Abstract

We propose and numerically demonstrate that a reconfigurable nanocavity can be created in a graphene-loaded Si photonic crystal waveguide. The cavity formation is caused by the local mode-gap modulation induced by electrostatic gate-tuning of graphene. Although most recent graphene photonic devices are based on a change in the imaginary part of the refractive index, here we make use of a change in the real part of the refractive index for gated graphene. We clarify that nanocavities can be formed in two different cases, red-shifted and blue-shifted tunings. These novel formation mechanisms enable us to create and annihilate a nanocavity in a reconfigurable way by varying the gate voltage, which is promising for novel control in photonic processing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
  33. V. Narasimhan and S. -Y. Park, “An Ion Gel as a Low-Cost, Spin-Coatable, High-Capacitance Dielectric for Electrowetting-on-Dielectric (EWOD),” Langmuir 31(30), 8512–8518 (2015).
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    [Crossref]

2018 (1)

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

2016 (3)

H. Dalir, Y. Xia, Y. Wang, and X. Zhang, “Athermal broadband graphene optical modulator with 35 GHz speed,” ACS Photonics 3(9), 1564–1568 (2016).
[Crossref]

Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 Gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10(2), 307–316 (2016).
[Crossref]

M. T. Mihnev, F. Kadi, C. J. Divin, T. Winzer, S. Lee, C.-H. Liu, Z. Zhong, C. Berger, W. A. de Heer, E. Malic, A. Knorr, and T. B. Norris, “Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene,” Nat. Commun. 7(1), 11617 (2016).
[Crossref]

2015 (3)

M. Mohsin, D. Neumaier, D. Schall, M. Otto, C. Matheisen, A. L. Giesecke, A. A. Sagade, and H. Kurz, “Experimental verification of electro-refractive phase modulation in graphene,” Sci. Rep. 5(1), 10967 (2015).
[Crossref]

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9(8), 511–514 (2015).
[Crossref]

V. Narasimhan and S. -Y. Park, “An Ion Gel as a Low-Cost, Spin-Coatable, High-Capacitance Dielectric for Electrowetting-on-Dielectric (EWOD),” Langmuir 31(30), 8512–8518 (2015).
[Crossref]

2014 (1)

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

2013 (1)

X. Gan, R. J. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, A. Szep, D. Walker Jr, J. Hone, T. F. Heinz, and D. Englund, “High-contrast electrooptic modulation of a photonic crystal nanocavity by electrical gating of graphene,” Nano Lett. 13(2), 691–696 (2013).
[Crossref]

2012 (2)

K. H. Lee, M. S. Kang, S. Zhang, Y. Gu, T. P. Lodge, and C. D. Frisbe, “Cut and Stick Rubbery Ion Gels as High Capacitance Gate Dielectrics,” Adv. Mater. 24(32), 4457–4462 (2012).
[Crossref]

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[Crossref]

2011 (6)

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]

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).
[Crossref]

T. C. Nguyen, M. Otani, and S. Okada, “Semiconducting Electronic Property of Graphene Adsorbed on (0001) Surfaces of SiO2,” Phys. Rev. Lett. 106(10), 106801 (2011).
[Crossref]

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref]

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]

A. Yokoo, T. Tanabe, E. Kuramochi, and M. Notomi, “Ultrahigh-Q nanocavities written with a nanoprobe,” Nano Lett. 11(9), 3634–3642 (2011).
[Crossref]

2010 (4)

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73(9), 096501 (2010).
[Crossref]

B. J. Kim, H. Jang, S. K. Lee, B. H. Hong, J. H. Ahn, and J. H. Cho, “High-performance flexible graphene field effect transistors with ion gel gate dielectrics,” Nano Lett. 10(9), 3464–3466 (2010).
[Crossref]

H. Wang, J. H. Strait, P. A. George, S. Shivaraman, V. B. Shields, M. Chandrashekhar, J. Hwang, F. Rana, M. G. Spencer, C. S. Ruiz-Vargas, and J. Park, “Ultrafast relaxation dynamics of hot optical phonons in graphene,” Appl. Phys. Lett. 96(8), 081917 (2010).
[Crossref]

F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97(25), 253110 (2010).
[Crossref]

2008 (4)

W.-K. Tse, E. H. Hwang, and S. D. Sarma, “Ballistic hot electron transport in graphene,” Appl. Phys. Lett. 93(2), 023128 (2008).
[Crossref]

J. H. Cho, J. Lee, Y. Xia, B. Kim, Y. He, M. J. Renn, T. P. Lodge, and C. D. Frisbie, “Printable ion-gel gate dielectrics for low-voltage polymer thin-film transistors on plastic,” Nat. Mater. 7(11), 900–906 (2008).
[Crossref]

M. Notomi and H. Taniyama, “On-demand ultrahigh-Q cavity formation and photon pinning via dynamic waveguide tuning,” Opt. Express 16(23), 18657–18666 (2008).
[Crossref]

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]

2007 (6)

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1(1), 49–52 (2007).
[Crossref]

Y. Takahashi, H. Hagino, Y. Tanaka, B.-S. Song, T. Asano, and S. Noda, “High-Q nanocavity with a 2-ns photon lifetime,” Opt. Express 15(25), 17206–17213 (2007).
[Crossref]

S. Tomljenovic-Hanic, M. J. Steel, C. Martijn de Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Opt. Lett. 32(5), 542–544 (2007).
[Crossref]

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. D. Sarma, H. L. Stormer, and P. Kim, “Measurement of Scattering Rate and Minimum Conductivity in Graphene,” Phys. Rev. Lett. 99(24), 246803 (2007).
[Crossref]

J. Lee, M. J. Panzer, Y. He, T. P. Lodge, and C. D. Frisbie, “Ion gel gated polymer thin-film transistors,” J. Am. Chem. Soc. 129(15), 4532–4533 (2007).
[Crossref]

2006 (2)

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[Crossref]

R. Herrmann, T. Sunner, T. Hein, A. Loffler, M. Kamp, and A. Forchel, “Ultrahigh-quality photonic crystal cavity in GaAs,” Opt. Lett. 31(9), 1229–1231 (2006).
[Crossref]

2005 (1)

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

Absil, P.

Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 Gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10(2), 307–316 (2016).
[Crossref]

Adam, S.

Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. D. Sarma, H. L. Stormer, and P. Kim, “Measurement of Scattering Rate and Minimum Conductivity in Graphene,” Phys. Rev. Lett. 99(24), 246803 (2007).
[Crossref]

Ahn, J. H.

B. J. Kim, H. Jang, S. K. Lee, B. H. Hong, J. H. Ahn, and J. H. Cho, “High-performance flexible graphene field effect transistors with ion gel gate dielectrics,” Nano Lett. 10(9), 3464–3466 (2010).
[Crossref]

Akahane, Y.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

Asano, T.

Y. Takahashi, H. Hagino, Y. Tanaka, B.-S. Song, T. Asano, and S. Noda, “High-Q nanocavity with a 2-ns photon lifetime,” Opt. Express 15(25), 17206–17213 (2007).
[Crossref]

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

Asselberghs, I.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 Gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10(2), 307–316 (2016).
[Crossref]

Bao, J.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

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]

Berger, C.

M. T. Mihnev, F. Kadi, C. J. Divin, T. Winzer, S. Lee, C.-H. Liu, Z. Zhong, C. Berger, W. A. de Heer, E. Malic, A. Knorr, and T. B. Norris, “Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene,” Nat. Commun. 7(1), 11617 (2016).
[Crossref]

Bolotin, K.

Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. D. Sarma, H. L. Stormer, and P. Kim, “Measurement of Scattering Rate and Minimum Conductivity in Graphene,” Phys. Rev. Lett. 99(24), 246803 (2007).
[Crossref]

Boudouris, B. W.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref]

Brems, S.

Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 Gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10(2), 307–316 (2016).
[Crossref]

Breusing, M.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).
[Crossref]

Cardenas, J.

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9(8), 511–514 (2015).
[Crossref]

Chandrashekhar, M.

H. Wang, J. H. Strait, P. A. George, S. Shivaraman, V. B. Shields, M. Chandrashekhar, J. Hwang, F. Rana, M. G. Spencer, C. S. Ruiz-Vargas, and J. Park, “Ultrafast relaxation dynamics of hot optical phonons in graphene,” Appl. Phys. Lett. 96(8), 081917 (2010).
[Crossref]

Chen, B.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

Chen, C. F.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref]

Cho, J. H.

B. J. Kim, H. Jang, S. K. Lee, B. H. Hong, J. H. Ahn, and J. H. Cho, “High-performance flexible graphene field effect transistors with ion gel gate dielectrics,” Nano Lett. 10(9), 3464–3466 (2010).
[Crossref]

J. H. Cho, J. Lee, Y. Xia, B. Kim, Y. He, M. J. Renn, T. P. Lodge, and C. D. Frisbie, “Printable ion-gel gate dielectrics for low-voltage polymer thin-film transistors on plastic,” Nat. Mater. 7(11), 900–906 (2008).
[Crossref]

Comfort, E. S.

F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97(25), 253110 (2010).
[Crossref]

Contestabile, G.

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Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 Gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10(2), 307–316 (2016).
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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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M. T. Mihnev, F. Kadi, C. J. Divin, T. Winzer, S. Lee, C.-H. Liu, Z. Zhong, C. Berger, W. A. de Heer, E. Malic, A. Knorr, and T. B. Norris, “Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene,” Nat. Commun. 7(1), 11617 (2016).
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Kang, M. S.

K. H. Lee, M. S. Kang, S. Zhang, Y. Gu, T. P. Lodge, and C. D. Frisbe, “Cut and Stick Rubbery Ion Gels as High Capacitance Gate Dielectrics,” Adv. Mater. 24(32), 4457–4462 (2012).
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J. H. Cho, J. Lee, Y. Xia, B. Kim, Y. He, M. J. Renn, T. P. Lodge, and C. D. Frisbie, “Printable ion-gel gate dielectrics for low-voltage polymer thin-film transistors on plastic,” Nat. Mater. 7(11), 900–906 (2008).
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B. J. Kim, H. Jang, S. K. Lee, B. H. Hong, J. H. Ahn, and J. H. Cho, “High-performance flexible graphene field effect transistors with ion gel gate dielectrics,” Nano Lett. 10(9), 3464–3466 (2010).
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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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M. T. Mihnev, F. Kadi, C. J. Divin, T. Winzer, S. Lee, C.-H. Liu, Z. Zhong, C. Berger, W. A. de Heer, E. Malic, A. Knorr, and T. B. Norris, “Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene,” Nat. Commun. 7(1), 11617 (2016).
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M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).
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J. H. Cho, J. Lee, Y. Xia, B. Kim, Y. He, M. J. Renn, T. P. Lodge, and C. D. Frisbie, “Printable ion-gel gate dielectrics for low-voltage polymer thin-film transistors on plastic,” Nat. Mater. 7(11), 900–906 (2008).
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J. Lee, M. J. Panzer, Y. He, T. P. Lodge, and C. D. Frisbie, “Ion gel gated polymer thin-film transistors,” J. Am. Chem. Soc. 129(15), 4532–4533 (2007).
[Crossref]

Lee, J. U.

F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97(25), 253110 (2010).
[Crossref]

Lee, K. H.

K. H. Lee, M. S. Kang, S. Zhang, Y. Gu, T. P. Lodge, and C. D. Frisbe, “Cut and Stick Rubbery Ion Gels as High Capacitance Gate Dielectrics,” Adv. Mater. 24(32), 4457–4462 (2012).
[Crossref]

Lee, S.

M. T. Mihnev, F. Kadi, C. J. Divin, T. Winzer, S. Lee, C.-H. Liu, Z. Zhong, C. Berger, W. A. de Heer, E. Malic, A. Knorr, and T. B. Norris, “Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene,” Nat. Commun. 7(1), 11617 (2016).
[Crossref]

Lee, S. K.

B. J. Kim, H. Jang, S. K. Lee, B. H. Hong, J. H. Ahn, and J. H. Cho, “High-performance flexible graphene field effect transistors with ion gel gate dielectrics,” Nano Lett. 10(9), 3464–3466 (2010).
[Crossref]

Lee, Y. H. D.

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9(8), 511–514 (2015).
[Crossref]

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X. Gan, R. J. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, A. Szep, D. Walker Jr, J. Hone, T. F. Heinz, and D. Englund, “High-contrast electrooptic modulation of a photonic crystal nanocavity by electrical gating of graphene,” Nano Lett. 13(2), 691–696 (2013).
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W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

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W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

Li, Z. Q.

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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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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C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9(8), 511–514 (2015).
[Crossref]

I. Datta, C. T. Phare, A. Dutt, A. Mohanty, and M. Lipson, “Integrated Graphene Electro-Optic Phase Modulator,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper STu3N.5.

Liu, C.-H.

M. T. Mihnev, F. Kadi, C. J. Divin, T. Winzer, S. Lee, C.-H. Liu, Z. Zhong, C. Berger, W. A. de Heer, E. Malic, A. Knorr, and T. B. Norris, “Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene,” Nat. Commun. 7(1), 11617 (2016).
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M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[Crossref]

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]

Liu, W.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref]

Lodge, T. P.

K. H. Lee, M. S. Kang, S. Zhang, Y. Gu, T. P. Lodge, and C. D. Frisbe, “Cut and Stick Rubbery Ion Gels as High Capacitance Gate Dielectrics,” Adv. Mater. 24(32), 4457–4462 (2012).
[Crossref]

J. H. Cho, J. Lee, Y. Xia, B. Kim, Y. He, M. J. Renn, T. P. Lodge, and C. D. Frisbie, “Printable ion-gel gate dielectrics for low-voltage polymer thin-film transistors on plastic,” Nat. Mater. 7(11), 900–906 (2008).
[Crossref]

J. Lee, M. J. Panzer, Y. He, T. P. Lodge, and C. D. Frisbie, “Ion gel gated polymer thin-film transistors,” J. Am. Chem. Soc. 129(15), 4532–4533 (2007).
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Loh, K. P.

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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C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref]

Mak, K. F.

X. Gan, R. J. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, A. Szep, D. Walker Jr, J. Hone, T. F. Heinz, and D. Englund, “High-contrast electrooptic modulation of a photonic crystal nanocavity by electrical gating of graphene,” Nano Lett. 13(2), 691–696 (2013).
[Crossref]

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M. T. Mihnev, F. Kadi, C. J. Divin, T. Winzer, S. Lee, C.-H. Liu, Z. Zhong, C. Berger, W. A. de Heer, E. Malic, A. Knorr, and T. B. Norris, “Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene,” Nat. Commun. 7(1), 11617 (2016).
[Crossref]

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).
[Crossref]

Martijn de Sterke, C.

Martin, M. C.

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]

Matheisen, C.

M. Mohsin, D. Neumaier, D. Schall, M. Otto, C. Matheisen, A. L. Giesecke, A. A. Sagade, and H. Kurz, “Experimental verification of electro-refractive phase modulation in graphene,” Sci. Rep. 5(1), 10967 (2015).
[Crossref]

Meng, C.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
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Figures (7)

Fig. 1.
Fig. 1. The complex refractive index of graphene as a function of the Fermi level. The black and red lines show the real and imaginary part of the refractive index. The blue line shows the normalized sheet conductivity representing the absorption loss in graphene.
Fig. 2.
Fig. 2. Local modulation of the mode gap induced by the refractive-index modulation of graphene. The light green area illustrates the frequency range of the mode gap along the PhC line-defect waveguide. (Left) Red-shift tuning. A nanocavity mode is created in the center region where the mode-gap edge is shifted lower. (Center) No cavity is formed. (Right) Blue-shift tuning. A nanocavity is created in the center region. The mode-gap edge of the surrounding barrier regions is shifted higher.
Fig. 3.
Fig. 3. Schematic of a graphene-loaded PhC waveguide. Graphene is loaded on the surface of the PhC waveguide in the green-shaded region.
Fig. 4.
Fig. 4. Cavity formation using the red-shift modulation. Graphene is loaded on the central region. (a, b, c) Electric field distribution Ey of Si PhC waveguide (a) without graphene, (b) with graphene (EF = 0.40 eV), and (c) with graphene (EF = 0.48 eV). The green area shows the graphene. (d) Calculated cavity wavelength as a function of the Fermi level. The shaded area shows the mode gap. (e) Calculated Q and effective mode volume as a function of the Fermi level. Blank squares indicate that the simulated values do not show enough convergence.
Fig. 5.
Fig. 5. Cavity formation using the blue shift modulation. Graphene is loaded on two barrier regions. (a, b) Electric field distribution Ey of a graphene-loaded Si PhC waveguide at (a) EF = 0.48 eV and (b) EF = 0.80 eV (The green area shows graphene. (c) Calculated Q and effective mode volume as a function of the Fermi level. Blank squares indicate that the simulated values do not show enough convergence. (d) Calculated cavity wavelength as a function of the Fermi level.
Fig. 6.
Fig. 6. Calculated the dependences of cavity performance on the cavity length about red-shift modulation with EF = 0.40 eV and 0.42 eV. (a) Effective mode volume. (b) Q factor.
Fig. 7.
Fig. 7. Calculated the dependences of cavity performance on the cavity length about blue-shift modulation with EF = 0.70 eV and 0.80 eV. (a) Effective mode volume. (b) Q factor.

Equations (5)

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σ i n t e r = σ 0 2 ( t a n h ( ( ω + 2 | E F | ) 2 4 k B T ) + t a n h ( ( ω 2 | E F | ) 2 4 k B T ) ) i σ 0 2 π l n [ ( ω + 2 | E F | ) 2 ( ω 2 | E F | ) 2 + ( 2 k B T ) 2 ]
σ i n t r a = i k B T 8 σ 0 π ( ω + i τ 1 ) [ E F k B T + 2 l n ( e x p ( E F k B T + 1 ) ]
σ 0 = e 2 / 4 2
ε = ε 0 + i σ i n t e r + σ i n t r a t ω
n = μ ε / μ 0 ε 0

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