Abstract

In this Letter, we report an approach to controlling the bistability of double-coupled photonic crystal cavities with a nanoelectromechanical comb drive, in which the optical force and thermo-optic effect form a feedback mechanism to the effective index of the cavities, and the gap width between the cavities is steered by the comb drive. A model based on temporal coupled mode theory is established to analyze this approach. Hysteresis loops characterizing the bistability are experimentally achieved by sweeping the gap width forward and in reverse. In addition, the experiments also demonstrate that the bistability is tunable by varying the input light power.

© 2013 Optical Society of America

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  10. F. Tian, G. Zhou, F. S. Chau, J. Deng, and R. Akkipeddi, Appl. Phys. Lett. 102, 081101 (2013).
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    [CrossRef]

2013

F. Tian, G. Zhou, F. S. Chau, J. Deng, and R. Akkipeddi, Appl. Phys. Lett. 102, 081101 (2013).
[CrossRef]

F. Tian, G. Zhou, Y. Du, F. S. Chau, J. Deng, X. Tang, and R. Akkipeddi, Opt. Express 21, 18398 (2013).
[CrossRef]

2012

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Llic, and M. Loncar, Nat. Commun. 3, 846 (2012).
[CrossRef]

Y. F. Yu, J. B. Zhang, T. Bourouina, and A. Q. Liu, Appl. Phys. Lett. 100, 093108 (2012).
[CrossRef]

F. Tian, G. Zhou, F. S. Chau, J. Deng, Y. Du, X. Tang, R. Akkipeddi, and Y. C. Loke, Opt. Express 20, 27697 (2012).
[CrossRef]

2010

2009

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, Appl. Phys. Lett. 95, 031102 (2009).
[CrossRef]

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. Fornel, Phys. Rev. B 80, 033103 (2009).

2008

E. Bulgan, Y. Kanamori, and K. Hane, Appl. Phys. Lett. 92, 101110 (2008).
[CrossRef]

2007

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, Nat. Photonics 1, 49 (2007).
[CrossRef]

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. L. Kwong, Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

2006

Akkipeddi, R.

Bourouina, T.

Y. F. Yu, J. B. Zhang, T. Bourouina, and A. Q. Liu, Appl. Phys. Lett. 100, 093108 (2012).
[CrossRef]

Brissinger, D.

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. Fornel, Phys. Rev. B 80, 033103 (2009).

Bulgan, E.

E. Bulgan, Y. Kanamori, and K. Hane, Appl. Phys. Lett. 92, 101110 (2008).
[CrossRef]

Bulu, I.

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Llic, and M. Loncar, Nat. Commun. 3, 846 (2012).
[CrossRef]

Chau, F. S.

Chew, X.

Cluzel, B.

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. Fornel, Phys. Rev. B 80, 033103 (2009).

Coillet, A.

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. Fornel, Phys. Rev. B 80, 033103 (2009).

Deng, J.

Deotare, P. B.

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Llic, and M. Loncar, Nat. Commun. 3, 846 (2012).
[CrossRef]

Q. Quan, P. B. Deotare, and M. Loncar, Appl. Phys. Lett. 96, 203102 (2010).
[CrossRef]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, Appl. Phys. Lett. 95, 031102 (2009).
[CrossRef]

Du, Y.

Dumas, C.

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. Fornel, Phys. Rev. B 80, 033103 (2009).

Fornel, F.

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. Fornel, Phys. Rev. B 80, 033103 (2009).

Frank, I. W.

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Llic, and M. Loncar, Nat. Commun. 3, 846 (2012).
[CrossRef]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, Appl. Phys. Lett. 95, 031102 (2009).
[CrossRef]

Grelu, P.

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. Fornel, Phys. Rev. B 80, 033103 (2009).

Hane, K.

E. Bulgan, Y. Kanamori, and K. Hane, Appl. Phys. Lett. 92, 101110 (2008).
[CrossRef]

Husko, C.

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. L. Kwong, Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Kanamori, Y.

E. Bulgan, Y. Kanamori, and K. Hane, Appl. Phys. Lett. 92, 101110 (2008).
[CrossRef]

Khan, M.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, Appl. Phys. Lett. 95, 031102 (2009).
[CrossRef]

Kuramochi, E.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, Nat. Photonics 1, 49 (2007).
[CrossRef]

Kwong, D. L.

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. L. Kwong, Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Li, Q.

Lipson, M.

Liu, A. Q.

Y. F. Yu, J. B. Zhang, T. Bourouina, and A. Q. Liu, Appl. Phys. Lett. 100, 093108 (2012).
[CrossRef]

Llic, R.

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Llic, and M. Loncar, Nat. Commun. 3, 846 (2012).
[CrossRef]

Loke, Y. C.

Loncar, M.

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Llic, and M. Loncar, Nat. Commun. 3, 846 (2012).
[CrossRef]

Q. Quan, P. B. Deotare, and M. Loncar, Appl. Phys. Lett. 96, 203102 (2010).
[CrossRef]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, Appl. Phys. Lett. 95, 031102 (2009).
[CrossRef]

McCutcheon, M. W.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, Appl. Phys. Lett. 95, 031102 (2009).
[CrossRef]

Notomi, M.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, Nat. Photonics 1, 49 (2007).
[CrossRef]

Qiu, M.

Quan, Q.

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Llic, and M. Loncar, Nat. Commun. 3, 846 (2012).
[CrossRef]

Q. Quan, P. B. Deotare, and M. Loncar, Appl. Phys. Lett. 96, 203102 (2010).
[CrossRef]

Reano, R. M.

Roels, J.

D. V. Thourhout and J. Roels, Nat. Photonics 4, 211 (2010).
[CrossRef]

Shinya, A.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, Nat. Photonics 1, 49 (2007).
[CrossRef]

Su, Y.

Sun, P.

Tanabe, T.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, Nat. Photonics 1, 49 (2007).
[CrossRef]

Tang, X.

Taniyama, H.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, Nat. Photonics 1, 49 (2007).
[CrossRef]

Thourhout, D. V.

D. V. Thourhout and J. Roels, Nat. Photonics 4, 211 (2010).
[CrossRef]

Tian, F.

Wang, T.

Wong, C. W.

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. L. Kwong, Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Xu, Q.

Yan, M.

Yang, X.

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. L. Kwong, Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Yu, M.

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. L. Kwong, Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Yu, Y. F.

Y. F. Yu, J. B. Zhang, T. Bourouina, and A. Q. Liu, Appl. Phys. Lett. 100, 093108 (2012).
[CrossRef]

Zhang, J. B.

Y. F. Yu, J. B. Zhang, T. Bourouina, and A. Q. Liu, Appl. Phys. Lett. 100, 093108 (2012).
[CrossRef]

Zhang, Y.

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Llic, and M. Loncar, Nat. Commun. 3, 846 (2012).
[CrossRef]

Zhou, G.

Appl. Phys. Lett.

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. L. Kwong, Appl. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Y. F. Yu, J. B. Zhang, T. Bourouina, and A. Q. Liu, Appl. Phys. Lett. 100, 093108 (2012).
[CrossRef]

E. Bulgan, Y. Kanamori, and K. Hane, Appl. Phys. Lett. 92, 101110 (2008).
[CrossRef]

F. Tian, G. Zhou, F. S. Chau, J. Deng, and R. Akkipeddi, Appl. Phys. Lett. 102, 081101 (2013).
[CrossRef]

Q. Quan, P. B. Deotare, and M. Loncar, Appl. Phys. Lett. 96, 203102 (2010).
[CrossRef]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, Appl. Phys. Lett. 95, 031102 (2009).
[CrossRef]

Nat. Commun.

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Llic, and M. Loncar, Nat. Commun. 3, 846 (2012).
[CrossRef]

Nat. Photonics

D. V. Thourhout and J. Roels, Nat. Photonics 4, 211 (2010).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, Nat. Photonics 1, 49 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. Fornel, Phys. Rev. B 80, 033103 (2009).

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Figures (4)

Fig. 1.
Fig. 1.

(a) SEM image of the fabricated device used to control the bistability of the double-coupled cavities, (b) magnified SEM image of the coupled cavities with the calculated electric field profile for the second-order even mode, (c) measured wavelength shift of the resonance peak of the second-order even mode driven by a voltage switching from 0 to 10 V, and (d) wavelength detuning of the second-order even mode under various applied voltages.

Fig. 2.
Fig. 2.

(a) and (b) Relations between the light energy inside cavities |A|2 and the gap change Δg given by Eqs. (3) (curves) and (4) (straight line), respectively; (a) when the frequency of input light, ω/2π, decreases, a falling point from high energy state to low energy state can be observed; (b) when the frequency of input light, ω/2π, increases, a rising point from low energy state to high energy state can be observed; and (c) hysteresis loop consists of a measured curve of forward sweep (blue) and hypothetical curve of reverse sweep (red).

Fig. 3.
Fig. 3.

Relations between the light energy of the inner cavities |A|2 and the optical-force-induced gap change Δg given by Eqs. (5) (curves) and (6) (straight line). (a) Launched by light energy |S0|2 of 40 mW, falling and rising points exist at comb-drive-controlled gap changes of 5.2 and 10.6nm, respectively; (b) launched by light energy, |S0|2, of 53 mW, falling and rising points exist at comb-drive-controlled gap changes of 1.8 and 10nm, respectively.

Fig. 4.
Fig. 4.

(a) Curve including falling and rising points is measured by applying a triangular wave to the comb drive; (b) and (c) launched by power of 0.3 mW (b) and 0.35 mW (c), respectively; (c) hysteresis loops are formed by sweeping the gap width forward and in reverse.

Equations (6)

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dAdt=iω0A4AτwAτi+2τwS0,
dAdt=i(ω0+gOMΔg+gTO|A|2)A4AτwAτi+2τwS0,
i(ωω0gOMΔggTO|A|2)A4AτwAτi+2τwS0=0.
Fopt=gOM|A|2/ωgOM|A|2/ω0=k×Δg,
i[ωFixedω0gOM(ΔgOF+ΔgCD)gTO|A|2]A4AτwAτi+2τwS0=0,
gOM|A|2/ω0=k×ΔgOF.

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