Abstract

We propose and numerically study an on-chip graphene-silicon hybrid electro-optic (EO) modulator operating at the telecommunication band, which is implemented by a compact 1D photonic crystal nanobeam (PCN) cavity coupled to a bus waveguide with a graphene sheet on top. Through electrically tuning the Fermi level of the graphene, both the quality factor and the resonance wavelength can be significantly changed, thus the in-plane lightwave can be efficiently modulated. Based on finite-difference time-domain (FDTD) simulation results, the proposed modulator can provide a large free spectral range (FSR) of 125.6 nm, a high modulation speed of 133 GHz, and a large modulation depth of ~12.5 dB in a small modal volume, promising a high performance EO modulator for wavelength-division multiplexed (WDM) optical communication systems.

© 2015 Optical Society of America

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    [Crossref]
  5. K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
    [Crossref] [PubMed]
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  7. M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12(3), 1482–1485 (2012).
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  8. 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]
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    [Crossref]
  10. Q. Xu, B. Schmidt, J. Shakya, and M. Lipson, “Cascaded silicon micro-ring modulators for WDM optical interconnection,” Opt. Express 14(20), 9431–9435 (2006).
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  11. Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-µm radius,” Opt. Express 16(6), 4309–4315 (2008).
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  12. P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
    [Crossref]
  13. Q. Quan and M. Loncar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19(19), 18529–18542 (2011).
    [Crossref] [PubMed]
  14. J. Hendrickson, R. Soref, J. Sweet, and W. Buchwald, “Ultrasensitive silicon photonic-crystal nanobeam electro-optical modulator: design and simulation,” Opt. Express 22(3), 3271–3283 (2014).
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    [Crossref]
  17. 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]
  18. 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]
  19. S. Shen, K. Wu, L. Sun, and C. Jiang, “Theoretical study of graphene-silicon nitride-silicon hybrid photonic crystal waveguides for four-wave mixing enhancement,” Appl. Opt. 54(12), 3640–3644 (2015).
    [Crossref]
  20. 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]
  21. Z. L. Lu and W. S. Zhao, “Nanoscale electro-optic modulators based on graphene-slot waveguides,” J. Opt. Soc. Am. B 29(6), 1490–1496 (2012).
    [Crossref]
  22. C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
    [Crossref]
  23. C. Qiu, J. Chen, Y. Xia, and Q. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep. 2, 855 (2012).
    [Crossref] [PubMed]
  24. M. Xu, F. Li, T. Wang, J. Y. Wu, L. Y. Lu, L. J. Zhou, and Y. K. Su, “Design of an electro-optic modulator based on a silicon-plasmonic hybrid phase shifter,” J. Lightwave Technol. 31(8), 1170–1177 (2013).
    [Crossref]
  25. P. Dong, S. Liao, D. Feng, H. Liang, D. Zheng, R. Shafiiha, C. C. Kung, W. Qian, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low V-pp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express 17(25), 22484–22490 (2009).
    [Crossref] [PubMed]
  26. D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
    [Crossref]
  27. C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 10, 1038 (2015).

2015 (2)

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 10, 1038 (2015).

S. Shen, K. Wu, L. Sun, and C. Jiang, “Theoretical study of graphene-silicon nitride-silicon hybrid photonic crystal waveguides for four-wave mixing enhancement,” Appl. Opt. 54(12), 3640–3644 (2015).
[Crossref]

2014 (3)

J. Hendrickson, R. Soref, J. Sweet, and W. Buchwald, “Ultrasensitive silicon photonic-crystal nanobeam electro-optical modulator: design and simulation,” Opt. Express 22(3), 3271–3283 (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]

W. Du, E. P. Li, and R. Hao, “Tunability analysis of a graphene-embedded ring modulator,” IEEE Photonics Technol. Lett. 26(20), 2008–2011 (2014).
[Crossref]

2013 (4)

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]

W. S. Fegadolli, J. E. B. Oliveira, V. R. Almeida, and A. Scherer, “Compact and low power consumption tunable photonic crystal nanobeam cavity,” Opt. Express 21(3), 3861–3871 (2013).
[Crossref] [PubMed]

M. Xu, F. Li, T. Wang, J. Y. Wu, L. Y. Lu, L. J. Zhou, and Y. K. Su, “Design of an electro-optic modulator based on a silicon-plasmonic hybrid phase shifter,” J. Lightwave Technol. 31(8), 1170–1177 (2013).
[Crossref]

2012 (6)

Z. L. Lu and W. S. Zhao, “Nanoscale electro-optic modulators based on graphene-slot waveguides,” J. Opt. Soc. Am. B 29(6), 1490–1496 (2012).
[Crossref]

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

C. Qiu, J. Chen, Y. Xia, and Q. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep. 2, 855 (2012).
[Crossref] [PubMed]

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (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]

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]

2011 (2)

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]

Q. Quan and M. Loncar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19(19), 18529–18542 (2011).
[Crossref] [PubMed]

2009 (3)

P. Dong, S. Liao, D. Feng, H. Liang, D. Zheng, R. Shafiiha, C. C. Kung, W. Qian, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low V-pp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express 17(25), 22484–22490 (2009).
[Crossref] [PubMed]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

A. V. Krishnamoorthy, R. Ho, X. Z. Zheng, H. Schwetman, J. Lexau, P. Koka, G. L. Li, I. Shubin, and J. E. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97(7), 1337–1361 (2009).
[Crossref]

2008 (3)

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]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-µm radius,” Opt. Express 16(6), 4309–4315 (2008).
[Crossref] [PubMed]

2006 (2)

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

Q. Xu, B. Schmidt, J. Shakya, and M. Lipson, “Cascaded silicon micro-ring modulators for WDM optical interconnection,” Opt. Express 14(20), 9431–9435 (2006).
[Crossref] [PubMed]

1999 (1)

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

1987 (1)

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

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]

Alic, N.

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Almeida, V. R.

Asghari, M.

Beausoleil, R. G.

Bennett, B. R.

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[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]

Buchwald, W.

Cardenas, J.

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 10, 1038 (2015).

Chen, H. S.

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]

Chen, J.

C. Qiu, J. Chen, Y. Xia, and Q. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep. 2, 855 (2012).
[Crossref] [PubMed]

Cho, D. J.

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]

Cunningham, J. E.

A. V. Krishnamoorthy, R. Ho, X. Z. Zheng, H. Schwetman, J. Lexau, P. Koka, G. L. Li, I. Shubin, and J. E. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97(7), 1337–1361 (2009).
[Crossref]

Deotare, P. B.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

Dong, P.

Du, W.

W. Du, E. P. Li, and R. Hao, “Tunability analysis of a graphene-embedded ring modulator,” IEEE Photonics Technol. Lett. 26(20), 2008–2011 (2014).
[Crossref]

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]

Fan, S. H.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Fattal, D.

Fedeli, J. M.

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Fegadolli, W. S.

Feng, D.

Frank, I. W.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

Fudenberg, G.

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]

Gao, W.

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]

Gardes, F. Y.

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Geng, B.

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]

Hao, R.

W. Du, E. P. Li, and R. Hao, “Tunability analysis of a graphene-embedded ring modulator,” IEEE Photonics Technol. Lett. 26(20), 2008–2011 (2014).
[Crossref]

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]

Haus, H. A.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Heinz, T. F.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Hendrickson, J.

Ho, R.

A. V. Krishnamoorthy, R. Ho, X. Z. Zheng, H. Schwetman, J. Lexau, P. Koka, G. L. Li, I. Shubin, and J. E. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97(7), 1337–1361 (2009).
[Crossref]

Hone, 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]

Hu, Y.

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Jiang, C.

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. F.

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]

Joannopoulos, J. D.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

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] [PubMed]

Khan, M.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

Khan, M. J.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Kim, 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]

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]

Kim, K.

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]

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]

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).
[Crossref]

Koka, P.

A. V. Krishnamoorthy, R. Ho, X. Z. Zheng, H. Schwetman, J. Lexau, P. Koka, G. L. Li, I. Shubin, and J. E. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97(7), 1337–1361 (2009).
[Crossref]

Kono, J.

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]

Krishnamoorthy, A. V.

A. V. Krishnamoorthy, R. Ho, X. Z. Zheng, H. Schwetman, J. Lexau, P. Koka, G. L. Li, I. Shubin, and J. E. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97(7), 1337–1361 (2009).
[Crossref]

P. Dong, S. Liao, D. Feng, H. Liang, D. Zheng, R. Shafiiha, C. C. Kung, W. Qian, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low V-pp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express 17(25), 22484–22490 (2009).
[Crossref] [PubMed]

Kung, C. C.

Kuo, B. P. P.

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[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 10, 1038 (2015).

Lexau, J.

A. V. Krishnamoorthy, R. Ho, X. Z. Zheng, H. Schwetman, J. Lexau, P. Koka, G. L. Li, I. Shubin, and J. E. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97(7), 1337–1361 (2009).
[Crossref]

Li, E. P.

W. Du, E. P. Li, and R. Hao, “Tunability analysis of a graphene-embedded ring modulator,” IEEE Photonics Technol. Lett. 26(20), 2008–2011 (2014).
[Crossref]

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]

Li, F.

Li, G.

Li, G. L.

A. V. Krishnamoorthy, R. Ho, X. Z. Zheng, H. Schwetman, J. Lexau, P. Koka, G. L. Li, I. Shubin, and J. E. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97(7), 1337–1361 (2009).
[Crossref]

Liang, H.

Liao, S.

Lipson, M.

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 10, 1038 (2015).

Q. Xu, B. Schmidt, J. Shakya, and M. Lipson, “Cascaded silicon micro-ring modulators for WDM optical interconnection,” Opt. Express 14(20), 9431–9435 (2006).
[Crossref] [PubMed]

Liu, M.

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]

Loncar, M.

Q. Quan and M. Loncar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19(19), 18529–18542 (2011).
[Crossref] [PubMed]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

Lu, L. Y.

Lu, Z. L.

Lui, C. H.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Majumdar, A.

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]

Mak, K. F.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Manolatou, C.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Mashanovich, G. Z.

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

McCutcheon, M. W.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

Misewich, J. A.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Myslivets, E.

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Oliveira, J. E. B.

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 10, 1038 (2015).

Qian, W.

Qiu, C.

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]

C. Qiu, J. Chen, Y. Xia, and Q. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep. 2, 855 (2012).
[Crossref] [PubMed]

Quan, Q.

Radic, S.

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Reed, G. T.

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Regan, W.

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]

Scherer, A.

Schmidt, B.

Schwetman, H.

A. V. Krishnamoorthy, R. Ho, X. Z. Zheng, H. Schwetman, J. Lexau, P. Koka, G. L. Li, I. Shubin, and J. E. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97(7), 1337–1361 (2009).
[Crossref]

Sfeir, M. Y.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Shafiiha, R.

Shakya, J.

Shen, S.

Shen, Y. R.

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]

Shi, S.

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]

Shu, J.

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]

Shubin, I.

A. V. Krishnamoorthy, R. Ho, X. Z. Zheng, H. Schwetman, J. Lexau, P. Koka, G. L. Li, I. Shubin, and J. E. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97(7), 1337–1361 (2009).
[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]

Son, H.

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]

Soref, R.

Soref, R. A.

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[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, Y. K.

Sun, L.

Sweet, J.

Thomson, D. J.

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[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] [PubMed]

Vajtai, R.

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]

Villeneuve, P. R.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

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]

Wang, F.

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, T.

Wu, J. Y.

Wu, K.

Wu, Y.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Xia, Y.

C. Qiu, J. Chen, Y. Xia, and Q. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep. 2, 855 (2012).
[Crossref] [PubMed]

Xu, M.

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]

C. Qiu, J. Chen, Y. Xia, and Q. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep. 2, 855 (2012).
[Crossref] [PubMed]

Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-µm radius,” Opt. Express 16(6), 4309–4315 (2008).
[Crossref] [PubMed]

Q. Xu, B. Schmidt, J. Shakya, and M. Lipson, “Cascaded silicon micro-ring modulators for WDM optical interconnection,” Opt. Express 14(20), 9431–9435 (2006).
[Crossref] [PubMed]

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).
[Crossref]

Yin, 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]

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]

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]

Zhao, W. S.

Zheng, D.

Zheng, X.

Zheng, X. Z.

A. V. Krishnamoorthy, R. Ho, X. Z. Zheng, H. Schwetman, J. Lexau, P. Koka, G. L. Li, I. Shubin, and J. E. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97(7), 1337–1361 (2009).
[Crossref]

Zhou, L. J.

Zlatanovic, S.

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

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. (2)

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]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

IEEE J. Quantum Electron. (2)

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

IEEE J. Sel. Top Quantum Electron. (1)

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

IEEE Photonics Technol. Lett. (2)

W. Du, E. P. Li, and R. Hao, “Tunability analysis of a graphene-embedded ring modulator,” IEEE Photonics Technol. Lett. 26(20), 2008–2011 (2014).
[Crossref]

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

J. Lightwave Technol. (1)

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

Nano Lett. (4)

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

Nat. Photonics (1)

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 10, 1038 (2015).

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] [PubMed]

Opt. Express (6)

Phys. Rev. Lett. (1)

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Proc. IEEE (1)

A. V. Krishnamoorthy, R. Ho, X. Z. Zheng, H. Schwetman, J. Lexau, P. Koka, G. L. Li, I. Shubin, and J. E. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97(7), 1337–1361 (2009).
[Crossref]

Sci. Rep. (1)

C. Qiu, J. Chen, Y. Xia, and Q. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep. 2, 855 (2012).
[Crossref] [PubMed]

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]

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Figures (3)

Fig. 1
Fig. 1 (a) Schematic perspective view of the proposed EO modulator. Note that there is no graphene covering the air holes of the PCN cavity. (b) Top-view of the PCN cavity. The PCN cavity is symmetric with respect to its center. (c) The model of the PCN cavity as a single-mode optical resonator coupled with a bus waveguide. (d) The cross-section of the proposed device corresponding to the red dashed line in (a).
Fig. 2
Fig. 2 (a) Real part, imaginary part, and magnitude of the calculated anisotropic in-plane permittivity of graphene under different Fermi levels. (b) The real and imaginary parts of effective modal index of 500 × 220 nm2 single-mode silicon waveguide with graphene on top as a function of the Fermi level. The inset is the electric field distribution profile of the TE mode. All the simulations are performed at an operation wavelength of 1550 nm.
Fig. 3
Fig. 3 (a) Normalized transmission spectra of the proposed device at different Fermi levels. (b) Normalized transmission spectrum ranging from 1400 nm to 1670 nm at Ef = 0.9 eV. Inset shows zoom-in view of the spectrum ranging from 1545 nm to 1553 nm. (c) Relative resonance wavelength shift defined as the resonance wavelength detuning from the resonance wavelength at Ef = 0.9 eV. (d) Calculated intrinsic quality factor. (e) Normalized transmission at 1549.3 nm.

Tables (2)

Tables Icon

Table 1 Designed structural parameters of the PCN cavity

Tables Icon

Table 2 Comparison with state-of-the-art silicon-based EO modulators

Equations (7)

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

ε g ' ( E f ) = 1 + e 2 8 π E p ε 0 d ln ( E p + 2 | E f | ) 2 + Γ 2 ( E p 2 | E f | ) 2 + Γ 2 e 2 π ε 0 d | E f | E p 2 + ( 1 / τ ) 2 ,
ε g " ( E f ) = e 2 4 E p ε 0 d [ 1 + 1 π ( tan 1 E p 2 | E f | Γ tan 1 E p + 2 | E f | Γ ) + e 2 π τ E p ε 0 d | E f | E p 2 + ( 1 / τ ) 2 ,
d a d t = [ j ( ω ω 0 ) 1 2 τ 0 | κ 1 | 2 + | κ 2 | 2 2 ] a + k 1 S 1 + ,
S 2 + = S 1 + κ 1 a ,
a = k 1 S 1 + i ( ω ω 0 ) + ( | κ 1 | 2 + | κ 2 | 2 ) / 2 + 1 / 2 τ 0 ,
T = | S 2 + | 2 | S 1 + | 2 = Q c 2 λ 2 + [ 2 Q i Q c ( λ λ 0 ) ] 2 ( Q c + Q i ) 2 λ 2 + [ 2 Q i Q c ( λ λ 0 ) ] 2 ,
E f = V f π ( n 0 + C p | V g | q ) ,

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