Abstract

We present a hybrid graphene–silicon waveguide, which consists of a lateral slot waveguide with three layers of graphene flakes inside. Through a theoretical analysis, an effective index variation for about 0.05 is found in the waveguide by applying a voltage on the graphene. We designed a Mach–Zehnder modulator based on this waveguide and demonstrated it can process signals nearly chirp-free. The calculation shows that the driving voltage is only 1 V even if the length of the arm is shortened to be 43.54 μm. An extinction up to 34.7 dB and a minimum chirp parameter of 0.006 are obtained. Its insertion loss is roughly 1.37dB. This modulator consumes low power and has a small footprint. It can potentially be ultrafast as well as CMOS compatible.

© 2013 Optical Society of America

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2012 (11)

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, Nano Lett. 12, 2773 (2012).
[CrossRef]

M. Liu, X. Yin, and X. Zhang, Nano Lett. 12, 1482 (2012).
[CrossRef]

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, Nat. Nanotechnol. 7, 330 (2012).
[CrossRef]

S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. D. Abajo, Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef]

K. V. Acoleyen, J. Roels, P. Mechet, T. Claes, D. V. Thourhout, and R. Baets, IEEE Photon. J. 4, 779 (2012).
[CrossRef]

Z. Luo, N. J. Pinto, Y. Davila, and A. T. C. Johnson, Appl. Phys. Lett. 100, 253108 (2012).
[CrossRef]

Q. Bao and K. P. Loh, ACS Nano 6, 3677 (2012).
[CrossRef]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

Z. Lu and W. Zhao, J. Opt. Soc. Am. B 29, 1490 (2012).
[CrossRef]

C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, Opt. Express 20, 22398 (2012).
[CrossRef]

H. Yi, Q. Long, W. Tan, L. Li, X. Wang, and Z. Zhou, Opt. Express 20, 27562 (2012).
[CrossRef]

2011 (7)

S. H. Choi, Y. L. Kim, and K. M. Byun, Opt. Express 19, 458 (2011).
[CrossRef]

Y. Wei, Y. Zhao, J. Yang, M. Wang, and X. Jiang, J. Lightwave Technol. 29, 1011 (2011).
[CrossRef]

J. T. Kim and S.-Y. Choi, Opt. Express 19, 24557 (2011).
[CrossRef]

T. Sohier and B. Yu, Appl. Phys. Lett. 98, 213104 (2011).
[CrossRef]

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, Nat. Photonics 5, 411 (2011).
[CrossRef]

2010 (3)

2009 (2)

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photonics 3, 216 (2009).
[CrossRef]

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, Nat. Nanotechnol. 4, 839 (2009).
[CrossRef]

2008 (1)

G. W. Hanson, J. Appl. Phys. 103, 064302 (2008).
[CrossRef]

2007 (1)

S. A. Mikhailov and K. Ziegler, Phys. Rev. Lett. 99, 016803 (2007).
[CrossRef]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

1993 (1)

R. A. Jishi, M. S. Dresselhaus, and G. Dresselhaus, Phys. Rev. B 48, 11385 (1993).
[CrossRef]

Abajo, F. J. G. D.

S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. D. Abajo, Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef]

Acoleyen, K. V.

K. V. Acoleyen, J. Roels, P. Mechet, T. Claes, D. V. Thourhout, and R. Baets, IEEE Photon. J. 4, 779 (2012).
[CrossRef]

Andrews, A. M.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, Nano Lett. 12, 2773 (2012).
[CrossRef]

Avouris, P.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, Nat. Nanotechnol. 7, 330 (2012).
[CrossRef]

T. Mueller, F. Xia, and P. Avouris, Nat. Photonics 4, 297 (2010).
[CrossRef]

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, Nat. Nanotechnol. 4, 839 (2009).
[CrossRef]

Baets, R.

K. V. Acoleyen, J. Roels, P. Mechet, T. Claes, D. V. Thourhout, and R. Baets, IEEE Photon. J. 4, 779 (2012).
[CrossRef]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photonics 3, 216 (2009).
[CrossRef]

Bao, Q.

Q. Bao and K. P. Loh, ACS Nano 6, 3677 (2012).
[CrossRef]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, Nat. Photonics 5, 411 (2011).
[CrossRef]

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photonics 3, 216 (2009).
[CrossRef]

Bogaerts, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photonics 3, 216 (2009).
[CrossRef]

Byun, K. M.

Carini, J. L.

Chandra, B.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, Nat. Nanotechnol. 7, 330 (2012).
[CrossRef]

Choi, S. H.

Choi, S.-Y.

Chu, H. S.

Claes, T.

K. V. Acoleyen, J. Roels, P. Mechet, T. Claes, D. V. Thourhout, and R. Baets, IEEE Photon. J. 4, 779 (2012).
[CrossRef]

Davila, Y.

Z. Luo, N. J. Pinto, Y. Davila, and A. T. C. Johnson, Appl. Phys. Lett. 100, 253108 (2012).
[CrossRef]

Detz, H.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, Nano Lett. 12, 2773 (2012).
[CrossRef]

Diederich, F.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photonics 3, 216 (2009).
[CrossRef]

Dresselhaus, G.

R. A. Jishi, M. S. Dresselhaus, and G. Dresselhaus, Phys. Rev. B 48, 11385 (1993).
[CrossRef]

Dresselhaus, M. S.

R. A. Jishi, M. S. Dresselhaus, and G. Dresselhaus, Phys. Rev. B 48, 11385 (1993).
[CrossRef]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Dumon, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photonics 3, 216 (2009).
[CrossRef]

Engheta, N.

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photonics 3, 216 (2009).
[CrossRef]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Freitag, M.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, Nat. Nanotechnol. 7, 330 (2012).
[CrossRef]

Freude, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photonics 3, 216 (2009).
[CrossRef]

Furchi, M.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, Nano Lett. 12, 2773 (2012).
[CrossRef]

Geim, A. K.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Geng, B.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Gould, P. L.

Grigorenko, A. N.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Hanson, G. W.

G. W. Hanson, J. Appl. Phys. 103, 064302 (2008).
[CrossRef]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Jiang, X.

Jin, Y.

Jishi, R. A.

R. A. Jishi, M. S. Dresselhaus, and G. Dresselhaus, Phys. Rev. B 48, 11385 (1993).
[CrossRef]

Johnson, A. T. C.

Z. Luo, N. J. Pinto, Y. Davila, and A. T. C. Johnson, Appl. Phys. Lett. 100, 253108 (2012).
[CrossRef]

Ju, L.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Kim, J. T.

Kim, Y. L.

Klang, P.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, Nano Lett. 12, 2773 (2012).
[CrossRef]

Koh, W. S.

Koos, C.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photonics 3, 216 (2009).
[CrossRef]

Koppens, F. H. L.

S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. D. Abajo, Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef]

Leuthold, J.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photonics 3, 216 (2009).
[CrossRef]

Li, E. P.

Li, L.

Li, X.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, Nat. Nanotechnol. 7, 330 (2012).
[CrossRef]

Lilley, G.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, Nano Lett. 12, 2773 (2012).
[CrossRef]

Lim, C. H. Y. X.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, Nat. Photonics 5, 411 (2011).
[CrossRef]

Lin, Y.-M.

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, Nat. Nanotechnol. 4, 839 (2009).
[CrossRef]

Liu, M.

M. Liu, X. Yin, and X. Zhang, Nano Lett. 12, 1482 (2012).
[CrossRef]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Loh, K. P.

Q. Bao and K. P. Loh, ACS Nano 6, 3677 (2012).
[CrossRef]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, Nat. Photonics 5, 411 (2011).
[CrossRef]

Long, Q.

Lu, Z.

Luo, Z.

Z. Luo, N. J. Pinto, Y. Davila, and A. T. C. Johnson, Appl. Phys. Lett. 100, 253108 (2012).
[CrossRef]

Mechet, P.

K. V. Acoleyen, J. Roels, P. Mechet, T. Claes, D. V. Thourhout, and R. Baets, IEEE Photon. J. 4, 779 (2012).
[CrossRef]

Michinobu, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photonics 3, 216 (2009).
[CrossRef]

Mikhailov, S. A.

S. A. Mikhailov and K. Ziegler, Phys. Rev. Lett. 99, 016803 (2007).
[CrossRef]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Mueller, T.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, Nano Lett. 12, 2773 (2012).
[CrossRef]

T. Mueller, F. Xia, and P. Avouris, Nat. Photonics 4, 297 (2010).
[CrossRef]

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, Nat. Nanotechnol. 4, 839 (2009).
[CrossRef]

Ni, Z.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, Nat. Photonics 5, 411 (2011).
[CrossRef]

Novoselov, K. S.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Pechkis, J. A.

Pinto, N. J.

Z. Luo, N. J. Pinto, Y. Davila, and A. T. C. Johnson, Appl. Phys. Lett. 100, 253108 (2012).
[CrossRef]

Polini, M.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

Pospischil, A.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, Nano Lett. 12, 2773 (2012).
[CrossRef]

Roels, J.

K. V. Acoleyen, J. Roels, P. Mechet, T. Claes, D. V. Thourhout, and R. Baets, IEEE Photon. J. 4, 779 (2012).
[CrossRef]

Rogers, C. E.

Schrenk, W.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, Nano Lett. 12, 2773 (2012).
[CrossRef]

Sohier, T.

T. Sohier and B. Yu, Appl. Phys. Lett. 98, 213104 (2011).
[CrossRef]

Strasser, G.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, Nano Lett. 12, 2773 (2012).
[CrossRef]

Tan, W.

Tang, D. Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, Nat. Photonics 5, 411 (2011).
[CrossRef]

Thongrattanasiri, S.

S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. D. Abajo, Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef]

Thourhout, D. V.

K. V. Acoleyen, J. Roels, P. Mechet, T. Claes, D. V. Thourhout, and R. Baets, IEEE Photon. J. 4, 779 (2012).
[CrossRef]

Tulevski, G.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, Nat. Nanotechnol. 7, 330 (2012).
[CrossRef]

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Unterrainer, K.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, Nano Lett. 12, 2773 (2012).
[CrossRef]

Urich, A.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, Nano Lett. 12, 2773 (2012).
[CrossRef]

Vakil, A.

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

Valdes-Garcia, A.

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, Nat. Nanotechnol. 4, 839 (2009).
[CrossRef]

Vallaitis, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photonics 3, 216 (2009).
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Figures (4)

Fig. 1.
Fig. 1.

Illustration of the Mach–Zehnder modulator structure. (a) 3D view of the device, (b) 2D vertical view of the modulator, and (c) 2D cross section of the modulator’s arm. One metal electrode is brought into contact with the first and third graphene layers. Another metal electrode is brought into contact with the second graphene layer. The refractive indices of Si, SiO2, and Si3N4 are 3.47, 1.447, and 1.98 in the simulation, respectively.

Fig. 2.
Fig. 2.

(a) Optical mode profile in the GSW for TM modes, (b) permittivity of graphene under different graphene chemical potentials, and (c) variation of the effective index in the modulator arm under different graphene chemical potentials. All the simulations and analyses are based on λ=1550nm and T=300K.

Fig. 3.
Fig. 3.

(a) Illustration of the push–pull modulation effect. The lateral axis shows the applied voltage on the graphene in the first modulator arm. The red curve stands for the phase change in the first arm, while the blue one stands for the second arm. The green curve refers to the normalized transmission power of the output signals. (b) Chirp parameter for a 10 GHz sinusoidal modulation signal.

Fig. 4.
Fig. 4.

Open circles represent the phase-modulating ability under different temperatures. The triangles represent light absorption peak values under different temperatures. The dashed lines are fitted curves for the circles and triangles.

Equations (6)

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

εg=1+i·σωε0Δ=1Im(σ)ωε0Δ+i·Re(σ)ωε0Δ,
σintra=ie2π2(ω+i2Γ)[0ε(fd(ε)εfd(ε)ε)dε],
σinter=ie2(ω+i2Γ)π2[0fd(ε)fd(ε)(ω+i2Γ)24(ε/)2dε],
μc=νFπ|η(Vg+V0)|,
T(Φ)=14×[eIm(β1)L+eIm(β2)L+2eIm(β1)L+Im(β2)L2cos(Φ)],
αchirp=2(d(Δφ1+Δφ2)dt)/(1T(Φ)dT(Φ)dt).

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