Abstract

We theoretically studied in terahertz frequency regime optical bistability of graphene placed at the interface between thin dielectric layers. We solved self-consistently the nonlinear wave equations containing the third-order optical conductivity of graphene in four-layer structures and obtained hysteresis response of the transmitted power as a function of the incident power. We numerically observed that the critical powers for the up and down transitions and the Fermi-energy of graphene required for terahertz optical bistability can be reduced by carefully choosing material properties and the thicknesses of dielectric layers. Furthermore, these values can be substantially decreased when graphene as a randomly stacked multilayer structure is asymmetrically located in thin dielectric layers.

© 2017 Optical Society of America

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References

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  1. S. D. Smith, “Lasers, nonlinear optics and optical computers,” Nature 316, 319–324 (1985).
    [Crossref]
  2. E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982).
    [Crossref]
  3. Robert W. Boyd, Nonlinear Optics (Elsevier Inc., 2008).
  4. Michael P. Marder, Condensed Matter Physics (John Wiley & Sons, Inc., 2010).
    [Crossref]
  5. M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
    [Crossref] [PubMed]
  6. G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).
    [Crossref] [PubMed]
  7. Sergio G. Rodrigo, S. Carretero-Palacios, F. J. García-Vidal, and L. Martín-Moreno, “Metallic slit arrays filled with third-order nonlinear media: Optical Kerr effect and third-harmonic generation,” Phys. Rev. B 83, 235425 (2011).
    [Crossref]
  8. S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Theory of the linear and nonlinear optical properties of semiconductor microcrystallites,” Phys. Rev. B 35, 8113–8125 (1987).
    [Crossref]
  9. Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
    [Crossref]
  10. K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
    [Crossref] [PubMed]
  11. Thomas Christensen, Wei Yan, Antti-Pekka Jauho, Martijn Wubs, and N Asger Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92, 121407(R) (2015).
    [Crossref]
  12. J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: Effects of phenomenological relaxation and finite temperature,” Phys. Rev. B 91, 235320 (2015).
    [Crossref]
  13. S. A. Mikhailov, “Quantum theory of the third-order nonlinear electrodynamic effects of graphene,” Phys. Rev. B 93, 085403 (2016).
    [Crossref]
  14. 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,” Nature Photon. 6, 554–559 (2012).
    [Crossref]
  15. Qiaoliang Bao, Jianqiang Chen, Yuanjiang Xiang, Kai Zhang, Shaojuan Li, Xiaofang Jiang, Qing-Hua Xu, Kian Ping Loh, and T. Venkatesan, “ Graphene Nanobubbles: A new optical nonlinear material,” Adv. Optical Mater. 3, 744–749 (2015).
    [Crossref]
  16. Yuanjiang Xiang, Xiaoyu Dai, Jun Guo, Shuangchun Wen, and Dingyuan Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,”, Appl. Phys. Lett. 104, 051108 (2014).
    [Crossref]
  17. Xiaoyu Dai, Leyong Jiang, and Yuanjiang Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5, 12271 (2015).
    [Crossref] [PubMed]
  18. Xiaoyu Dai, Leyong Jiang, and Yuanjiang Xiang, “ Tunable optical bistability of dielectric/nonlinear graphene/dielectric heterostructures,”, Opt. Express 23, 6497–6508 (2015).
    [Crossref] [PubMed]
  19. In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
    [Crossref]
  20. E. Lidorikis, K. Busch, Qiming Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090 (1997).
    [Crossref]
  21. I. H. Baek, K. J. Ahn, B. J. Kang, S. Bae, B. H. Hong, D.-I. Yeom, K. Lee, Y. U. Jeong, and F. Rotermund, “Terahertz transmission and sheet conductivity of randomly stacked multi-layer graphene,” Appl. Phys. Lett. 102, 191109 (2013).
    [Crossref]
  22. N. M. R. Peres, Yu. V. Bludov, Jaime E. Santos, Antti-Pekka Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
    [Crossref]
  23. Jason Horng, Chi-Fan Chen, Baisong Geng, Caglar Girit, Yuanbo Zhang, Zhao Hao, Hans A. Bechtel, Michael Martin, Alex Zettl, Michael F. Crommie, Y. Ron Shen, and Feng Wang, “ Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
    [Crossref]
  24. R. Bonifacio and L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18, 1129–1144 (1978).
    [Crossref]

2017 (1)

In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
[Crossref]

2016 (1)

S. A. Mikhailov, “Quantum theory of the third-order nonlinear electrodynamic effects of graphene,” Phys. Rev. B 93, 085403 (2016).
[Crossref]

2015 (5)

Thomas Christensen, Wei Yan, Antti-Pekka Jauho, Martijn Wubs, and N Asger Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92, 121407(R) (2015).
[Crossref]

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: Effects of phenomenological relaxation and finite temperature,” Phys. Rev. B 91, 235320 (2015).
[Crossref]

Qiaoliang Bao, Jianqiang Chen, Yuanjiang Xiang, Kai Zhang, Shaojuan Li, Xiaofang Jiang, Qing-Hua Xu, Kian Ping Loh, and T. Venkatesan, “ Graphene Nanobubbles: A new optical nonlinear material,” Adv. Optical Mater. 3, 744–749 (2015).
[Crossref]

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

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

2014 (2)

Yuanjiang Xiang, Xiaoyu Dai, Jun Guo, Shuangchun Wen, and Dingyuan Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,”, Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

N. M. R. Peres, Yu. V. Bludov, Jaime E. Santos, Antti-Pekka Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
[Crossref]

2013 (1)

I. H. Baek, K. J. Ahn, B. J. Kang, S. Bae, B. H. Hong, D.-I. Yeom, K. Lee, Y. U. Jeong, and F. Rotermund, “Terahertz transmission and sheet conductivity of randomly stacked multi-layer graphene,” Appl. Phys. Lett. 102, 191109 (2013).
[Crossref]

2012 (2)

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,” Nature Photon. 6, 554–559 (2012).
[Crossref]

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

2011 (2)

Sergio G. Rodrigo, S. Carretero-Palacios, F. J. García-Vidal, and L. Martín-Moreno, “Metallic slit arrays filled with third-order nonlinear media: Optical Kerr effect and third-harmonic generation,” Phys. Rev. B 83, 235425 (2011).
[Crossref]

Jason Horng, Chi-Fan Chen, Baisong Geng, Caglar Girit, Yuanbo Zhang, Zhao Hao, Hans A. Bechtel, Michael Martin, Alex Zettl, Michael F. Crommie, Y. Ron Shen, and Feng Wang, “ Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

2010 (2)

Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
[Crossref]

M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
[Crossref] [PubMed]

2006 (1)

G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).
[Crossref] [PubMed]

1997 (1)

E. Lidorikis, K. Busch, Qiming Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090 (1997).
[Crossref]

1987 (1)

S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Theory of the linear and nonlinear optical properties of semiconductor microcrystallites,” Phys. Rev. B 35, 8113–8125 (1987).
[Crossref]

1985 (1)

S. D. Smith, “Lasers, nonlinear optics and optical computers,” Nature 316, 319–324 (1985).
[Crossref]

1982 (1)

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

1978 (1)

R. Bonifacio and L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18, 1129–1144 (1978).
[Crossref]

Abraham, E.

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

Ahn, Jong-Hyun

Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
[Crossref]

Ahn, K.

M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
[Crossref] [PubMed]

Ahn, K. J.

I. H. Baek, K. J. Ahn, B. J. Kang, S. Bae, B. H. Hong, D.-I. Yeom, K. Lee, Y. U. Jeong, and F. Rotermund, “Terahertz transmission and sheet conductivity of randomly stacked multi-layer graphene,” Appl. Phys. Lett. 102, 191109 (2013).
[Crossref]

Ahn, Kwang Jun

In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
[Crossref]

Ahn, Y. H.

M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
[Crossref] [PubMed]

Asger Mortensen, N

Thomas Christensen, Wei Yan, Antti-Pekka Jauho, Martijn Wubs, and N Asger Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92, 121407(R) (2015).
[Crossref]

Bae, S.

I. H. Baek, K. J. Ahn, B. J. Kang, S. Bae, B. H. Hong, D.-I. Yeom, K. Lee, Y. U. Jeong, and F. Rotermund, “Terahertz transmission and sheet conductivity of randomly stacked multi-layer graphene,” Appl. Phys. Lett. 102, 191109 (2013).
[Crossref]

Bae, Sukang

In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
[Crossref]

Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
[Crossref]

Baek, I. H.

I. H. Baek, K. J. Ahn, B. J. Kang, S. Bae, B. H. Hong, D.-I. Yeom, K. Lee, Y. U. Jeong, and F. Rotermund, “Terahertz transmission and sheet conductivity of randomly stacked multi-layer graphene,” Appl. Phys. Lett. 102, 191109 (2013).
[Crossref]

Baek, In Hyung

In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
[Crossref]

Balakrishnan, Jayakumar

Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
[Crossref]

Bao, Qiaoliang

Qiaoliang Bao, Jianqiang Chen, Yuanjiang Xiang, Kai Zhang, Shaojuan Li, Xiaofang Jiang, Qing-Hua Xu, Kian Ping Loh, and T. Venkatesan, “ Graphene Nanobubbles: A new optical nonlinear material,” Adv. Optical Mater. 3, 744–749 (2015).
[Crossref]

Bechtel, Hans A.

Jason Horng, Chi-Fan Chen, Baisong Geng, Caglar Girit, Yuanbo Zhang, Zhao Hao, Hans A. Bechtel, Michael Martin, Alex Zettl, Michael F. Crommie, Y. Ron Shen, and Feng Wang, “ Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Bernien, H.

M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
[Crossref] [PubMed]

Bludov, Yu. V.

N. M. R. Peres, Yu. V. Bludov, Jaime E. Santos, Antti-Pekka Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
[Crossref]

Bonifacio, R.

R. Bonifacio and L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18, 1129–1144 (1978).
[Crossref]

Boyd, Robert W.

Robert W. Boyd, Nonlinear Optics (Elsevier Inc., 2008).

Busch, K.

E. Lidorikis, K. Busch, Qiming Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090 (1997).
[Crossref]

Carretero-Palacios, S.

Sergio G. Rodrigo, S. Carretero-Palacios, F. J. García-Vidal, and L. Martín-Moreno, “Metallic slit arrays filled with third-order nonlinear media: Optical Kerr effect and third-harmonic generation,” Phys. Rev. B 83, 235425 (2011).
[Crossref]

Chan, C. T.

E. Lidorikis, K. Busch, Qiming Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090 (1997).
[Crossref]

Chemla, D. S.

S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Theory of the linear and nonlinear optical properties of semiconductor microcrystallites,” Phys. Rev. B 35, 8113–8125 (1987).
[Crossref]

Chen, Chi-Fan

Jason Horng, Chi-Fan Chen, Baisong Geng, Caglar Girit, Yuanbo Zhang, Zhao Hao, Hans A. Bechtel, Michael Martin, Alex Zettl, Michael F. Crommie, Y. Ron Shen, and Feng Wang, “ Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Chen, Jianqiang

Qiaoliang Bao, Jianqiang Chen, Yuanjiang Xiang, Kai Zhang, Shaojuan Li, Xiaofang Jiang, Qing-Hua Xu, Kian Ping Loh, and T. Venkatesan, “ Graphene Nanobubbles: A new optical nonlinear material,” Adv. Optical Mater. 3, 744–749 (2015).
[Crossref]

Cheng, J. L.

J. L. Cheng, N. Vermeulen, and J. E. Sipe, “Third-order nonlinearity of graphene: Effects of phenomenological relaxation and finite temperature,” Phys. Rev. B 91, 235320 (2015).
[Crossref]

Choe, J. H.

M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
[Crossref] [PubMed]

Choi, Sun Young

In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
[Crossref]

Christensen, Thomas

Thomas Christensen, Wei Yan, Antti-Pekka Jauho, Martijn Wubs, and N Asger Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92, 121407(R) (2015).
[Crossref]

Colombo, L.

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

Crommie, Michael F.

Jason Horng, Chi-Fan Chen, Baisong Geng, Caglar Girit, Yuanbo Zhang, Zhao Hao, Hans A. Bechtel, Michael Martin, Alex Zettl, Michael F. Crommie, Y. Ron Shen, and Feng Wang, “ Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Dai, Xiaoyu

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

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

Yuanjiang Xiang, Xiaoyu Dai, Jun Guo, Shuangchun Wen, and Dingyuan Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,”, Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

Fal’ko, V. I.

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

García-Vidal, F. J.

Sergio G. Rodrigo, S. Carretero-Palacios, F. J. García-Vidal, and L. Martín-Moreno, “Metallic slit arrays filled with third-order nonlinear media: Optical Kerr effect and third-harmonic generation,” Phys. Rev. B 83, 235425 (2011).
[Crossref]

Gellert, P. R.

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

Geng, Baisong

Jason Horng, Chi-Fan Chen, Baisong Geng, Caglar Girit, Yuanbo Zhang, Zhao Hao, Hans A. Bechtel, Michael Martin, Alex Zettl, Michael F. Crommie, Y. Ron Shen, and Feng Wang, “ Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Girit, Caglar

Jason Horng, Chi-Fan Chen, Baisong Geng, Caglar Girit, Yuanbo Zhang, Zhao Hao, Hans A. Bechtel, Michael Martin, Alex Zettl, Michael F. Crommie, Y. Ron Shen, and Feng Wang, “ Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Gu, T.

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,” Nature Photon. 6, 554–559 (2012).
[Crossref]

Guo, Jun

Yuanjiang Xiang, Xiaoyu Dai, Jun Guo, Shuangchun Wen, and Dingyuan Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,”, Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

Hamm, Joachim

In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
[Crossref]

Hao, Zhao

Jason Horng, Chi-Fan Chen, Baisong Geng, Caglar Girit, Yuanbo Zhang, Zhao Hao, Hans A. Bechtel, Michael Martin, Alex Zettl, Michael F. Crommie, Y. Ron Shen, and Feng Wang, “ Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Hess, Ortwin

In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
[Crossref]

Hone, J.

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,” Nature Photon. 6, 554–559 (2012).
[Crossref]

Hong, B. H.

I. H. Baek, K. J. Ahn, B. J. Kang, S. Bae, B. H. Hong, D.-I. Yeom, K. Lee, Y. U. Jeong, and F. Rotermund, “Terahertz transmission and sheet conductivity of randomly stacked multi-layer graphene,” Appl. Phys. Lett. 102, 191109 (2013).
[Crossref]

Hong, Byung

In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
[Crossref]

Hong, Byung Hee

Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
[Crossref]

Horng, Jason

Jason Horng, Chi-Fan Chen, Baisong Geng, Caglar Girit, Yuanbo Zhang, Zhao Hao, Hans A. Bechtel, Michael Martin, Alex Zettl, Michael F. Crommie, Y. Ron Shen, and Feng Wang, “ Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
[Crossref]

Iijima, Sumio

Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
[Crossref]

Jauho, Antti-Pekka

Thomas Christensen, Wei Yan, Antti-Pekka Jauho, Martijn Wubs, and N Asger Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92, 121407(R) (2015).
[Crossref]

N. M. R. Peres, Yu. V. Bludov, Jaime E. Santos, Antti-Pekka Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
[Crossref]

Jeong, Y. U.

I. H. Baek, K. J. Ahn, B. J. Kang, S. Bae, B. H. Hong, D.-I. Yeom, K. Lee, Y. U. Jeong, and F. Rotermund, “Terahertz transmission and sheet conductivity of randomly stacked multi-layer graphene,” Appl. Phys. Lett. 102, 191109 (2013).
[Crossref]

Jeong, Young Uk

In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
[Crossref]

Jiang, Leyong

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

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

Jiang, Xiaofang

Qiaoliang Bao, Jianqiang Chen, Yuanjiang Xiang, Kai Zhang, Shaojuan Li, Xiaofang Jiang, Qing-Hua Xu, Kian Ping Loh, and T. Venkatesan, “ Graphene Nanobubbles: A new optical nonlinear material,” Adv. Optical Mater. 3, 744–749 (2015).
[Crossref]

Kang, B. J.

I. H. Baek, K. J. Ahn, B. J. Kang, S. Bae, B. H. Hong, D.-I. Yeom, K. Lee, Y. U. Jeong, and F. Rotermund, “Terahertz transmission and sheet conductivity of randomly stacked multi-layer graphene,” Appl. Phys. Lett. 102, 191109 (2013).
[Crossref]

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In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
[Crossref]

Kim, B. J.

M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
[Crossref] [PubMed]

Kim, D.-s.

M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
[Crossref] [PubMed]

Kim, H.-s.

M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
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Kim, H.-T.

M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
[Crossref] [PubMed]

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Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
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Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (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, 192–200 (2012).
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Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
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Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
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M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
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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,” Nature Photon. 6, 554–559 (2012).
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M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
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I. H. Baek, K. J. Ahn, B. J. Kang, S. Bae, B. H. Hong, D.-I. Yeom, K. Lee, Y. U. Jeong, and F. Rotermund, “Terahertz transmission and sheet conductivity of randomly stacked multi-layer graphene,” Appl. Phys. Lett. 102, 191109 (2013).
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Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
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Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
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E. Lidorikis, K. Busch, Qiming Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090 (1997).
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Qiaoliang Bao, Jianqiang Chen, Yuanjiang Xiang, Kai Zhang, Shaojuan Li, Xiaofang Jiang, Qing-Hua Xu, Kian Ping Loh, and T. Venkatesan, “ Graphene Nanobubbles: A new optical nonlinear material,” Adv. Optical Mater. 3, 744–749 (2015).
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Qiaoliang Bao, Jianqiang Chen, Yuanjiang Xiang, Kai Zhang, Shaojuan Li, Xiaofang Jiang, Qing-Hua Xu, Kian Ping Loh, and T. Venkatesan, “ Graphene Nanobubbles: A new optical nonlinear material,” Adv. Optical Mater. 3, 744–749 (2015).
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Sergio G. Rodrigo, S. Carretero-Palacios, F. J. García-Vidal, and L. Martín-Moreno, “Metallic slit arrays filled with third-order nonlinear media: Optical Kerr effect and third-harmonic generation,” Phys. Rev. B 83, 235425 (2011).
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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,” Nature Photon. 6, 554–559 (2012).
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In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
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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, 192–200 (2012).
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In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
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Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
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M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
[Crossref] [PubMed]

Park, Jae-Sung

Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
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M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
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M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
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N. M. R. Peres, Yu. V. Bludov, Jaime E. Santos, Antti-Pekka Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
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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,” Nature Photon. 6, 554–559 (2012).
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Jason Horng, Chi-Fan Chen, Baisong Geng, Caglar Girit, Yuanbo Zhang, Zhao Hao, Hans A. Bechtel, Michael Martin, Alex Zettl, Michael F. Crommie, Y. Ron Shen, and Feng Wang, “ Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
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In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
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N. M. R. Peres, Yu. V. Bludov, Jaime E. Santos, Antti-Pekka Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
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S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Theory of the linear and nonlinear optical properties of semiconductor microcrystallites,” Phys. Rev. B 35, 8113–8125 (1987).
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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, 192–200 (2012).
[Crossref] [PubMed]

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M. Seo, J. Kyoung, H. Park, S. Koo, H.-s. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-s. Kim, “Active terahertz nanoantennas based on VO2 phase transition,“ Nano Lett. 10, 2064–2068 (2010).
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Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros Özyilmaz, Jong-Hyun Ahn, Byung Hee Hong, and Sumio Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nature Nanotech. 5, 574–578 (2010).
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E. Lidorikis, K. Busch, Qiming Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090 (1997).
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Yuanjiang Xiang, Xiaoyu Dai, Jun Guo, Shuangchun Wen, and Dingyuan Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,”, Appl. Phys. Lett. 104, 051108 (2014).
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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,” Nature Photon. 6, 554–559 (2012).
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N. M. R. Peres, Yu. V. Bludov, Jaime E. Santos, Antti-Pekka Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
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Qiaoliang Bao, Jianqiang Chen, Yuanjiang Xiang, Kai Zhang, Shaojuan Li, Xiaofang Jiang, Qing-Hua Xu, Kian Ping Loh, and T. Venkatesan, “ Graphene Nanobubbles: A new optical nonlinear material,” Adv. Optical Mater. 3, 744–749 (2015).
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Jason Horng, Chi-Fan Chen, Baisong Geng, Caglar Girit, Yuanbo Zhang, Zhao Hao, Hans A. Bechtel, Michael Martin, Alex Zettl, Michael F. Crommie, Y. Ron Shen, and Feng Wang, “ Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011).
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Yuanjiang Xiang, Xiaoyu Dai, Jun Guo, Shuangchun Wen, and Dingyuan Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,”, Appl. Phys. Lett. 104, 051108 (2014).
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Thomas Christensen, Wei Yan, Antti-Pekka Jauho, Martijn Wubs, and N Asger Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92, 121407(R) (2015).
[Crossref]

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G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).
[Crossref] [PubMed]

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Xiaoyu Dai, Leyong Jiang, and Yuanjiang Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5, 12271 (2015).
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In Hyung Baek, Joachim Hamm, Kwang Jun Ahn, Bong Joo Kang, Sang Soon Oh, Sukang Bae, Sun Young Choi, Byung Hong, Dong-Il Yeom, Bumki Min, Ortwin Hess, Young Uk Jeong, and Fabian Rotermund, “Boosting the terahertz nonlinearity of graphene by orientation disorder,” 2D Mater. 4, 025035 (2017).
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Figures (4)

Fig. 1
Fig. 1

(a) The sample geometry considered in this study. Graphene with optical conductivity σg is sandwiched by two finite dielectric layers 1 and 2 with thicknesses d1 and d2. (b) THz OB of graphene at the interface between 1 = 3 = 2.25 and 2 = 4 = 1 (EF = 1.2 eV, ω = 2π THz). The hysteresis curve is bounded by two lines, Pt /Pi = Smax for σg = 0 and Pt /Pi = Smin for σ3 = 0. The critical powers for the up- and down-transition are read as Pu = 36.7 MW/cm2 and Pd = 27.8 MW/cm2, respectively.

Fig. 2
Fig. 2

(a) The second criterion for THz OB of graphene in single interface system (na = 1, nb = 1.5) as a function of frequency for different values of Fermi-energy. (b) THz OB of graphene for different values of EF for the same conditions as (a).

Fig. 3
Fig. 3

(a) THz OB of graphene in an asymmetric four-layered system. The physical parameters used are 1 = 2 = 1.552, 3 = 4 = 1.52, d1 = 200 nm, d2 = 2200 nm, and EF = 0.9 eV. (b) THz OB of a bilayer graphene in an asymmetric four-layered system. The physical parameters used are 1 = 2 = 1.552, 3 = 4 = 1.52, d1 = 600 nm, d2 = 4800 nm, and EF = 0.4 eV.

Fig. 4
Fig. 4

(a) THz OB of graphene in an asymmetric four-layered system for different values of thickness d1 with a fixed ratio d2/d1 = 11. Otherwise, the same physical parameters as Fig. 3(a) are used. (b) THz OB of graphene in an asymmetric four-layered system for different ratios d2/d1 with a fixed value of d1 = 200 nm. Otherwise, the same physical parameters as Fig. 3(a) are used.

Equations (13)

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E x ( z ) = { E 0 e i k 3 z ( z + d 1 ) + r e i k 3 z ( z + d 1 ) ( z < d 1 ) A 1 e i k 1 z z + B 1 e i k 1 z z ( d 1 < z < 0 ) A 2 e i k 2 z ( z d 2 ) + B e e i k 2 z ( z d 2 ) ( 0 < z < d 2 ) t e i k 4 z ( z d 2 ) ( z > d 2 ) ,
σ 1 ( ω ) = σ 1 r + i σ 1 i = 2 e 0 2 k B T π 2 i ω + i Γ log [ 2 cosh ( E F 2 k B T ) ]
σ 3 ( ω ) = 3 4 e 0 2 ( e 0 v F ) 2 π 2 E F { 2 ( Γ 2 + ω 2 ) ( Γ i ω ) + 1 ( Γ i ω ) 2 ( Γ 2 i ω ) }
σ 3 i = i 9 8 e 0 2 ( e 0 v F ) 2 π 2 E F ω 3 for ω Γ
E 0 = [ n 2 2 n 1 ( a 1 b 1 ) ( a 2 b 2 ) + 1 2 ( a 1 + b 1 ) ( a 2 + b 2 ) + Z 0 σ 1 2 n 1 ( a 1 b 1 ) ( a 2 + b 2 ) ] t Z 0 σ 3 2 n 1 ( a 1 b 1 ) ( a 2 + b 2 ) 3 t 3 = α t β t 3
a 1 = 1 2 ( 1 + k 1 z k 3 z ) e i k 1 z d 1 , b 1 = 1 2 ( 1 k 1 z k 3 z ) e i k 1 z d 1 ,
a 2 = 1 2 ( 1 + k 4 z k 2 z ) e i k 2 z d 2 , b 2 = 1 2 ( 1 k 4 z k 2 z ) e i k 2 z d 2 .
Y = | E 0 | 2 = | α | 2 t 2 ( α β * + α * β ) t 4 + | β | 2 t 6 = A X C X 2 + B X 3
d Y d X = 3 B X 2 2 C X + A = 0 X d / u = 1 3 B ( C ± C 2 3 A B ) .
C > C 2 3 A B and C 2 > 3 A B .
E 0 = [ 1 3 ( n a n b + 1 ) + Z 0 σ 1 r 2 n b + i Z 0 σ 1 i 2 n b ( 1 σ 3 i σ 1 i t 2 ) ] t .
| Z 0 σ 1 i | > 3 | ( n a + n b ) + Z 0 σ 1 r | .
X d / u = 1 3 σ 1 i σ 3 i ( 1 ± 1 ( n a + n b Z 0 σ 1 i ) 2 ) .