Abstract

Forces arising from overlap between the guided waves of parallel, microphotonic waveguides are calculated. Both attractive and repulsive forces, determined by the choice of relative input phase, are found. Using realistic parameters for a silicon-on-insulator material system, we estimate that the forces are large enough to cause observable displacements. Our results illustrate the potential for a broader class of optically tunable microphotonic devices and microstructured artificial materials.

© 2005 Optical Society of America

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  1. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
    [CrossRef] [PubMed]
  2. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Science 249, 749 (1990).
    [CrossRef] [PubMed]
  3. P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 035422 (2001).
    [CrossRef]
  4. S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, Phys. Rev. Lett. 89, 283901 (2002).
    [CrossRef]
  5. S. K. Mohanty, J. T. Andrews, and P. K. Gupta, Opt. Express 12, 2749 (2004).
    [CrossRef]
  6. M. I. Antonoyiannakis and J. B. Pendry, Phys. Rev. B 60, 2363 (1999).
    [CrossRef]
  7. 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]
  8. K. Okamoto and S. Kawata, Phys. Rev. Lett. 83, 4534 (1999).
    [CrossRef]
  9. P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 123601 (2002).
    [CrossRef]
  10. L. N. Ng, M. N. Zervas, J. S. Wilkinson, and B. J. Luff, Appl. Phys. Lett. 76, 1993 (2000).
    [CrossRef]
  11. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995), p. 34.
  12. M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery-mode resonators,” submitted to Opt. Express.
  13. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998), Sec. 6.7.
  14. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
    [CrossRef] [PubMed]
  15. E. Lidorikis, M. M. Sigalas, E. E. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 81, 1405 (1998).
    [CrossRef]
  16. H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
    [CrossRef]
  17. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, Opt. Lett. 29, 1209 (2004).
    [CrossRef] [PubMed]
  18. S. D. Senturia, Microsystem Design (Kluwer Academic, 2001).
  19. D. W. Carr, S. Evoy, L. Sekaric, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 75, 920 (1999).
    [CrossRef]
  20. M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Appl. Phys. Lett. 85, 1466 (2004).
    [CrossRef]

2004

S. K. Mohanty, J. T. Andrews, and P. K. Gupta, Opt. Express 12, 2749 (2004).
[CrossRef]

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Appl. Phys. Lett. 85, 1466 (2004).
[CrossRef]

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, Opt. Lett. 29, 1209 (2004).
[CrossRef] [PubMed]

2002

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 123601 (2002).
[CrossRef]

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

2001

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 035422 (2001).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

2000

H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
[CrossRef]

L. N. Ng, M. N. Zervas, J. S. Wilkinson, and B. J. Luff, Appl. Phys. Lett. 76, 1993 (2000).
[CrossRef]

1999

M. I. Antonoyiannakis and J. B. Pendry, Phys. Rev. B 60, 2363 (1999).
[CrossRef]

D. W. Carr, S. Evoy, L. Sekaric, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 75, 920 (1999).
[CrossRef]

K. Okamoto and S. Kawata, Phys. Rev. Lett. 83, 4534 (1999).
[CrossRef]

1998

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]

E. Lidorikis, M. M. Sigalas, E. E. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 81, 1405 (1998).
[CrossRef]

1990

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

1989

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef] [PubMed]

Almeida, V. R.

Andrews, J. T.

S. K. Mohanty, J. T. Andrews, and P. K. Gupta, Opt. Express 12, 2749 (2004).
[CrossRef]

Antonoyiannakis, M. I.

M. I. Antonoyiannakis and J. B. Pendry, Phys. Rev. B 60, 2363 (1999).
[CrossRef]

Barrios, C. A.

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]

Burns, M. M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef] [PubMed]

Capasso, F.

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery-mode resonators,” submitted to Opt. Express.

Carr, D. W.

D. W. Carr, S. Evoy, L. Sekaric, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 75, 920 (1999).
[CrossRef]

Carruthers, A. E.

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Chaumet, P. C.

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 123601 (2002).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 035422 (2001).
[CrossRef]

Craighead, H. G.

D. W. Carr, S. Evoy, L. Sekaric, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 75, 920 (1999).
[CrossRef]

Dholakia, K.

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, Phys. Rev. Lett. 89, 283901 (2002).
[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]

Economou, E. E.

E. Lidorikis, M. M. Sigalas, E. E. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 81, 1405 (1998).
[CrossRef]

Evoy, S.

D. W. Carr, S. Evoy, L. Sekaric, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 75, 920 (1999).
[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]

Fournier, J.-M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef] [PubMed]

Golovchenko, J. A.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef] [PubMed]

Gupta, P. K.

S. K. Mohanty, J. T. Andrews, and P. K. Gupta, Opt. Express 12, 2749 (2004).
[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]

Ibanescu, M.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Appl. Phys. Lett. 85, 1466 (2004).
[CrossRef]

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery-mode resonators,” submitted to Opt. Express.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998), Sec. 6.7.

Jimba, Y.

H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
[CrossRef]

Joannopoulos, J. D.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Appl. Phys. Lett. 85, 1466 (2004).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery-mode resonators,” submitted to Opt. Express.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995), p. 34.

Johnson, S. G.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Appl. Phys. Lett. 85, 1466 (2004).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery-mode resonators,” submitted to Opt. Express.

Kawata, S.

K. Okamoto and S. Kawata, Phys. Rev. Lett. 83, 4534 (1999).
[CrossRef]

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]

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]

Lidorikis, E.

E. Lidorikis, M. M. Sigalas, E. E. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 81, 1405 (1998).
[CrossRef]

Lipson, M.

Loncar, M.

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery-mode resonators,” submitted to Opt. Express.

Luff, B. J.

L. N. Ng, M. N. Zervas, J. S. Wilkinson, and B. J. Luff, Appl. Phys. Lett. 76, 1993 (2000).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995), p. 34.

Miyazaki, H.

H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
[CrossRef]

Mohanty, S. K.

S. K. Mohanty, J. T. Andrews, and P. K. Gupta, Opt. Express 12, 2749 (2004).
[CrossRef]

Ng, L. N.

L. N. Ng, M. N. Zervas, J. S. Wilkinson, and B. J. Luff, Appl. Phys. Lett. 76, 1993 (2000).
[CrossRef]

Nieto-Vesperinas, M.

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 123601 (2002).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 035422 (2001).
[CrossRef]

Okamoto, K.

K. Okamoto and S. Kawata, Phys. Rev. Lett. 83, 4534 (1999).
[CrossRef]

Parpia, J. M.

D. W. Carr, S. Evoy, L. Sekaric, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 75, 920 (1999).
[CrossRef]

Pendry, J. B.

M. I. Antonoyiannakis and J. B. Pendry, Phys. Rev. B 60, 2363 (1999).
[CrossRef]

Povinelli, M. L.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Appl. Phys. Lett. 85, 1466 (2004).
[CrossRef]

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery-mode resonators,” submitted to Opt. Express.

Rahmani, A.

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 123601 (2002).
[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]

Sekaric, L.

D. W. Carr, S. Evoy, L. Sekaric, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 75, 920 (1999).
[CrossRef]

Senturia, S. D.

S. D. Senturia, Microsystem Design (Kluwer Academic, 2001).

Sigalas, M. M.

E. Lidorikis, M. M. Sigalas, E. E. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 81, 1405 (1998).
[CrossRef]

Smythe, E. J.

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery-mode resonators,” submitted to Opt. Express.

Soukoulis, C. M.

E. Lidorikis, M. M. Sigalas, E. E. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 81, 1405 (1998).
[CrossRef]

Tatarkova, S. A.

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Wilkinson, J. S.

L. N. Ng, M. N. Zervas, J. S. Wilkinson, and B. J. Luff, Appl. Phys. Lett. 76, 1993 (2000).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995), p. 34.

Xu, Q.

Zervas, M. N.

L. N. Ng, M. N. Zervas, J. S. Wilkinson, and B. J. Luff, Appl. Phys. Lett. 76, 1993 (2000).
[CrossRef]

Appl. Phys. Lett.

L. N. Ng, M. N. Zervas, J. S. Wilkinson, and B. J. Luff, Appl. Phys. Lett. 76, 1993 (2000).
[CrossRef]

D. W. Carr, S. Evoy, L. Sekaric, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 75, 920 (1999).
[CrossRef]

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Appl. Phys. Lett. 85, 1466 (2004).
[CrossRef]

Opt. Express

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

S. K. Mohanty, J. T. Andrews, and P. K. Gupta, Opt. Express 12, 2749 (2004).
[CrossRef]

Opt. Lett.

Phys. Rev. B

M. I. Antonoyiannakis and J. B. Pendry, Phys. Rev. B 60, 2363 (1999).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 035422 (2001).
[CrossRef]

H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
[CrossRef]

Phys. Rev. Lett.

E. Lidorikis, M. M. Sigalas, E. E. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 81, 1405 (1998).
[CrossRef]

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef] [PubMed]

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]

K. Okamoto and S. Kawata, Phys. Rev. Lett. 83, 4534 (1999).
[CrossRef]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 123601 (2002).
[CrossRef]

Science

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

Other

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995), p. 34.

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery-mode resonators,” submitted to Opt. Express.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998), Sec. 6.7.

S. D. Senturia, Microsystem Design (Kluwer Academic, 2001).

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Figures (2)

Fig. 1
Fig. 1

(a) High-index ( n = 3.45 ) linear waveguides with square cross section a × a separated by distance d. (b) Dispersion relation for varying waveguide separations for modes with y-odd vector symmetry. Insets, E y of waveguide modes ( d a = 1.0 ) for modes lying above and below the infinite-separation limit, indicated by the black solid curve. (c) Normalized force per unit length as a function of separation at fixed frequency ν a c = a λ = 0.2 . The left and bottom axes are in dimensionless units; the right and top axes are in physical units with P = 100 mW , λ = 1.55 μ m , and a = 310 nm . Solid curves are calculated by the stress tensor method; symbols are calculated from Eq. (1).

Fig. 2
Fig. 2

(a) Schematic of suspended section of two coupled waveguides. (b) Displacement of each waveguide as a function of position along the waveguide. L = 30 μ m , h = a , d a = 0.15 , a λ = 0.2 , λ = 1.55 μ m , and P = 100 mW . (c) Displacement at the center of the suspended section (nanometers) as a function of power and length of suspended section. The white region shown is where waveguides are in contact.

Equations (2)

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

F = d U d ξ k = d ( N ω ) d ξ k = N d ω d ξ k = 1 ω d ω d ξ k U
E I d 4 w d x 4 = q ( w ) q d + 2 α ω ,

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