Abstract

In this paper we investigate the optical forces induced by localized optical modes propagating along three parallel waveguides, of which only the central one is free to move. In this configuration, when all three waveguides are identical, the components of the optical-force acting on the free beam are decoupled along the axis of symmetry. As a result, two dimensional optomechanical control of the central waveguide, like single-mode optical trapping, can be achieved. We also study non symmetric configurations, that can be used, for example, to tailor the position of the optical trap. Unlike other techniques that rely on buckling, multi-mode excitation or radiation-pressure, single-mode optomechanical-operation should help the realization of faster and simpler on-chip positioning of a single nanobeam since most of the parameters involved can be controlled with great precision.

© 2013 Optical Society of America

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  1. R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys.79, 1197–1216 (2007).
    [CrossRef]
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  3. H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, a. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett.102, 023103 (2013).
    [CrossRef]
  4. X Zhao, J M Tsai, H Cai, X M Ji, J Zhou, M H Bao, Y P Huang, D L Kwong, and Q Liu, “A nano-opto-mechanical pressure sensor via ring resonator,” Opt. Express20, 8535–8542, (2012).
    [CrossRef] [PubMed]
  5. D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics4, 211–217 (2010).
    [CrossRef]
  6. J. Ma and M.L. Povinelli, “Applications of optomechanical effects for on-chip manipulation of light signals,” Curr. Op. in. Sol. St. and Mat. Sci16, 82–90 (2012).
  7. V. Intaraprasonk and S. Fan, “Nonvolatile bistable all-optical switch from mechanical buckling,” Appl. Phys. Lett.98, 241104 (2011).
    [CrossRef]
  8. A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics6, 768–772 (2012).
    [CrossRef]
  9. J. Rosenberg, L. Qiang, and P. Oskar, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics3, 478–483 (2009).
    [CrossRef]
  10. A. Butsch, M. S. Kang, T. G. Euser, J. R. Koehler, S. Rammler, R. Keding, and P. S. J. Russell, “Optomechanical nonlinearity in dual-nanoweb structure suspended inside capillary fiber,” Phys. Rev. Lett.109, 183904 (2012).
    [CrossRef] [PubMed]
  11. M.L. Povinelli, M. Loncar, M. Ibanescu, E.J. Smythe, S.G. Johnson, F. Capasso, and J.D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett.30, 3042–3044 (2005).
    [CrossRef] [PubMed]
  12. G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature (London)462, 633–636 (2009).
    [CrossRef]
  13. V. Intaraprasonk and S. Fan, “An optical equilibrium in lateral waveguide-resonator optical force,” http://arxiv.org/abs/1306.2417 .
  14. P. A. Favuzzi, R. Bardoux, T. Asano, Y. Kawakami, and S. Noda, “Ab-initio design of nanophotonic waveguides for tunable, bidirectional optical forces,” Opt. Express20, 24488–24495 (2012).
    [CrossRef] [PubMed]
  15. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).
  16. M. Eichenfield, J. Chan, R.M. Camacho, K.J. Vahala, and O. Painter, “Optomechanical crystals,” Nature (London)462, 78–82 (2009).
    [CrossRef]
  17. M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics3, 464–468 (2009).
    [CrossRef]
  18. M. Li, W. H. P. Pernice, and H. X. Tang, “Broadband all-photonic transduction of nanocantilevers,” Nat. Nanotechnology4, 377–382 (2009).
    [CrossRef]
  19. C. L. Yu, H. Kim, N. De Leon, I. W. Frank, J. T. Robinson, M. McCutcheon, M. Liu, M. D. Lukin, M. Loncar, and H. Park, “Stretchable photonic crystal cavity with wide frequency tunability,” Nano Lett.13, 248–252 (2013).
    [CrossRef]
  20. Y. Chen, H. Li, and M. Li, “Flexible and tunable silicon photonic circuits on plastic substrates,” Scientific Reports2, 622 (2012).
    [CrossRef] [PubMed]

2013

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, a. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett.102, 023103 (2013).
[CrossRef]

C. L. Yu, H. Kim, N. De Leon, I. W. Frank, J. T. Robinson, M. McCutcheon, M. Liu, M. D. Lukin, M. Loncar, and H. Park, “Stretchable photonic crystal cavity with wide frequency tunability,” Nano Lett.13, 248–252 (2013).
[CrossRef]

2012

Y. Chen, H. Li, and M. Li, “Flexible and tunable silicon photonic circuits on plastic substrates,” Scientific Reports2, 622 (2012).
[CrossRef] [PubMed]

A. Butsch, M. S. Kang, T. G. Euser, J. R. Koehler, S. Rammler, R. Keding, and P. S. J. Russell, “Optomechanical nonlinearity in dual-nanoweb structure suspended inside capillary fiber,” Phys. Rev. Lett.109, 183904 (2012).
[CrossRef] [PubMed]

X Zhao, J M Tsai, H Cai, X M Ji, J Zhou, M H Bao, Y P Huang, D L Kwong, and Q Liu, “A nano-opto-mechanical pressure sensor via ring resonator,” Opt. Express20, 8535–8542, (2012).
[CrossRef] [PubMed]

P. A. Favuzzi, R. Bardoux, T. Asano, Y. Kawakami, and S. Noda, “Ab-initio design of nanophotonic waveguides for tunable, bidirectional optical forces,” Opt. Express20, 24488–24495 (2012).
[CrossRef] [PubMed]

J. Ma and M.L. Povinelli, “Applications of optomechanical effects for on-chip manipulation of light signals,” Curr. Op. in. Sol. St. and Mat. Sci16, 82–90 (2012).

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics6, 768–772 (2012).
[CrossRef]

2011

V. Intaraprasonk and S. Fan, “Nonvolatile bistable all-optical switch from mechanical buckling,” Appl. Phys. Lett.98, 241104 (2011).
[CrossRef]

2010

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics4, 211–217 (2010).
[CrossRef]

2009

J. Rosenberg, L. Qiang, and P. Oskar, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics3, 478–483 (2009).
[CrossRef]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature (London)462, 633–636 (2009).
[CrossRef]

M. Eichenfield, J. Chan, R.M. Camacho, K.J. Vahala, and O. Painter, “Optomechanical crystals,” Nature (London)462, 78–82 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics3, 464–468 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, “Broadband all-photonic transduction of nanocantilevers,” Nat. Nanotechnology4, 377–382 (2009).
[CrossRef]

2007

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys.79, 1197–1216 (2007).
[CrossRef]

2005

Asano, T.

Bao, M H

Bardoux, R.

Blasius, T. D.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics6, 768–772 (2012).
[CrossRef]

Butsch, A.

A. Butsch, M. S. Kang, T. G. Euser, J. R. Koehler, S. Rammler, R. Keding, and P. S. J. Russell, “Optomechanical nonlinearity in dual-nanoweb structure suspended inside capillary fiber,” Phys. Rev. Lett.109, 183904 (2012).
[CrossRef] [PubMed]

Cai, H

Cai, H.

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, a. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett.102, 023103 (2013).
[CrossRef]

Camacho, R.M.

M. Eichenfield, J. Chan, R.M. Camacho, K.J. Vahala, and O. Painter, “Optomechanical crystals,” Nature (London)462, 78–82 (2009).
[CrossRef]

Capasso, F.

Chan, J.

M. Eichenfield, J. Chan, R.M. Camacho, K.J. Vahala, and O. Painter, “Optomechanical crystals,” Nature (London)462, 78–82 (2009).
[CrossRef]

Chen, L.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature (London)462, 633–636 (2009).
[CrossRef]

Chen, Y.

Y. Chen, H. Li, and M. Li, “Flexible and tunable silicon photonic circuits on plastic substrates,” Scientific Reports2, 622 (2012).
[CrossRef] [PubMed]

De Leon, N.

C. L. Yu, H. Kim, N. De Leon, I. W. Frank, J. T. Robinson, M. McCutcheon, M. Liu, M. D. Lukin, M. Loncar, and H. Park, “Stretchable photonic crystal cavity with wide frequency tunability,” Nano Lett.13, 248–252 (2013).
[CrossRef]

Ding, L.

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, a. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett.102, 023103 (2013).
[CrossRef]

Dong, B.

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, a. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett.102, 023103 (2013).
[CrossRef]

Eichenfield, M.

M. Eichenfield, J. Chan, R.M. Camacho, K.J. Vahala, and O. Painter, “Optomechanical crystals,” Nature (London)462, 78–82 (2009).
[CrossRef]

Euser, T. G.

A. Butsch, M. S. Kang, T. G. Euser, J. R. Koehler, S. Rammler, R. Keding, and P. S. J. Russell, “Optomechanical nonlinearity in dual-nanoweb structure suspended inside capillary fiber,” Phys. Rev. Lett.109, 183904 (2012).
[CrossRef] [PubMed]

Fan, S.

V. Intaraprasonk and S. Fan, “Nonvolatile bistable all-optical switch from mechanical buckling,” Appl. Phys. Lett.98, 241104 (2011).
[CrossRef]

V. Intaraprasonk and S. Fan, “An optical equilibrium in lateral waveguide-resonator optical force,” http://arxiv.org/abs/1306.2417 .

Favuzzi, P. A.

Frank, I. W.

C. L. Yu, H. Kim, N. De Leon, I. W. Frank, J. T. Robinson, M. McCutcheon, M. Liu, M. D. Lukin, M. Loncar, and H. Park, “Stretchable photonic crystal cavity with wide frequency tunability,” Nano Lett.13, 248–252 (2013).
[CrossRef]

Gondarenko, A.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature (London)462, 633–636 (2009).
[CrossRef]

Heckenberg, N. R.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys.79, 1197–1216 (2007).
[CrossRef]

Huang, Y P

Ibanescu, M.

Intaraprasonk, V.

V. Intaraprasonk and S. Fan, “Nonvolatile bistable all-optical switch from mechanical buckling,” Appl. Phys. Lett.98, 241104 (2011).
[CrossRef]

V. Intaraprasonk and S. Fan, “An optical equilibrium in lateral waveguide-resonator optical force,” http://arxiv.org/abs/1306.2417 .

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998).

Ji, X M

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).

Joannopoulos, J.D.

Johnson, S.G.

Kang, M. S.

A. Butsch, M. S. Kang, T. G. Euser, J. R. Koehler, S. Rammler, R. Keding, and P. S. J. Russell, “Optomechanical nonlinearity in dual-nanoweb structure suspended inside capillary fiber,” Phys. Rev. Lett.109, 183904 (2012).
[CrossRef] [PubMed]

Kawakami, Y.

Keding, R.

A. Butsch, M. S. Kang, T. G. Euser, J. R. Koehler, S. Rammler, R. Keding, and P. S. J. Russell, “Optomechanical nonlinearity in dual-nanoweb structure suspended inside capillary fiber,” Phys. Rev. Lett.109, 183904 (2012).
[CrossRef] [PubMed]

Kim, H.

C. L. Yu, H. Kim, N. De Leon, I. W. Frank, J. T. Robinson, M. McCutcheon, M. Liu, M. D. Lukin, M. Loncar, and H. Park, “Stretchable photonic crystal cavity with wide frequency tunability,” Nano Lett.13, 248–252 (2013).
[CrossRef]

Koehler, J. R.

A. Butsch, M. S. Kang, T. G. Euser, J. R. Koehler, S. Rammler, R. Keding, and P. S. J. Russell, “Optomechanical nonlinearity in dual-nanoweb structure suspended inside capillary fiber,” Phys. Rev. Lett.109, 183904 (2012).
[CrossRef] [PubMed]

Krause, A. G.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics6, 768–772 (2012).
[CrossRef]

Kwong, D L

Kwong, D. L.

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, a. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett.102, 023103 (2013).
[CrossRef]

Li, H.

Y. Chen, H. Li, and M. Li, “Flexible and tunable silicon photonic circuits on plastic substrates,” Scientific Reports2, 622 (2012).
[CrossRef] [PubMed]

Li, M.

Y. Chen, H. Li, and M. Li, “Flexible and tunable silicon photonic circuits on plastic substrates,” Scientific Reports2, 622 (2012).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics3, 464–468 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, “Broadband all-photonic transduction of nanocantilevers,” Nat. Nanotechnology4, 377–382 (2009).
[CrossRef]

Lin, Q.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics6, 768–772 (2012).
[CrossRef]

Lipson, M.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature (London)462, 633–636 (2009).
[CrossRef]

Liu, a. Q.

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, a. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett.102, 023103 (2013).
[CrossRef]

Liu, M.

C. L. Yu, H. Kim, N. De Leon, I. W. Frank, J. T. Robinson, M. McCutcheon, M. Liu, M. D. Lukin, M. Loncar, and H. Park, “Stretchable photonic crystal cavity with wide frequency tunability,” Nano Lett.13, 248–252 (2013).
[CrossRef]

Liu, Q

Lo, G. Q.

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, a. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett.102, 023103 (2013).
[CrossRef]

Loncar, M.

C. L. Yu, H. Kim, N. De Leon, I. W. Frank, J. T. Robinson, M. McCutcheon, M. Liu, M. D. Lukin, M. Loncar, and H. Park, “Stretchable photonic crystal cavity with wide frequency tunability,” Nano Lett.13, 248–252 (2013).
[CrossRef]

M.L. Povinelli, M. Loncar, M. Ibanescu, E.J. Smythe, S.G. Johnson, F. Capasso, and J.D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett.30, 3042–3044 (2005).
[CrossRef] [PubMed]

Lukin, M. D.

C. L. Yu, H. Kim, N. De Leon, I. W. Frank, J. T. Robinson, M. McCutcheon, M. Liu, M. D. Lukin, M. Loncar, and H. Park, “Stretchable photonic crystal cavity with wide frequency tunability,” Nano Lett.13, 248–252 (2013).
[CrossRef]

Ma, J.

J. Ma and M.L. Povinelli, “Applications of optomechanical effects for on-chip manipulation of light signals,” Curr. Op. in. Sol. St. and Mat. Sci16, 82–90 (2012).

McCutcheon, M.

C. L. Yu, H. Kim, N. De Leon, I. W. Frank, J. T. Robinson, M. McCutcheon, M. Liu, M. D. Lukin, M. Loncar, and H. Park, “Stretchable photonic crystal cavity with wide frequency tunability,” Nano Lett.13, 248–252 (2013).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).

Nieminen, T. A.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys.79, 1197–1216 (2007).
[CrossRef]

Noda, S.

Oskar, P.

J. Rosenberg, L. Qiang, and P. Oskar, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics3, 478–483 (2009).
[CrossRef]

Painter, O.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics6, 768–772 (2012).
[CrossRef]

M. Eichenfield, J. Chan, R.M. Camacho, K.J. Vahala, and O. Painter, “Optomechanical crystals,” Nature (London)462, 78–82 (2009).
[CrossRef]

Park, H.

C. L. Yu, H. Kim, N. De Leon, I. W. Frank, J. T. Robinson, M. McCutcheon, M. Liu, M. D. Lukin, M. Loncar, and H. Park, “Stretchable photonic crystal cavity with wide frequency tunability,” Nano Lett.13, 248–252 (2013).
[CrossRef]

Pernice, W. H. P.

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics3, 464–468 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, “Broadband all-photonic transduction of nanocantilevers,” Nat. Nanotechnology4, 377–382 (2009).
[CrossRef]

Pfeifer, R. N. C.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys.79, 1197–1216 (2007).
[CrossRef]

Povinelli, M.L.

J. Ma and M.L. Povinelli, “Applications of optomechanical effects for on-chip manipulation of light signals,” Curr. Op. in. Sol. St. and Mat. Sci16, 82–90 (2012).

M.L. Povinelli, M. Loncar, M. Ibanescu, E.J. Smythe, S.G. Johnson, F. Capasso, and J.D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett.30, 3042–3044 (2005).
[CrossRef] [PubMed]

Qiang, L.

J. Rosenberg, L. Qiang, and P. Oskar, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics3, 478–483 (2009).
[CrossRef]

Rammler, S.

A. Butsch, M. S. Kang, T. G. Euser, J. R. Koehler, S. Rammler, R. Keding, and P. S. J. Russell, “Optomechanical nonlinearity in dual-nanoweb structure suspended inside capillary fiber,” Phys. Rev. Lett.109, 183904 (2012).
[CrossRef] [PubMed]

Robinson, J. T.

C. L. Yu, H. Kim, N. De Leon, I. W. Frank, J. T. Robinson, M. McCutcheon, M. Liu, M. D. Lukin, M. Loncar, and H. Park, “Stretchable photonic crystal cavity with wide frequency tunability,” Nano Lett.13, 248–252 (2013).
[CrossRef]

Roels, J.

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics4, 211–217 (2010).
[CrossRef]

Rosenberg, J.

J. Rosenberg, L. Qiang, and P. Oskar, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics3, 478–483 (2009).
[CrossRef]

Rubinsztein-Dunlop, H.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys.79, 1197–1216 (2007).
[CrossRef]

Russell, P. S. J.

A. Butsch, M. S. Kang, T. G. Euser, J. R. Koehler, S. Rammler, R. Keding, and P. S. J. Russell, “Optomechanical nonlinearity in dual-nanoweb structure suspended inside capillary fiber,” Phys. Rev. Lett.109, 183904 (2012).
[CrossRef] [PubMed]

Smythe, E.J.

Tang, H. X.

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics3, 464–468 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, “Broadband all-photonic transduction of nanocantilevers,” Nat. Nanotechnology4, 377–382 (2009).
[CrossRef]

Tao, J. F.

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, a. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett.102, 023103 (2013).
[CrossRef]

Tsai, J M

Tsai, J. M.

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, a. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett.102, 023103 (2013).
[CrossRef]

Vahala, K.J.

M. Eichenfield, J. Chan, R.M. Camacho, K.J. Vahala, and O. Painter, “Optomechanical crystals,” Nature (London)462, 78–82 (2009).
[CrossRef]

Van Thourhout, D.

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics4, 211–217 (2010).
[CrossRef]

Wiederhecker, G. S.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature (London)462, 633–636 (2009).
[CrossRef]

Winger, M.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics6, 768–772 (2012).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).

Yu, C. L.

C. L. Yu, H. Kim, N. De Leon, I. W. Frank, J. T. Robinson, M. McCutcheon, M. Liu, M. D. Lukin, M. Loncar, and H. Park, “Stretchable photonic crystal cavity with wide frequency tunability,” Nano Lett.13, 248–252 (2013).
[CrossRef]

Zhao, X

Zhou, J

Appl. Phys. Lett.

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, a. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett.102, 023103 (2013).
[CrossRef]

V. Intaraprasonk and S. Fan, “Nonvolatile bistable all-optical switch from mechanical buckling,” Appl. Phys. Lett.98, 241104 (2011).
[CrossRef]

Curr. Op. in. Sol. St. and Mat. Sci

J. Ma and M.L. Povinelli, “Applications of optomechanical effects for on-chip manipulation of light signals,” Curr. Op. in. Sol. St. and Mat. Sci16, 82–90 (2012).

Nano Lett.

C. L. Yu, H. Kim, N. De Leon, I. W. Frank, J. T. Robinson, M. McCutcheon, M. Liu, M. D. Lukin, M. Loncar, and H. Park, “Stretchable photonic crystal cavity with wide frequency tunability,” Nano Lett.13, 248–252 (2013).
[CrossRef]

Nat. Nanotechnology

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Figures (6)

Fig. 1
Fig. 1

Schematic of the system studied in which only the central waveguide is free to move. The height and thickness of the waveguides is h = a and t = 0.5a. The thickness of the thin SiO2 layers is t0 = 0.5a. The waveguides are made of Silicon and the separation between the external beams is fixed to 2ds + t, where ds = 0.25a.

Fig. 2
Fig. 2

(a) Force per unit energy as a function of a displacement dz/a for the Yodd-Zeven(1), Yodd-Zodd, Yodd-Zeven(2) and Yeven-Zodd modes at a constant axial wave-vector kx = π/a. In the inset we show a schematic of the geometry in use where a is the unit length, t0 is the thickness of the SiO2 support layer equal to 0.5a and the height and thickness of the waveguides is h = a and t = 0.5a respectively. (b) Dispersion diagram showing the five lowest frequency modes for the same geometry shown in (a) when all waveguides are evenly spaced. The field distribution of these modes at kx = π/a are shown in the first row of Fig. 3 and in Fig. 5(b). (c) Force per unit energy as a function of the displacement dz/a for the Yodd-Zeven, Yeven-Zodd, Yodd-Zodd and Yeven-Zeven fundamental modes at a constant axial wave-vector kx = π/a between two parallel waveguides with identical parameters to those shown in (a).

Fig. 3
Fig. 3

In-plane Eyz vector-field distribution (larger arrows mean more intense) with the total |E|2 in the background (darker is more intense) for the Yodd-Zeven(1), Yodd-Zodd, Yodd-Zeven(2) and Yeven-Zodd modes at kx = π/a. For the first row dz = 0 and for the second row dz = 0.075a. No displacement along the y-axis (dy = 0) is considered. All arrows lengths and color scales share the same normalization.

Fig. 4
Fig. 4

(a) Normalize force per unit energy as a function of a displacement dy/a for the Yodd-Zeven(1), Yodd-Zodd, Yodd-Zeven(2) and Yeven-Zodd modes at a constant axial wave-vector kx = π/a. (b) Schematic of the geometry in use where a is the height of the blocks and t0 is the thickness of the SiO2 support layer equal to 0.5a and the height and thickness of the waveguides is h = a and t = 0.5a respectively. (c) detail of (a), approximately of the box shown in clear green. (d) In-plane Eyz vector-field distribution (larger arrows mean more intense) with the total |E|2 in the background (darker is more intense) for the same geometry and modes described in (b). All arrows lengths and color scales share the same normalization.

Fig. 5
Fig. 5

(a) Normalized force per unit energy as a function of a displacement dz/a and dy/a for the Yeven-Zeven mode at a constant axial wave-vector kx = π/a for the same geometry shown in the inset of Fig. 2(a). (b) In-plane Eyz vector-field distribution (larger arrows mean more intense) with the total |E|2 in the background (darker is more intense) of the Yeven-Zeven mode for three different displacements of the central beam. All arrows lengths and color scales share the same normalization

Fig. 6
Fig. 6

(a) Normalized force per unit energy as a function of a displacement dy/a for the Yodd-Zeven(1), Yodd-Zodd, Yodd-Zeven(2) and Yeven-Zodd modes at a constant axial wave-vector kx = π/a. The height of the waveguides is h = a, tb = 0.25a, t = 0.5a, t0 = 0.5a and, when all waveguides lay on the same plane, the walls of the external waveguides are parallel to the walls of the central waveguide. (b) Dimensionless force as a function of a displacement dz/a for the Yodd-Zeven(1), Yodd-Zodd, Yodd-Zeven(2) and Yeven-Zodd modes at a constant axial wave-vector kx = π/a. In the inset we show the schematic of the geometry in use where a is the unit length, h = a, ta = 0.55a, tb = 0.5a, tc = 0.45a and t0 = 0.5a.

Tables (1)

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Table 1 Summary of the behavior of the force for each mode.

Equations (1)

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F U / a = A Δ ε 2 ( | E | | | 2 + 1 ε 1 ε 2 | D | 2 ) n d A V ε | E | 2 d V .

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