Abstract

Graphene, as a type of flexible and electrically adjustable two-dimensional material, has exceptional optical and electrical properties that make it possible to be used in modulators. However, the poor interaction between optical fields and a single atom graphene layer prevents the easy implementation of graphene modulators. Currently available devices often require a larger overlap area of graphene to obtain the desired phase or amplitude modulation, which results in a rather large footprint and high capacitance and consequently increases the energy consumption and reduces the modulation speed. In this paper, a localized plasmonic-enhanced waveguide modulator with high-speed tunability using graphene is proposed for telecommunication applications. Strong modulation of the transmission takes place due to the enhanced interaction between the ultrathin plasmon patches and the graphene, when the plasmons are tuned on- and off-resonance by the gate-tunable graphene. A 400 GHz modulation rate using low gated-voltages with an active device area of 0.2 μm2 and a low consumption of only 0.5 fJ/bit is achieved, which paves the way for ultrafast low-energy optical waveguide modulation and switching.

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

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2017 (5)

M. Mohsin, D. Schall, M. Otto, B. Chmielak, S. Suckow, and D. Neumaier, “Towards the Predicted High Performance of Waveguide Integrated Electro-Refractive Phase Modulators Based on Graphene,” IEEE Photonics J. 9(1), 1–7 (2017).
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Z. Ma, M. H. Tahersima, S. Khan, and V. J. Sorger, “Two-Dimensional Material-Based Mode Confinement Engineering in Electro-Optic Modulators,” IEEE J. Sel. Top. Quantum Electron. 23(1), 81–88 (2017).
[Crossref]

X. Peng, R. Hao, Z. Ye, P. Qin, W. Chen, H. Chen, X. Jin, D. Yang, and E. Li, “Highly efficient graphene-on-gap modulator by employing the hybrid plasmonic effect,” Opt. Lett. 42(9), 1736–1739 (2017).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, Y. Huang, J. Q. Liu, L. L. Wang, and S. C. Wen, “Multi-band perfect plasmonic absorptions using rectangular graphene gratings,” Opt. Lett. 42(15), 3052–3055 (2017).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, Y. Huang, J. Q. Liu, L. L. Wang, and S. C. Wen, “Graphene surface plasmons with dielectric metasurfaces,” J. Lightwave Technol. 35(20), 4553–4558 (2017).
[Crossref]

2016 (4)

B. H. Huang, W. B. Lu, X. B. Li, J. Wang, and Z. G. Liu, “Waveguide-coupled hybrid plasmonic modulator based on graphene,” Appl. Opt. 55(21), 5598–5602 (2016).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, L. L. Wang, B. Sun, J. Q. Liu, and S. C. Wen, “Dynamically tunable plasmonically induced transparency in sinusoidally curved and planar graphene layers,” Opt. Express 24(16), 17886–17899 (2016).
[Crossref] [PubMed]

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

2015 (11)

L. Vivien, “Computer technology: Silicon chips lighten up,” Nature 528(7583), 483–484 (2015).
[Crossref] [PubMed]

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref] [PubMed]

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]

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J.-K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J.-Y. Park, F. Rotermund, and D.-I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
[Crossref] [PubMed]

J. S. Shin and J. T. Kim, “Broadband silicon optical modulator using a graphene-integrated hybrid plasmonic waveguide,” Nanotechnology 26(36), 365201 (2015).
[Crossref] [PubMed]

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref] [PubMed]

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref] [PubMed]

X. Yin, M. Schäferling, A. K. Michel, A. Tittl, M. Wuttig, T. Taubner, and H. Giessen, “Active chiral plasmonics,” Nano Lett. 15(7), 4255–4260 (2015).
[Crossref] [PubMed]

S. Das, A. Salandrino, J. Z. Wu, and R. Hui, “Near-infrared electro-optic modulator based on plasmonic graphene,” Opt. Lett. 40(7), 1516–1519 (2015).
[Crossref] [PubMed]

T. Pan, C. Qiu, J. Wu, X. Jiang, B. Liu, Y. Yang, H. Zhou, R. Soref, and Y. Su, “Analysis of an electro-optic modulator based on a graphene-silicon hybrid 1D photonic crystal nanobeam cavity,” Opt. Express 23(18), 23357–23364 (2015).
[Crossref] [PubMed]

2014 (4)

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
[Crossref] [PubMed]

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] [PubMed]

C. Qiu, W. Gao, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 μm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14(12), 6811–6815 (2014).
[Crossref] [PubMed]

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] [PubMed]

2013 (3)

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

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

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[Crossref] [PubMed]

2012 (5)

A. G. Brolo, “Plasmonics for future biosensors,” Nat. Photonics 6(11), 709–713 (2012).
[Crossref]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

M. Midrio, S. Boscolo, M. Moresco, M. Romagnoli, C. De Angelis, A. Locatelli, and A. D. Capobianco, “Graphene-assisted critically-coupled optical ring modulator,” Opt. Express 20(21), 23144–23155 (2012).
[Crossref] [PubMed]

J. Kim, H. Son, D. J. Cho, B. Geng, W. Regan, S. Shi, K. Kim, A. Zettl, Y.-R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
[Crossref] [PubMed]

M. Liu, X. Yin, and X. Zhang, “Double-Layer Graphene Optical Modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[Crossref] [PubMed]

2011 (2)

K. Kim, J. Y. Choi, T. Kim, S. H. Cho, and H. J. Chung, “A role for graphene in silicon-based semiconductor devices,” Nature 479(7373), 338–344 (2011).
[Crossref] [PubMed]

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

2010 (1)

2008 (1)

G. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Ahn, K. J.

E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J.-K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J.-Y. Park, F. Rotermund, and D.-I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
[Crossref] [PubMed]

Ahn, Y. H.

E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J.-K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J.-Y. Park, F. Rotermund, and D.-I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
[Crossref] [PubMed]

Ajayan, P. M.

C. Qiu, W. Gao, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 μm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14(12), 6811–6815 (2014).
[Crossref] [PubMed]

Albella, P.

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref] [PubMed]

Alloatti, L.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref] [PubMed]

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, M. Popovic, and V. Stojanovic, “A 45nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in Symposium on VLSI Circuits, (2015), pp. C122–C123.
[Crossref]

Ansell, D.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref] [PubMed]

Asanovic, K.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref] [PubMed]

Atabaki, A.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, M. Popovic, and V. Stojanovic, “A 45nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in Symposium on VLSI Circuits, (2015), pp. C122–C123.
[Crossref]

Atabaki, A. H.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
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Avizienis, R. R.

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Vivien, L.

L. Vivien, “Computer technology: Silicon chips lighten up,” Nature 528(7583), 483–484 (2015).
[Crossref] [PubMed]

Vuckovic, J.

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[Crossref] [PubMed]

Wade, M.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, M. Popovic, and V. Stojanovic, “A 45nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in Symposium on VLSI Circuits, (2015), pp. C122–C123.
[Crossref]

Wade, M. T.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref] [PubMed]

Wagner, M.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

Wang, F.

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[Crossref] [PubMed]

J. Kim, H. Son, D. J. Cho, B. Geng, W. Regan, S. Shi, K. Kim, A. Zettl, Y.-R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
[Crossref] [PubMed]

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

Wang, J.

Wang, L.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

Wang, L. L.

Wang, Z.

Waterman, A. S.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref] [PubMed]

Wen, S. C.

Wu, J.

Wu, J. Z.

Wuttig, M.

X. Yin, M. Schäferling, A. K. Michel, A. Tittl, M. Wuttig, T. Taubner, and H. Giessen, “Active chiral plasmonics,” Nano Lett. 15(7), 4255–4260 (2015).
[Crossref] [PubMed]

Xia, S. X.

Xiao, S.

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

Xu, Q.

C. Qiu, W. Gao, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 μm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14(12), 6811–6815 (2014).
[Crossref] [PubMed]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Yang, D.

Yang, L. Z.

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

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).
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Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
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Ye, Z.

Yeom, D.-I.

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E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J.-K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J.-Y. Park, F. Rotermund, and D.-I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
[Crossref] [PubMed]

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X. Yin, M. Schäferling, A. K. Michel, A. Tittl, M. Wuttig, T. Taubner, and H. Giessen, “Active chiral plasmonics,” Nano Lett. 15(7), 4255–4260 (2015).
[Crossref] [PubMed]

M. Liu, X. Yin, and X. Zhang, “Double-Layer Graphene Optical Modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[Crossref] [PubMed]

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

Yu, N.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Yvind, K.

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

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] [PubMed]

Zettl, A.

J. Kim, H. Son, D. J. Cho, B. Geng, W. Regan, S. Shi, K. Kim, A. Zettl, Y.-R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
[Crossref] [PubMed]

Zhai, X.

Zhang, X.

M. Liu, X. Yin, and X. Zhang, “Double-Layer Graphene Optical Modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[Crossref] [PubMed]

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

Zhang, Y.

Zhou, H.

Zhu, X.

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

ACS Nano (1)

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. Hao, W. Du, H. S. Chen, X. F. Jin, L. Z. Yang, and E. P. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
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IEEE J. Sel. Top. Quantum Electron. (1)

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G. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
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X. Yin, M. Schäferling, A. K. Michel, A. Tittl, M. Wuttig, T. Taubner, and H. Giessen, “Active chiral plasmonics,” Nano Lett. 15(7), 4255–4260 (2015).
[Crossref] [PubMed]

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

J. Kim, H. Son, D. J. Cho, B. Geng, W. Regan, S. Shi, K. Kim, A. Zettl, Y.-R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
[Crossref] [PubMed]

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[Crossref] [PubMed]

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
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[Crossref] [PubMed]

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

C. Qiu, W. Gao, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 μm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14(12), 6811–6815 (2014).
[Crossref] [PubMed]

M. Liu, X. Yin, and X. Zhang, “Double-Layer Graphene Optical Modulator,” Nano Lett. 12(3), 1482–1485 (2012).
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Nanotechnology (1)

J. S. Shin and J. T. Kim, “Broadband silicon optical modulator using a graphene-integrated hybrid plasmonic waveguide,” Nanotechnology 26(36), 365201 (2015).
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Nat. Commun. (3)

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
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Nat. Photonics (4)

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
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G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
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Nature (4)

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

L. Vivien, “Computer technology: Silicon chips lighten up,” Nature 528(7583), 483–484 (2015).
[Crossref] [PubMed]

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
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Opt. Lett. (3)

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C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, M. Popovic, and V. Stojanovic, “A 45nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in Symposium on VLSI Circuits, (2015), pp. C122–C123.
[Crossref]

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,” arXiv:1610.05352 (2016)

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Figures (6)

Fig. 1
Fig. 1 (a) 3D view and (b) cross-sectional view of the proposed waveguide electro-optic modulator integrated with metal patches and graphene. The outer edges of the patches along the z direction are aligned with the edge of the waveguide, where the spacing of edges is 400 nm. The gap between patches in the z direction is wgap, and the thickness of the metal patches is t. wx and wz are the widths of the patch in the x and z directions, respectively. The inset in Fig. 1(a) shows an electric field intensity cutplane aligned with the x-z plane at the middle of the metal patch thickness where t = 3 nm, wx = wz = 110 nm and wgap = 100 nm, and wavelength is 1.55 µm.
Fig. 2
Fig. 2 Transmission characteristics of the waveguides. (a) Electric field profile of the silicon waveguide in the x-z cutplane without the metal patches. The areas of the dotted boxes represent the locations where the patch array will be placed. (b) Optical transmission spectrum with t = 3 nm, wx = 110 nm, wz = 100 nm and wgap = 100 nm. The two insets show the electric field resonant intensity profiles of the metal patches in the z and x directions corresponding to the two resonant peaks of the transmission spectrum, respectively.
Fig. 3
Fig. 3 Transmission spectra of the waveguide with different patches’ sizes. The thickness of the metal patch t is 3 nm, and the gap size wgap is 100 nm. In the left of Fig. 3(a), wz is 110 nm, and wx varies from 90 to 120 nm with a 10-nm step. In the right of Fig. 3(a), wx is at 110 nm, and wz varies from 90 to 120 nm with a 10-nm step. (b) The transmission spectra with patch sizes of wx = wz = 95 nm, 100 nm, 105 nm and 110 nm, respectively. (c) The electric field distribution corresponding to the three resonance peaks of two transmission spectrum with patch sizes of wx = 110 nm, wz = 100 nm, and wx = wz = 110 nm as red circle marked in Figs. 3(a) and 3(b).
Fig. 4
Fig. 4 Electrical control of the plasmon resonance. (a) Transmission spectra (colour scale) are plotted as a function of the wavelength and chemical potential with t = 3 nm, wx = wz = 110 nm and wgap = 100 nm. (b–c) Real (εr) and imaginary (εi) parts of the graphene in-plane permittivity are calculated using the Kubo formula at temperature T = 300 K for different wavelengths in single-layer graphene. The carrier relaxation time used in the calculation is τ = 10−13 s. (d–f) The corresponding properties of resonance wavelength, intensity and peak width as a function of chemical potential in graphene.
Fig. 5
Fig. 5 The plasmon resonant wavelength as a function of chemical potential of graphene with different thicknesses, t = 3-4 nm, of the metal patches (width of wx = wz = 115 nm, and gap size of wgap = 100 nm).
Fig. 6
Fig. 6 Optical modulation based on the active graphene sheet. The transmission spectra of the device as a function of different bias voltages of graphene with wx = wz = 110 nm, t = 3 nm and wgap = 100 nm. When the bias voltage is 1.9 V, the modulator is in the states of ON, and when the bias voltage is more than 2.4 V, the modulator is in the states of OFF. So with different bias voltages, a wideband modulation can be achieved as shown in the inset.

Equations (2)

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( Δω/ω )=( Δε | E | 2 d r 3 /2 ε | E | 2 d r 3 )
σ( ω, μ c ,τ,T )= i e 2 ( ω+i τ 1 ) π 2 [ 1 ( ω+i τ 1 ) 2 0 ξ( f d ( ξ ) ξ f d ( ξ ) ξ ) dξ 0 f d ( ξ ) f d ( ξ ) ( ω+i τ 1 ) 2 4 ( ξ/ ) 2 dξ ]

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