Abstract

Graphene has attracted a high level of research interest because of its outstanding electronic transport properties and optical properties. Based on the Kubo formalism and the Maxwell equations, it’s demonstrated that the optical conductivity of graphene can be controlled through the applied voltage. And we find that the graphene-oxide-silicon (GOS) based waveguide can be made into either the electro-absorptive or electron-refractive modulators. Using graphene as the active medium, we present a new electro-refractive Mach-Zender interferometer based on the GOS structure. This new GOS-based electron-refractive modulation mechanism can enable novel architectures for on-chip optical communications.

© 2012 OSA

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  3. L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express 19(12), 11841–11851 (2011).
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    [CrossRef] [PubMed]
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  22. X. L. Wen and Y. L. Long, “An implementation of a root-finding algorithm for transcendental functions in a complex plane,” J. Numer. Methods & Comput. Appl. No. 2, 88–92 (1994).
  23. 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]

2012 (6)

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

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

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[CrossRef] [PubMed]

T. Gu, N. Petrone, J. F. McMillan, A. V. D. Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[CrossRef]

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[CrossRef] [PubMed]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Components for silicon plasmonic nanocircuits based on horizontal Cu-SiO₂-Si-SiO₂-Cu nanoplasmonic waveguides,” Opt. Express 20(6), 5867–5881 (2012).
[CrossRef] [PubMed]

2011 (4)

L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express 19(12), 11841–11851 (2011).
[CrossRef] [PubMed]

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]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. Xuan, Y. Wang, C. H. Y. X. Lim, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

2010 (1)

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[CrossRef]

2008 (4)

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]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

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

G. W. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallel-plate waveguide,” J. Appl. Phys. 104(8), 084314 (2008).
[CrossRef]

2007 (3)

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

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

J. Yan, Y. Zhang, P. Kim, and A. Pinczuk, “Electric Field Effect Tuning of Electron-Phonon Coupling in Graphene,” Phys. Rev. Lett. 98(16), 166802 (2007).
[CrossRef] [PubMed]

2005 (1)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

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(6975), 615–618 (2004).
[CrossRef] [PubMed]

1994 (1)

X. L. Wen and Y. L. Long, “An implementation of a root-finding algorithm for transcendental functions in a complex plane,” J. Numer. Methods & Comput. Appl. No. 2, 88–92 (1994).

1987 (1)

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

Alloatti, L.

Baets, R.

Bao, Q.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. Xuan, Y. Wang, C. H. Y. X. Lim, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Barklund, A.

Bennett, B. R.

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

Bogaerts, W.

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]

Carbotte, J. P.

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

Cho, S. H.

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]

Choi, J. Y.

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]

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[CrossRef] [PubMed]

Chung, H. J.

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]

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(6975), 615–618 (2004).
[CrossRef] [PubMed]

Crommie, M.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

de Abajo, F. J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[CrossRef] [PubMed]

Dinu, R.

Dumon, P.

Fedeli, J.

Fournier, M.

Freude, W.

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]

Gardes, F. Y.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[CrossRef]

Geim, A. K.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 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(7349), 64–67 (2011).
[CrossRef] [PubMed]

Girit, C.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

Gu, T.

T. Gu, N. Petrone, J. F. McMillan, A. V. D. Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[CrossRef]

Gusynin, V. P.

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

Haley, C.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. Xuan, Y. Wang, C. H. Y. X. Lim, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Hanson, G. W.

G. W. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallel-plate waveguide,” J. Appl. Phys. 104(8), 084314 (2008).
[CrossRef]

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

Hillerkuss, D.

Hone, J.

T. Gu, N. Petrone, J. F. McMillan, A. V. D. Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[CrossRef]

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]

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, Z.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[CrossRef] [PubMed]

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(6975), 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(7349), 64–67 (2011).
[CrossRef] [PubMed]

Kaneko, R.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[CrossRef] [PubMed]

Kawayama, I.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[CrossRef] [PubMed]

Kim, K.

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]

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]

J. Yan, Y. Zhang, P. Kim, and A. Pinczuk, “Electric Field Effect Tuning of Electron-Phonon Coupling in Graphene,” Phys. Rev. Lett. 98(16), 166802 (2007).
[CrossRef] [PubMed]

Kim, T.

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]

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]

Koester, S. J.

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

Kono, J.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[CrossRef] [PubMed]

Koos, C.

Koppens, F. H. L.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[CrossRef] [PubMed]

Korn, D.

Kwong, D. L.

T. Gu, N. Petrone, J. F. McMillan, A. V. D. Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[CrossRef]

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Components for silicon plasmonic nanocircuits based on horizontal Cu-SiO₂-Si-SiO₂-Cu nanoplasmonic waveguides,” Opt. Express 20(6), 5867–5881 (2012).
[CrossRef] [PubMed]

Leuthold, J.

Li, J.

Li, M.

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

Liao, L.

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(6975), 615–618 (2004).
[CrossRef] [PubMed]

Lim, C. H. Y. X.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. Xuan, Y. Wang, C. H. Y. X. Lim, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Lipson, M.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Liu, A.

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(6975), 615–618 (2004).
[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]

Lo, G. Q.

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Components for silicon plasmonic nanocircuits based on horizontal Cu-SiO₂-Si-SiO₂-Cu nanoplasmonic waveguides,” Opt. Express 20(6), 5867–5881 (2012).
[CrossRef] [PubMed]

T. Gu, N. Petrone, J. F. McMillan, A. V. D. Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[CrossRef]

Loh, K. P.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. Xuan, Y. Wang, C. H. Y. X. Lim, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Long, Y. L.

X. L. Wen and Y. L. Long, “An implementation of a root-finding algorithm for transcendental functions in a complex plane,” J. Numer. Methods & Comput. Appl. No. 2, 88–92 (1994).

Manjavacas, A.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[CrossRef] [PubMed]

Mashanovich, G.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[CrossRef]

McMillan, J. F.

T. Gu, N. Petrone, J. F. McMillan, A. V. D. Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[CrossRef]

Nanot, S.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[CrossRef] [PubMed]

Ni, Z.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. Xuan, Y. Wang, C. H. Y. X. Lim, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

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(6975), 615–618 (2004).
[CrossRef] [PubMed]

Novoselov, K. S.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

Palmer, R.

Paniccia, M.

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(6975), 615–618 (2004).
[CrossRef] [PubMed]

Petrone, N.

T. Gu, N. Petrone, J. F. McMillan, A. V. D. Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[CrossRef]

Pinczuk, A.

J. Yan, Y. Zhang, P. Kim, and A. Pinczuk, “Electric Field Effect Tuning of Electron-Phonon Coupling in Graphene,” Phys. Rev. Lett. 98(16), 166802 (2007).
[CrossRef] [PubMed]

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Reed, G. T.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[CrossRef]

Ren, L.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[CrossRef] [PubMed]

Rubin, 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(6975), 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(6975), 615–618 (2004).
[CrossRef] [PubMed]

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Sharapov, S. G.

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

Shen, Y. R.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

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]

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]

Sun, Z.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[CrossRef] [PubMed]

Tang, D. Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. Xuan, Y. Wang, C. H. Y. X. Lim, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Thomson, D. J.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[CrossRef]

Thongrattanasiri, S.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[CrossRef] [PubMed]

Tian, C.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

Tonouchi, M.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[CrossRef] [PubMed]

Tour, J. M.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[CrossRef] [PubMed]

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]

Wang, B.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. Xuan, Y. Wang, C. H. Y. X. Lim, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Wang, F.

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

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

Wang, Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. Xuan, Y. Wang, C. H. Y. X. Lim, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Wen, X. L.

X. L. Wen and Y. L. Long, “An implementation of a root-finding algorithm for transcendental functions in a complex plane,” J. Numer. Methods & Comput. Appl. No. 2, 88–92 (1994).

Wieland, J.

Wong, C. W.

T. Gu, N. Petrone, J. F. McMillan, A. V. D. Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[CrossRef]

Xu, Q.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Xuan, Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. Xuan, Y. Wang, C. H. Y. X. Lim, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Yan, J.

J. Yan, Y. Zhang, P. Kim, and A. Pinczuk, “Electric Field Effect Tuning of Electron-Phonon Coupling in Graphene,” Phys. Rev. Lett. 98(16), 166802 (2007).
[CrossRef] [PubMed]

Yan, Z.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[CrossRef] [PubMed]

Yao, J.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[CrossRef] [PubMed]

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]

Yu, H.

Yu, M.

T. Gu, N. Petrone, J. F. McMillan, A. V. D. Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[CrossRef]

Zande, A. V. D.

T. Gu, N. Petrone, J. F. McMillan, A. V. D. Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[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(7349), 64–67 (2011).
[CrossRef] [PubMed]

Zettl, A.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

Zhang, H.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. Xuan, Y. Wang, C. H. Y. X. Lim, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

Zhang, Q.

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (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]

Zhang, Y.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

J. Yan, Y. Zhang, P. Kim, and A. Pinczuk, “Electric Field Effect Tuning of Electron-Phonon Coupling in Graphene,” Phys. Rev. Lett. 98(16), 166802 (2007).
[CrossRef] [PubMed]

Zhu, S. Y.

ACS Nano (1)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

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

IEEE J. Quantum Electron. (1)

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

J. Appl. Phys. (2)

G. W. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallel-plate waveguide,” J. Appl. Phys. 104(8), 084314 (2008).
[CrossRef]

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

J. Numer. Methods & Comput. Appl. No. (1)

X. L. Wen and Y. L. Long, “An implementation of a root-finding algorithm for transcendental functions in a complex plane,” J. Numer. Methods & Comput. Appl. No. 2, 88–92 (1994).

J. Phys. Condens. Matter (1)

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

Nano Lett. (2)

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[CrossRef] [PubMed]

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

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

Nat. Photonics (3)

T. Gu, N. Petrone, J. F. McMillan, A. V. D. Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[CrossRef]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. Xuan, Y. Wang, C. H. Y. X. Lim, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[CrossRef]

Nature (4)

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]

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(6975), 615–618 (2004).
[CrossRef] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Rev. Lett. (1)

J. Yan, Y. Zhang, P. Kim, and A. Pinczuk, “Electric Field Effect Tuning of Electron-Phonon Coupling in Graphene,” Phys. Rev. Lett. 98(16), 166802 (2007).
[CrossRef] [PubMed]

Science (1)

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[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]

Other (1)

H. Li, Y. Anugrah, S. J. Koester, and M. Li, “Optical absorption in graphene integrated on silicon waveguides,” arXiv: 1205.4050v1, 2012.

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Figures (6)

Fig. 1
Fig. 1

2D model in which graphene is considered as a conductive interface between Oxide (Al2O3) and air. During the calculation, the oxide is defined as Al2O3.ε0 = 1.4552,ε1 = 3.4552,ε2 = 1.7462,ε3 = 1. Inset is the cross-section of the GOS waveguide. G represents graphene in the inset figure.

Fig. 2
Fig. 2

Interband and intraband conductivity (unit of S) as a function of chemical potential at wavelength 1550 nm,T = 300 K,τ = 5 × 10−13 s.

Fig. 3
Fig. 3

the effective index of the TM mode varies with d2 (the thickness of the oxide layer), the left inset is the mode distribution of Hy and Ex when d1 = 250 nm, d2 = 10 nm.

Fig. 4
Fig. 4

the effective index and the loss of the TM mode varies with μ c (the chemical potential of graphene) when d1 = 250 nm, d2 = 10 nm.

Fig. 5
Fig. 5

The sketch map of the GOS based MZI. (a) is the schematic 3D drawing of the MZI. (b) is the vertical show of the MZI. (c) is the cross section of the MZI-arm;

Fig. 6
Fig. 6

The transmission of the GOS MZI varies with the chemical potential.

Equations (10)

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

×H=ε ε r E t +σE
×E=μ H t
( 2 x 2 + 2 z 2 + ε i k 0 2 ) H y (x,z)=0
n ^ ×( E + E )=0 n ^ ×( H + H )=σE lim x± E,H=0
arctan( T 2 Q 3 )+arctan( T 1 )+mπ= γ 1 d 1 Q 3 = 1Rtanh( γ 2 d 2 ) Rtanh( γ 2 d 2 ) R= ε 3 γ 2 ε 2 γ 3 ( σ γ 3 jω ε 3 ε 1 )
σ( ω, μ c ,τ,T )= j e 2 (ωj τ 1 ) π 2 [ 1 ( ωj τ 1 ) 2 0 ξ( f d ( ξ ) ξ f d ( ξ ) ξ )dξ 0 f d ( ξ ) f d ( ξ ) ( ωj τ 1 ) 2 4 ( ξ/ ) 2 dξ ]
σ intra (ω)=j e 2 k B T π 2 (ωj τ 1 ) [ μ c k B T +2ln( e μ c / k B T +1 ) ]
σ inter (ω)= j e 2 4π ln( 2| μ c |(ωj τ 1 ) 2| μ c |+(ωj τ 1 ) )
| μ c || E F ( V g ) |= ν F π| a 0 ( V g V Dirac ) |
T(λ)= 1 4 ×[ exp( α 0 L)+exp( α 1 L)+2exp( α 0 L+ α 1 L 2 )cos(Δϕ) ]

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