Abstract

In this paper, the low-threshold optical bistability (OB) of a reflected light beam at terahertz frequencies is achieved by using a multilayer structure where monolayer graphene is coated on one-dimensional photonic crystal (1D PC) separated by a top layer. This low-threshold OB phenomenon originates from the enhancement of the electrical field owing to the excitation of optical Tamm states (OTSs) at the interface between the graphene and 1D PC. It is found that the hysterical behavior of the reflected light can be electrically controlled by properly varying the applied voltage on the graphene. Moreover, the bistable behavior of the proposed structure is proved sensitive to incidence angle and the dispersion characteristics of the top layer, thus making this configuration a prime candidate for future experimental investigation at the terahertz range.

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

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  11. A. Grieco, B. Slutsky, D. T. H. Tan, S. Zamek, M. P. Nezhad, and Y. Fainman, “Optical bistability in a Silicon Waveguide Distributed Bragg Reflector Fabry–Pérot Resonator,” J. Lightwave Technol. 30(14), 2352–2355 (2012).
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  18. 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(11), 1856–1858 (2012).
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  21. 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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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  26. X. Dai, L. Jiang, and Y. Xiang, “Tunable optical bistability of dielectric/nonlinear graphene/dielectric heterostructures,” Opt. Express 23(5), 6497–6508 (2015).
    [Crossref] [PubMed]
  27. 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. Photonics 6(8), 554–559 (2012).
    [Crossref]
  28. Q. L. Bao, J. Q. Chen, Y. J. Xiang, K. Zhang, S. J. Li, X. F. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
    [Crossref]
  29. A. V. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B Condens. Matter Mater. Phys. 72(23), 233102 (2005).
    [Crossref]
  30. M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B Condens. Matter Mater. Phys. 76(16), 165415 (2007).
    [Crossref]
  31. S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B Condens. Matter Mater. Phys. 79(8), 085416 (2009).
    [Crossref]
  32. M. V. Pyatnov, S. Y. Vetrov, and I. V. Timofeev, “Tunable hybrid optical modes in a bounded cholesteric liquid crystal with a twist defect,” Phys. Rev. E 97(3-1), 032703 (2018).
    [Crossref] [PubMed]
  33. M. Parker, E. Harbord, A. Young, P. Androvitsaneas, J. Rarity, and R. Oulton, “Tamm plasmons for efficient interaction of telecom wavelength photons and quantum dots,” IET Optoelectron. 12(1), 11–14 (2018).
    [Crossref]
  34. A. R. Gubaydullin, C. Symonds, J. Bellessa, K. A. Ivanov, E. D. Kolykhalova, M. E. Sasin, A. Lemaitre, P. Senellart, G. Pozina, and M. A. Kaliteevski, “Enhancement of spontaneous emission in Tamm plasmon structures,” Sci. Rep. 7(1), 9014 (2017).
    [Crossref] [PubMed]
  35. H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Opt. Lett. 35(24), 4112–4114 (2010).
    [Crossref] [PubMed]
  36. G. Lu, K. Yu, Z. Wen, and J. Chen, “Semiconducting graphene: converting graphene from semimetal to semiconductor,” Nanoscale 5(4), 1353–1368 (2013).
    [Crossref] [PubMed]
  37. X. Wang, X. Jiang, Q. You, J. Guo, X. Y. Dai, and Y. J. Xiang, “Tunable and multichannel terahertz perfect absorber due to Tamm surface plasmons with grapheme,” Photonic research,  5(6), 536–542 (2017).
  38. Y. Kang, J. J. Walish, T. Gorishnyy, and E. L. Thomas, “Broad-wavelength-range chemically tunable block-copolymer photonic gels,” Nat. Mater. 6(12), 957–960 (2007).
    [Crossref] [PubMed]
  39. A. Reina, H. Son, L. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and Identification of Single- and Few-Layer Graphene on Arbitrary Substrates,” J. Phys. Chem. C 112(46), 17741–17744 (2008).
    [Crossref]
  40. Y. V. Bludov, A. Ferreira, N. M. R. Peres, and M. I. Vasilevskiy, “A primer on surface plasmon-polaritons in grapheme,” Int. J. Mod. Phys. B 27(10), 1341001 (2013).
    [Crossref]
  41. Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
    [Crossref] [PubMed]
  42. 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 Condens. Matter Mater. Phys. 90(12), 125425 (2014).
    [Crossref]

2018 (5)

W. Yu, P. Ma, H. Sun, L. Gao, and R. E. Noskov, “Optical tristability and ultrafast Fano switching in nonlinear magnetoplasmonic nanoparticles,” Phys. Rev. B 97(7), 075128 (2018).
[Crossref]

L. Pickup, K. Kalinin, A. Askitopoulos, Z. Hatzopoulos, P. G. Savvidis, N. G. Berloff, and P. G. Lagoudakis, “Optical Bistability under Nonresonant Excitation in Spinor Polariton Condensates,” Phys. Rev. Lett. 120(22), 225301 (2018).
[Crossref] [PubMed]

M. V. Pyatnov, S. Y. Vetrov, and I. V. Timofeev, “Tunable hybrid optical modes in a bounded cholesteric liquid crystal with a twist defect,” Phys. Rev. E 97(3-1), 032703 (2018).
[Crossref] [PubMed]

M. Parker, E. Harbord, A. Young, P. Androvitsaneas, J. Rarity, and R. Oulton, “Tamm plasmons for efficient interaction of telecom wavelength photons and quantum dots,” IET Optoelectron. 12(1), 11–14 (2018).
[Crossref]

M. Kim, S. Kim, and S. Kim, “Optical bistability based on hyperbolic metamaterials,” Opt. Express 26(9), 11620–11632 (2018).
[Crossref] [PubMed]

2017 (4)

J. Guo, L. Jiang, Y. Jia, X. Dai, Y. Xiang, and D. Fan, “Low threshold optical bistability in one-dimensional gratings based on graphene plasmonics,” Opt. Express 25(6), 5972–5981 (2017).
[Crossref] [PubMed]

K. Zhang and L. Gao, “Optical bistability in graphene-wrapped dielectric nanowires,” Opt. Express 25(12), 13747–13759 (2017).
[Crossref] [PubMed]

A. R. Gubaydullin, C. Symonds, J. Bellessa, K. A. Ivanov, E. D. Kolykhalova, M. E. Sasin, A. Lemaitre, P. Senellart, G. Pozina, and M. A. Kaliteevski, “Enhancement of spontaneous emission in Tamm plasmon structures,” Sci. Rep. 7(1), 9014 (2017).
[Crossref] [PubMed]

X. Wang, X. Jiang, Q. You, J. Guo, X. Y. Dai, and Y. J. Xiang, “Tunable and multichannel terahertz perfect absorber due to Tamm surface plasmons with grapheme,” Photonic research,  5(6), 536–542 (2017).

2015 (4)

X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5(1), 12271 (2015).
[Crossref] [PubMed]

Q. L. Bao, J. Q. Chen, Y. J. Xiang, K. Zhang, S. J. Li, X. F. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
[Crossref]

X. Dai, L. Jiang, and Y. Xiang, “Tunable optical bistability of dielectric/nonlinear graphene/dielectric heterostructures,” Opt. Express 23(5), 6497–6508 (2015).
[Crossref] [PubMed]

K. Nozaki, A. Lacraz, A. Shinya, S. Matsuo, T. Sato, K. Takeda, E. Kuramochi, and M. Notomi, “All-optical switching for 10-Gb/s packet data by using an ultralow-power optical bistability of photonic-crystal nanocavities,” Opt. Express 23(23), 30379–30392 (2015).
[Crossref] [PubMed]

2014 (3)

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]

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]

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 Condens. Matter Mater. Phys. 90(12), 125425 (2014).
[Crossref]

2013 (3)

Y. V. Bludov, A. Ferreira, N. M. R. Peres, and M. I. Vasilevskiy, “A primer on surface plasmon-polaritons in grapheme,” Int. J. Mod. Phys. B 27(10), 1341001 (2013).
[Crossref]

G. Lu, K. Yu, Z. Wen, and J. Chen, “Semiconducting graphene: converting graphene from semimetal to semiconductor,” Nanoscale 5(4), 1353–1368 (2013).
[Crossref] [PubMed]

Z. Wang and B. Yu, “Optical bistability via dual electromagnetically induced transparency in a coupled quantum-well nanostructure,” J. Appl. Phys. 113(11), 113101 (2013).
[Crossref]

2012 (4)

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]

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. Photonics 6(8), 554–559 (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(11), 1856–1858 (2012).
[Crossref] [PubMed]

A. Grieco, B. Slutsky, D. T. H. Tan, S. Zamek, M. P. Nezhad, and Y. Fainman, “Optical bistability in a Silicon Waveguide Distributed Bragg Reflector Fabry–Pérot Resonator,” J. Lightwave Technol. 30(14), 2352–2355 (2012).
[Crossref]

2010 (2)

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

H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Opt. Lett. 35(24), 4112–4114 (2010).
[Crossref] [PubMed]

2009 (2)

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B Condens. Matter Mater. Phys. 79(8), 085416 (2009).
[Crossref]

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

2008 (3)

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]

J. H. Chen, C. Jang, S. Xiao, M. Ishigami, and M. S. Fuhrer, “Intrinsic and extrinsic performance limits of graphene devices on SiO2.,” Nat. Nanotechnol. 3(4), 206–209 (2008).
[Crossref] [PubMed]

A. Reina, H. Son, L. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and Identification of Single- and Few-Layer Graphene on Arbitrary Substrates,” J. Phys. Chem. C 112(46), 17741–17744 (2008).
[Crossref]

2007 (3)

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B Condens. Matter Mater. Phys. 76(16), 165415 (2007).
[Crossref]

Y. Kang, J. J. Walish, T. Gorishnyy, and E. L. Thomas, “Broad-wavelength-range chemically tunable block-copolymer photonic gels,” Nat. Mater. 6(12), 957–960 (2007).
[Crossref] [PubMed]

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

2005 (4)

A. V. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B Condens. Matter Mater. Phys. 72(23), 233102 (2005).
[Crossref]

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13(7), 2678–2687 (2005).
[Crossref] [PubMed]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30(19), 2575–2577 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

P. Wen, M. Sanchez, M. Gross, and S. Esener, “Vertical-cavity optical AND gate,” Opt. Commun. 219(1), 383–387 (2003).
[Crossref]

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]

1986 (1)

Abram, R. A.

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B Condens. Matter Mater. Phys. 79(8), 085416 (2009).
[Crossref]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B Condens. Matter Mater. Phys. 76(16), 165415 (2007).
[Crossref]

Almeida, V. R.

Androvitsaneas, P.

M. Parker, E. Harbord, A. Young, P. Androvitsaneas, J. Rarity, and R. Oulton, “Tamm plasmons for efficient interaction of telecom wavelength photons and quantum dots,” IET Optoelectron. 12(1), 11–14 (2018).
[Crossref]

Askitopoulos, A.

L. Pickup, K. Kalinin, A. Askitopoulos, Z. Hatzopoulos, P. G. Savvidis, N. G. Berloff, and P. G. Lagoudakis, “Optical Bistability under Nonresonant Excitation in Spinor Polariton Condensates,” Phys. Rev. Lett. 120(22), 225301 (2018).
[Crossref] [PubMed]

Bao, Q.

Bao, Q. L.

Q. L. Bao, J. Q. Chen, Y. J. Xiang, K. Zhang, S. J. Li, X. F. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
[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]

Bellessa, J.

A. R. Gubaydullin, C. Symonds, J. Bellessa, K. A. Ivanov, E. D. Kolykhalova, M. E. Sasin, A. Lemaitre, P. Senellart, G. Pozina, and M. A. Kaliteevski, “Enhancement of spontaneous emission in Tamm plasmon structures,” Sci. Rep. 7(1), 9014 (2017).
[Crossref] [PubMed]

Berloff, N. G.

L. Pickup, K. Kalinin, A. Askitopoulos, Z. Hatzopoulos, P. G. Savvidis, N. G. Berloff, and P. G. Lagoudakis, “Optical Bistability under Nonresonant Excitation in Spinor Polariton Condensates,” Phys. Rev. Lett. 120(22), 225301 (2018).
[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 Condens. Matter Mater. Phys. 90(12), 125425 (2014).
[Crossref]

Y. V. Bludov, A. Ferreira, N. M. R. Peres, and M. I. Vasilevskiy, “A primer on surface plasmon-polaritons in grapheme,” Int. J. Mod. Phys. B 27(10), 1341001 (2013).
[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]

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]

Brand, S.

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B Condens. Matter Mater. Phys. 79(8), 085416 (2009).
[Crossref]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B Condens. Matter Mater. Phys. 76(16), 165415 (2007).
[Crossref]

Castro Neto, A. H.

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Savvidis, P. G.

L. Pickup, K. Kalinin, A. Askitopoulos, Z. Hatzopoulos, P. G. Savvidis, N. G. Berloff, and P. G. Lagoudakis, “Optical Bistability under Nonresonant Excitation in Spinor Polariton Condensates,” Phys. Rev. Lett. 120(22), 225301 (2018).
[Crossref] [PubMed]

Scalora, 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]

Schwab, M. G.

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

Senellart, P.

A. R. Gubaydullin, C. Symonds, J. Bellessa, K. A. Ivanov, E. D. Kolykhalova, M. E. Sasin, A. Lemaitre, P. Senellart, G. Pozina, and M. A. Kaliteevski, “Enhancement of spontaneous emission in Tamm plasmon structures,” Sci. Rep. 7(1), 9014 (2017).
[Crossref] [PubMed]

Shelykh, I. A.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B Condens. Matter Mater. Phys. 76(16), 165415 (2007).
[Crossref]

A. V. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B Condens. Matter Mater. Phys. 72(23), 233102 (2005).
[Crossref]

Shen, J. T.

Shinya, A.

Slutsky, B.

Son, H.

A. Reina, H. Son, L. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and Identification of Single- and Few-Layer Graphene on Arbitrary Substrates,” J. Phys. Chem. C 112(46), 17741–17744 (2008).
[Crossref]

Stormer, H. L.

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]

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Sun, H.

W. Yu, P. Ma, H. Sun, L. Gao, and R. E. Noskov, “Optical tristability and ultrafast Fano switching in nonlinear magnetoplasmonic nanoparticles,” Phys. Rev. B 97(7), 075128 (2018).
[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]

Symonds, C.

A. R. Gubaydullin, C. Symonds, J. Bellessa, K. A. Ivanov, E. D. Kolykhalova, M. E. Sasin, A. Lemaitre, P. Senellart, G. Pozina, and M. A. Kaliteevski, “Enhancement of spontaneous emission in Tamm plasmon structures,” Sci. Rep. 7(1), 9014 (2017).
[Crossref] [PubMed]

Takeda, K.

Tan, D. T. H.

Tan, Y. W.

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Tanabe, T.

Tang, D.

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, S.

Thomas, E. L.

Y. Kang, J. J. Walish, T. Gorishnyy, and E. L. Thomas, “Broad-wavelength-range chemically tunable block-copolymer photonic gels,” Nat. Mater. 6(12), 957–960 (2007).
[Crossref] [PubMed]

Timofeev, I. V.

M. V. Pyatnov, S. Y. Vetrov, and I. V. Timofeev, “Tunable hybrid optical modes in a bounded cholesteric liquid crystal with a twist defect,” Phys. Rev. E 97(3-1), 032703 (2018).
[Crossref] [PubMed]

Tocci, M. D.

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]

van der Zande, A.

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. Photonics 6(8), 554–559 (2012).
[Crossref]

Vasilevskiy, M. I.

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 Condens. Matter Mater. Phys. 90(12), 125425 (2014).
[Crossref]

Y. V. Bludov, A. Ferreira, N. M. R. Peres, and M. I. Vasilevskiy, “A primer on surface plasmon-polaritons in grapheme,” Int. J. Mod. Phys. B 27(10), 1341001 (2013).
[Crossref]

Venkatesan, T.

Q. L. Bao, J. Q. Chen, Y. J. Xiang, K. Zhang, S. J. Li, X. F. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
[Crossref]

Vetrov, S. Y.

M. V. Pyatnov, S. Y. Vetrov, and I. V. Timofeev, “Tunable hybrid optical modes in a bounded cholesteric liquid crystal with a twist defect,” Phys. Rev. E 97(3-1), 032703 (2018).
[Crossref] [PubMed]

Virally, S.

Walish, J. J.

Y. Kang, J. J. Walish, T. Gorishnyy, and E. L. Thomas, “Broad-wavelength-range chemically tunable block-copolymer photonic gels,” Nat. Mater. 6(12), 957–960 (2007).
[Crossref] [PubMed]

Wang, K.

Wang, X.

X. Wang, X. Jiang, Q. You, J. Guo, X. Y. Dai, and Y. J. Xiang, “Tunable and multichannel terahertz perfect absorber due to Tamm surface plasmons with grapheme,” Photonic research,  5(6), 536–542 (2017).

Wang, Z.

Z. Wang and B. Yu, “Optical bistability via dual electromagnetically induced transparency in a coupled quantum-well nanostructure,” J. Appl. Phys. 113(11), 113101 (2013).
[Crossref]

Wen, P.

P. Wen, M. Sanchez, M. Gross, and S. Esener, “Vertical-cavity optical AND gate,” Opt. Commun. 219(1), 383–387 (2003).
[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(5), 051108 (2014).
[Crossref]

Wen, Z.

G. Lu, K. Yu, Z. Wen, and J. Chen, “Semiconducting graphene: converting graphene from semimetal to semiconductor,” Nanoscale 5(4), 1353–1368 (2013).
[Crossref] [PubMed]

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. Photonics 6(8), 554–559 (2012).
[Crossref]

Xiang, Y.

J. Guo, L. Jiang, Y. Jia, X. Dai, Y. Xiang, and D. Fan, “Low threshold optical bistability in one-dimensional gratings based on graphene plasmonics,” Opt. Express 25(6), 5972–5981 (2017).
[Crossref] [PubMed]

X. Dai, L. Jiang, and Y. Xiang, “Tunable optical bistability of dielectric/nonlinear graphene/dielectric heterostructures,” Opt. Express 23(5), 6497–6508 (2015).
[Crossref] [PubMed]

X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5(1), 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]

Xiang, Y. J.

X. Wang, X. Jiang, Q. You, J. Guo, X. Y. Dai, and Y. J. Xiang, “Tunable and multichannel terahertz perfect absorber due to Tamm surface plasmons with grapheme,” Photonic research,  5(6), 536–542 (2017).

Q. L. Bao, J. Q. Chen, Y. J. Xiang, K. Zhang, S. J. Li, X. F. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
[Crossref]

Xiao, S.

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]

J. H. Chen, C. Jang, S. Xiao, M. Ishigami, and M. S. Fuhrer, “Intrinsic and extrinsic performance limits of graphene devices on SiO2.,” Nat. Nanotechnol. 3(4), 206–209 (2008).
[Crossref] [PubMed]

Xu, Q. H.

Q. L. Bao, J. Q. Chen, Y. J. Xiang, K. Zhang, S. J. Li, X. F. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
[Crossref]

Yang, G.

You, Q.

X. Wang, X. Jiang, Q. You, J. Guo, X. Y. Dai, and Y. J. Xiang, “Tunable and multichannel terahertz perfect absorber due to Tamm surface plasmons with grapheme,” Photonic research,  5(6), 536–542 (2017).

Young, A.

M. Parker, E. Harbord, A. Young, P. Androvitsaneas, J. Rarity, and R. Oulton, “Tamm plasmons for efficient interaction of telecom wavelength photons and quantum dots,” IET Optoelectron. 12(1), 11–14 (2018).
[Crossref]

Yu, B.

Z. Wang and B. Yu, “Optical bistability via dual electromagnetically induced transparency in a coupled quantum-well nanostructure,” J. Appl. Phys. 113(11), 113101 (2013).
[Crossref]

Yu, K.

G. Lu, K. Yu, Z. Wen, and J. Chen, “Semiconducting graphene: converting graphene from semimetal to semiconductor,” Nanoscale 5(4), 1353–1368 (2013).
[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. Photonics 6(8), 554–559 (2012).
[Crossref]

Yu, W.

W. Yu, P. Ma, H. Sun, L. Gao, and R. E. Noskov, “Optical tristability and ultrafast Fano switching in nonlinear magnetoplasmonic nanoparticles,” Phys. Rev. B 97(7), 075128 (2018).
[Crossref]

Zamek, S.

Zhang, H.

Zhang, K.

K. Zhang and L. Gao, “Optical bistability in graphene-wrapped dielectric nanowires,” Opt. Express 25(12), 13747–13759 (2017).
[Crossref] [PubMed]

Q. L. Bao, J. Q. Chen, Y. J. Xiang, K. Zhang, S. J. Li, X. F. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
[Crossref]

Zhang, Y.

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Zhou, H.

Zhou, L.

Zhu, B.

Adv. Opt. Mater. (1)

Q. L. Bao, J. Q. Chen, Y. J. Xiang, K. Zhang, S. J. Li, X. F. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
[Crossref]

Appl. Phys. Lett. (2)

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]

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]

IET Optoelectron. (1)

M. Parker, E. Harbord, A. Young, P. Androvitsaneas, J. Rarity, and R. Oulton, “Tamm plasmons for efficient interaction of telecom wavelength photons and quantum dots,” IET Optoelectron. 12(1), 11–14 (2018).
[Crossref]

Int. J. Mod. Phys. B (1)

Y. V. Bludov, A. Ferreira, N. M. R. Peres, and M. I. Vasilevskiy, “A primer on surface plasmon-polaritons in grapheme,” Int. J. Mod. Phys. B 27(10), 1341001 (2013).
[Crossref]

J. Appl. Phys. (1)

Z. Wang and B. Yu, “Optical bistability via dual electromagnetically induced transparency in a coupled quantum-well nanostructure,” J. Appl. Phys. 113(11), 113101 (2013).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

J. Phys. Chem. C (1)

A. Reina, H. Son, L. Jiao, B. Fan, M. S. Dresselhaus, Z. Liu, and J. Kong, “Transferring and Identification of Single- and Few-Layer Graphene on Arbitrary Substrates,” J. Phys. Chem. C 112(46), 17741–17744 (2008).
[Crossref]

Nanoscale (1)

G. Lu, K. Yu, Z. Wen, and J. Chen, “Semiconducting graphene: converting graphene from semimetal to semiconductor,” Nanoscale 5(4), 1353–1368 (2013).
[Crossref] [PubMed]

Nat. Mater. (2)

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

Y. Kang, J. J. Walish, T. Gorishnyy, and E. L. Thomas, “Broad-wavelength-range chemically tunable block-copolymer photonic gels,” Nat. Mater. 6(12), 957–960 (2007).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

J. H. Chen, C. Jang, S. Xiao, M. Ishigami, and M. S. Fuhrer, “Intrinsic and extrinsic performance limits of graphene devices on SiO2.,” Nat. Nanotechnol. 3(4), 206–209 (2008).
[Crossref] [PubMed]

Nat. Photonics (2)

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[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. Photonics 6(8), 554–559 (2012).
[Crossref]

Nat. Phys. (1)

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]

Nature (2)

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]

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Opt. Commun. (1)

P. Wen, M. Sanchez, M. Gross, and S. Esener, “Vertical-cavity optical AND gate,” Opt. Commun. 219(1), 383–387 (2003).
[Crossref]

Opt. Express (6)

Opt. Lett. (5)

Photonic research (1)

X. Wang, X. Jiang, Q. You, J. Guo, X. Y. Dai, and Y. J. Xiang, “Tunable and multichannel terahertz perfect absorber due to Tamm surface plasmons with grapheme,” Photonic research,  5(6), 536–542 (2017).

Phys. Rev. B (1)

W. Yu, P. Ma, H. Sun, L. Gao, and R. E. Noskov, “Optical tristability and ultrafast Fano switching in nonlinear magnetoplasmonic nanoparticles,” Phys. Rev. B 97(7), 075128 (2018).
[Crossref]

Phys. Rev. B Condens. Matter Mater. Phys. (4)

A. V. Kavokin, I. A. Shelykh, and G. Malpuech, “Lossless interface modes at the boundary between two periodic dielectric structures,” Phys. Rev. B Condens. Matter Mater. Phys. 72(23), 233102 (2005).
[Crossref]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B Condens. Matter Mater. Phys. 76(16), 165415 (2007).
[Crossref]

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B Condens. Matter Mater. Phys. 79(8), 085416 (2009).
[Crossref]

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 Condens. Matter Mater. Phys. 90(12), 125425 (2014).
[Crossref]

Phys. Rev. E (1)

M. V. Pyatnov, S. Y. Vetrov, and I. V. Timofeev, “Tunable hybrid optical modes in a bounded cholesteric liquid crystal with a twist defect,” Phys. Rev. E 97(3-1), 032703 (2018).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

L. Pickup, K. Kalinin, A. Askitopoulos, Z. Hatzopoulos, P. G. Savvidis, N. G. Berloff, and P. G. Lagoudakis, “Optical Bistability under Nonresonant Excitation in Spinor Polariton Condensates,” Phys. Rev. Lett. 120(22), 225301 (2018).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

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]

Sci. Rep. (2)

X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5(1), 12271 (2015).
[Crossref] [PubMed]

A. R. Gubaydullin, C. Symonds, J. Bellessa, K. A. Ivanov, E. D. Kolykhalova, M. E. Sasin, A. Lemaitre, P. Senellart, G. Pozina, and M. A. Kaliteevski, “Enhancement of spontaneous emission in Tamm plasmon structures,” Sci. Rep. 7(1), 9014 (2017).
[Crossref] [PubMed]

Other (1)

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).

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Figures (6)

Fig. 1
Fig. 1 Schematic diagram of the investigated Tamm plasmon structure, where the top layer is inserted between nonlinear graphene and 1D PC. A plane wave of amplitude E i is incident on the structure with incident angle θ, giving rise to a reflected and a transmitted wave with amplitude E r and E t , respectively. F i and B i  (i=1~n) are the amplitudes of the transmitted and reflected waves inside the dielectric slabs.

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Fig. 2
Fig. 2 (a) Reflectance as functions of wavelength at different Fermi energies for TE-polarized wave. The normalized electric field profile distributions in the graphene-1D PC configuration without (b) and with (c) the covering of nonlinear graphene. (d) The dependencies of the reflectance on the input light intensity at different Fermi energies of the graphene.

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Fig. 3
Fig. 3 (a) The dependencies of the reflected electric field E r on the input light intensity E i at different Fermi energies of the graphene. (b) The dependencies of the switch-up and switch-down threshold electric fields on the Fermi energy of the graphene.

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Fig. 4
Fig. 4 (a) Reflectance, and (b) reflected electric field E r as functions of the input light intensity E i at different incident angles.

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Fig. 5
Fig. 5 The influence of the properties of incident light on the reflected optical bistable phenomena for different work wavelengths.

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Fig. 6
Fig. 6 The influence of the properties of incident light on the reflected optical bistable phenomena for (a) different refractive index of top layer, and (b) different thicknesses of top layer.

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Equations (6)

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

σ 0 ≈ i e 2 E F π ℏ 2 ( ω+i/τ ) ,
σ 3 =−i 9 8 e 4 ν F 2 π ℏ 2 E F ω 3 .
{ E 0y = E i e i k 0z z e i k x x + E r e −i k 0z z e i k x x ,                                         (3a)  H 0x =− k 0z μ 0 ω E i e i k 0z z e i k x x + k 0z μ 0 ω E r e −i k 0z z e i k x x ,                          (3b) H 0z = k x μ 0 ω E i e i k 0z z e i k x x + k x μ 0 ω E r e −i k 0z z e i k x x ,                            (3c)
{ E 1y = F 1 e i k tz z e i k x x + B 1 e −i k tz z e i k x x ,                                         (4a) H 1x =− k tz μ 0 ω F 1 e i k tz z e i k x x + k tz μ 0 ω B 1 e −i k tz z e i k x x ,                         (4b) H 1z = k x μ 0 ω F 1 e i k tz z e i k x x + k x μ 0 ω B 1 e −i k tz z e i k x x .                            (4c)
{ E my = F m e i k ζz [ z−( d t +α d a +β d b ) ] e i k x x + B m e −i k ζz [ z−( d t +α d a +β d b ) ] e i k x x ,                         (5a) H mx =− k ζz μ 0 ω F m e i k ζz [ z−( d t +α d a +β d b ) ] e i k x x + k ζz μ 0 ω B m e −i k ζz [ z−( d t +α d a +β d b ) ] e i k x x ,        (5b) H mz = k x μ 0 ω F m e i k ζz [ z−( d t +α d a +β d b ) ] e i k x x + k x μ 0 ω B m e −i k ζz [ z−( d t +α d a +β d b ) ] e i k x x .           (5c)
{ E ( n+1 )y = E t e i k 0z [ z−( d t +N( d a + d b ) ) ] e i k x x ,                                   (6a) H ( n+1 )x =− k 0z μ 0 ω E t e i k 0z [ z−( d t +N( d a + d b ) ) ] e i k x x ,                          (6b) H ( n+1 )z = k x μ 0 ω E t e i k 0z [ z−( d t +N( d a + d b ) ) ] e i k x x ,                             (6c)

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