Abstract

All-optical tunable filters are basic elements for various micro-optical circuits. Obtaining all-optical tunability remains a challenge for micro-optical circuits. Optical forces with significant effects in nanophotonic systems provide new ways for wavelength tuning. In this Letter, the optomechanical effects in two-dimensional photonic crystal cavities are investigated. Simulations based on the finite element method demonstrate that forces arise in single and coupled cavities with movable rods inside. The optical force controls the positions of the movable rods and, thus, the resonance wavelength of the cavity, based on which tunable filter is designed. The operating wavelength of the cavity or the filter for the signal can be tuned by a control light with a different frequency. The results have potential applications for various integrated circuits.

© 2013 Optical Society of America

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2012 (1)

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

2010 (2)

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

J. Wang, H. Wang, X. Chen, and Y. Yu, J. Mater. Sci. 45, 2688 (2010).
[CrossRef]

2009 (3)

W. H. P. Pernice, M. Li, and H. X. Tang, Opt. Express 17, 1806 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef]

2008 (2)

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef]

H. Taniyama, M. Notomi, E. Kuramochi, T. Yamamoto, Y. Yoshikawa, Y. Torii, and T. Kuga, Phys. Rev. B 78, 165129 (2008).

2007 (3)

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

A. Mizrahi and L. Schachter, Opt. Lett. 32, 692 (2007).
[CrossRef]

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).
[CrossRef]

2006 (1)

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef]

2005 (3)

2003 (1)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

1998 (1)

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Akahane, Y.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[CrossRef]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

Asano, T.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[CrossRef]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

Baehr-Jones, T.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef]

Bayer, M.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Bulu, I.

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

Capasso, F.

Chen, L.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef]

Chen, X.

J. Wang, H. Wang, X. Chen, and Y. Yu, J. Mater. Sci. 45, 2688 (2010).
[CrossRef]

Deotare, P. B.

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

Dremin, A. A.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Eaves, D.

D. Eaves, Handbook of Polymer Foams (Smithers Rapra, 2004).

Eichenfield, M.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

Forchel, A.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Frank, I. W.

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

Gondarenko, A.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef]

Gutbrod, T.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Hochberg, M.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef]

Ibanescu, M.

Ilic, R.

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

Ippen, E. P.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Knipp, P. A.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Kuga, T.

H. Taniyama, M. Notomi, E. Kuramochi, T. Yamamoto, Y. Yoshikawa, Y. Torii, and T. Kuga, Phys. Rev. B 78, 165129 (2008).

Kulakovskii, V. D.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Kuramochi, E.

H. Taniyama, M. Notomi, E. Kuramochi, T. Yamamoto, Y. Yoshikawa, Y. Torii, and T. Kuga, Phys. Rev. B 78, 165129 (2008).

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef]

Li, M.

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

W. H. P. Pernice, M. Li, and H. X. Tang, Opt. Express 17, 1806 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef]

Lipson, M.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef]

Loncar, M.

Michael, C. P.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

Mitsugi, S.

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef]

Mizrahi, A.

Noda, S.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[CrossRef]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

Notomi, M.

H. Taniyama, M. Notomi, E. Kuramochi, T. Yamamoto, Y. Yoshikawa, Y. Torii, and T. Kuga, Phys. Rev. B 78, 165129 (2008).

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef]

Painter, O.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

Perahia, R.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

Pernice, W. H. P.

W. H. P. Pernice, M. Li, and H. X. Tang, Opt. Express 17, 1806 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef]

Popovic, M. A.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).
[CrossRef]

Povinelli, M. L.

Quan, Q.

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

Rakich, P. T.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).
[CrossRef]

Reinecke, T. L.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Reithmaier, J. P.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Roels, J.

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

Schachter, L.

Smythe, E. J.

Soljacic, M.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).
[CrossRef]

Song, B.-S.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[CrossRef]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

Tang, H. X.

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

W. H. P. Pernice, M. Li, and H. X. Tang, Opt. Express 17, 1806 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef]

Taniyama, H.

H. Taniyama, M. Notomi, E. Kuramochi, T. Yamamoto, Y. Yoshikawa, Y. Torii, and T. Kuga, Phys. Rev. B 78, 165129 (2008).

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef]

Torii, Y.

H. Taniyama, M. Notomi, E. Kuramochi, T. Yamamoto, Y. Yoshikawa, Y. Torii, and T. Kuga, Phys. Rev. B 78, 165129 (2008).

Van Thourhout, D.

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

Wang, H.

J. Wang, H. Wang, X. Chen, and Y. Yu, J. Mater. Sci. 45, 2688 (2010).
[CrossRef]

Wang, J.

J. Wang, H. Wang, X. Chen, and Y. Yu, J. Mater. Sci. 45, 2688 (2010).
[CrossRef]

Wiederhecker, G. S.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef]

Xiong, C.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef]

Yamamoto, T.

H. Taniyama, M. Notomi, E. Kuramochi, T. Yamamoto, Y. Yoshikawa, Y. Torii, and T. Kuga, Phys. Rev. B 78, 165129 (2008).

Yoshikawa, Y.

H. Taniyama, M. Notomi, E. Kuramochi, T. Yamamoto, Y. Yoshikawa, Y. Torii, and T. Kuga, Phys. Rev. B 78, 165129 (2008).

Yu, Y.

J. Wang, H. Wang, X. Chen, and Y. Yu, J. Mater. Sci. 45, 2688 (2010).
[CrossRef]

Zhang, Y.

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

J. Mater. Sci. (1)

J. Wang, H. Wang, X. Chen, and Y. Yu, J. Mater. Sci. 45, 2688 (2010).
[CrossRef]

Nat. Commun. (1)

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

Nat. Mater. (1)

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[CrossRef]

Nat. Photonics (4)

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

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

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

Nature (3)

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. B (1)

H. Taniyama, M. Notomi, E. Kuramochi, T. Yamamoto, Y. Yoshikawa, Y. Torii, and T. Kuga, Phys. Rev. B 78, 165129 (2008).

Phys. Rev. Lett. (2)

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef]

Other (1)

D. Eaves, Handbook of Polymer Foams (Smithers Rapra, 2004).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Two-dimensional photonic crystal with a movable rod in red inside the point defect cavity. The red rod can move along the x axis. (b) Ez (z-component of the electric field) of the cavity eigenmode in the xy plane. (c) Eigenfrequency and quality factor as functions of the red rod’s position. Parameter l is the displacement of the red rod to the center of the cavity.

Fig. 2.
Fig. 2.

Relation between the PFCC (γ) and the position of the movable rod in a single point defect cavity.

Fig. 3.
Fig. 3.

(a) Two cavities with movable rods (in red) inside form a coupled system. The red rod can move along the x axis at the same time toward the opposite direction. (b) Ez (z component of the electric field) of the antisymmetric and symmetric eigenmodes in the xy plane that can be generated in the system. (c) Eigenfrequency and quality factor versus the position of the red rods. Parameter l is the displacement of the right-side movable rod to the center of the right-side cavity.

Fig. 4.
Fig. 4.

Influence of the position of the movable rods on the PFCC (γ) in the system with two coupled point defect cavities.

Fig. 5.
Fig. 5.

(a) Schematic of the tunable filter. The control light is applied to change the positions of the movable rods. (b) The resonant frequency is tuned from 110.40 to 108.95 THz when the rods move from l=0.4 to 0.3 μm.

Fig. 6.
Fig. 6.

(a) Field distribution Ez when there is only the signal with the frequency of 110.40 THz for the red rods in the initial position (l=0.4μm), showing large output signal power. (b) Field distribution Ez in the xy plane when there is only the control light (odd mode, 103.62 THz) in the xy plane. (c) Field distribution Ez for both the signal (110.40 THz) and the control (103.62 THz); the red rods have been moved by the control light to l=0.3μm, in which the cavities are tuned by the control light, showing small output signal power, i.e., the signal channel is blocked. (d) Field distribution Ez for both the signal (108.95 THz) and control (103.62 THz) when the control-produced force is acting on the red rods and it maintains the position of l=0.3μm.

Equations (4)

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

F=Ul=1ωωlU,
Q=ω·UPloss=ω·UP.
γ=FP=Qω2ωl.
Ep=Fdl.

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