Abstract

Graphene’s conductivity at optical frequencies can be varied upon injection of carriers. In the present paper, this effect is used to modulate losses of an optical wave traveling inside a ring cavity. This way an optical modulator based on the critical–coupling concept first introduced by Yariv can be realized. Through numerical simulations, we show that a modulator featuring a bandwidth as large as 100 GHz can be designed with switching energy in the order of few fJ per bit. Also, we show that operations with driving voltages below 1.2 volt could be obtained, thus making the proposed modulator compatible with requirements of low–voltage CMOS technology.

© 2012 Optical Society of America

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References

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  1. A. Yariv, “Critical coupling and its control in optical waveguide–ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002).
    [Crossref]
  2. R. A. Soref and B. R. Bennett, “Kramers–Kronig analysis of electro–optical switching in silicon,” Proc. SPIE 704, 32–37 (1987).
  3. J. P. Lorenzo and R. A. Soref, “1.3 μm electro–optic silicon switch,” J. Appl. Phys. 51, 6–8 (1987).
  4. L. Friedman, R. A. Soref, and J. P. Lorenzo, “Silicon double–injection electro–optic modulator with junction gate control,” J. Appl. Phys. 63, 1831–1839 (1988).
    [Crossref]
  5. S. R. Giguere, L. Friedman, R. A. Soref, and J. P. Lorenzo, “Simulation studies of silicon electro–optic waveguide devices,” J. Appl. Phys. 68, 4964–4970 (1990).
    [Crossref]
  6. G. V. Treyez, P. G. May, and J. M. Halbout, “Silicon optical modulators at 1.3 micrometer based on free–carrier absorption,” IEEE Electron. Dev. Lett. 12, 276–278 (1991).
    [Crossref]
  7. G. V. Treyez, P. G. May, and J. M. Halbout, “Silicon Mach–Zehnder waveguide inteferometers based on the plasma dispersion effect,” Appl. Phys. Lett. 59, 771–773 (1991).
    [Crossref]
  8. U. Fischer, B. Schuppert, and K. Petermann, “Integrated optical switches in silicon based on SiGe–waveguides,” IEEE Photon. Technol. Lett. 5, 785–787 (1993).
    [Crossref]
  9. H. C. Huang and T. C. Lo, “Simulation and analysis of silicon electro–optic modulators utilizing the carrier–dispersion effect and impact–ionization mechanism,” J. Appl. Phys. 74, 1521–1582 (1993).
    [Crossref]
  10. A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, “Silicon electro–optic modulator based on a three-terminal device integrated in a low–loss single–mode SOI waveguide,” J. Lightwave Technol. 15, 505–518 (1997).
    [Crossref]
  11. A. Sciuto, S. Libertino, A. Alessandria, S. Coffa, and G. Coppola, “Design, fabrication and testing of an integrated Si–based light modulator,” J. Lightwave Technol. 21, 228–235 (2003).
    [Crossref]
  12. C. A. Barrios, V. R. de Almeida, and M. Lipson, “Low–power–consumption short–length and high–modulation–depth silicon electrooptic modulator,” J. Lightwave Technol. 21, 1089–1098 (2003).
    [Crossref]
  13. A. Liu, R. Jones, L. Liao, D. Samara–Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high–speed silicon optical modulator based on a metal–oxide semiconductor capacitor,” Nature 427, 615–618 (2004).
    [Crossref] [PubMed]
  14. A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaki, and M. Paniccia, “High–speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
    [Crossref] [PubMed]
  15. Q. Xu, S. Manipatrumi, B. Schmidt, J. Shakya, and M. Lipson, “12.5 Gbit/s carrier–injection–based silicon microring silicon modulators,” Opt. Express 15, 430–436 (2007).
    [Crossref] [PubMed]
  16. Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-μm radius,” Opt. Express 16, 4309–4315 (2008).
    [Crossref] [PubMed]
  17. P. Dong, R. Shafiiha, S. Liao, H. Liang, N.-N. Feng, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Ashgari, “Wavelength-tunable silicon microring modulator,” Opt. Express 18, 10941–10946 (2010).
    [Crossref] [PubMed]
  18. W. A. Zortman, M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-power high-speed silicon microdisk modulators,” in Proc. Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference (CLEO/QELS) (San Jose, Calif., 2004), paper CThJ4.
  19. M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Ultralow power silicon microdisk modulators and switches,” in Proc. of the 5th IEEE International Conference on Group IV Photonics (Cardiff, Wales, 2008).
  20. 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, 64–67 (2011).
    [Crossref] [PubMed]
  21. M. Liu, X. Yin, and X. Zhang, “Double–layer graphene optical modulator,” Nano Lett. 12, 1482–1485 (2012).
    [Crossref] [PubMed]
  22. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
    [Crossref] [PubMed]
  23. T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
    [Crossref]
  24. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2008).
    [Crossref]
  25. G. W. Hanson, “Dyadic Green’s function and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
    [Crossref]
  26. CST Microwave Studio 2012. Darmstadt, Germany.
  27. T. Barwicz and H. A. Haus, “Three-dimensional analysis of scattering losses due to sidewall roughness in microphotonic waveguides,” J. Lightwave Technol. 23, 2719–2732 (2005).
    [Crossref]
  28. K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 23, 1888–1890 (2001).
    [Crossref]
  29. M. Moresco, M. Romagnoli, S. Boscolo, and M. Midrio, “Method for Characterization of Si waveguide propagation loss,” submitted to Opt. Express (2012).
  30. A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
    [Crossref] [PubMed]
  31. C. T. DeRose, M. R. Watts, D. C. Trotter, D. L. Luck, G. N. Nielson, and R. W. Young, “Silicon microring modulator with integrated heater and temperature sensor for thermal control,” in Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2010, paper CThJ3.

2012 (2)

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

M. Moresco, M. Romagnoli, S. Boscolo, and M. Midrio, “Method for Characterization of Si waveguide propagation loss,” submitted to Opt. Express (2012).

2011 (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, 64–67 (2011).
[Crossref] [PubMed]

2010 (1)

2008 (5)

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

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
[Crossref] [PubMed]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2008).
[Crossref]

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

2007 (3)

2005 (1)

2004 (1)

A. Liu, R. Jones, L. Liao, D. Samara–Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high–speed silicon optical modulator based on a metal–oxide semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

2003 (2)

2002 (1)

A. Yariv, “Critical coupling and its control in optical waveguide–ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002).
[Crossref]

2001 (1)

K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 23, 1888–1890 (2001).
[Crossref]

1997 (1)

A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, “Silicon electro–optic modulator based on a three-terminal device integrated in a low–loss single–mode SOI waveguide,” J. Lightwave Technol. 15, 505–518 (1997).
[Crossref]

1993 (2)

U. Fischer, B. Schuppert, and K. Petermann, “Integrated optical switches in silicon based on SiGe–waveguides,” IEEE Photon. Technol. Lett. 5, 785–787 (1993).
[Crossref]

H. C. Huang and T. C. Lo, “Simulation and analysis of silicon electro–optic modulators utilizing the carrier–dispersion effect and impact–ionization mechanism,” J. Appl. Phys. 74, 1521–1582 (1993).
[Crossref]

1991 (2)

G. V. Treyez, P. G. May, and J. M. Halbout, “Silicon optical modulators at 1.3 micrometer based on free–carrier absorption,” IEEE Electron. Dev. Lett. 12, 276–278 (1991).
[Crossref]

G. V. Treyez, P. G. May, and J. M. Halbout, “Silicon Mach–Zehnder waveguide inteferometers based on the plasma dispersion effect,” Appl. Phys. Lett. 59, 771–773 (1991).
[Crossref]

1990 (1)

S. R. Giguere, L. Friedman, R. A. Soref, and J. P. Lorenzo, “Simulation studies of silicon electro–optic waveguide devices,” J. Appl. Phys. 68, 4964–4970 (1990).
[Crossref]

1988 (1)

L. Friedman, R. A. Soref, and J. P. Lorenzo, “Silicon double–injection electro–optic modulator with junction gate control,” J. Appl. Phys. 63, 1831–1839 (1988).
[Crossref]

1987 (2)

R. A. Soref and B. R. Bennett, “Kramers–Kronig analysis of electro–optical switching in silicon,” Proc. SPIE 704, 32–37 (1987).

J. P. Lorenzo and R. A. Soref, “1.3 μm electro–optic silicon switch,” J. Appl. Phys. 51, 6–8 (1987).

Alessandria, A.

Ashgari, M.

Balandin, A. A.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
[Crossref] [PubMed]

Bao, W.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
[Crossref] [PubMed]

Barrios, C. A.

Barwicz, T.

Beausoleil, R. G.

Bennett, B. R.

R. A. Soref and B. R. Bennett, “Kramers–Kronig analysis of electro–optical switching in silicon,” Proc. SPIE 704, 32–37 (1987).

Boscolo, S.

M. Moresco, M. Romagnoli, S. Boscolo, and M. Midrio, “Method for Characterization of Si waveguide propagation loss,” submitted to Opt. Express (2012).

Calizo, I.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
[Crossref] [PubMed]

Cerrina, F.

K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 23, 1888–1890 (2001).
[Crossref]

Chetrit, Y.

Ciftcioglu, B.

Coffa, S.

Cohen, O.

A. Liu, R. Jones, L. Liao, D. Samara–Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high–speed silicon optical modulator based on a metal–oxide semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Coppola, G.

Cutolo, A.

A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, “Silicon electro–optic modulator based on a three-terminal device integrated in a low–loss single–mode SOI waveguide,” J. Lightwave Technol. 15, 505–518 (1997).
[Crossref]

de Almeida, V. R.

DeRose, C. T.

C. T. DeRose, M. R. Watts, D. C. Trotter, D. L. Luck, G. N. Nielson, and R. W. Young, “Silicon microring modulator with integrated heater and temperature sensor for thermal control,” in Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2010, paper CThJ3.

Dong, P.

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2008).
[Crossref]

Fattal, D.

Feng, D.

Feng, N.-N.

Fischer, U.

U. Fischer, B. Schuppert, and K. Petermann, “Integrated optical switches in silicon based on SiGe–waveguides,” IEEE Photon. Technol. Lett. 5, 785–787 (1993).
[Crossref]

Friedman, L.

S. R. Giguere, L. Friedman, R. A. Soref, and J. P. Lorenzo, “Simulation studies of silicon electro–optic waveguide devices,” J. Appl. Phys. 68, 4964–4970 (1990).
[Crossref]

L. Friedman, R. A. Soref, and J. P. Lorenzo, “Silicon double–injection electro–optic modulator with junction gate control,” J. Appl. Phys. 63, 1831–1839 (1988).
[Crossref]

Geim, A. K.

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref] [PubMed]

Geng, B.

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, 64–67 (2011).
[Crossref] [PubMed]

Ghosh, S.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
[Crossref] [PubMed]

Giguere, S. R.

S. R. Giguere, L. Friedman, R. A. Soref, and J. P. Lorenzo, “Simulation studies of silicon electro–optic waveguide devices,” J. Appl. Phys. 68, 4964–4970 (1990).
[Crossref]

Halbout, J. M.

G. V. Treyez, P. G. May, and J. M. Halbout, “Silicon Mach–Zehnder waveguide inteferometers based on the plasma dispersion effect,” Appl. Phys. Lett. 59, 771–773 (1991).
[Crossref]

G. V. Treyez, P. G. May, and J. M. Halbout, “Silicon optical modulators at 1.3 micrometer based on free–carrier absorption,” IEEE Electron. Dev. Lett. 12, 276–278 (1991).
[Crossref]

Hanson, G. W.

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

Haus, H. A.

Huang, H. C.

H. C. Huang and T. C. Lo, “Simulation and analysis of silicon electro–optic modulators utilizing the carrier–dispersion effect and impact–ionization mechanism,” J. Appl. Phys. 74, 1521–1582 (1993).
[Crossref]

Iodice, M.

A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, “Silicon electro–optic modulator based on a three-terminal device integrated in a low–loss single–mode SOI waveguide,” J. Lightwave Technol. 15, 505–518 (1997).
[Crossref]

Izhaki, N.

Jones, R.

A. Liu, R. Jones, L. Liao, D. Samara–Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high–speed silicon optical modulator based on a metal–oxide semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

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, 64–67 (2011).
[Crossref] [PubMed]

Kimerling, L. C.

K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 23, 1888–1890 (2001).
[Crossref]

Krishnamoorthy, A. V.

Lau, C. N.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
[Crossref] [PubMed]

Lee, K. K.

K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 23, 1888–1890 (2001).
[Crossref]

Lentine, A. L.

M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Ultralow power silicon microdisk modulators and switches,” in Proc. of the 5th IEEE International Conference on Group IV Photonics (Cardiff, Wales, 2008).

W. A. Zortman, M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-power high-speed silicon microdisk modulators,” in Proc. Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference (CLEO/QELS) (San Jose, Calif., 2004), paper CThJ4.

Li, G.

Liang, H.

Liao, L.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaki, and M. Paniccia, “High–speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
[Crossref] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara–Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high–speed silicon optical modulator based on a metal–oxide semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Liao, S.

Libertino, S.

Lim, D. R.

K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 23, 1888–1890 (2001).
[Crossref]

Lipson, M.

Liu, A.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaki, and M. Paniccia, “High–speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
[Crossref] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara–Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high–speed silicon optical modulator based on a metal–oxide semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Liu, M.

M. Liu, X. Yin, and X. Zhang, “Double–layer graphene optical modulator,” Nano Lett. 12, 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, 64–67 (2011).
[Crossref] [PubMed]

Lo, T. C.

H. C. Huang and T. C. Lo, “Simulation and analysis of silicon electro–optic modulators utilizing the carrier–dispersion effect and impact–ionization mechanism,” J. Appl. Phys. 74, 1521–1582 (1993).
[Crossref]

Lorenzo, J. P.

S. R. Giguere, L. Friedman, R. A. Soref, and J. P. Lorenzo, “Simulation studies of silicon electro–optic waveguide devices,” J. Appl. Phys. 68, 4964–4970 (1990).
[Crossref]

L. Friedman, R. A. Soref, and J. P. Lorenzo, “Silicon double–injection electro–optic modulator with junction gate control,” J. Appl. Phys. 63, 1831–1839 (1988).
[Crossref]

J. P. Lorenzo and R. A. Soref, “1.3 μm electro–optic silicon switch,” J. Appl. Phys. 51, 6–8 (1987).

Luck, D. L.

C. T. DeRose, M. R. Watts, D. C. Trotter, D. L. Luck, G. N. Nielson, and R. W. Young, “Silicon microring modulator with integrated heater and temperature sensor for thermal control,” in Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2010, paper CThJ3.

Manipatrumi, S.

May, P. G.

G. V. Treyez, P. G. May, and J. M. Halbout, “Silicon Mach–Zehnder waveguide inteferometers based on the plasma dispersion effect,” Appl. Phys. Lett. 59, 771–773 (1991).
[Crossref]

G. V. Treyez, P. G. May, and J. M. Halbout, “Silicon optical modulators at 1.3 micrometer based on free–carrier absorption,” IEEE Electron. Dev. Lett. 12, 276–278 (1991).
[Crossref]

Miao, F.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
[Crossref] [PubMed]

Midrio, M.

M. Moresco, M. Romagnoli, S. Boscolo, and M. Midrio, “Method for Characterization of Si waveguide propagation loss,” submitted to Opt. Express (2012).

Moresco, M.

M. Moresco, M. Romagnoli, S. Boscolo, and M. Midrio, “Method for Characterization of Si waveguide propagation loss,” submitted to Opt. Express (2012).

Nguyen, H.

Nicolaescu, R.

A. Liu, R. Jones, L. Liao, D. Samara–Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high–speed silicon optical modulator based on a metal–oxide semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Nielson, G. N.

C. T. DeRose, M. R. Watts, D. C. Trotter, D. L. Luck, G. N. Nielson, and R. W. Young, “Silicon microring modulator with integrated heater and temperature sensor for thermal control,” in Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2010, paper CThJ3.

Novoselov, K. S.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref] [PubMed]

Paniccia, M.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaki, and M. Paniccia, “High–speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
[Crossref] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara–Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high–speed silicon optical modulator based on a metal–oxide semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Peres, N. M. R.

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

Petermann, K.

U. Fischer, B. Schuppert, and K. Petermann, “Integrated optical switches in silicon based on SiGe–waveguides,” IEEE Photon. Technol. Lett. 5, 785–787 (1993).
[Crossref]

Romagnoli, M.

M. Moresco, M. Romagnoli, S. Boscolo, and M. Midrio, “Method for Characterization of Si waveguide propagation loss,” submitted to Opt. Express (2012).

Rubin, D.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaki, and M. Paniccia, “High–speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
[Crossref] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara–Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high–speed silicon optical modulator based on a metal–oxide semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Samara–Rubio, D.

A. Liu, R. Jones, L. Liao, D. Samara–Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high–speed silicon optical modulator based on a metal–oxide semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Schmidt, B.

Schuppert, B.

U. Fischer, B. Schuppert, and K. Petermann, “Integrated optical switches in silicon based on SiGe–waveguides,” IEEE Photon. Technol. Lett. 5, 785–787 (1993).
[Crossref]

Sciuto, A.

Shafiiha, R.

Shakya, J.

Shin, J.

K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 23, 1888–1890 (2001).
[Crossref]

Soref, R. A.

S. R. Giguere, L. Friedman, R. A. Soref, and J. P. Lorenzo, “Simulation studies of silicon electro–optic waveguide devices,” J. Appl. Phys. 68, 4964–4970 (1990).
[Crossref]

L. Friedman, R. A. Soref, and J. P. Lorenzo, “Silicon double–injection electro–optic modulator with junction gate control,” J. Appl. Phys. 63, 1831–1839 (1988).
[Crossref]

J. P. Lorenzo and R. A. Soref, “1.3 μm electro–optic silicon switch,” J. Appl. Phys. 51, 6–8 (1987).

R. A. Soref and B. R. Bennett, “Kramers–Kronig analysis of electro–optical switching in silicon,” Proc. SPIE 704, 32–37 (1987).

Spirito, P.

A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, “Silicon electro–optic modulator based on a three-terminal device integrated in a low–loss single–mode SOI waveguide,” J. Lightwave Technol. 15, 505–518 (1997).
[Crossref]

Stauber, T.

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

Teweldebrhan, D.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
[Crossref] [PubMed]

Treyez, G. V.

G. V. Treyez, P. G. May, and J. M. Halbout, “Silicon Mach–Zehnder waveguide inteferometers based on the plasma dispersion effect,” Appl. Phys. Lett. 59, 771–773 (1991).
[Crossref]

G. V. Treyez, P. G. May, and J. M. Halbout, “Silicon optical modulators at 1.3 micrometer based on free–carrier absorption,” IEEE Electron. Dev. Lett. 12, 276–278 (1991).
[Crossref]

Trotter, D. C.

C. T. DeRose, M. R. Watts, D. C. Trotter, D. L. Luck, G. N. Nielson, and R. W. Young, “Silicon microring modulator with integrated heater and temperature sensor for thermal control,” in Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2010, paper CThJ3.

W. A. Zortman, M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-power high-speed silicon microdisk modulators,” in Proc. Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference (CLEO/QELS) (San Jose, Calif., 2004), paper CThJ4.

M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Ultralow power silicon microdisk modulators and switches,” in Proc. of the 5th IEEE International Conference on Group IV Photonics (Cardiff, Wales, 2008).

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, 64–67 (2011).
[Crossref] [PubMed]

Vakil, A.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2008).
[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, 64–67 (2011).
[Crossref] [PubMed]

Watts, M. R.

C. T. DeRose, M. R. Watts, D. C. Trotter, D. L. Luck, G. N. Nielson, and R. W. Young, “Silicon microring modulator with integrated heater and temperature sensor for thermal control,” in Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2010, paper CThJ3.

M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Ultralow power silicon microdisk modulators and switches,” in Proc. of the 5th IEEE International Conference on Group IV Photonics (Cardiff, Wales, 2008).

W. A. Zortman, M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-power high-speed silicon microdisk modulators,” in Proc. Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference (CLEO/QELS) (San Jose, Calif., 2004), paper CThJ4.

Xu, Q.

Yariv, A.

A. Yariv, “Critical coupling and its control in optical waveguide–ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002).
[Crossref]

Yin, X.

M. Liu, X. Yin, and X. Zhang, “Double–layer graphene optical modulator,” Nano Lett. 12, 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, 64–67 (2011).
[Crossref] [PubMed]

Young, R. W.

C. T. DeRose, M. R. Watts, D. C. Trotter, D. L. Luck, G. N. Nielson, and R. W. Young, “Silicon microring modulator with integrated heater and temperature sensor for thermal control,” in Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2010, paper CThJ3.

M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Ultralow power silicon microdisk modulators and switches,” in Proc. of the 5th IEEE International Conference on Group IV Photonics (Cardiff, Wales, 2008).

W. A. Zortman, M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-power high-speed silicon microdisk modulators,” in Proc. Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference (CLEO/QELS) (San Jose, Calif., 2004), paper CThJ4.

Zeni, L.

A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, “Silicon electro–optic modulator based on a three-terminal device integrated in a low–loss single–mode SOI waveguide,” J. Lightwave Technol. 15, 505–518 (1997).
[Crossref]

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, 64–67 (2011).
[Crossref] [PubMed]

Zhang, X.

M. Liu, X. Yin, and X. Zhang, “Double–layer graphene optical modulator,” Nano Lett. 12, 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, 64–67 (2011).
[Crossref] [PubMed]

Zheng, X.

Zortman, W. A.

W. A. Zortman, M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-power high-speed silicon microdisk modulators,” in Proc. Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference (CLEO/QELS) (San Jose, Calif., 2004), paper CThJ4.

Appl. Phys. Lett. (1)

G. V. Treyez, P. G. May, and J. M. Halbout, “Silicon Mach–Zehnder waveguide inteferometers based on the plasma dispersion effect,” Appl. Phys. Lett. 59, 771–773 (1991).
[Crossref]

IEEE Electron. Dev. Lett. (1)

G. V. Treyez, P. G. May, and J. M. Halbout, “Silicon optical modulators at 1.3 micrometer based on free–carrier absorption,” IEEE Electron. Dev. Lett. 12, 276–278 (1991).
[Crossref]

IEEE Photon. Technol. Lett. (2)

U. Fischer, B. Schuppert, and K. Petermann, “Integrated optical switches in silicon based on SiGe–waveguides,” IEEE Photon. Technol. Lett. 5, 785–787 (1993).
[Crossref]

A. Yariv, “Critical coupling and its control in optical waveguide–ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002).
[Crossref]

J. Appl. Phys. (5)

J. P. Lorenzo and R. A. Soref, “1.3 μm electro–optic silicon switch,” J. Appl. Phys. 51, 6–8 (1987).

L. Friedman, R. A. Soref, and J. P. Lorenzo, “Silicon double–injection electro–optic modulator with junction gate control,” J. Appl. Phys. 63, 1831–1839 (1988).
[Crossref]

S. R. Giguere, L. Friedman, R. A. Soref, and J. P. Lorenzo, “Simulation studies of silicon electro–optic waveguide devices,” J. Appl. Phys. 68, 4964–4970 (1990).
[Crossref]

H. C. Huang and T. C. Lo, “Simulation and analysis of silicon electro–optic modulators utilizing the carrier–dispersion effect and impact–ionization mechanism,” J. Appl. Phys. 74, 1521–1582 (1993).
[Crossref]

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

J. Lightwave Technol. (4)

Nano Lett. (2)

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
[Crossref] [PubMed]

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

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[Crossref] [PubMed]

Nature (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, 64–67 (2011).
[Crossref] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara–Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high–speed silicon optical modulator based on a metal–oxide semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (1)

K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 23, 1888–1890 (2001).
[Crossref]

Phys. Rev. B (1)

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

Proc. SPIE (1)

R. A. Soref and B. R. Bennett, “Kramers–Kronig analysis of electro–optical switching in silicon,” Proc. SPIE 704, 32–37 (1987).

Science (1)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2008).
[Crossref]

Other (4)

CST Microwave Studio 2012. Darmstadt, Germany.

W. A. Zortman, M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-power high-speed silicon microdisk modulators,” in Proc. Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference (CLEO/QELS) (San Jose, Calif., 2004), paper CThJ4.

M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Ultralow power silicon microdisk modulators and switches,” in Proc. of the 5th IEEE International Conference on Group IV Photonics (Cardiff, Wales, 2008).

C. T. DeRose, M. R. Watts, D. C. Trotter, D. L. Luck, G. N. Nielson, and R. W. Young, “Silicon microring modulator with integrated heater and temperature sensor for thermal control,” in Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2010, paper CThJ3.

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Figures (6)

Fig. 1
Fig. 1 Left: transmission curve as a function of the ring transmission α for t=0.8 at resonance. Inset: schematic diagram of the ring structure, with definition of the straight waveguide and ring single pass transmission, t and α, respectively. Right: the layout of the graphene–assisted optical ring modulator we have used in our simulations. The dashed area is the region where graphene is present.

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Fig. 2
Fig. 2 Left panel: Schematic diagram (not to scale) of the ring waveguide. Light blue is the silicon core, yellow is alumina and red is graphene, respectively. Silica cladding is not shown. Right panel: Power density and lines of force of the electric field of the fundamental TE mode.

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Fig. 3
Fig. 3 Left panel: Conductivity of graphene for chemical potential μC = 0.3 eV (solid line) and μC = 0.5 eV (dashed line) for T=300 K. The vertical line highlights value of the conductivity for photons with free-space wavelength equal to 1550 nm. Right panel: relation between carrier density and chemical potential for an isolated sheet of graphene.

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Fig. 4
Fig. 4 Left panel: a plot from CST main window, showing the structure used in the simulation performed to compute bending losses along with the mesh. The ocher, blu and red regions are the silicon core, alumina coating and graphene layers, respectively. Though barely observable, two layers of graphene are present. Right panel: bending loss in the absence and presence of the two graphene layers (solid and dashed lines, respectively). The graphene conductivity is set equal to σHigh.

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Fig. 5
Fig. 5 Left panel: Transmission in a critically–coupled ring with gap g = 100 nm, average radius equal to 5 μm for graphene conductivity σ = σHigh (solid line) and σ = σLow (dashed curve). Right panel: numerically computed 6 dB bandwidth versus the gap distance g.

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Fig. 6
Fig. 6 Left panel: Estimate of the energy required for switching with a pseudo–random bit–sequence (PRBS) in a ring modulator with oxide being constituted by a 7 nm thick layer of alumina (εrel,diel = 10 at microwaves). Right panel: numerically evaluated dependence of the required switching energy versus the available bandwidth.

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Equations (15)

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[ b 1 b 2 ] = [ t k * − k t ] [ a 1 a 2 ] ,         with         | t | 2 + | k | 2 = 1             and           a 2 = α b 2 e i φ .
T = | b 1 a 1 | 2 = ( α − | t | ) 2 ( 1 − α | t | ) 2 .
σ R ( ω ) ≃ σ 0 2 ( tanh h ¯ ω + 2 μ C 4 k B T + tanh h ¯ ω − 2 μ C 4 k B T ) .
σ 0 = e 2 4 h ¯ ≃ 6.0853 × 10 − 5 Siemens .
σ High = 0.98 σ 0 h Graphene ≃ 1.75 × 10 5 S / m ,                         σ Low = 0.02 σ 0 h Graphene ≃ 3.58 × 10 3 S / m .
n s = 2 π h ¯ 2 v F 2 ∫ 0 + ∞ ε [ f d ( ε ) − f d ( ε + 2 μ C ) ] d ε ,
No   graphene n eff = 2.2576 Graphene   with   low   conductivity   ( σ = σ Low , ε = ε Low ) n eff = 2.2543 − i 8.42 × 10 − 5 Graphene   with   high   conductivity   ( σ = σ High , ε = ε High ) n eff = 2.2546 − i 3.79 × 10 − 3
A High ≃ 0.13 dB / μ m ⋅ L Graphene + 1.4 × 10 − 3   dB / μ m ( L Ring − L Graphene ) ≃ 1.34   dB ,
A Low ≃ 2.8 × 10 − 3 dB / μ m ⋅ L Graphene + 1.4 × 10 − 3 dB / μ m ( L Ring − L Graphene ) ≃ 0.058   dB
E PRBS = 1 2 Q ON 2 − Q OFF 2 2 C
Q ON = ρ ON e S ,             S = ψ Graphene R Ave W
C = ε 0 ε rel , diel S h diel
V ON , OFF = Q ON , OFF C = ρ ON , OFF e ε 0 ε rel , diel h diel
E PRBS = 1 2 ( ρ ON 2 − ρ OFF 2 ) e 2 h diel S 2 ε 0 ε rel , diel .
Δ n Si n Si ≃ Δ f f → Δ n Si ≃ 0.125   THz 200   THz 12 ≃ 2 × 10 − 3 .

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