Abstract

We employ the finite-difference time-domain method to calculate the dominant short range forces in optomechanical devices, Casimir and gradient optical forces. Numerical results are obtained for typical silicon optomechanical devices and are compared to metallic reference structures, taking into account geometric and frequency dispersion of silicon. Our results indicate that although a small gap is desirable for operating optomechanical devices, the Casimir force offsets the gradient force in strongly coupled optomechanical devices, which has to be taken into account in the design of optical force tunable devices.

© 2010 OSA

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  1. M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
    [CrossRef] [PubMed]
  2. W. Mo Li and P. H. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
    [CrossRef]
  3. M. Li, W. H. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009).
    [CrossRef]
  4. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
    [CrossRef] [PubMed]
  5. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
    [CrossRef] [PubMed]
  6. G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
    [CrossRef] [PubMed]
  7. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
    [CrossRef] [PubMed]
  8. W. H. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
    [CrossRef] [PubMed]
  9. 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(22), 3042–3044 (2005).
    [CrossRef] [PubMed]
  10. A. Mizrahi and L. Schächter, “Mirror manipulation by attractive and repulsive forces of guided waves,” Opt. Express 13(24), 9804–9811 (2005).
    [CrossRef] [PubMed]
  11. H. B. G. Casimir, “On the attraction between two perfectly conducting plates,” Proc. K. Ned. Akad. Wet. 51, 793 (1948).
  12. S. K. Lamoreaux, “Demonstration of the Casimir Force in the 0.6 to 6μm Range,” Phys. Rev. Lett. 78(1), 5–8 (1997).
    [CrossRef]
  13. H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Quantum mechanical actuation of microelectromechanical systems by the Casimir force,” Science 291(5510), 1941–1944 (2001).
    [CrossRef] [PubMed]
  14. M. Bordag, U. Mohideen, and V. M. Mostepanenko, “New developments in the Casimir effect,” Phys. Rep. 353(1–3), 1–205 (2001).
    [CrossRef]
  15. S. K. Lamoreaux, “The Casimir force: background, experiments, and applications,” Rep. Prog. Phys. 68(1), 201–236 (2005).
    [CrossRef]
  16. F. Capasso, J. N. Munday, D. Iannuzzi, and H. B. Chan, “Casimir Forces and Quantum Electrodynamical Torques: Physics and Nanomechanics,” IEEE J. Sel. Top. Quantum Electron. 13(2), 400–414 (2007).
    [CrossRef]
  17. F. M. Serry, D. Walliser, and M. G. Jordan, “The role of the casimir effect in the static deflection and stiction of membrane strips in microelectromechanical systems (MEMS),” J. Appl. Phys. 84(5), 2501 (1998).
    [CrossRef]
  18. J. Ma and M. L. Povinelli, “Large tuning of birefringence in two strip silicon waveguides via optomechanical motion,” Opt. Express 17(20), 17818–17828 (2009).
    [CrossRef] [PubMed]
  19. I. W. Frank, P. B. Deotare, M. W. McCutcheon, and M. Lončar, “Programmable photonic crystal nanobeam cavities,” Opt. Express 18(8), 8705 (2010).
    [CrossRef] [PubMed]
  20. J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics 3(8), 478–483 (2009).
    [CrossRef]
  21. T. Emig, A. Hanke, R. Golestanian, and M. Kardar, “Probing the strong boundary shape dependence of the Casimir force,” Phys. Rev. Lett. 87(26), 260402 (2001).
    [CrossRef]
  22. H. Gies and K. Klingmuller, “Worldline algorithms for Casimir configurations,” Phys. Rev. D Part. Fields Gravit. Cosmol. 74(4), 045002 (2006).
    [CrossRef]
  23. A. Rodriguez, M. Ibanescu, D. Iannuzzi, F. Capasso, J. D. Joannopoulos, and S. G. Johnson, “Computation and visualization of Casimir forces in arbitrary geometries: nonmonotonic lateral-wall forces and the failure of proximity-force approximations,” Phys. Rev. Lett. 99(8), 080401 (2007).
    [CrossRef] [PubMed]
  24. A. W. Rodriguez, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Casimir forces in the time domain: Theory,” Phys. Rev. A 80(1), 012115 (2009).
    [CrossRef]
  25. A. P. McCauley, A. W. Rodriguez, J. D. Joannopoulos, and S. G. Johnson, “Casimir forces in the time domain: Applications,” Phys. Rev. A 81(1), 012119 (2010).
    [CrossRef]
  26. B. V. Deriagin, I. I. Abrikosova, and E. M. Lifshitz, “Direct measurement of molecular attraction between solids separated by a narrow gap,” Quart. Rev. 10(3), 295 (1956).
    [CrossRef]
  27. L. Bergström, “Hamaker constants of inorganic materials,” Adv. Colloid Interface Sci. 70, 125–169 (1997).
    [CrossRef]

2010 (2)

I. W. Frank, P. B. Deotare, M. W. McCutcheon, and M. Lončar, “Programmable photonic crystal nanobeam cavities,” Opt. Express 18(8), 8705 (2010).
[CrossRef] [PubMed]

A. P. McCauley, A. W. Rodriguez, J. D. Joannopoulos, and S. G. Johnson, “Casimir forces in the time domain: Applications,” Phys. Rev. A 81(1), 012119 (2010).
[CrossRef]

2009 (9)

A. W. Rodriguez, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Casimir forces in the time domain: Theory,” Phys. Rev. A 80(1), 012115 (2009).
[CrossRef]

J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics 3(8), 478–483 (2009).
[CrossRef]

W. Mo Li and P. H. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
[CrossRef]

M. Li, W. H. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009).
[CrossRef]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

W. H. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
[CrossRef] [PubMed]

J. Ma and M. L. Povinelli, “Large tuning of birefringence in two strip silicon waveguides via optomechanical motion,” Opt. Express 17(20), 17818–17828 (2009).
[CrossRef] [PubMed]

2008 (2)

M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[CrossRef] [PubMed]

2007 (2)

F. Capasso, J. N. Munday, D. Iannuzzi, and H. B. Chan, “Casimir Forces and Quantum Electrodynamical Torques: Physics and Nanomechanics,” IEEE J. Sel. Top. Quantum Electron. 13(2), 400–414 (2007).
[CrossRef]

A. Rodriguez, M. Ibanescu, D. Iannuzzi, F. Capasso, J. D. Joannopoulos, and S. G. Johnson, “Computation and visualization of Casimir forces in arbitrary geometries: nonmonotonic lateral-wall forces and the failure of proximity-force approximations,” Phys. Rev. Lett. 99(8), 080401 (2007).
[CrossRef] [PubMed]

2006 (1)

H. Gies and K. Klingmuller, “Worldline algorithms for Casimir configurations,” Phys. Rev. D Part. Fields Gravit. Cosmol. 74(4), 045002 (2006).
[CrossRef]

2005 (3)

2001 (3)

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Quantum mechanical actuation of microelectromechanical systems by the Casimir force,” Science 291(5510), 1941–1944 (2001).
[CrossRef] [PubMed]

M. Bordag, U. Mohideen, and V. M. Mostepanenko, “New developments in the Casimir effect,” Phys. Rep. 353(1–3), 1–205 (2001).
[CrossRef]

T. Emig, A. Hanke, R. Golestanian, and M. Kardar, “Probing the strong boundary shape dependence of the Casimir force,” Phys. Rev. Lett. 87(26), 260402 (2001).
[CrossRef]

1998 (1)

F. M. Serry, D. Walliser, and M. G. Jordan, “The role of the casimir effect in the static deflection and stiction of membrane strips in microelectromechanical systems (MEMS),” J. Appl. Phys. 84(5), 2501 (1998).
[CrossRef]

1997 (2)

S. K. Lamoreaux, “Demonstration of the Casimir Force in the 0.6 to 6μm Range,” Phys. Rev. Lett. 78(1), 5–8 (1997).
[CrossRef]

L. Bergström, “Hamaker constants of inorganic materials,” Adv. Colloid Interface Sci. 70, 125–169 (1997).
[CrossRef]

1956 (1)

B. V. Deriagin, I. I. Abrikosova, and E. M. Lifshitz, “Direct measurement of molecular attraction between solids separated by a narrow gap,” Quart. Rev. 10(3), 295 (1956).
[CrossRef]

1948 (1)

H. B. G. Casimir, “On the attraction between two perfectly conducting plates,” Proc. K. Ned. Akad. Wet. 51, 793 (1948).

Abrikosova, I. I.

B. V. Deriagin, I. I. Abrikosova, and E. M. Lifshitz, “Direct measurement of molecular attraction between solids separated by a narrow gap,” Quart. Rev. 10(3), 295 (1956).
[CrossRef]

Aksyuk, V. A.

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Quantum mechanical actuation of microelectromechanical systems by the Casimir force,” Science 291(5510), 1941–1944 (2001).
[CrossRef] [PubMed]

Baehr-Jones, T.

M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[CrossRef] [PubMed]

Bergström, L.

L. Bergström, “Hamaker constants of inorganic materials,” Adv. Colloid Interface Sci. 70, 125–169 (1997).
[CrossRef]

Bishop, D. J.

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Quantum mechanical actuation of microelectromechanical systems by the Casimir force,” Science 291(5510), 1941–1944 (2001).
[CrossRef] [PubMed]

Bordag, M.

M. Bordag, U. Mohideen, and V. M. Mostepanenko, “New developments in the Casimir effect,” Phys. Rep. 353(1–3), 1–205 (2001).
[CrossRef]

Camacho, R.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

Capasso, F.

F. Capasso, J. N. Munday, D. Iannuzzi, and H. B. Chan, “Casimir Forces and Quantum Electrodynamical Torques: Physics and Nanomechanics,” IEEE J. Sel. Top. Quantum Electron. 13(2), 400–414 (2007).
[CrossRef]

A. Rodriguez, M. Ibanescu, D. Iannuzzi, F. Capasso, J. D. Joannopoulos, and S. G. Johnson, “Computation and visualization of Casimir forces in arbitrary geometries: nonmonotonic lateral-wall forces and the failure of proximity-force approximations,” Phys. Rev. Lett. 99(8), 080401 (2007).
[CrossRef] [PubMed]

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(22), 3042–3044 (2005).
[CrossRef] [PubMed]

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Quantum mechanical actuation of microelectromechanical systems by the Casimir force,” Science 291(5510), 1941–1944 (2001).
[CrossRef] [PubMed]

Casimir, H. B. G.

H. B. G. Casimir, “On the attraction between two perfectly conducting plates,” Proc. K. Ned. Akad. Wet. 51, 793 (1948).

Chan, H. B.

F. Capasso, J. N. Munday, D. Iannuzzi, and H. B. Chan, “Casimir Forces and Quantum Electrodynamical Torques: Physics and Nanomechanics,” IEEE J. Sel. Top. Quantum Electron. 13(2), 400–414 (2007).
[CrossRef]

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Quantum mechanical actuation of microelectromechanical systems by the Casimir force,” Science 291(5510), 1941–1944 (2001).
[CrossRef] [PubMed]

Chan, J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

Chen, L.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

Deotare, P. B.

Deriagin, B. V.

B. V. Deriagin, I. I. Abrikosova, and E. M. Lifshitz, “Direct measurement of molecular attraction between solids separated by a narrow gap,” Quart. Rev. 10(3), 295 (1956).
[CrossRef]

Eichenfield, M.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

Emig, T.

T. Emig, A. Hanke, R. Golestanian, and M. Kardar, “Probing the strong boundary shape dependence of the Casimir force,” Phys. Rev. Lett. 87(26), 260402 (2001).
[CrossRef]

Fong, K. Y.

Frank, I. W.

Gies, H.

H. Gies and K. Klingmuller, “Worldline algorithms for Casimir configurations,” Phys. Rev. D Part. Fields Gravit. Cosmol. 74(4), 045002 (2006).
[CrossRef]

Golestanian, R.

T. Emig, A. Hanke, R. Golestanian, and M. Kardar, “Probing the strong boundary shape dependence of the Casimir force,” Phys. Rev. Lett. 87(26), 260402 (2001).
[CrossRef]

Gondarenko, A.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

Hanke, A.

T. Emig, A. Hanke, R. Golestanian, and M. Kardar, “Probing the strong boundary shape dependence of the Casimir force,” Phys. Rev. Lett. 87(26), 260402 (2001).
[CrossRef]

Hochberg, M.

M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[CrossRef] [PubMed]

Iannuzzi, D.

F. Capasso, J. N. Munday, D. Iannuzzi, and H. B. Chan, “Casimir Forces and Quantum Electrodynamical Torques: Physics and Nanomechanics,” IEEE J. Sel. Top. Quantum Electron. 13(2), 400–414 (2007).
[CrossRef]

A. Rodriguez, M. Ibanescu, D. Iannuzzi, F. Capasso, J. D. Joannopoulos, and S. G. Johnson, “Computation and visualization of Casimir forces in arbitrary geometries: nonmonotonic lateral-wall forces and the failure of proximity-force approximations,” Phys. Rev. Lett. 99(8), 080401 (2007).
[CrossRef] [PubMed]

Ibanescu, M.

A. Rodriguez, M. Ibanescu, D. Iannuzzi, F. Capasso, J. D. Joannopoulos, and S. G. Johnson, “Computation and visualization of Casimir forces in arbitrary geometries: nonmonotonic lateral-wall forces and the failure of proximity-force approximations,” Phys. Rev. Lett. 99(8), 080401 (2007).
[CrossRef] [PubMed]

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(22), 3042–3044 (2005).
[CrossRef] [PubMed]

Joannopoulos, J. D.

A. P. McCauley, A. W. Rodriguez, J. D. Joannopoulos, and S. G. Johnson, “Casimir forces in the time domain: Applications,” Phys. Rev. A 81(1), 012119 (2010).
[CrossRef]

A. W. Rodriguez, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Casimir forces in the time domain: Theory,” Phys. Rev. A 80(1), 012115 (2009).
[CrossRef]

A. Rodriguez, M. Ibanescu, D. Iannuzzi, F. Capasso, J. D. Joannopoulos, and S. G. Johnson, “Computation and visualization of Casimir forces in arbitrary geometries: nonmonotonic lateral-wall forces and the failure of proximity-force approximations,” Phys. Rev. Lett. 99(8), 080401 (2007).
[CrossRef] [PubMed]

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(22), 3042–3044 (2005).
[CrossRef] [PubMed]

Johnson, S. G.

A. P. McCauley, A. W. Rodriguez, J. D. Joannopoulos, and S. G. Johnson, “Casimir forces in the time domain: Applications,” Phys. Rev. A 81(1), 012119 (2010).
[CrossRef]

A. W. Rodriguez, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Casimir forces in the time domain: Theory,” Phys. Rev. A 80(1), 012115 (2009).
[CrossRef]

A. Rodriguez, M. Ibanescu, D. Iannuzzi, F. Capasso, J. D. Joannopoulos, and S. G. Johnson, “Computation and visualization of Casimir forces in arbitrary geometries: nonmonotonic lateral-wall forces and the failure of proximity-force approximations,” Phys. Rev. Lett. 99(8), 080401 (2007).
[CrossRef] [PubMed]

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(22), 3042–3044 (2005).
[CrossRef] [PubMed]

Jordan, M. G.

F. M. Serry, D. Walliser, and M. G. Jordan, “The role of the casimir effect in the static deflection and stiction of membrane strips in microelectromechanical systems (MEMS),” J. Appl. Phys. 84(5), 2501 (1998).
[CrossRef]

Kardar, M.

T. Emig, A. Hanke, R. Golestanian, and M. Kardar, “Probing the strong boundary shape dependence of the Casimir force,” Phys. Rev. Lett. 87(26), 260402 (2001).
[CrossRef]

Kippenberg, T. J.

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[CrossRef] [PubMed]

Kleiman, R. N.

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Quantum mechanical actuation of microelectromechanical systems by the Casimir force,” Science 291(5510), 1941–1944 (2001).
[CrossRef] [PubMed]

Klingmuller, K.

H. Gies and K. Klingmuller, “Worldline algorithms for Casimir configurations,” Phys. Rev. D Part. Fields Gravit. Cosmol. 74(4), 045002 (2006).
[CrossRef]

Lamoreaux, S. K.

S. K. Lamoreaux, “The Casimir force: background, experiments, and applications,” Rep. Prog. Phys. 68(1), 201–236 (2005).
[CrossRef]

S. K. Lamoreaux, “Demonstration of the Casimir Force in the 0.6 to 6μm Range,” Phys. Rev. Lett. 78(1), 5–8 (1997).
[CrossRef]

Li, M.

W. H. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
[CrossRef] [PubMed]

M. Li, W. H. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009).
[CrossRef]

M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[CrossRef] [PubMed]

Lifshitz, E. M.

B. V. Deriagin, I. I. Abrikosova, and E. M. Lifshitz, “Direct measurement of molecular attraction between solids separated by a narrow gap,” Quart. Rev. 10(3), 295 (1956).
[CrossRef]

Lin, Q.

J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics 3(8), 478–483 (2009).
[CrossRef]

Lipson, M.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

Loncar, M.

Ma, J.

McCauley, A. P.

A. P. McCauley, A. W. Rodriguez, J. D. Joannopoulos, and S. G. Johnson, “Casimir forces in the time domain: Applications,” Phys. Rev. A 81(1), 012119 (2010).
[CrossRef]

A. W. Rodriguez, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Casimir forces in the time domain: Theory,” Phys. Rev. A 80(1), 012115 (2009).
[CrossRef]

McCutcheon, M. W.

Mizrahi, A.

Mo Li, W.

W. Mo Li and P. H. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
[CrossRef]

Mohideen, U.

M. Bordag, U. Mohideen, and V. M. Mostepanenko, “New developments in the Casimir effect,” Phys. Rep. 353(1–3), 1–205 (2001).
[CrossRef]

Mostepanenko, V. M.

M. Bordag, U. Mohideen, and V. M. Mostepanenko, “New developments in the Casimir effect,” Phys. Rep. 353(1–3), 1–205 (2001).
[CrossRef]

Munday, J. N.

F. Capasso, J. N. Munday, D. Iannuzzi, and H. B. Chan, “Casimir Forces and Quantum Electrodynamical Torques: Physics and Nanomechanics,” IEEE J. Sel. Top. Quantum Electron. 13(2), 400–414 (2007).
[CrossRef]

Painter, O.

J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics 3(8), 478–483 (2009).
[CrossRef]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

Pernice, W. H.

W. H. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
[CrossRef] [PubMed]

M. Li, W. H. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

a) The geometry used for the determination of both the gradient optical force and the Casimir force. Overlaid is the profile of the odd optical mode, responsible for the generation of repulsive gradient force.

Fig. 2
Fig. 2

a): The Casimir force calculated for square coupled nano-beams composed of perfectly conducting metal, in dependence of waveguide separation. The width of the waveguide is varied from 100nm (black) to 2000nm (purple). The Casimir force decays exponentially with increasing gap and linearly with increasing waveguide width. b) The equivalent calculation for waveguides made from pure silicon, taking into account the frequency dispersion of silicon. Compared to the metallic case, the Casimir force is reduced by a factor of 3 for small separations, increasing to a factor of 10-20 for large gaps.

Fig. 3
Fig. 3

a) The Casimir force for waveguides with a fixed height of 220nm in dependence of waveguide separation, for perfectly conducting and silicon materials. The upper curves correspond the metallic waveguides (larger Casimir force), while the lower curves correspond the silicon waveguides. As expected from theory, the Casimir force shows only weak dependence on the waveguide width. b) The Casimir force ratio between metal and silicon waveguides.

Fig. 4
Fig. 4

(a) The calculated repulsive optical force in dependence of waveguide separation and waveguide width, for waveguides of 220nm height. The corresponding Casimir force is shown by the dashed orange line. (b) The amount of optical power required for the cancellation of the Casimir force. The power is determined in dependence of waveguide separation and waveguide width.

Equations (1)

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ε S i ( i ω ) = ε + ω 0 2 ε 0 ε ω 2 + ω 0 2

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