Abstract

The suspended triple-layer graphene modulator is firstly investigated theoretically. We find there appear two modulation depths for electro-absorption modulation. The light-graphene interaction is enhanced to its maximum by our designed waveguide structure. The highest modulation depth for electro-absorption modulation can be 0.834 dB/µm, causing a 3-dB footprint of only 0.94 µm2. For electro-refractive modulation, there appear several 100% modulations with a much smaller π-phase shift length of only 11.3 µm. This modulator also shows great potential for high-speed modulation with a prediction value of 759.85 GHz, while the switch energy can be as low as 0.61 fJ/bit with low applied voltage. Moreover, the verification simulation by COMSOL is also presented, which shows very good agreement with our calculation results, and the figure of merit (defined as the ratio of modulation depth to insertion loss) of this modulator can be 2105. We believe these results can pave the way to design practical high-speed, compact-footprint, and high-efficiency devices.

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

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  30. J. Liu, H. Liang, M. Zhang, and H. Su, “THz wave in double-metal-film waveguides and its application of analysis wavelength,” Appl. Opt. 54(28), 8406–8411 (2015).
    [Crossref]
  31. C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on Graphene-Oxide-Silicon waveguide,” Opt. Express 20(20), 22398–22405 (2012).
    [Crossref]
  32. C.-C. Lee, S. Suzuki, W. Xie, and T. R. Schibli, “Broadband graphene electro-optic modulators with sub-wavelength thickness,” Opt. Express 20(5), 5264–5269 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref]
  35. F. Xia, V. Perebeinos, Y. Lin, Y. Wu, and P. Avouris, “The origins and limits of metal–graphene junction resistance,” Nat. Nanotechnol. 6(3), 179–184 (2011).
    [Crossref]
  36. G. Kovacevica and S. Yamashita, “Design optimizations for a high-speed two-layer graphene optical modulator on silicon,” IEICE Electron. Express 13(14), 20160499 (2016).
    [Crossref]

2018 (1)

J. Liu and Y. Liu, “Ultrafast suspended self-biasing graphene modulator with ultrahigh figure of merit,” Opt. Commun. 427, 439–446 (2018).
[Crossref]

2017 (3)

Y. Ding, X. Guan, X. Zhu, H. Hu, S. I. Bozhevolnyi, L. K. Oxenløwe, N. A. Mortensen, and S. Xiao, “Efficient graphene based electro-optical modulator enabled by interfacing plasmonic slot and silicon waveguides,” Nanoscale 9(40), 15576–15581 (2017).
[Crossref]

X. Hu and J. Wang, “High figure of merit graphene modulator based on long-range hybrid plasmonic slot waveguide,” IEEE J. Quantum Electron. 53(3), 1–8 (2017).
[Crossref]

M. Fan, H. Yang, P. Zheng, G. Hu, B. Yun, and Y. Cui, “Multilayer graphene electro-absorption optical modulator based on double-stripe silicon nitride waveguide,” Opt. Express 25(18), 21619–21629 (2017).
[Crossref]

2016 (4)

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

H. Dalir, Y. Xia, Y. Wang, and X. Zhang, “Athermal Broadband Graphene Optical Modulator with 35 GHz Speed,” ACS Photon. 3(9), 1564–1568 (2016).
[Crossref]

R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
[Crossref]

G. Kovacevica and S. Yamashita, “Design optimizations for a high-speed two-layer graphene optical modulator on silicon,” IEICE Electron. Express 13(14), 20160499 (2016).
[Crossref]

2015 (5)

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]

J. Liu, H. Liang, M. Zhang, and H. Su, “THz wave transmission within the metal-clad antiresonant reflecting hollow waveguides,” Appl. Opt. 54(14), 4549–4555 (2015).
[Crossref]

J. Liu, H. Liang, M. Zhang, and H. Su, “THz wave transmission within the metal film coated double-dielectric-slab waveguides and the tunable filter application,” Opt. Commun. 351, 103–108 (2015).
[Crossref]

J. Liu, H. Liang, M. Zhang, and H. Su, “THz wave in double-metal-film waveguides and its application of analysis wavelength,” Appl. Opt. 54(28), 8406–8411 (2015).
[Crossref]

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, S. F. Yu, and Q. J. Wang, “Integrated Terahertz Graphene Modulator with 100% Modulation Depth,” ACS Photon. 2(11), 1559–1566 (2015).
[Crossref]

2014 (6)

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. Javier García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

L. Yang, T. Hu, A. Shen, C. Pei, B. Yang, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Ultracompact optical modulator based on graphene-silica metamaterial,” Opt. Lett. 39(7), 1909–1912 (2014).
[Crossref]

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]

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref]

S. Ye, Z. Wang, L. Tang, Y. Zhang, R. Lu, and Y. Liu, “Electro-absorption optical modulator using dual-graphene-on-graphene configuration,” Opt. Express 22(21), 26173–26180 (2014).
[Crossref]

M. Tamagnone, A. Fallahi, J. R. Mosig, and J. Perruisseau-Carrier, “Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices,” Nat. Photonics 8(7), 556–563 (2014).
[Crossref]

2013 (3)

R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
[Crossref]

J. Gosciniak and D. T. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24(18), 185202 (2013).
[Crossref]

Z.-B. Liu, M. Feng, W.-S. Jiang, W. Xin, P. Wang, Q.-W. Sheng, Y.-G. Liu, D. N. Wang, W.-Y. Zhou, and J.-G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

2012 (5)

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

S. J. Koester and M. Li, “High-speed waveguide-coupled graphene-on-graphene optical modulators,” Appl. Phys. Lett. 100(17), 171107 (2012).
[Crossref]

C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on Graphene-Oxide-Silicon waveguide,” Opt. Express 20(20), 22398–22405 (2012).
[Crossref]

C.-C. Lee, S. Suzuki, W. Xie, and T. R. Schibli, “Broadband graphene electro-optic modulators with sub-wavelength thickness,” Opt. Express 20(5), 5264–5269 (2012).
[Crossref]

N. K. Emani, T. F. Chung, X. J. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltasseva, “Electrically Tunable Damping of Plasmonic Resonances with Graphene,” Nano Lett. 12(10), 5202–5206 (2012).
[Crossref]

2011 (2)

F. Xia, V. Perebeinos, Y. Lin, Y. Wu, and P. Avouris, “The origins and limits of metal–graphene junction resistance,” Nat. Nanotechnol. 6(3), 179–184 (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]

2009 (1)

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

2008 (2)

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
[Crossref]

X. Du, I. Skachko, A. Barker, and E. Andrei, “Approaching ballistic transport in suspended graphene,” Nat. Nanotechnol. 3(8), 491–495 (2008).
[Crossref]

2007 (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

2001 (2)

R. Mendis and D. Grischkowsky, “THz interconnect with low-loss and low-group velocity dispersion,” IEEE Microw. Wireless Compon. Lett. 11(11), 444–446 (2001).
[Crossref]

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-κ gate dielectrics: Current status and materials properties considerations,” J. Appl. Phys. 89(10), 5243–5275 (2001).
[Crossref]

Absil, P.

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

Ajayan, P. M.

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. Javier García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

An, J.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

Andrei, E.

X. Du, I. Skachko, A. Barker, and E. Andrei, “Approaching ballistic transport in suspended graphene,” Nat. Nanotechnol. 3(8), 491–495 (2008).
[Crossref]

Anthony, J. M.

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-κ gate dielectrics: Current status and materials properties considerations,” J. Appl. Phys. 89(10), 5243–5275 (2001).
[Crossref]

Asselberghs, I.

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

Avouris, P.

F. Xia, V. Perebeinos, Y. Lin, Y. Wu, and P. Avouris, “The origins and limits of metal–graphene junction resistance,” Nat. Nanotechnol. 6(3), 179–184 (2011).
[Crossref]

Banerjee, S. K.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[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]

Barker, A.

X. Du, I. Skachko, A. Barker, and E. Andrei, “Approaching ballistic transport in suspended graphene,” Nat. Nanotechnol. 3(8), 491–495 (2008).
[Crossref]

Bolotin, K. I.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
[Crossref]

Boltasseva, A.

N. K. Emani, T. F. Chung, X. J. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltasseva, “Electrically Tunable Damping of Plasmonic Resonances with Graphene,” Nano Lett. 12(10), 5202–5206 (2012).
[Crossref]

Bozhevolnyi, S. I.

Y. Ding, X. Guan, X. Zhu, H. Hu, S. I. Bozhevolnyi, L. K. Oxenløwe, N. A. Mortensen, and S. Xiao, “Efficient graphene based electro-optical modulator enabled by interfacing plasmonic slot and silicon waveguides,” Nanoscale 9(40), 15576–15581 (2017).
[Crossref]

Brems, S.

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

Cai, W.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

Campenhout, J. V.

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

Capasso, F.

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref]

Carbotte, J. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[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]

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, H.

R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
[Crossref]

Chen, Y. P.

N. K. Emani, T. F. Chung, X. J. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltasseva, “Electrically Tunable Damping of Plasmonic Resonances with Graphene,” Nano Lett. 12(10), 5202–5206 (2012).
[Crossref]

Chung, T. F.

N. K. Emani, T. F. Chung, X. J. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltasseva, “Electrically Tunable Damping of Plasmonic Resonances with Graphene,” Nano Lett. 12(10), 5202–5206 (2012).
[Crossref]

Colombo, L.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

Cui, Y.

Dai, T.

Dalir, H.

H. Dalir, Y. Xia, Y. Wang, and X. Zhang, “Athermal Broadband Graphene Optical Modulator with 35 GHz Speed,” ACS Photon. 3(9), 1564–1568 (2016).
[Crossref]

Davies, A. G.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, S. F. Yu, and Q. J. Wang, “Integrated Terahertz Graphene Modulator with 100% Modulation Depth,” ACS Photon. 2(11), 1559–1566 (2015).
[Crossref]

Ding, Y.

Y. Ding, X. Guan, X. Zhu, H. Hu, S. I. Bozhevolnyi, L. K. Oxenløwe, N. A. Mortensen, and S. Xiao, “Efficient graphene based electro-optical modulator enabled by interfacing plasmonic slot and silicon waveguides,” Nanoscale 9(40), 15576–15581 (2017).
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R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
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Du, X.

X. Du, I. Skachko, A. Barker, and E. Andrei, “Approaching ballistic transport in suspended graphene,” Nat. Nanotechnol. 3(8), 491–495 (2008).
[Crossref]

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N. K. Emani, T. F. Chung, X. J. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltasseva, “Electrically Tunable Damping of Plasmonic Resonances with Graphene,” Nano Lett. 12(10), 5202–5206 (2012).
[Crossref]

Fallahi, A.

M. Tamagnone, A. Fallahi, J. R. Mosig, and J. Perruisseau-Carrier, “Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices,” Nat. Photonics 8(7), 556–563 (2014).
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Fang, 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]

Fang, Z.

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. Javier García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

Feng, M.

Z.-B. Liu, M. Feng, W.-S. Jiang, W. Xin, P. Wang, Q.-W. Sheng, Y.-G. Liu, D. N. Wang, W.-Y. Zhou, and J.-G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
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K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
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M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
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J. Gosciniak and D. T. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24(18), 185202 (2013).
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R. Mendis and D. Grischkowsky, “THz interconnect with low-loss and low-group velocity dispersion,” IEEE Microw. Wireless Compon. Lett. 11(11), 444–446 (2001).
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Y. Ding, X. Guan, X. Zhu, H. Hu, S. I. Bozhevolnyi, L. K. Oxenløwe, N. A. Mortensen, and S. Xiao, “Efficient graphene based electro-optical modulator enabled by interfacing plasmonic slot and silicon waveguides,” Nanoscale 9(40), 15576–15581 (2017).
[Crossref]

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V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
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Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. Javier García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

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R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
[Crossref]

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R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
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R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
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K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
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R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
[Crossref]

Hu, G.

Hu, H.

Y. Ding, X. Guan, X. Zhu, H. Hu, S. I. Bozhevolnyi, L. K. Oxenløwe, N. A. Mortensen, and S. Xiao, “Efficient graphene based electro-optical modulator enabled by interfacing plasmonic slot and silicon waveguides,” Nanoscale 9(40), 15576–15581 (2017).
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Hu, X.

X. Hu and J. Wang, “High figure of merit graphene modulator based on long-range hybrid plasmonic slot waveguide,” IEEE J. Quantum Electron. 53(3), 1–8 (2017).
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G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, S. F. Yu, and Q. J. Wang, “Integrated Terahertz Graphene Modulator with 100% Modulation Depth,” ACS Photon. 2(11), 1559–1566 (2015).
[Crossref]

Hu, Y.

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

Hu, Z.

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]

Huyghebaert, C.

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

Javier García de Abajo, F.

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. Javier García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

Jiang, W.-S.

Z.-B. Liu, M. Feng, W.-S. Jiang, W. Xin, P. Wang, Q.-W. Sheng, Y.-G. Liu, D. N. Wang, W.-Y. Zhou, and J.-G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Jiang, X.

Jiang, Z.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
[Crossref]

Jin, X.

R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
[Crossref]

Jin, Y.

Ju, L.

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]

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X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
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Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref]

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N. K. Emani, T. F. Chung, X. J. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltasseva, “Electrically Tunable Damping of Plasmonic Resonances with Graphene,” Nano Lett. 12(10), 5202–5206 (2012).
[Crossref]

Kim, P.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
[Crossref]

Kim, S.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
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Klima, M.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
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R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
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S. J. Koester and M. Li, “High-speed waveguide-coupled graphene-on-graphene optical modulators,” Appl. Phys. Lett. 100(17), 171107 (2012).
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Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
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Kou, R.

R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
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G. Kovacevica and S. Yamashita, “Design optimizations for a high-speed two-layer graphene optical modulator on silicon,” IEICE Electron. Express 13(14), 20160499 (2016).
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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).
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Li, E.

R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
[Crossref]

Li, L. H.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, S. F. Yu, and Q. J. Wang, “Integrated Terahertz Graphene Modulator with 100% Modulation Depth,” ACS Photon. 2(11), 1559–1566 (2015).
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S. J. Koester and M. Li, “High-speed waveguide-coupled graphene-on-graphene optical modulators,” Appl. Phys. Lett. 100(17), 171107 (2012).
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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, X.

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]

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
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Li, Y.

Liang, G.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, S. F. Yu, and Q. J. Wang, “Integrated Terahertz Graphene Modulator with 100% Modulation Depth,” ACS Photon. 2(11), 1559–1566 (2015).
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Liang, H. K.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, S. F. Yu, and Q. J. Wang, “Integrated Terahertz Graphene Modulator with 100% Modulation Depth,” ACS Photon. 2(11), 1559–1566 (2015).
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Lin, Y.

F. Xia, V. Perebeinos, Y. Lin, Y. Wu, and P. Avouris, “The origins and limits of metal–graphene junction resistance,” Nat. Nanotechnol. 6(3), 179–184 (2011).
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Linfield, E. H.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, S. F. Yu, and Q. J. Wang, “Integrated Terahertz Graphene Modulator with 100% Modulation Depth,” ACS Photon. 2(11), 1559–1566 (2015).
[Crossref]

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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).
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J. Liu and Y. Liu, “Ultrafast suspended self-biasing graphene modulator with ultrahigh figure of merit,” Opt. Commun. 427, 439–446 (2018).
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J. Liu, H. Liang, M. Zhang, and H. Su, “THz wave transmission within the metal film coated double-dielectric-slab waveguides and the tunable filter application,” Opt. Commun. 351, 103–108 (2015).
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J. Liu, H. Liang, M. Zhang, and H. Su, “THz wave in double-metal-film waveguides and its application of analysis wavelength,” Appl. Opt. 54(28), 8406–8411 (2015).
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J. Liu, H. Liang, M. Zhang, and H. Su, “THz wave transmission within the metal-clad antiresonant reflecting hollow waveguides,” Appl. Opt. 54(14), 4549–4555 (2015).
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Liu, M.

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]

Liu, Y.

J. Liu and Y. Liu, “Ultrafast suspended self-biasing graphene modulator with ultrahigh figure of merit,” Opt. Commun. 427, 439–446 (2018).
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S. Ye, Z. Wang, L. Tang, Y. Zhang, R. Lu, and Y. Liu, “Electro-absorption optical modulator using dual-graphene-on-graphene configuration,” Opt. Express 22(21), 26173–26180 (2014).
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Liu, Y.-G.

Z.-B. Liu, M. Feng, W.-S. Jiang, W. Xin, P. Wang, Q.-W. Sheng, Y.-G. Liu, D. N. Wang, W.-Y. Zhou, and J.-G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Liu, Z.

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. Javier García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

Liu, Z.-B.

Z.-B. Liu, M. Feng, W.-S. Jiang, W. Xin, P. Wang, Q.-W. Sheng, Y.-G. Liu, D. N. Wang, W.-Y. Zhou, and J.-G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Loncar, M.

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref]

Lu, R.

Mendis, R.

R. Mendis and D. Grischkowsky, “THz interconnect with low-loss and low-group velocity dispersion,” IEEE Microw. Wireless Compon. Lett. 11(11), 444–446 (2001).
[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).
[Crossref]

Mortensen, N. A.

Y. Ding, X. Guan, X. Zhu, H. Hu, S. I. Bozhevolnyi, L. K. Oxenløwe, N. A. Mortensen, and S. Xiao, “Efficient graphene based electro-optical modulator enabled by interfacing plasmonic slot and silicon waveguides,” Nanoscale 9(40), 15576–15581 (2017).
[Crossref]

Mosig, J. R.

M. Tamagnone, A. Fallahi, J. R. Mosig, and J. Perruisseau-Carrier, “Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices,” Nat. Photonics 8(7), 556–563 (2014).
[Crossref]

Nah, J.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

Nakajima, H.

R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
[Crossref]

Ni, X. J.

N. K. Emani, T. F. Chung, X. J. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltasseva, “Electrically Tunable Damping of Plasmonic Resonances with Graphene,” Nano Lett. 12(10), 5202–5206 (2012).
[Crossref]

Nordlander, P.

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. Javier García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

Oxenløwe, L. K.

Y. Ding, X. Guan, X. Zhu, H. Hu, S. I. Bozhevolnyi, L. K. Oxenløwe, N. A. Mortensen, and S. Xiao, “Efficient graphene based electro-optical modulator enabled by interfacing plasmonic slot and silicon waveguides,” Nanoscale 9(40), 15576–15581 (2017).
[Crossref]

Pantouvaki, M.

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

Pei, C.

Perebeinos, V.

F. Xia, V. Perebeinos, Y. Lin, Y. Wu, and P. Avouris, “The origins and limits of metal–graphene junction resistance,” Nat. Nanotechnol. 6(3), 179–184 (2011).
[Crossref]

Perruisseau-Carrier, J.

M. Tamagnone, A. Fallahi, J. R. Mosig, and J. Perruisseau-Carrier, “Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices,” Nat. Photonics 8(7), 556–563 (2014).
[Crossref]

Phare, C. T.

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]

Piner, R.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

Ruoff, R. S.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

Schibli, T. R.

Schlather, A. E.

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. Javier García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

Shankar, R.

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref]

Sharapov, S. G.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

Shen, A.

Shen, Y.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, S. F. Yu, and Q. J. Wang, “Integrated Terahertz Graphene Modulator with 100% Modulation Depth,” ACS Photon. 2(11), 1559–1566 (2015).
[Crossref]

Shen, Y. R.

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]

Sheng, Q.-W.

Z.-B. Liu, M. Feng, W.-S. Jiang, W. Xin, P. Wang, Q.-W. Sheng, Y.-G. Liu, D. N. Wang, W.-Y. Zhou, and J.-G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Sikes, K. J.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
[Crossref]

Skachko, I.

X. Du, I. Skachko, A. Barker, and E. Andrei, “Approaching ballistic transport in suspended graphene,” Nat. Nanotechnol. 3(8), 491–495 (2008).
[Crossref]

Song, Y.

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref]

Stormer, H. L.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
[Crossref]

Su, H.

Suzuki, S.

Tamagnone, M.

M. Tamagnone, A. Fallahi, J. R. Mosig, and J. Perruisseau-Carrier, “Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices,” Nat. Photonics 8(7), 556–563 (2014).
[Crossref]

Tan, D. T.

J. Gosciniak and D. T. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24(18), 185202 (2013).
[Crossref]

Tang, L.

Thourhout, D. V.

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

Tian, J.-G.

Z.-B. Liu, M. Feng, W.-S. Jiang, W. Xin, P. Wang, Q.-W. Sheng, Y.-G. Liu, D. N. Wang, W.-Y. Zhou, and J.-G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Tong, L.

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]

Tsuchizawa, T.

R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
[Crossref]

Tutuc, E.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

Ulin-Avila, E.

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]

Velamakanni, A.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

Wallace, R. M.

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-κ gate dielectrics: Current status and materials properties considerations,” J. Appl. Phys. 89(10), 5243–5275 (2001).
[Crossref]

Wang, D. N.

Z.-B. Liu, M. Feng, W.-S. Jiang, W. Xin, P. Wang, Q.-W. Sheng, Y.-G. Liu, D. N. Wang, W.-Y. Zhou, and J.-G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Wang, H.

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]

Wang, J.

X. Hu and J. Wang, “High figure of merit graphene modulator based on long-range hybrid plasmonic slot waveguide,” IEEE J. Quantum Electron. 53(3), 1–8 (2017).
[Crossref]

Wang, P.

Z.-B. Liu, M. Feng, W.-S. Jiang, W. Xin, P. Wang, Q.-W. Sheng, Y.-G. Liu, D. N. Wang, W.-Y. Zhou, and J.-G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Wang, Q. J.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, S. F. Yu, and Q. J. Wang, “Integrated Terahertz Graphene Modulator with 100% Modulation Depth,” ACS Photon. 2(11), 1559–1566 (2015).
[Crossref]

Wang, Y.

H. Dalir, Y. Xia, Y. Wang, and X. Zhang, “Athermal Broadband Graphene Optical Modulator with 35 GHz Speed,” ACS Photon. 3(9), 1564–1568 (2016).
[Crossref]

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. Javier García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

Wang, Z.

Warabi, K.

R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
[Crossref]

Wilk, G. D.

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-κ gate dielectrics: Current status and materials properties considerations,” J. Appl. Phys. 89(10), 5243–5275 (2001).
[Crossref]

Wu, Y.

F. Xia, V. Perebeinos, Y. Lin, Y. Wu, and P. Avouris, “The origins and limits of metal–graphene junction resistance,” Nat. Nanotechnol. 6(3), 179–184 (2011).
[Crossref]

Xia, F.

F. Xia, V. Perebeinos, Y. Lin, Y. Wu, and P. Avouris, “The origins and limits of metal–graphene junction resistance,” Nat. Nanotechnol. 6(3), 179–184 (2011).
[Crossref]

Xia, Y.

H. Dalir, Y. Xia, Y. Wang, and X. Zhang, “Athermal Broadband Graphene Optical Modulator with 35 GHz Speed,” ACS Photon. 3(9), 1564–1568 (2016).
[Crossref]

Xiao, S.

Y. Ding, X. Guan, X. Zhu, H. Hu, S. I. Bozhevolnyi, L. K. Oxenløwe, N. A. Mortensen, and S. Xiao, “Efficient graphene based electro-optical modulator enabled by interfacing plasmonic slot and silicon waveguides,” Nanoscale 9(40), 15576–15581 (2017).
[Crossref]

Xiao, Y.

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]

Xie, W.

Xin, W.

Z.-B. Liu, M. Feng, W.-S. Jiang, W. Xin, P. Wang, Q.-W. Sheng, Y.-G. Liu, D. N. Wang, W.-Y. Zhou, and J.-G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Xu, C.

Xu, Y.

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]

Yamada, K.

R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
[Crossref]

Yamamoto, T.

R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
[Crossref]

Yamashita, S.

G. Kovacevica and S. Yamashita, “Design optimizations for a high-speed two-layer graphene optical modulator on silicon,” IEICE Electron. Express 13(14), 20160499 (2016).
[Crossref]

Yang, B.

Yang, D.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

Yang, H.

Yang, J.

Yang, L.

Yao, Y.

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref]

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications (Oxford University, 2007).

Ye, S.

Yin, X.

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]

Yu, H.

Yu, S. F.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, S. F. Yu, and Q. J. Wang, “Integrated Terahertz Graphene Modulator with 100% Modulation Depth,” ACS Photon. 2(11), 1559–1566 (2015).
[Crossref]

Yu, X.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, S. F. Yu, and Q. J. Wang, “Integrated Terahertz Graphene Modulator with 100% Modulation Depth,” ACS Photon. 2(11), 1559–1566 (2015).
[Crossref]

Yun, B.

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Zhang, M.

Zhang, X.

H. Dalir, Y. Xia, Y. Wang, and X. Zhang, “Athermal Broadband Graphene Optical Modulator with 35 GHz Speed,” ACS Photon. 3(9), 1564–1568 (2016).
[Crossref]

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]

Zhang, Y.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, S. F. Yu, and Q. J. Wang, “Integrated Terahertz Graphene Modulator with 100% Modulation Depth,” ACS Photon. 2(11), 1559–1566 (2015).
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S. Ye, Z. Wang, L. Tang, Y. Zhang, R. Lu, and Y. Liu, “Electro-absorption optical modulator using dual-graphene-on-graphene configuration,” Opt. Express 22(21), 26173–26180 (2014).
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Zheng, P.

Zhou, W.-Y.

Z.-B. Liu, M. Feng, W.-S. Jiang, W. Xin, P. Wang, Q.-W. Sheng, Y.-G. Liu, D. N. Wang, W.-Y. Zhou, and J.-G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Zhu, X.

Y. Ding, X. Guan, X. Zhu, H. Hu, S. I. Bozhevolnyi, L. K. Oxenløwe, N. A. Mortensen, and S. Xiao, “Efficient graphene based electro-optical modulator enabled by interfacing plasmonic slot and silicon waveguides,” Nanoscale 9(40), 15576–15581 (2017).
[Crossref]

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. Javier García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

ACS Photon. (2)

H. Dalir, Y. Xia, Y. Wang, and X. Zhang, “Athermal Broadband Graphene Optical Modulator with 35 GHz Speed,” ACS Photon. 3(9), 1564–1568 (2016).
[Crossref]

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, S. F. Yu, and Q. J. Wang, “Integrated Terahertz Graphene Modulator with 100% Modulation Depth,” ACS Photon. 2(11), 1559–1566 (2015).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

S. J. Koester and M. Li, “High-speed waveguide-coupled graphene-on-graphene optical modulators,” Appl. Phys. Lett. 100(17), 171107 (2012).
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R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
[Crossref]

R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
[Crossref]

IEEE J. Quantum Electron. (1)

X. Hu and J. Wang, “High figure of merit graphene modulator based on long-range hybrid plasmonic slot waveguide,” IEEE J. Quantum Electron. 53(3), 1–8 (2017).
[Crossref]

IEEE Microw. Wireless Compon. Lett. (1)

R. Mendis and D. Grischkowsky, “THz interconnect with low-loss and low-group velocity dispersion,” IEEE Microw. Wireless Compon. Lett. 11(11), 444–446 (2001).
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IEICE Electron. Express (1)

G. Kovacevica and S. Yamashita, “Design optimizations for a high-speed two-layer graphene optical modulator on silicon,” IEICE Electron. Express 13(14), 20160499 (2016).
[Crossref]

J. Appl. Phys. (1)

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-κ gate dielectrics: Current status and materials properties considerations,” J. Appl. Phys. 89(10), 5243–5275 (2001).
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J. Phys. Condens. Matter (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
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Laser Photon. Rev. (1)

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

Laser Phys. Lett. (1)

Z.-B. Liu, M. Feng, W.-S. Jiang, W. Xin, P. Wang, Q.-W. Sheng, Y.-G. Liu, D. N. Wang, W.-Y. Zhou, and J.-G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Nano Lett. (5)

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]

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. Javier García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

N. K. Emani, T. F. Chung, X. J. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltasseva, “Electrically Tunable Damping of Plasmonic Resonances with Graphene,” Nano Lett. 12(10), 5202–5206 (2012).
[Crossref]

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref]

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

Nanoscale (1)

Y. Ding, X. Guan, X. Zhu, H. Hu, S. I. Bozhevolnyi, L. K. Oxenløwe, N. A. Mortensen, and S. Xiao, “Efficient graphene based electro-optical modulator enabled by interfacing plasmonic slot and silicon waveguides,” Nanoscale 9(40), 15576–15581 (2017).
[Crossref]

Nanotechnology (1)

J. Gosciniak and D. T. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24(18), 185202 (2013).
[Crossref]

Nat. Nanotechnol. (2)

X. Du, I. Skachko, A. Barker, and E. Andrei, “Approaching ballistic transport in suspended graphene,” Nat. Nanotechnol. 3(8), 491–495 (2008).
[Crossref]

F. Xia, V. Perebeinos, Y. Lin, Y. Wu, and P. Avouris, “The origins and limits of metal–graphene junction resistance,” Nat. Nanotechnol. 6(3), 179–184 (2011).
[Crossref]

Nat. Photonics (2)

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]

M. Tamagnone, A. Fallahi, J. R. Mosig, and J. Perruisseau-Carrier, “Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices,” Nat. Photonics 8(7), 556–563 (2014).
[Crossref]

Nature (1)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Opt. Commun. (2)

J. Liu and Y. Liu, “Ultrafast suspended self-biasing graphene modulator with ultrahigh figure of merit,” Opt. Commun. 427, 439–446 (2018).
[Crossref]

J. Liu, H. Liang, M. Zhang, and H. Su, “THz wave transmission within the metal film coated double-dielectric-slab waveguides and the tunable filter application,” Opt. Commun. 351, 103–108 (2015).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Science (1)

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

Solid State Commun. (1)

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
[Crossref]

Other (1)

A. Yariv, Optical Electronics in Modern Communications (Oxford University, 2007).

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Figures (10)

Fig. 1.
Fig. 1. (a) The structure of suspended triple-layer graphene waveguide modulator. (b) The movement of carriers when the triple-layer graphene modulator is biased. (c) The equivalent circuit of the suspended triple-layer graphene modulator.
Fig. 2.
Fig. 2. Shows the fabrication steps of the device. The fabrication starts from the silicon waveguide with a trench in the middle caused by etching, as shown in (a). In (b), a prepared graphene sheet is mechanically transferred. (c) Deposit of a thick insulator. (d) Mechanically transfer the middle graphene layer. (e) Deposit of the other thick insulator. (f) Mechanically transfer the up side graphene layer.
Fig. 3.
Fig. 3. MPA (black line) and mode index (red dash line) of TE mode in the suspended triple-layer graphene modulator as a function of chemical potential µc of the side graphene layers.
Fig. 4.
Fig. 4. (a) The modulation depths (both Δα1 and Δα2) change as a function of insulator thickness w at λ =1.55 µm for different dielectric: ɛ1 = 3.06, 16, and 22, respectively. (b) The highest modulation depth (black line) for different insulator permittivity ɛ1 and the corresponding optimized dielectric thickness (red line) for both modulation depth 1 and 2, respectively.
Fig. 5.
Fig. 5. (a) The mode profile as a function of coordinate x when µc = 0.3 eV at λ = 1.55 m, ɛ1 = 22, and w = 17 nm (black line), 5 nm (red dashed line) and 50 nm (blue dotted line). (b) The corresponding mode amplitude in the side graphene layers.
Fig. 6.
Fig. 6. The mode power transmittance of the modulator as a function of incident wavelength when µc = 0.3 eV (black line), 0.4 eV (red dashed line) and 0.5 eV (blue dotted line).
Fig. 7.
Fig. 7. The transmittance of the M-Z modulator as a function of the difference of the side-layer chemical potential (Δµc) between two arms when L = 12 µm (black line), 34 µm (red dashed line), and 68 µm (blue dotted line).
Fig. 8.
Fig. 8. (a) The applied voltage as a function of side-layer chemical potential μc: black line: ɛ1 = 10, wopt = 30 nm, red line: ɛ1 = 22, wopt = 17 nm; (b) The applied voltage and corresponding energy consumption as a function of permittivity ɛ1 of the insulator when w is at wopt and μc = 0.3 eV.
Fig. 9.
Fig. 9. The mode profile in the longitudinal transmission direction at different wavelength: λ = 2.5 µm (a), λ = 1.5 µm (b), λ = 0.6 µm (c) when ɛ1 = 22, μc = 0.3 eV. Simulated by COMSOL.
Fig. 10.
Fig. 10. The scattering parameter S21 as a function of wavelength at μc = 0.1 eV (black solid line), 0.2 eV (red dashed line), 0.3 eV (blue dotted line), 0.4 eV (green dashed dotted line), and 0.5 eV (pink dashed dotted dotted line). Simulated by COMSOL.

Equations (9)

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

1 R t o t a l = 1 1.5 R + 1 1.5 R = 4 3 R
C t o t a l = 2 C
f 3dB = 1 2 π R total C total = 1 3 π R C
E y ( x ) = { A 10 e h 4 ( x 3 δ / 2 w ) x 3 δ / 2 + w A 6 e h 3 ( x δ / 2 w ) + A 7 e h 3 ( x δ / 2 w ) δ / 2 + w x 3 δ / 2 + w A 2 cos h 2 ( x δ / 2 ) + A 3 sin h 2 ( x δ / 2 ) δ / 2 x δ / 2 + w A 1 cos ( h 1 x ) δ / 2 x δ / 2 A 4 cos h 2 ( x + δ / 2 ) + A 5 sin h 2 ( x + δ / 2 ) δ / 2 w x δ / 2 A 8 e h 3 ( x + δ / 2 + w ) + A 9 e h 3 ( x + δ / 2 + w ) 3 δ / 2 w x δ / 2 w A 10 e h 4 ( x + 3 δ / 2 + w ) x 3 δ / 2 w ,
tan ( h 1 δ / 2 ) = P 1 + P 2 P 3 + P 4 ,
α = 10 Log [ T max ]
FOM = Δ α / α
T ( Δ μ c ) = 1 4 × [ exp ( α 0 L ) + exp ( α 1 L ) + 2 exp ( α 0 L + α 1 L 2 ) cos ( Δ ϕ ) ]
V g = e w π ε 1 ε 0 2 v F 2 0 ς [ ( e ς μ c k B T + 1 ) 1 ( e ς + μ c k B T + 1 ) 1 ]d ς ,

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