301 (2014).
[Crossref]

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature,” Phys. Rev. B 91, 235320 (2016).
[Crossref]

Phys. Rev. B (erratum) (2)

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature,” Phys. Rev. B (erratum) 93, 039904 (2016).
[Crossref]

S. A. Mikhailov, “Quantum theory of third-harmonic generation in graphene,” Phys. Rev. B (erratum) 91, 039904 (2014).
[Crossref]

Phys. Rev. Lett. (14)

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

M. I. Molina, A. E. Miroshnichenko, and Y. S. Kivshar, “Surface bound states in the continuum,” Phys. Rev. Lett. 108, 070401 (2012).
[Crossref]

J. Lee, B. Zhen, S. L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
[Crossref]

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound states in the continuum in photonics,” Phys. Rev. Lett. 100, 183902 (2008).
[Crossref]

X. Yao and A. Belyanin, “Giant optical nonlinearity of graphene in a strong magnetic field,” Phys. Rev. Lett. 108, 255503 (2012).
[Crossref]

M. Tokman, X. Yao, and A. Belyanin, “Generation of entangled photons in graphene in a strong magnetic field,” Phys. Rev. Lett. 110, 077404 (2013).
[Crossref]

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref]

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

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref]

F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112, 213903 (2014).
[Crossref]

Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Analytical perspective for bound states in the continuum in photonic crystal slabs,” Phys. Rev. Lett. 113, 037401 (2014).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

K. Ziegler, “Robust transport properties in graphene,” Phys. Rev. Lett. 97, 266802 (2006).
[Crossref]

Phys. Rev. X (1)

S.-Y. Hong, J. I. Dadap, N. Petrone, P.-C. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).
[Crossref]

RSC Adv. (1)

H. Nasari and M. S. Abrishamian, “Electrically tunable, plasmon resonance enhanced terahertz third harmonic generation via graphene,” RSC Adv. 6, 50190–50200 (2016).
[Crossref]

Sci. Rep. (2)

M. Zhang and X. D. Zhang, “Ultrasensitive optical absorption in graphene based on bound states in the continuum,” Sci. Rep. 5, 8266 (2015).
[Crossref]

S. M. Rao, A. Lyons, T. Roger, M. Clerici, N. I. Zheludev, and D. Faccio, “Geometries for the coherent control of four-wave mixing in graphene multilayers,” Sci. Rep. 5, 15399 (2015).
[Crossref]

Other (1)

E. D. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).

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 (8)

Fig. 1.
Fig. 1. (a) Diagram of the sphere-graphene-slab structure and the TH generation process. The spheres are arranged in a square lattice with lattice constant a ; the thickness of the dielectric slab is d , and the monolayer graphene is put at the interface between the monolayer dielectric spheres and the dielectric slab. When a plane wave with angular frequency ω is incident on the structure at the incident angle θ i , the transmitted and reflected TH fields are generated due to the third-order nonlinear effect of graphene. Inset shows graphene layer with up medium denoted by 1 and down medium marked by 2. (b) Schematic of the degenerate FWM process in the three-layer structure. The pump beam at frequency ω 1 and the probe beam at frequency ω 2 are incident on the structure with arbitrary incident angles θ 1 and θ 2 . Because of the third nonlinear effect of the graphene, the transmitted and reflected beams at FWM frequency ω 3 = 2 ω 1 ω 2 are generated with angle θ 3 . The angle θ 3 is determined by the in-plane phase-matching condition.
Fig. 2.
Fig. 2. (a) The absorption as a function of the wavelength λ when the Fermi energy is taken as E f = 0.23    eV (black line) and E f = 0.7    eV (red line). Inset shows the conductivity of the graphene. (b) The electric field distribution at the graphene location below the bottom of the spheres when the Fermi energy is taken as E f = 0.23    eV (black line) and E f = 0.7    eV (red line).
Fig. 3.
Fig. 3. Transmitted (F1), reflected (F2), and total (F3) TH conversions in the three-layer structure and freestanding graphene as a function of the FF wavelength λ when the Fermi energy is taken as (a)  E f = 0.23    eV and (b)  E f = 0.7    eV . The TH enhancement G3 of TH signal in the three-layer structure compared with that in the freestanding graphene as a function of the FF wavelength λ for (c) different radius r s of the spheres or (d) various thickness d of the slab, the Fermi energy in (c) and (d) is taken as E f = 0.23    eV .
Fig. 4.
Fig. 4. TH enhancement of the (a) and (b) transmitted and (c) and (d) reflected TH beams as a function of the fundamental wavelength and the incident angle for S-(P) polarized pump beam. (e) and (f) show the absorption spectra of the three-layer structure. The bound states are denoted by S1, S2, and S3 (P1 and P2) for S-(P) polarized wave.
Fig. 5.
Fig. 5. (a) Schematic of the FWM progress in the three-layer structure when all the waves are at the same wavelength; the incident angles of the pump and probe beams are 0° and θ , respectively; the angle of the generated FWM wave is equal to θ because of phase-match condition. (b) and (c) correspond to T and R of the transmitted and reflected FWM beams as a function of the FF wavelength and incident angle of the probe beam. The T and R in the three-layer structure and freestanding graphene as a function of the fundamental wavelength at θ = 16.09 ° corresponding to the maxima when the Fermi energy is taken as (d)  E f = 0.23    eV and (e)  E f = 0.7    eV . The blue and pink lines show the absorption spectra under only one incident beam at the incident angles θ = 0 ° and θ = 16.09 ° , respectively.
Fig. 6.
Fig. 6. Transmission ( T ) and reflection ( R ) as a function of the phase difference between the two parts of the pump beam with the same intensity.
Fig. 7.
Fig. 7. (a) Schematic of the FWM progress in the three-layer structure when the wavelengths of the pump and probe beams ( λ 1 and λ 2 ) are not equal, the incident angles of the pump and probe beams are θ 1 = 0 ° and θ 2 , respectively. (b) and (c) correspond to the transmitted and reflected FWM beams as a function of the wavelength λ 1 and incident angle θ 2 of the probe beam. The wavelength of the probe beam is taken as λ 2 = 1760.29    nm .
Fig. 8.
Fig. 8. T and R in the three-layer structure and freestanding graphene as a function of the wavelength λ 1 with θ 2 = 60 ° , which correspond to a peak when the Fermi energy is taken as (a)  E f = 0.23    eV and (c)  E f = 0.7    eV , respectively. (b) Blue and pink lines show the absorption as a function of the wavelengths of the pump or FWM beams ( λ 1 or λ 3 ) under one incident beam at the incident angles 0° and θ 3 , respectively; the two relations are put together via phase match condition.

Equations (47)

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

σ = σ intra + σ inter ,
σ intra = j e 2 k B T π 2 ( ω + j γ ) [ E F k B T + 2 In ( e E F / k B T + 1 ) ] ,
σ inter = j e 2 ( ω + j γ ) π 2 0 d ϵ f d ( ϵ ) f d ( ϵ ) ( ω + j γ ) 2 4 ( ϵ / ) 2 .
n × [ E 2 ( r , 3 ω ) E 1 ( r , 3 ω ) ] | z = 0 = 0 ,
n × [ H 2 ( r , 3 ω ) H 1 ( r , 3 ω ) ] | z = 0 = σ E 1 ( r , 3 ω ) | z = 0 + J ( 3 ) ( 3 ω ) ,
E 1 ( r , 3 ω ) = E 1 i ( 3 ω ) e i ( q x x + q 1 z z 3 ω t ) + E 1 r ( 3 ω ) e i ( q x x q 1 z z 3 ω t ) ,
E 2 ( r , 3 ω ) = E 2 t ( 3 ω ) e i ( q x x + q 2 z z 3 ω t ) .
E 2 x t ( 3 ω ) = T x ( 1 , 2 ) E 1 x i ( 3 ω ) + C T x ( 1 , 2 ) ,
E 2 y t ( 3 ω ) = T y ( 1 , 2 ) E 1 y i ( 3 ω ) + C T y ( 1 , 2 ) ,
E 1 x r ( 3 ω ) = R x ( 1 , 2 ) E 1 x i ( 3 ω ) + C R x ( 1 , 2 ) ,
E 1 y r ( 3 ω ) = R y ( 1 , 2 ) E 1 y i ( 3 ω ) + C R y ( 1 , 2 ) ,
T x ( 1 , 2 ) = 2 q 2 z / ϵ 2 q 1 z / ϵ 1 + q 2 z / ϵ 2 + q 1 z q 2 z σ / ( ω ϵ 0 ϵ 1 ϵ 2 ) ,
T y ( 1 , 2 ) = 2 q 1 z q 1 z + q 2 z + ω μ 0 σ ,
R x ( 1 , 2 ) = q 2 z / ϵ 2 q 1 z / ϵ 1 q 1 z q 2 z σ / ( ω ϵ 0 ϵ 1 ϵ 2 ) q 1 z / ϵ 1 + q 2 z / ϵ 2 + q 1 z q 2 z σ / ( ω ϵ 0 ϵ 1 ϵ 2 ) ,
R y ( 1 , 2 ) = q 1 z q 2 z ω μ 0 σ q 1 z + q 2 z + ω μ 0 σ .
C T x ( 1 , 2 ) = J x ( 3 ) ( 3 ω ) q 1 z q 2 z σ / ( ω ϵ 0 ϵ 1 ϵ 2 ) q 1 z / ϵ 1 + q 2 z / ϵ 2 + q 1 z q 2 z σ / ( ω ϵ 0 ϵ 1 ϵ 2 ) ,
C T y ( 1 , 2 ) = J y ( 3 ) ( 3 ω ) ω μ 0 q 1 z + q 2 z + ω μ 0 σ ,
C R x ( 1 , 2 ) = J x ( 3 ) ( 3 ω ) q 1 z q 2 z σ / ( ω ϵ 0 ϵ 1 ϵ 2 ) q 1 z / ϵ 1 + q 2 z / ϵ 2 + q 1 z q 2 z σ / ( ω ϵ 0 ϵ 1 ϵ 2 ) = C T x ( 1 , 2 ) ,
C R y ( 1 , 2 ) = J y ( 3 ) ( 3 ω ) ω μ 0 q 1 z + q 2 z + ω μ 0 σ = C T y ( 1 , 2 ) ,
E in ( tr , rf ) ± ( r , 3 ω ) = l = 1 2 m n E in ( tr , rf ) , l , m n ± ( 3 ω ) e i ( k m n x x + k m n y y ± k m n z z ) u ^ l ,
E tr , l s ( 3 ω ) = l = 1 2 N l l s s E in , l s ( 3 ω ) + D l s s ,
E r f , l s ( 3 ω ) = l = 1 2 N l l s s E in , l s ( 3 ω ) + D l s s ,
N l l s s = ( N x s s cos 2 ϕ + N y s s sin 2 ϕ ( N x s s N y s s ) sin ϕ cos ϕ ( N x s s N y s s ) sin ϕ cos ϕ N x s s sin 2 ϕ + N y s s cos 2 ϕ ) ,
D l s s = ( cos ϕ D x s s sin ϕ D y s s sin ϕ D x s s + cos ϕ D y s s ) ,
( E 2 + ( 3 ω ) E 1 ( 3 ω ) ) = ( Q 2 I Q 2 II Q 2 III Q 2 IV ) ( E 1 + ( 3 ω ) E 2 ( 3 ω ) ) + ( C 2 I C 2 II ) ,
Q 1,2 I = Q 2 I [ 1 Q 1 II Q 2 III ] 1 Q 1 I ,
Q 1 , 2 II = Q 2 II + Q 2 I Q 1 II [ 1 Q 2 III Q 1 II ] 1 Q 2 IV ,
Q 1 , 2 III = Q 1 III + Q 1 IV Q 2 III [ 1 Q 1 II Q 2 III ] 1 Q 1 I ,
Q 1,2 IV = Q 1 IV [ 1 Q 2 III Q 1 II ] 1 Q 2 IV ,
C 1 , 2 I = Q 2 I [ 1 Q 1 II Q 2 III ] 1 [ Q 1 II C 2 II + C 1 I ] + C 2 I ,
C 1,2 II = Q n IV [ 1 Q 2 III Q 1 II ] 1 [ Q 2 III C 1 I + C 2 II ] + C 1 II ,
( E 3 + ( 3 ω ) E 0 ( 3 ω ) ) = ( Q 1,2 , 3 I Q 1,2 , 3 II Q 1,2 , 3 III Q 1,2 , 3 IV ) ( E 0 + ( 3 ω ) E 3 ( 3 ω ) ) + ( C 1,2 , 3 I C 1,2 , 3 II ) = ( Q 1,2 , 3 I Q 1,2 , 3 II Q 1,2 , 3 III Q 1,2 , 3 IV ) ( 0 0 ) + ( C 1,2 , 3 I C 1,2 , 3 II ) .
I t ( 3 ω ) = 1 2 ϵ 0 l , m n [ E 3 , l , m n + ( 3 ω ) ] [ E 3 , l , m n + ( 3 ω ) ] * ,
I r ( 3 ω ) = 1 2 ϵ 0 l , m n [ E 0 , l , m n ( 3 ω ) ] [ E 0 , l , m n ( 3 ω ) ] * .
I i ( ω ) = 1 2 ϵ 0 l , m n [ E i , l , m n + ( ω ) ] [ E i , l , m n + ( ω ) ] * .
F 1 = I t ( 3 ω ) I i ( ω ) , F 2 = I r ( 3 ω ) I i ( ω ) , F 3 = I t ( 3 ω ) + I r ( 3 ω ) I i ( ω ) .
G 1 = I t ( 3 ω ) I 0 t ( 3 ω ) , G 2 = I r ( 3 ω ) I 0 r ( 3 ω ) , G 3 = I t ( 3 ω ) + I r ( 3 ω ) I 0 t ( 3 ω ) + I 0 r ( 3 ω ) ,
E 1 ( 2,3 ) ( r , ω 1 ( 2,3 ) ) = E 1 ( 2,3 ) + ( r , ω 1 ( 2,3 ) ) + E 1 ( 2,3 ) ( r , ω 1 ( 2,3 ) ) = m n E 1 ( 2,3 ) m n ( z ) e i ( k 1 ( 2,3 ) m n x x + k 1 ( 2,3 ) m n y y ω 1 ( 2,3 ) t ) = m n [ E 1 ( 2,3 ) m n + ( z ) + E 1 ( 2,3 ) m n ( z ) ] e i ( k 1 ( 2,3 ) m n x x + k 1 ( 2,3 ) m n y y ω 1 ( 2,3 ) t ) ,
P x ( ω 3 ) = ϵ 0 χ ( 3 ) E 1 x ( r , ω 1 ) E 2 x * ( r , ω 2 ) E 1 x ( r , ω 1 ) | z = 0 = ϵ 0 χ ( 3 ) otmnrs E 1 o t x ( z ) E 2 m n x * ( z ) E 1 r s x ( z ) | z = 0 × e i ( k 3 x x + G o m + r x x + k 3 y y + G t n + s y y ω 3 t ) .
P 1 x ( ω 0 ) = ϵ 0 χ ( 3 ) ( 3 E 1 x E 1 x * E 1 x + 6 E 2 x E 2 x * E 1 x + 6 E 3 x E 3 x * E 1 x + 6 E 2 x E 1 x * E 3 x ) = ϵ 0 χ ( 3 ) otmnrs P 1 x , otmnrs e i ( G o m + n x x + G t n + s y y ω 0 t ) ,
P 2 x ( ω 0 ) = ϵ 0 χ ( 3 ) ( 3 E 2 x E 2 x * E 2 x + 6 E 3 x E 3 x * E 2 x + 6 E 1 x E 1 x * E 2 x + 3 E 1 x E 3 x * E 1 x ) = ϵ 0 χ ( 3 ) otmnrs P 2 x , otmnrs e i [ ( k 2 x + G o m + r t n + s , x ) x + ( k 2 y + G o m + r t n + s , y ) y ω 0 t ] ,
P 3 x ( ω 0 ) = ϵ 0 χ ( 3 ) ( 3 E 3 x E 3 x * E 3 x + 6 E 1 x E 1 x * E 3 x + 6 E 2 x E 2 x * E 3 x + 3 E 1 x E 2 x * E 1 x ) = ϵ 0 χ ( 3 ) otmnrs P 3 x , otmnrs e i [ ( k 2 x + G o m + r t n + s x ) x + ( k 2 y + G o m + r t n + s y ) y ω 0 t ] ,
P 1 x , otmnrs = 3 E 1 o t x E 1 m n x * E 1 r s x + 6 E 2 o t x E 2 m n x * E 1 r s x + 6 E 3 o t x E 3 m n x * E 1 r s x + 6 E 2 o t x E 1 m n x * E 3 r s x ,
P 2 x , otmnrs = 6 E 1 o t x E 1 m n x * E 2 r s x + 3 E 2 o t x E 2 m n x * E 2 r s x + 6 E 3 o t x E 3 m n x * E 2 r s x + 3 E 1 o t x E 3 m n x * E 1 r s x ,
P 3 x , otmnrs = 3 E 1 o t x E 2 m n x * E 1 r s x + 6 E 1 o t x E 1 m n x * E 3 r s x + 6 E 2 o t x E 2 m n x * E 3 r s x + 3 E 3 o t x E 3 m n x * E 3 r s x .
T = I 3 t / I 2 , T = I 3 r / I 2 .
{ ω 3 = 2 ω 1 ω 2 2 π c λ 3 = 2 2 π c λ 1 2 π c λ 2 k 3 x = 2 k 1 x k 2 x 2 π λ 3 sin θ 3 = 2 2 π λ 1 · 0 2 π λ 2 sin θ 2 .

Metrics