Abstract

We report observation of optical bistability and enhanced thermal nonlinearity in a graphene–silicon waveguide resonator. Photo-induced Joule heating in the graphene layer gives rise to a temperature increase in the silicon waveguide core and a corresponding thermo-optic shift in the resonance of the Fabry–Perot resonator. Measurement of the nonlinear resonance spectra showed a 9-fold increase in the effective thermal nonlinear index due to the graphene layer compared with a bare silicon waveguide.

© 2013 Optical Society of America

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    [CrossRef]

2014

Z. Cheng, H. K. Tsang, X. Wang, K. Xu, and J. B. Xu, IEEE J. Sel. Topics Quantum Electron. 20, 1 (2014).

2012

J. Kang, D. Shin, S. Bae, and B. H. Hong, Nanoscale 4, 5527 (2012).
[CrossRef]

H. Li, Y. Anugrah, S. J. Koester, and M. Li, Appl. Phys. Lett. 101, 111110 (2012).

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, Nat. Photonics 6, 554 (2012).
[CrossRef]

J. T. Kim and C. G. Choi, Opt. Express 20, 3556 (2012).

A. Grieco, B. Slutsky, D. T. H. Tan, S. Zamek, M. P. Nezhad, and Y. Fainman, J. Lightwave Technol. 30, 2352 (2012).
[CrossRef]

A. Locatelli, A. Capobianco, M. Midrio, S. Boscolo, and C. De Angelis, Opt. Express 20, 28479 (2012).
[CrossRef]

2011

D. Perron, M. Wu, C. Horvath, D. Bachman, and V. Van, Opt. Lett. 36, 2731 (2011).
[CrossRef]

Z. Yan, Z. Peng, Z. Sun, J. Yao, Y. Zhu, Z. Liu, P. M. Ajayan, and J. M. Tour, ACS Nano 5, 8187 (2011).

2008

L. A. Falkovsky, J. Phys. Conf. Ser. 129, 012004 (2008).
[CrossRef]

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Nano Lett. 8, 902 (2008).

1986

Ajayan, P. M.

Z. Yan, Z. Peng, Z. Sun, J. Yao, Y. Zhu, Z. Liu, P. M. Ajayan, and J. M. Tour, ACS Nano 5, 8187 (2011).

Anugrah, Y.

H. Li, Y. Anugrah, S. J. Koester, and M. Li, Appl. Phys. Lett. 101, 111110 (2012).

Bachman, D.

Bae, S.

J. Kang, D. Shin, S. Bae, and B. H. Hong, Nanoscale 4, 5527 (2012).
[CrossRef]

Balandin, A. A.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Nano Lett. 8, 902 (2008).

Bao, W.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Nano Lett. 8, 902 (2008).

Boscolo, S.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008), pp. 359–365.

Calizo, I.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Nano Lett. 8, 902 (2008).

Capobianco, A.

Cariou, J. M.

Cheng, Z.

Z. Cheng, H. K. Tsang, X. Wang, K. Xu, and J. B. Xu, IEEE J. Sel. Topics Quantum Electron. 20, 1 (2014).

Choi, C. G.

De Angelis, C.

Dugas, J.

Fainman, Y.

Falkovsky, L. A.

L. A. Falkovsky, J. Phys. Conf. Ser. 129, 012004 (2008).
[CrossRef]

Ghosh, S.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Nano Lett. 8, 902 (2008).

Grieco, A.

Gu, T.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, Nat. Photonics 6, 554 (2012).
[CrossRef]

Hone, J.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, Nat. Photonics 6, 554 (2012).
[CrossRef]

Hong, B. H.

J. Kang, D. Shin, S. Bae, and B. H. Hong, Nanoscale 4, 5527 (2012).
[CrossRef]

Horvath, C.

Kang, J.

J. Kang, D. Shin, S. Bae, and B. H. Hong, Nanoscale 4, 5527 (2012).
[CrossRef]

Kim, J. T.

Koester, S. J.

H. Li, Y. Anugrah, S. J. Koester, and M. Li, Appl. Phys. Lett. 101, 111110 (2012).

Kwong, D. L.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, Nat. Photonics 6, 554 (2012).
[CrossRef]

Lau, C. N.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Nano Lett. 8, 902 (2008).

Li, H.

H. Li, Y. Anugrah, S. J. Koester, and M. Li, Appl. Phys. Lett. 101, 111110 (2012).

Li, M.

H. Li, Y. Anugrah, S. J. Koester, and M. Li, Appl. Phys. Lett. 101, 111110 (2012).

Liu, Z.

Z. Yan, Z. Peng, Z. Sun, J. Yao, Y. Zhu, Z. Liu, P. M. Ajayan, and J. M. Tour, ACS Nano 5, 8187 (2011).

Lo, G. Q.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, Nat. Photonics 6, 554 (2012).
[CrossRef]

Locatelli, A.

Martin, L.

McMillan, J. F.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, Nat. Photonics 6, 554 (2012).
[CrossRef]

Miao, F.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Nano Lett. 8, 902 (2008).

Michel, P.

Midrio, M.

Nezhad, M. P.

Peng, Z.

Z. Yan, Z. Peng, Z. Sun, J. Yao, Y. Zhu, Z. Liu, P. M. Ajayan, and J. M. Tour, ACS Nano 5, 8187 (2011).

Perron, D.

Petrone, N.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, Nat. Photonics 6, 554 (2012).
[CrossRef]

Shin, D.

J. Kang, D. Shin, S. Bae, and B. H. Hong, Nanoscale 4, 5527 (2012).
[CrossRef]

Slutsky, B.

Sun, Z.

Z. Yan, Z. Peng, Z. Sun, J. Yao, Y. Zhu, Z. Liu, P. M. Ajayan, and J. M. Tour, ACS Nano 5, 8187 (2011).

Tan, D. T. H.

Teweldebrhan, D.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Nano Lett. 8, 902 (2008).

Tour, J. M.

Z. Yan, Z. Peng, Z. Sun, J. Yao, Y. Zhu, Z. Liu, P. M. Ajayan, and J. M. Tour, ACS Nano 5, 8187 (2011).

Tsang, H. K.

Z. Cheng, H. K. Tsang, X. Wang, K. Xu, and J. B. Xu, IEEE J. Sel. Topics Quantum Electron. 20, 1 (2014).

Van, V.

van der Zande, A.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, Nat. Photonics 6, 554 (2012).
[CrossRef]

Wang, X.

Z. Cheng, H. K. Tsang, X. Wang, K. Xu, and J. B. Xu, IEEE J. Sel. Topics Quantum Electron. 20, 1 (2014).

Wong, C. W.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, Nat. Photonics 6, 554 (2012).
[CrossRef]

Wu, M.

Xu, J. B.

Z. Cheng, H. K. Tsang, X. Wang, K. Xu, and J. B. Xu, IEEE J. Sel. Topics Quantum Electron. 20, 1 (2014).

Xu, K.

Z. Cheng, H. K. Tsang, X. Wang, K. Xu, and J. B. Xu, IEEE J. Sel. Topics Quantum Electron. 20, 1 (2014).

Yan, Z.

Z. Yan, Z. Peng, Z. Sun, J. Yao, Y. Zhu, Z. Liu, P. M. Ajayan, and J. M. Tour, ACS Nano 5, 8187 (2011).

Yao, J.

Z. Yan, Z. Peng, Z. Sun, J. Yao, Y. Zhu, Z. Liu, P. M. Ajayan, and J. M. Tour, ACS Nano 5, 8187 (2011).

Yu, M.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, Nat. Photonics 6, 554 (2012).
[CrossRef]

Zamek, S.

Zhu, Y.

Z. Yan, Z. Peng, Z. Sun, J. Yao, Y. Zhu, Z. Liu, P. M. Ajayan, and J. M. Tour, ACS Nano 5, 8187 (2011).

ACS Nano

Z. Yan, Z. Peng, Z. Sun, J. Yao, Y. Zhu, Z. Liu, P. M. Ajayan, and J. M. Tour, ACS Nano 5, 8187 (2011).

Appl. Opt.

Appl. Phys. Lett.

H. Li, Y. Anugrah, S. J. Koester, and M. Li, Appl. Phys. Lett. 101, 111110 (2012).

IEEE J. Sel. Topics Quantum Electron.

Z. Cheng, H. K. Tsang, X. Wang, K. Xu, and J. B. Xu, IEEE J. Sel. Topics Quantum Electron. 20, 1 (2014).

J. Lightwave Technol.

J. Phys. Conf. Ser.

L. A. Falkovsky, J. Phys. Conf. Ser. 129, 012004 (2008).
[CrossRef]

Nano Lett.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Nano Lett. 8, 902 (2008).

Nanoscale

J. Kang, D. Shin, S. Bae, and B. H. Hong, Nanoscale 4, 5527 (2012).
[CrossRef]

Nat. Photonics

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, Nat. Photonics 6, 554 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Other

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008), pp. 359–365.

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Figures (6)

Fig. 1.
Fig. 1.

(a) Optical micrograph of a graphene–Si waveguide with region of PMMA/graphene to the right. (b) Schematic of the graphene–Si waveguide. (c) Raman spectrograph of graphene fabricated with the CVD process.

Fig. 2.
Fig. 2.

Spectral response of the Si waveguide resonator without graphene for TM polarization.

Fig. 3.
Fig. 3.

Spectral responses of the graphene–Si waveguide resonator at varying input powers for (a) TE mode, (b) TM mode (solid lines are measurements, dashed lines are theoretical fits). (c) Dependence of the resonant wavelength shift on the input power.

Fig. 4.
Fig. 4.

Modal electric field distributions in the graphene–Si waveguide: (a) Ex, (b) Ez for TE polarization, (c) Ey, and (d) Ez for TM polarization.

Fig. 5.
Fig. 5.

Steady-state temperature distribution (relative to 295 K) at 5 mW input power for (a) TE mode, (b) TM mode in the graphene–Si waveguide, and (c) TM mode in bare Si waveguide without PMMA/graphene.

Fig. 6.
Fig. 6.

Steady-state transfer function of the graphene–Si waveguide resonator for TM polarization at 1550.138 nm (starred points are measurements; lines are obtained from the dispersive bistability model using experimentally measured thermal nonlinear index n2).

Tables (1)

Tables Icon

Table 1. Simulation and Experimental Results for the Effective Thermal Nonlinear Index n2

Equations (3)

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·(KT)=q,
q=12σ|E⃗|2,
σ=αnε0/μ0,

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