Abstract

We have established the theoretical relation of nonlinear optical response with respect to the dielectric/nonlinear graphene/dielectric heterostructures and further demonstrated the tunable optical bistability at terahertz frequencies. It is shown that the hysteretic behavior is strongly dependent on the Fermi energy of graphene, and the threshold electric fields could be correspondingly adjusted with the continuous tuning of Fermi Energy level. It is clear that the bistable thresholds can be lowered dramatically by decreasing the Fermi energy of graphene, at the same time the optical hysteresis width is narrowed. Moreover, we have confirmed that the optical bistability can be tuned by adjusting the incident illumination angle, or by varying the thickness and permittivity of the dielectric slabs. Our contribution might provide a new avenue of fabricating graphene based optical switching device that could even operate at terahertz regime.

© 2015 Optical Society of America

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    [Crossref]
  3. D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
    [Crossref] [PubMed]
  4. G. Assanto, Z. Wang, D. J. Hagan, and E. W. VanStryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
    [Crossref]
  5. H. Nihei and A. Okamoto, “Photonic crystal systems for high-speed optical memory device on an atomic scale,” Proc. SPIE 4416, 470–473 (2001).
    [Crossref]
  6. L. S. Yan, A. E. Willner, X. X. Wu, A. L. Yi, B. Antonella, Z. Y. Chen, and H. Y. Jiang, “All-optical signal processing for ultrahigh speed optical systems and networks,” J. Lightwave Technol. 30, 3760–3770 (2012).
    [Crossref]
  7. F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
    [Crossref]
  8. C. Min, P. Wang, C. Chen, Y. Deng, Y. Lu, H. Ming, T. Ning, Y. Zhou, and G. Yang, “All optical switching in subwavelength metallic grating structure containing nonlinear optical materials,” Opt. Lett. 33, 869–871 (2008).
    [Crossref] [PubMed]
  9. Y. Shen and G. P. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express 16, 8421–8426 (2008).
    [Crossref] [PubMed]
  10. N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007).
    [Crossref] [PubMed]
  11. P. Y. Chen, M. Farhat, and A. Alu, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106, 105503 (2011).
    [Crossref] [PubMed]
  12. P. Y. Chen and A. Alu, “Optical nanoantenna arrays loaded with nonlinear materials,” Phys. Rev. B 82, 235405 (2010).
    [Crossref]
  13. F. Zhou, Y. Liu, Z. Y. Li, and Y. Xia, “Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials,” Opt. Express 18, 13337–13344 (2010).
    [Crossref] [PubMed]
  14. 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] [PubMed]
  15. 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] [PubMed]
  16. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
    [Crossref] [PubMed]
  17. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
    [Crossref]
  18. 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] [PubMed]
  19. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
    [Crossref]
  20. E. Simsek, “Improving tuning range and sensitivity of localized SPR sensors with graphene,” Photon. Technol. Lett. 25, 867–870 (2013).
    [Crossref]
  21. B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 103, 011102 (2013).
  22. L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
    [Crossref] [PubMed]
  23. A. Andryieuski and A. V. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21, 9144–9155 (2013).
    [Crossref] [PubMed]
  24. L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
    [Crossref]
  25. Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
    [Crossref]
  26. Y. C. Fan, F. L. Zhang, Q. Zhao, Z. Y. Wei, and H. Q. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
    [Crossref] [PubMed]
  27. C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Phys. Rev. B 85, 245407 (2012).
    [Crossref]
  28. 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] [PubMed]
  29. 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]
  30. Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
    [Crossref]
  31. G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
    [Crossref]
  32. T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
    [Crossref]
  33. Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
    [Crossref]
  34. Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
    [Crossref]
  35. N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
    [Crossref]
  36. S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J Phys: Condens. Matter. 20, 384204 (2008).

2014 (3)

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
[Crossref]

Y. C. Fan, F. L. Zhang, Q. Zhao, Z. Y. Wei, and H. Q. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

2013 (5)

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

L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
[Crossref]

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
[Crossref]

E. Simsek, “Improving tuning range and sensitivity of localized SPR sensors with graphene,” Photon. Technol. Lett. 25, 867–870 (2013).
[Crossref]

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 103, 011102 (2013).

2012 (4)

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Phys. Rev. B 85, 245407 (2012).
[Crossref]

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] [PubMed]

L. S. Yan, A. E. Willner, X. X. Wu, A. L. Yi, B. Antonella, Z. Y. Chen, and H. Y. Jiang, “All-optical signal processing for ultrahigh speed optical systems and networks,” J. Lightwave Technol. 30, 3760–3770 (2012).
[Crossref]

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[Crossref]

2011 (5)

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (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] [PubMed]

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

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] [PubMed]

P. Y. Chen, M. Farhat, and A. Alu, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106, 105503 (2011).
[Crossref] [PubMed]

2010 (4)

P. Y. Chen and A. Alu, “Optical nanoantenna arrays loaded with nonlinear materials,” Phys. Rev. B 82, 235405 (2010).
[Crossref]

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

F. Zhou, Y. Liu, Z. Y. Li, and Y. Xia, “Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials,” Opt. Express 18, 13337–13344 (2010).
[Crossref] [PubMed]

2009 (3)

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

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

2008 (4)

C. Min, P. Wang, C. Chen, Y. Deng, Y. Lu, H. Ming, T. Ning, Y. Zhou, and G. Yang, “All optical switching in subwavelength metallic grating structure containing nonlinear optical materials,” Opt. Lett. 33, 869–871 (2008).
[Crossref] [PubMed]

Y. Shen and G. P. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express 16, 8421–8426 (2008).
[Crossref] [PubMed]

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J Phys: Condens. Matter. 20, 384204 (2008).

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
[Crossref]

2007 (1)

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007).
[Crossref] [PubMed]

2004 (1)

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

2003 (1)

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[Crossref] [PubMed]

2001 (1)

H. Nihei and A. Okamoto, “Photonic crystal systems for high-speed optical memory device on an atomic scale,” Proc. SPIE 4416, 470–473 (2001).
[Crossref]

1995 (1)

G. Assanto, Z. Wang, D. J. Hagan, and E. W. VanStryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[Crossref]

1982 (1)

E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982).
[Crossref]

Abraham, E.

E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982).
[Crossref]

Akimov, A. V.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[Crossref] [PubMed]

Alu, A.

P. Y. Chen, M. Farhat, and A. Alu, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106, 105503 (2011).
[Crossref] [PubMed]

P. Y. Chen and A. Alu, “Optical nanoantenna arrays loaded with nonlinear materials,” Phys. Rev. B 82, 235405 (2010).
[Crossref]

Andryieuski, A.

Antonella, B.

Assanto, G.

G. Assanto, Z. Wang, D. J. Hagan, and E. W. VanStryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[Crossref]

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] [PubMed]

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] [PubMed]

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

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Bechtel, H. A.

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

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] [PubMed]

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, Y. V.

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
[Crossref]

Bonaccorso, F.

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

Castro Neto, A. H.

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

Cheah, K. W.

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
[Crossref]

Chen, C.

Chen, H.

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
[Crossref]

Chen, J.

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Chen, P. Y.

P. Y. Chen, M. Farhat, and A. Alu, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106, 105503 (2011).
[Crossref] [PubMed]

P. Y. Chen and A. Alu, “Optical nanoantenna arrays loaded with nonlinear materials,” Phys. Rev. B 82, 235405 (2010).
[Crossref]

Chen, Z. L.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[Crossref]

Chen, Z. Y.

Chua, L. L.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[Crossref]

Clark, J.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[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]

Dai, X.

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
[Crossref]

Deng, Y.

Dijkhuis, J. I.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[Crossref] [PubMed]

Dubonos, S. V.

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

Fan, Y. C.

Y. C. Fan, F. L. Zhang, Q. Zhao, Z. Y. Wei, and H. Q. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
[Crossref]

Farhat, M.

P. Y. Chen, M. Farhat, and A. Alu, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106, 105503 (2011).
[Crossref] [PubMed]

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B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 103, 011102 (2013).

Vasilevskiy, M. I.

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
[Crossref]

Venkatesan, T.

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[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] [PubMed]

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] [PubMed]

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

Wang, F. Y.

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
[Crossref]

Wang, G. P.

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, P.

Wang, Q.

L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (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] [PubMed]

Wang, Y.

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

Wang, Z.

G. Assanto, Z. Wang, D. J. Hagan, and E. W. VanStryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[Crossref]

Wei, Z. Y.

Y. C. Fan, F. L. Zhang, Q. Zhao, Z. Y. Wei, and H. Q. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
[Crossref]

Wen, S.

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
[Crossref]

Willner, A. E.

Wong, C. W.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[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] [PubMed]

Wu, X. X.

Xia, Y.

Xiang, Y.

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
[Crossref]

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Xu, Q. H.

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

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Yakovlev, A. B.

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Phys. Rev. B 85, 245407 (2012).
[Crossref]

Yan, L. S.

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] [PubMed]

Yang, G.

Yi, A. L.

Yin, X.

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] [PubMed]

Yu, M.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[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] [PubMed]

Zettl, A.

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

Zhang, F. L.

Zhang, H.

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] [PubMed]

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

Zhang, K.

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Zhang, X.

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] [PubMed]

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] [PubMed]

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

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] [PubMed]

Zhao, Q.

Zhou, F.

Zhou, Y.

Zhu, S. N.

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
[Crossref]

Ziegler, K.

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J Phys: Condens. Matter. 20, 384204 (2008).

Adv. Funct. Mater. (1)

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “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. (4)

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 103, 011102 (2013).

G. Assanto, Z. Wang, D. J. Hagan, and E. W. VanStryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[Crossref]

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
[Crossref]

IEEE Photonic J. (1)

L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
[Crossref]

J Phys: Condens. Matter. (1)

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J Phys: Condens. Matter. 20, 384204 (2008).

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Nano. Lett. (1)

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] [PubMed]

Nat. Nanotechnol. (1)

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

Nat. Photon. (1)

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[Crossref]

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G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
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Nature (1)

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] [PubMed]

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[Crossref]

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
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H. M. Gibbs., Optical Bistability: Controlling Light with Light. (Academic Press, 1985).

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of a sandwiched structure, where the graphene sheet is inserted between two dielectric slabs. A plane wave of amplitude Ei is incident on the sandwiched structure with incident angle θ, giving rise to a reflected and a transmitted wave with amplitude ER and ET, respectively. A, B, C and D are the amplitudes of the transmitted and reflected waves inside the two dielectric slabs.

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Fig. 2
Fig. 2 The dependencies of the transmittance and reflectance on the incident angle for the sandwich structure with the insertion of graphene sheet (a) and without graphene sheet (b). Where EF = 0.8eV, λ = 100 μm, ε1 = ε4 = 1, ε2 = ε3 = 2.25, d2=d3 = 4 μm, τ−1 = 0, and T = 300 K.

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Fig. 3
Fig. 3 The dependencies of the transmitted electric field (a) and transmittance (b) on the input light intensity at different Fermi energy EF of the graphene. Where θ = 75°, other parameters have the same values as those in Fig. 2.

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Fig. 4
Fig. 4 The dependencies of the switch-up and switch-down threshold electric fields on the Fermi energy EF of the graphene. The parameters have the same values as those in Fig. 3.

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Fig. 5
Fig. 5 The influence of the properties of dielectric slabs 2 and 3 on the optical bistable phenomenon for (a) different thicknesses of dielectric slabs 2 and 3, and (b) different permittivities of dielectrics 2 and 3. Where ε2 = ε3 = 2.25 in (a) and d2=d3 = 4 μm in (b), other parameters have the same values as those in Fig. 3.

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Fig. 6
Fig. 6 The influence of the properties of incident light on the optical bistable phenomena for (a) different incident angle, and (b) different work wavelength. Where λ2 = 100 μm in (a) and θ = 75° in (b), other parameters have the same values as those in Fig. 3.

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Fig. 7
Fig. 7 The dependencies of the transmitted electric field and transmittance on the input electric field at different electron-phonon relaxation time τ of the graphene for wavelength λ = 100um in (a and b) and λ = 60um in (c and d). The parameters have the same values as those in Fig. 3.

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Equations (13)

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

σ intra = i e 2 k B T π h ¯ 2 ( ω + i / τ ) [ E F k B T + 2 ln ( e − E F k B T + 1 ) ] ,
σ inter = i e 2 4 π h ¯ ln | 2 E F − ( ω + i τ − 1 ) h ¯ 2 E F + ( ω + i τ − 1 ) h ¯ | ,
σ 3 = − i 3 32 e 2 π ( e ν F ) 2 E F ω 3     ( 1 + i α T ) ,
{ E 1 y = E i e i k 1 z ( z + d 2 ) e i k x x + E R e − i k 1 z ( z + d 2 ) e i k x x , H 1 x = − k 1 z μ 0 ω E i e i k 1 z ( z + d 2 ) e i k x x + k 1 z μ 0 ω E R e − i k 1 z ( z + d 2 ) e i k x x , H 1 z = k x μ 0 ω E i e i k 1 z ( z + d 2 ) e i k x x + k x μ 0 ω E R e − i k 1 z ( z + d 2 ) e i k x x ,
{ E 2 y = A e i k 2 z z e i k x x + B e − i k 2 z z e i k x x , H 2 x = − k 2 z μ 0 ω A e i k 2 z z e i k x x + k 2 z μ 0 ω B e − i k 2 z z e i k x x , H 2 z = k x μ 0 ω A e i k 2 z z e i k x x + k x μ 0 ω B e − i k 2 z z e i k x x ,
{ E 3 y = C e i k 3 z z e i k x x + D e − i k 3 z z e i k x x , H 3 x = − k 3 z μ 0 ω C e i k 3 z z e i k x x + k 3 z μ 0 ω D e − i k 3 z z e i k x x , H 3 z = k x μ 0 ω C e i k 3 z z e i k x x + k x μ 0 ω D e − i k 3 z z e i k x x ,
{ E 4 y = E T e i k 4 z ( z − d 3 ) e i k x x , H 4 x = − k 4 z μ 0 ω E T e i k 4 z ( z − d 3 ) e i k x x , H 4 z = k x μ 0 ω E T e i k 4 z ( z − d 3 ) e i k x x .
E i = E T 1 8 ( 1 + k 2 z k 1 z )     [ ( 1 − k 3 z k 2 z ) Δ + Θ ]     e − i k 2 z d 2 + E T 1 8 ( 1 − k 2 z k 1 z )     [ ( 1 + k 3 z k 2 z ) Δ − Θ ]     e i k 2 z d 2 ,
{ Δ = ( k 4 z k 3 z + 1 )     e − i k 3 z d 3 + ( 1 − k 4 z k 3 z )     e i k 3 z d 3 , Θ = 2 k 3 z k 2 z ( 1 + k 4 z k 3 z )     e − i k 3 z d 3 − μ 0 ω k 2 z ( σ 0 + 1 4 σ 3 | E T | 2 | Δ | 2 ) Δ .
Y = X | Π ( X ) | 2 ,
Π = 1 8 ( 1 + k 2 z k 1 z )     [ ( 1 − k 3 z k 2 z ) Δ + Θ ]     e − i k 2 z d 2 + 1 8 ( 1 − k 2 z k 1 z )     [ ( 1 + k 3 z k 2 z ) Δ − Θ ]     e i k 2 z d 2 .
Y = X | Σ ( X ) | 2 ,
{ Δ T M = ( k 4 z k 3 z ε 3 ε 4 + 1 )     e − i k 3 z d 3 − ( 1 − k 4 z k 3 z ε 3 ε 4 )     e i k 3 z d 3 , Θ T M = − k 2 z ε 2 ω ( σ 0 + 1 4 σ 3 X | k 2 z ε 0 ε 2 ω | 2 | k 3 z k 2 z ε 2 ε 3 | 2 | Δ T M | 2 )     ( k 3 z k 2 z ε 2 ε 3 Δ T M ) , Π T M = ( k 4 k 3 z ε 3 ε 4 + 1 )     e − i k 3 z d 3 + ( 1 − k 4 z k 3 z ε 3 ε 4 )     e i k 3 z d 3 + Θ T M , Σ = 1 8 ( k 2 z k 1 z ε 1 ε 2 + 1 )     ( Π T M + k 3 z k 2 z ε 2 ε 3 Δ T M )     e − i k 2 z d 2           + ( 1 − k 2 z k 1 z ε 1 ε 2 )     ( Π T M − k 3 z k 2 z ε 2 ε 3 Δ T M )     e i k 2 z d 2 .

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