Abstract

We have calculated the optically-induced force between coupled high-Q whispering gallery modes of microsphere resonators. Attractive and repulsive forces are found, depending whether the bi-sphere mode is symmetric or antisymmetric. The magnitude of the force is linearly proportional to the total power in the spheres and consequently linearly enhanced by Q. Forces on the order of 100 nN are found for Q=108, large enough to cause displacements in the range of 1μm when the sphere is attached to a fiber stem with spring constant 0.004 N/m.

© 2005 Optical Society of America

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  1. W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A 11, 963–983 (1994).
    [Crossref]
  2. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between microphotonic waveguides,” Opt. Lett. (to be published).
    [PubMed]
  3. V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A,  137, 393–397 (1989).
    [Crossref]
  4. L. Collot, V. Lefévre-Seguin, M. Brune, J.M. Raimond, and S. Haroche “Very high Q whispering gallery modes observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
    [Crossref]
  5. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of a whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997).
    [Crossref] [PubMed]
  6. D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, “High-Q measurements of fused-silica spheres in the near infrared,” Opt. Lett. 23, 247–249 (1998).
    [Crossref]
  7. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
    [Crossref] [PubMed]
  8. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Valhala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
    [Crossref] [PubMed]
  9. V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, “On the ultimate sensitivity in coordinate measurements,” Phys. Lett. A 179, 244–248 (1993).
    [Crossref]
  10. V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, “Coupling and tunability of whispering-gallery modes: a basis for coordinate meter,” Opt. Commun. 107, 41–48 (1994).
    [Crossref]
  11. H. Miyazaki and Y. Jimba, “Ab initio tight-binding description of morphology-dependent resonance in a bisphere,” Phys. Rev. B 62, 7976–7997 (2000).
    [Crossref]
  12. D. D. Smith, H. Chang, and K. A. Fuller, “Whispering-gallery mode splitting in coupled microresonators,” J. Opt. Soc. Am. B 20, 1967–1974 (2003).
    [Crossref]
  13. J.-P. Laine, B. E. Little, D. R. Lim, H. C. Tapalian, L. C. Kimerling, and H. A. Haus, “Microsphere resonator mode characterization by pedestal anti-resonant reflecting waveguide coupler,” IEEE Phot. Tech. Lett. 12, 1004–1006 (2000).
    [Crossref]
  14. B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am. A 10, 343–352 (1993).
    [Crossref]
  15. H. M. Lai, P.T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
    [Crossref] [PubMed]
  16. S. Götzinger, O. Benson, and V. Sandoghdar, “Towards controlled coupling between a high-Q whispering gallery mode and a single nanoparticle,” Appl. Phys. B 73, 825–828 (2001).
    [Crossref]
  17. D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” Proc. Inst. Electr. Eng. Part J. 140, 177–188 (1993).
  18. M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147–154 (1999).
    [Crossref]
  19. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209–1211 (2004).
    [Crossref] [PubMed]
  20. J.-P. Laine, H. C. Tapalian, B. E. Little, and H. A. Haus, “Acceleration sensor based on high-Q optical ,” Sensors and Actuators A 93, 1–7 (2001).
    [Crossref]
  21. T. B. Gabrielson, “Mechanical-thermal noise in micromachined acoustic and vibration sensors,” IEEE Trans. on Electron Devices  40, 903–909 (1993).
    [Crossref]
  22. W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefévre-Seguin, “Frequency tuning of the whispering-gallery modes of silica microspheres for cavity quantum electrodynamics and spectroscopy,” Opt. Lett. 26, 166–168 (2001).
    [Crossref]
  23. J. Israelachvili, Intermolecular and Surface Forces (Academic Press, London, 1992), Chap. 11.
  24. V. P. Mitrofanov, L. G. Prokhorov, and K. V. Tokmakov, “Variation of electric charge on prototype of ,” Phys. Lett. A 300, 370–374 (2002).
    [Crossref]
  25. J. Ng, C. T. Chan, P. Sheng, and Z. Lin, “Strong optical force induced by morphology dependent resonances,” Opt. Lett. 30, 1956–1958 (2005). An earlier version may be found at URL http://arxiv.org/abs/physics/0502020.
    [Crossref] [PubMed]
  26. M. I. Antonoyiannakis and J. B. Pendry, “Electromagnetic forces in photonic crystals,” Phys. Rev. B 60, 2363–2374 (1999).
    [Crossref]
  27. M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional reflector waveguide,” Appl. Phys. Lett. 85, 1466–1468 (2004).
    [Crossref]
  28. P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation theory for quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
    [Crossref] [PubMed]

2005 (1)

2004 (2)

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209–1211 (2004).
[Crossref] [PubMed]

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional reflector waveguide,” Appl. Phys. Lett. 85, 1466–1468 (2004).
[Crossref]

2003 (2)

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Valhala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref] [PubMed]

D. D. Smith, H. Chang, and K. A. Fuller, “Whispering-gallery mode splitting in coupled microresonators,” J. Opt. Soc. Am. B 20, 1967–1974 (2003).
[Crossref]

2002 (2)

V. P. Mitrofanov, L. G. Prokhorov, and K. V. Tokmakov, “Variation of electric charge on prototype of ,” Phys. Lett. A 300, 370–374 (2002).
[Crossref]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[Crossref] [PubMed]

2001 (3)

S. Götzinger, O. Benson, and V. Sandoghdar, “Towards controlled coupling between a high-Q whispering gallery mode and a single nanoparticle,” Appl. Phys. B 73, 825–828 (2001).
[Crossref]

J.-P. Laine, H. C. Tapalian, B. E. Little, and H. A. Haus, “Acceleration sensor based on high-Q optical ,” Sensors and Actuators A 93, 1–7 (2001).
[Crossref]

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefévre-Seguin, “Frequency tuning of the whispering-gallery modes of silica microspheres for cavity quantum electrodynamics and spectroscopy,” Opt. Lett. 26, 166–168 (2001).
[Crossref]

2000 (2)

J.-P. Laine, B. E. Little, D. R. Lim, H. C. Tapalian, L. C. Kimerling, and H. A. Haus, “Microsphere resonator mode characterization by pedestal anti-resonant reflecting waveguide coupler,” IEEE Phot. Tech. Lett. 12, 1004–1006 (2000).
[Crossref]

H. Miyazaki and Y. Jimba, “Ab initio tight-binding description of morphology-dependent resonance in a bisphere,” Phys. Rev. B 62, 7976–7997 (2000).
[Crossref]

1999 (2)

M. I. Antonoyiannakis and J. B. Pendry, “Electromagnetic forces in photonic crystals,” Phys. Rev. B 60, 2363–2374 (1999).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147–154 (1999).
[Crossref]

1998 (1)

1997 (1)

1994 (3)

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, “Coupling and tunability of whispering-gallery modes: a basis for coordinate meter,” Opt. Commun. 107, 41–48 (1994).
[Crossref]

P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation theory for quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
[Crossref] [PubMed]

W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A 11, 963–983 (1994).
[Crossref]

1993 (5)

B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am. A 10, 343–352 (1993).
[Crossref]

T. B. Gabrielson, “Mechanical-thermal noise in micromachined acoustic and vibration sensors,” IEEE Trans. on Electron Devices  40, 903–909 (1993).
[Crossref]

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” Proc. Inst. Electr. Eng. Part J. 140, 177–188 (1993).

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, “On the ultimate sensitivity in coordinate measurements,” Phys. Lett. A 179, 244–248 (1993).
[Crossref]

L. Collot, V. Lefévre-Seguin, M. Brune, J.M. Raimond, and S. Haroche “Very high Q whispering gallery modes observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

1990 (1)

H. M. Lai, P.T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

1989 (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A,  137, 393–397 (1989).
[Crossref]

Almeida, V. R.

Antonoyiannakis, M. I.

M. I. Antonoyiannakis and J. B. Pendry, “Electromagnetic forces in photonic crystals,” Phys. Rev. B 60, 2363–2374 (1999).
[Crossref]

Barber, P. W.

H. M. Lai, P.T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Barrios, C. A.

Benson, O.

S. Götzinger, O. Benson, and V. Sandoghdar, “Towards controlled coupling between a high-Q whispering gallery mode and a single nanoparticle,” Appl. Phys. B 73, 825–828 (2001).
[Crossref]

Birks, T. A.

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, “On the ultimate sensitivity in coordinate measurements,” Phys. Lett. A 179, 244–248 (1993).
[Crossref]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A,  137, 393–397 (1989).
[Crossref]

Brune, M.

L. Collot, V. Lefévre-Seguin, M. Brune, J.M. Raimond, and S. Haroche “Very high Q whispering gallery modes observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Capasso, F.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between microphotonic waveguides,” Opt. Lett. (to be published).
[PubMed]

Chan, C. T.

Chang, H.

Cheung, G.

Collot, L.

L. Collot, V. Lefévre-Seguin, M. Brune, J.M. Raimond, and S. Haroche “Very high Q whispering gallery modes observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Fuller, K. A.

Gabrielson, T. B.

T. B. Gabrielson, “Mechanical-thermal noise in micromachined acoustic and vibration sensors,” IEEE Trans. on Electron Devices  40, 903–909 (1993).
[Crossref]

Gorodetsky, M. L.

M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147–154 (1999).
[Crossref]

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, “Coupling and tunability of whispering-gallery modes: a basis for coordinate meter,” Opt. Commun. 107, 41–48 (1994).
[Crossref]

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, “On the ultimate sensitivity in coordinate measurements,” Phys. Lett. A 179, 244–248 (1993).
[Crossref]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A,  137, 393–397 (1989).
[Crossref]

Götzinger, S.

S. Götzinger, O. Benson, and V. Sandoghdar, “Towards controlled coupling between a high-Q whispering gallery mode and a single nanoparticle,” Appl. Phys. B 73, 825–828 (2001).
[Crossref]

Hare, J.

Haroche, S.

L. Collot, V. Lefévre-Seguin, M. Brune, J.M. Raimond, and S. Haroche “Very high Q whispering gallery modes observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Haus, H. A.

J.-P. Laine, H. C. Tapalian, B. E. Little, and H. A. Haus, “Acceleration sensor based on high-Q optical ,” Sensors and Actuators A 93, 1–7 (2001).
[Crossref]

J.-P. Laine, B. E. Little, D. R. Lim, H. C. Tapalian, L. C. Kimerling, and H. A. Haus, “Microsphere resonator mode characterization by pedestal anti-resonant reflecting waveguide coupler,” IEEE Phot. Tech. Lett. 12, 1004–1006 (2000).
[Crossref]

Hill, S. C.

H. M. Lai, P.T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Huang, W.-P.

Ibanescu, M.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional reflector waveguide,” Appl. Phys. Lett. 85, 1466–1468 (2004).
[Crossref]

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between microphotonic waveguides,” Opt. Lett. (to be published).
[PubMed]

Ilchenko, V. S.

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefévre-Seguin, “Frequency tuning of the whispering-gallery modes of silica microspheres for cavity quantum electrodynamics and spectroscopy,” Opt. Lett. 26, 166–168 (2001).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147–154 (1999).
[Crossref]

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, “High-Q measurements of fused-silica spheres in the near infrared,” Opt. Lett. 23, 247–249 (1998).
[Crossref]

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, “Coupling and tunability of whispering-gallery modes: a basis for coordinate meter,” Opt. Commun. 107, 41–48 (1994).
[Crossref]

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, “On the ultimate sensitivity in coordinate measurements,” Phys. Lett. A 179, 244–248 (1993).
[Crossref]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A,  137, 393–397 (1989).
[Crossref]

Israelachvili, J.

J. Israelachvili, Intermolecular and Surface Forces (Academic Press, London, 1992), Chap. 11.

Jacques, F.

Jimba, Y.

H. Miyazaki and Y. Jimba, “Ab initio tight-binding description of morphology-dependent resonance in a bisphere,” Phys. Rev. B 62, 7976–7997 (2000).
[Crossref]

Joannopoulos, J. D.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional reflector waveguide,” Appl. Phys. Lett. 85, 1466–1468 (2004).
[Crossref]

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between microphotonic waveguides,” Opt. Lett. (to be published).
[PubMed]

Johnson, B. R.

Johnson, S. G.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional reflector waveguide,” Appl. Phys. Lett. 85, 1466–1468 (2004).
[Crossref]

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between microphotonic waveguides,” Opt. Lett. (to be published).
[PubMed]

Kimble, H. J.

Kimerling, L. C.

J.-P. Laine, B. E. Little, D. R. Lim, H. C. Tapalian, L. C. Kimerling, and H. A. Haus, “Microsphere resonator mode characterization by pedestal anti-resonant reflecting waveguide coupler,” IEEE Phot. Tech. Lett. 12, 1004–1006 (2000).
[Crossref]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Valhala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[Crossref] [PubMed]

Knight, J. C.

Lai, H. M.

H. M. Lai, P.T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Laine, J.-P.

J.-P. Laine, H. C. Tapalian, B. E. Little, and H. A. Haus, “Acceleration sensor based on high-Q optical ,” Sensors and Actuators A 93, 1–7 (2001).
[Crossref]

J.-P. Laine, B. E. Little, D. R. Lim, H. C. Tapalian, L. C. Kimerling, and H. A. Haus, “Microsphere resonator mode characterization by pedestal anti-resonant reflecting waveguide coupler,” IEEE Phot. Tech. Lett. 12, 1004–1006 (2000).
[Crossref]

Lefévre-Seguin, V.

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefévre-Seguin, “Frequency tuning of the whispering-gallery modes of silica microspheres for cavity quantum electrodynamics and spectroscopy,” Opt. Lett. 26, 166–168 (2001).
[Crossref]

L. Collot, V. Lefévre-Seguin, M. Brune, J.M. Raimond, and S. Haroche “Very high Q whispering gallery modes observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Leung, P. T.

P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation theory for quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
[Crossref] [PubMed]

Leung, P.T.

H. M. Lai, P.T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Lim, D. R.

J.-P. Laine, B. E. Little, D. R. Lim, H. C. Tapalian, L. C. Kimerling, and H. A. Haus, “Microsphere resonator mode characterization by pedestal anti-resonant reflecting waveguide coupler,” IEEE Phot. Tech. Lett. 12, 1004–1006 (2000).
[Crossref]

Lin, Z.

Lipson, M.

Little, B. E.

J.-P. Laine, H. C. Tapalian, B. E. Little, and H. A. Haus, “Acceleration sensor based on high-Q optical ,” Sensors and Actuators A 93, 1–7 (2001).
[Crossref]

J.-P. Laine, B. E. Little, D. R. Lim, H. C. Tapalian, L. C. Kimerling, and H. A. Haus, “Microsphere resonator mode characterization by pedestal anti-resonant reflecting waveguide coupler,” IEEE Phot. Tech. Lett. 12, 1004–1006 (2000).
[Crossref]

Liu, S. Y.

P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation theory for quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
[Crossref] [PubMed]

Loncar, M.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between microphotonic waveguides,” Opt. Lett. (to be published).
[PubMed]

Long, R.

Love, J. D.

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” Proc. Inst. Electr. Eng. Part J. 140, 177–188 (1993).

Mabuchi, H.

Mitrofanov, V. P.

V. P. Mitrofanov, L. G. Prokhorov, and K. V. Tokmakov, “Variation of electric charge on prototype of ,” Phys. Lett. A 300, 370–374 (2002).
[Crossref]

Miyazaki, H.

H. Miyazaki and Y. Jimba, “Ab initio tight-binding description of morphology-dependent resonance in a bisphere,” Phys. Rev. B 62, 7976–7997 (2000).
[Crossref]

Ng, J.

Painter, O. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Valhala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref] [PubMed]

Pendry, J. B.

M. I. Antonoyiannakis and J. B. Pendry, “Electromagnetic forces in photonic crystals,” Phys. Rev. B 60, 2363–2374 (1999).
[Crossref]

Povinelli, M. L.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional reflector waveguide,” Appl. Phys. Lett. 85, 1466–1468 (2004).
[Crossref]

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between microphotonic waveguides,” Opt. Lett. (to be published).
[PubMed]

Prokhorov, L. G.

V. P. Mitrofanov, L. G. Prokhorov, and K. V. Tokmakov, “Variation of electric charge on prototype of ,” Phys. Lett. A 300, 370–374 (2002).
[Crossref]

Raimond, J.M.

L. Collot, V. Lefévre-Seguin, M. Brune, J.M. Raimond, and S. Haroche “Very high Q whispering gallery modes observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Rowland, D. R.

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” Proc. Inst. Electr. Eng. Part J. 140, 177–188 (1993).

Sandoghdar, V.

S. Götzinger, O. Benson, and V. Sandoghdar, “Towards controlled coupling between a high-Q whispering gallery mode and a single nanoparticle,” Appl. Phys. B 73, 825–828 (2001).
[Crossref]

Sheng, P.

Smith, D. D.

Smythe, E. J.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between microphotonic waveguides,” Opt. Lett. (to be published).
[PubMed]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Valhala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[Crossref] [PubMed]

Streed, E. W.

Tapalian, H. C.

J.-P. Laine, H. C. Tapalian, B. E. Little, and H. A. Haus, “Acceleration sensor based on high-Q optical ,” Sensors and Actuators A 93, 1–7 (2001).
[Crossref]

J.-P. Laine, B. E. Little, D. R. Lim, H. C. Tapalian, L. C. Kimerling, and H. A. Haus, “Microsphere resonator mode characterization by pedestal anti-resonant reflecting waveguide coupler,” IEEE Phot. Tech. Lett. 12, 1004–1006 (2000).
[Crossref]

Tokmakov, K. V.

V. P. Mitrofanov, L. G. Prokhorov, and K. V. Tokmakov, “Variation of electric charge on prototype of ,” Phys. Lett. A 300, 370–374 (2002).
[Crossref]

Tong, S. S.

P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation theory for quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
[Crossref] [PubMed]

Vahala, K. J.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[Crossref] [PubMed]

Valhala, K. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Valhala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref] [PubMed]

Vernooy, D. W.

von Klitzing, W.

Vyatchanin, S. P.

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, “Coupling and tunability of whispering-gallery modes: a basis for coordinate meter,” Opt. Commun. 107, 41–48 (1994).
[Crossref]

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, “On the ultimate sensitivity in coordinate measurements,” Phys. Lett. A 179, 244–248 (1993).
[Crossref]

Xu, Q.

Young, K.

P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation theory for quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
[Crossref] [PubMed]

H. M. Lai, P.T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Appl. Phys. B (1)

S. Götzinger, O. Benson, and V. Sandoghdar, “Towards controlled coupling between a high-Q whispering gallery mode and a single nanoparticle,” Appl. Phys. B 73, 825–828 (2001).
[Crossref]

Appl. Phys. Lett. (1)

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional reflector waveguide,” Appl. Phys. Lett. 85, 1466–1468 (2004).
[Crossref]

Europhys. Lett. (1)

L. Collot, V. Lefévre-Seguin, M. Brune, J.M. Raimond, and S. Haroche “Very high Q whispering gallery modes observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

IEEE Phot. Tech. Lett. (1)

J.-P. Laine, B. E. Little, D. R. Lim, H. C. Tapalian, L. C. Kimerling, and H. A. Haus, “Microsphere resonator mode characterization by pedestal anti-resonant reflecting waveguide coupler,” IEEE Phot. Tech. Lett. 12, 1004–1006 (2000).
[Crossref]

IEEE Trans. (1)

T. B. Gabrielson, “Mechanical-thermal noise in micromachined acoustic and vibration sensors,” IEEE Trans. on Electron Devices  40, 903–909 (1993).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

Nature (1)

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[Crossref] [PubMed]

Opt. Commun. (1)

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, “Coupling and tunability of whispering-gallery modes: a basis for coordinate meter,” Opt. Commun. 107, 41–48 (1994).
[Crossref]

Opt. Lett. (5)

Phys. Lett. A (3)

V. P. Mitrofanov, L. G. Prokhorov, and K. V. Tokmakov, “Variation of electric charge on prototype of ,” Phys. Lett. A 300, 370–374 (2002).
[Crossref]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A,  137, 393–397 (1989).
[Crossref]

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, “On the ultimate sensitivity in coordinate measurements,” Phys. Lett. A 179, 244–248 (1993).
[Crossref]

Phys. Rev. A (2)

H. M. Lai, P.T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation theory for quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
[Crossref] [PubMed]

Phys. Rev. B (2)

M. I. Antonoyiannakis and J. B. Pendry, “Electromagnetic forces in photonic crystals,” Phys. Rev. B 60, 2363–2374 (1999).
[Crossref]

H. Miyazaki and Y. Jimba, “Ab initio tight-binding description of morphology-dependent resonance in a bisphere,” Phys. Rev. B 62, 7976–7997 (2000).
[Crossref]

Phys. Rev. Lett. (1)

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Valhala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref] [PubMed]

Proc. Inst. Electr. Eng. Part J. (1)

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” Proc. Inst. Electr. Eng. Part J. 140, 177–188 (1993).

Sensors and Actuators A (1)

J.-P. Laine, H. C. Tapalian, B. E. Little, and H. A. Haus, “Acceleration sensor based on high-Q optical ,” Sensors and Actuators A 93, 1–7 (2001).
[Crossref]

Other (2)

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between microphotonic waveguides,” Opt. Lett. (to be published).
[PubMed]

J. Israelachvili, Intermolecular and Surface Forces (Academic Press, London, 1992), Chap. 11.

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Figures (2)

Fig. 1.
Fig. 1.

Force as a function of separation for coupled microspheres for two different angular mode numbers. Negative values indicate attractive forces. Left and bottom axes use dimensionless units. Right and top axes show the force as a function of distance in physical units, assuming a coupled input power of 1mW to each sphere and a Qo of 108. At a wavelength of 1.55 μm, l = m = 111 corresponds to a sphere radius (a) of 19.9 μm and l = m = 184 to a radius of 32.4 μm. Inset shows modal symmetries. For antisymmetric modes (top inset, upper two data curves), the electric field perpendicular to the page points in opposite directions in the two spheres. For symmetric modes (bottom inset, lower two data curves), the opposite is true. Red and blue correspond to electric fields pointing in and out of the page, respectively. Arrows indicate direction of propagation.

Fig. 2.
Fig. 2.

Magnitude of equilibrium displacement of a sphere due to the optical force as a function of the spring constant k of the attached fiber stem. The optical displacement is larger than 1000 times the estimated thermal displacement (solid black line) for spring constants greater than 0.002 N/m.

Equations (21)

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F = 1 ω d ω d ξ U = 1 ω o + Δ ω d ( ω o + Δ ω ) d ξ U 1 ω d Δ ω d ξ U ,
Δ ω ω o = 1 2 d V [ ( ε 2 1 ) E 1 2 + ( ε 1 1 ) E 2 2 ± ( ( ε 1 1 ) E 1 * · E 2 + ( ε 2 1 ) E 2 * · E 1 ) ] d V [ ε 1 E 1 2 + ε 2 E 2 2 ] ,
d V [ ( ε 2 1 ) E 1 2 + ( ε 1 1 ) E 2 2 ] ,
d V [ ( ε 1 1 ) E 1 * · E 2 + ( ε 2 1 ) E 2 * · E 1 ] .
F = ( F λ U ) U λ = ( F λ U ) P Q o ω o λ = ( F λ U ) P Q o 2 π c ,
F = d U d ξ
F = d ( N ħ ω ) d ξ = N ħ d ω d ξ = 1 ω d ω d ξ U
U = 1 4 π 1 2 Re [ d V ( E ξ * · D ξ + B ξ * · H ξ ) ]
× H ξ = i ω D ξ
× E ξ = i ω B ξ
E ξ * · ( × ξ H ξ ) H ξ * · ( × ξ E ξ ) = E ξ * · [ i ξ ω D ξ + i ω ξ D ξ ] + H ξ * · [ i ξ ω B ξ + i ω ξ B ξ ] .
b · ( × a ) = · ( a × b ) + a · ( × b )
ω ξ d V ( E ξ * · D ξ + B ξ * · H ξ ) = i ( ξ ω ) d V ( E ξ * · D ξ + B ξ * · H ξ )
ω ξ U = U ξ ω
F = U ξ = 1 ω ω ξ U ,
× × E i ( ω i c ) 2 ( ε i 1 ) E i = ( ω i c ) 2 E i
( Θ ˆ λ i A ˆ i ) ψ i = λ i ψ i
Θ ˆ ψ λ [ A ˆ 1 + A ˆ 2 ] | ψ = λ ψ ,
λ ( 0 ) { ψ 1 A ˆ 2 ψ 1 ± ψ 1 A ˆ 2 ψ 2 + ψ 1 A ˆ 2 ψ ( 1 ) } + λ ( 1 ) ψ 1 ( 1 + A ˆ 1 ) ψ 1 = 0
λ ( 0 ) { ψ 2 A ˆ 1 ψ 1 ± ψ 2 A ˆ 1 ψ 2 + ψ 2 A ˆ 1 ψ ( 1 ) } ± λ ( 1 ) ψ 2 ( 1 + A ˆ 2 ) ψ 2 = 0
1 2 λ ( 1 ) λ ( 0 ) = Δ ω ω o = 1 2 d V [ ( ε 2 1 ) E 1 2 + ( ε 1 1 ) E 2 2 ± ( ( ε 1 1 ) E 1 * · E 2 + ( ε 2 1 ) E 2 * · E 1 ) ] d V [ ε 1 E 1 2 + ε 2 E 2 2 ] .

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