Abstract

We investigate theoretically the optical bistability from a Fabry-Perot cavity with graphene in the terahertz (THz) frequency. It is demonstrated that the optical bistablility in this cavity can be realized due to the electric field enhancement and the giant third-order nonlinear conductivity of graphene. The optical bistable behavior is strongly dependent on the transmission amplitude of the mirror and the position of the graphene in the cavity. It is especially important that the hysterical behaviors of the transmitted light rely on the optical conductivity of graphene, making the Fabry-Perot cavity to be a good candidate for dynamic tunable optical bistable device in the THz frequencies, owing to the possibility of high tunability of graphene conductivity by means of external electrostatic or magnetostatic field.

© 2015 Optical Society of America

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  5. M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66(18), 2324–2326 (1995).
    [Crossref]
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  7. M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
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  8. P. Y. Chen, M. Farhat, and A. Alù, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106(10), 105503 (2011).
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  9. S. Tang, B. Zhu, S. Xiao, J. T. Shen, and L. Zhou, “Low-threshold optical bistabilities in ultrathin nonlinear metamaterials,” Opt. Lett. 39(11), 3212–3215 (2014).
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  10. M. F. Yanik, S. H. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83(14), 2739–2741 (2003).
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  11. F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in onedimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92(21), 211109 (2008).
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  12. W. Harshawardhan and G. S. Agarwal, “Controlling optical bistability using electromagnetic-field-induced transparency and quantum interferences,” Phys. Rev. A 53(3), 1812–1817 (1996).
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  13. A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67(4), 041801 (2003).
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    [Crossref]
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    [Crossref] [PubMed]
  18. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
    [Crossref]
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    [Crossref] [PubMed]
  20. A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
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  21. 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(7349), 64–67 (2011).
    [Crossref] [PubMed]
  22. Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
    [Crossref]
  23. F. Liu and E. Cubukcu, “Tunable omnidirectional strong light-matter interactions mediated by graphene surface plasmons,” Phys. Rev. B 88(11), 115439 (2013).
    [Crossref]
  24. F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
    [Crossref] [PubMed]
  25. Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
    [Crossref]
  26. E. Simsek, “Improving tuning range and sensitivity of localized SPR sensors with graphene,” IEEE Photonics Technol. Lett. 25(9), 867–870 (2013).
    [Crossref]
  27. A. Fallahi and J. Perruisseau-Carrier, “Design of tunable biperiodic graphene metasurfaces,” Phys. Rev. B 86(19), 195408 (2012).
    [Crossref]
  28. H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
    [Crossref] [PubMed]
  29. E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
    [Crossref] [PubMed]
  30. X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5, 12271 (2015).
    [Crossref] [PubMed]
  31. N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
    [Crossref]
  32. A. Ferreira, N. Peres, R. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (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(5), 051108 (2014).
    [Crossref]
  34. S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys. Condens. Matter 20(38), 384204 (2008).
    [Crossref] [PubMed]
  35. T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
    [Crossref] [PubMed]

2015 (1)

X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5, 12271 (2015).
[Crossref] [PubMed]

2014 (3)

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
[Crossref]

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104(5), 051108 (2014).
[Crossref]

S. Tang, B. Zhu, S. Xiao, J. T. Shen, and L. Zhou, “Low-threshold optical bistabilities in ultrathin nonlinear metamaterials,” Opt. Lett. 39(11), 3212–3215 (2014).
[Crossref] [PubMed]

2013 (3)

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

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

E. Simsek, “Improving tuning range and sensitivity of localized SPR sensors with graphene,” IEEE Photonics Technol. Lett. 25(9), 867–870 (2013).
[Crossref]

2012 (4)

A. Fallahi and J. Perruisseau-Carrier, “Design of tunable biperiodic graphene metasurfaces,” Phys. Rev. B 86(19), 195408 (2012).
[Crossref]

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

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
[Crossref] [PubMed]

A. Ferreira, N. Peres, R. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
[Crossref]

2011 (3)

P. Y. Chen, M. Farhat, and A. Alù, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106(10), 105503 (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(7349), 64–67 (2011).
[Crossref] [PubMed]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

2010 (2)

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref] [PubMed]

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

2009 (3)

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

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
[Crossref] [PubMed]

2008 (4)

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys. Condens. Matter 20(38), 384204 (2008).
[Crossref] [PubMed]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308–1310 (2008).
[Crossref] [PubMed]

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in onedimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92(21), 211109 (2008).
[Crossref]

2007 (1)

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

2004 (1)

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Tunable transmission and bistability in left-handed band-gap structures,” Appl. Phys. Lett. 85(9), 1451–1453 (2004).
[Crossref]

2003 (3)

M. F. Yanik, S. H. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83(14), 2739–2741 (2003).
[Crossref]

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67(4), 041801 (2003).
[Crossref]

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(21), 213903 (2003).
[Crossref] [PubMed]

2002 (1)

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[Crossref] [PubMed]

2001 (1)

H. Nihei and A. Okamoto, “Switching time of optical memory devices composed of photonic crystals with an impurity three-level atom,” Jpn. J. Appl. Phys. 40(1), 6835–6840 (2001).
[Crossref]

1996 (1)

W. Harshawardhan and G. S. Agarwal, “Controlling optical bistability using electromagnetic-field-induced transparency and quantum interferences,” Phys. Rev. A 53(3), 1812–1817 (1996).
[Crossref] [PubMed]

1995 (1)

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66(18), 2324–2326 (1995).
[Crossref]

1990 (1)

H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of two optical triodes,” Appl. Phys. Lett. 57(17), 1724–1726 (1990).
[Crossref]

1988 (1)

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52(11), 869–871 (1988).
[Crossref]

Agarwal, G. S.

W. Harshawardhan and G. S. Agarwal, “Controlling optical bistability using electromagnetic-field-induced transparency and quantum interferences,” Phys. Rev. A 53(3), 1812–1817 (1996).
[Crossref] [PubMed]

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(21), 213903 (2003).
[Crossref] [PubMed]

Alù, A.

P. Y. Chen, M. Farhat, and A. Alù, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106(10), 105503 (2011).
[Crossref] [PubMed]

Assanto, G.

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52(11), 869–871 (1988).
[Crossref]

Avouris, P.

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

F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
[Crossref] [PubMed]

Bao, Q.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Basov, D. N.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Blake, P.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308–1310 (2008).
[Crossref] [PubMed]

Bloemer, M. J.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66(18), 2324–2326 (1995).
[Crossref]

Bludov, Y. V.

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
[Crossref]

Bonaccorso, F.

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

Booth, T. J.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308–1310 (2008).
[Crossref] [PubMed]

Bowden, C. M.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66(18), 2324–2326 (1995).
[Crossref]

Brown, A.

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67(4), 041801 (2003).
[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(1), 109–162 (2009).
[Crossref]

Chandra, B.

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

Cheah, K. W.

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in onedimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92(21), 211109 (2008).
[Crossref]

Chen, P. Y.

P. Y. Chen, M. Farhat, and A. Alù, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106(10), 105503 (2011).
[Crossref] [PubMed]

Colombo, L.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
[Crossref] [PubMed]

Cubukcu, E.

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

Dai, X.

X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5, 12271 (2015).
[Crossref] [PubMed]

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104(5), 051108 (2014).
[Crossref]

Dai, Y.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

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(21), 213903 (2003).
[Crossref] [PubMed]

Dowling, J. P.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66(18), 2324–2326 (1995).
[Crossref]

Fal’ko, V. I.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
[Crossref] [PubMed]

Fallahi, A.

A. Fallahi and J. Perruisseau-Carrier, “Design of tunable biperiodic graphene metasurfaces,” Phys. Rev. B 86(19), 195408 (2012).
[Crossref]

Fan, S. H.

M. F. Yanik, S. H. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83(14), 2739–2741 (2003).
[Crossref]

Farhat, M.

P. Y. Chen, M. Farhat, and A. Alù, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106(10), 105503 (2011).
[Crossref] [PubMed]

Feise, M. W.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Tunable transmission and bistability in left-handed band-gap structures,” Appl. Phys. Lett. 85(9), 1451–1453 (2004).
[Crossref]

Ferrari, A. C.

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

Ferreira, A.

A. Ferreira, N. Peres, R. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
[Crossref]

Fink, Y.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[Crossref] [PubMed]

Freitag, M.

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

Garmire, E.

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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(7349), 64–67 (2011).
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Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
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F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in onedimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92(21), 211109 (2008).
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F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
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Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
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E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
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Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
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A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
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R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308–1310 (2008).
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N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
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A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
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R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308–1310 (2008).
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N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
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E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
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K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
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G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52(11), 869–871 (1988).
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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(21), 213903 (2003).
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M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Tunable transmission and bistability in left-handed band-gap structures,” Appl. Phys. Lett. 85(9), 1451–1453 (2004).
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Shen, J. T.

Shi, X.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
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A. Ferreira, N. Peres, R. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
[Crossref]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308–1310 (2008).
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G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52(11), 869–871 (1988).
[Crossref]

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Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Sun, Z.

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

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F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in onedimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92(21), 211109 (2008).
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Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104(5), 051108 (2014).
[Crossref]

Tang, D. Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
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M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66(18), 2324–2326 (1995).
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H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of two optical triodes,” Appl. Phys. Lett. 57(17), 1724–1726 (1990).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
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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(7349), 64–67 (2011).
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F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
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N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
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G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52(11), 869–871 (1988).
[Crossref]

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Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

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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(7349), 64–67 (2011).
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F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in onedimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92(21), 211109 (2008).
[Crossref]

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A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67(4), 041801 (2003).
[Crossref]

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Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
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Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104(5), 051108 (2014).
[Crossref]

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

F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
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Figures (6)

Fig. 1
Fig. 1 Schematic diagram of a Fabry-Perot cavity with the insertion of graphene sheet. A plane wave of amplitude E i is incident on the structure, giving rise to a reflected and a transmitted wave with amplitude E r and E t , respectively.
Fig. 2
Fig. 2 The reflectance (short dashed lines) and transmittance (solid lines) as a function of frequency for different Fermi energies in the Fabry-Perot cavity with graphene. Here, L l = L c /2 , τ=1250fs , T=300K and t m 2 =0.3 .
Fig. 3
Fig. 3 (a) The dependences of the transmitted electric field on the input light intensity at different Fermi energies E F of the graphene. (b) The dependences of the switch-up and switch-down threshold electric fields on the Fermi energy E F of the graphene.Here, L l = L c /2 , τ=1250fs , T=300K and t m 2 =0.3 .
Fig. 4
Fig. 4 The influences of mirror transmittance t m 2 (a) and cavity length L c (b) on the optical bistable phenomenon. Here, L l = L c /2 , τ=1250fs , T=300K and E F =0.1eV .
Fig. 5
Fig. 5 The dependences of the transmitted electric field on the input light intensity at different positions of graphene. Here, t m 2 =0.3 , τ=1250fs , T=300K and E F =0.1eV .
Fig. 6
Fig. 6 The dependences of the transmitted electric field (a) and transmittance (b) on the input light intensity at different relaxation times τ of the graphene. Here, L l = L c /2 , t m 2 =0.3 , T=300K and E F =0.1eV .

Equations (17)

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M m = 1 t m [ 1 | r m | | r m | 1 ],
σ intra = i e 2 k B T π 2 ( ω+i/τ ) [ E F k B T +2ln( e E F k B T +1) ],
σ inter = i e 2 4π ln| 2 E F ( ω+i τ 1 ) 2 E F +( ω+i τ 1 ) |,
σ 3 =i 9 8 e 4 ν F 2 π 2 E F ω 3 ,
M g =[ 1+ξ ξ ξ 1ξ ],
M= M m M f ( L l ) M g M f ( L r ) M m ,
M f ( Δx )=[ e ikΔx 0 0 e ikΔx ],
t= 1 M 11 ,r= M 21 M 11 ,
E t E i =t= t m 2 ( 1+ζ ) e ik L c 2ζ| r m |( 1ζ ) | r m | 2 e ik L c ,
Y=X | Π( X ) | 2 ,
Π= | [ 1+Z( σ 0 + σ 3 X ) ] e ik L c 2Z( σ 0 + σ 3 X )| r m |[ 1Z( σ 0 + σ 3 X ) ] | r m | 2 e ik L c | 2 | t m | 4 ,
Δ=4Im ( σ 3 ) 2 Z 4 ( | r m |+1 ) 8 { Im ( σ 0 ) 2 3 [ Re( σ 0 )+ ( 1| r m | ) Z( 1+| r m | ) ] 2 }>0.
Δ m =| Im( σ 0 ) | 3 Re( σ 0 ) 3 Z + 2 3 Z | r m | ( 1+| r m | ) .
Δ m =| Im( σ 0 ) | 3 Re( σ 0 ) 3 Z .
X ext,1 - Im( σ 0 ) 3Im( σ 3 ) = 8 ω 2 27 e 2 v F 2 E F 2 , X ext,2 - Im( σ 0 ) Im( σ 3 ) = 8 ω 2 9 e 2 v F 2 E F 2 .
ΔY 128 729 Z | t m | 4 e 2 π 2 v F 2 4 E F 4 .
{ | r m | 2 +2cos[ ( 2κ1 )π ]| r m |+1 }Z| Im( σ 0 ) |>1 | r m | 2 .

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