Abstract

We consider the resonant optical force acting on a pair of transparent microspheres by the excitation of morphology-dependent resonance (MDR). The bonding and antibonding modes of the MDR correspond to strong attraction and repulsion, respectively. The dependence of the force on separation and the role of absorption are discussed. At resonance, the force can be enhanced by orders of magnitude such that it will dominate other relevant forces. We found that a stable binding configuration can be induced by the resonant optical force.

© 2005 Optical Society of America

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References

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  1. J. Ng, Z. F Lin, C. T. Chan, and P. Sheng, “Photonic clusters,” http://arXiv.org/abs/cond-mat/0501733.
  2. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
    [CrossRef] [PubMed]
  3. S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, Phys. Rev. Lett. 89, 283901 (2002).
    [CrossRef]
  4. H. Xu and M. Kall, Phys. Rev. Lett. 89, 246802 (2002).
    [CrossRef]
  5. M. I. Antonoyiannakis and J. B. Pendry, Europhys. Lett. 40, 613 (1997).
    [CrossRef]
  6. T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
    [CrossRef]
  7. Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
    [CrossRef]
  8. Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Opt. Lett. 28, 2437 (2003).
    [CrossRef] [PubMed]
  9. Y. L. Xu, Appl. Opt. 34, 4573 (1995).
    [CrossRef] [PubMed]
  10. H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
    [CrossRef]
  11. V. Fraysse, L. Giraud, S. Gratton, and J. Langou, (European Centre for Research and Advanced Training in Scientific Computation, Toulouse, France, 2003).
  12. K. A. Fuller, Appl. Opt. 30, 4716 (1991).
    [CrossRef] [PubMed]
  13. See, e.g., J. Israelachvili, Intermolecular and Surface Forces, 2nd ed. (Academic, 1991).

2004 (1)

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

2003 (1)

2002 (2)

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

H. Xu and M. Kall, Phys. Rev. Lett. 89, 246802 (2002).
[CrossRef]

2000 (1)

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

1999 (1)

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

1997 (1)

M. I. Antonoyiannakis and J. B. Pendry, Europhys. Lett. 40, 613 (1997).
[CrossRef]

1995 (1)

1991 (1)

1989 (1)

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

Antonoyiannakis, M. I.

M. I. Antonoyiannakis and J. B. Pendry, Europhys. Lett. 40, 613 (1997).
[CrossRef]

Boland, J. J.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Bradley, A. L.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Burns, M. M.

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

Carruthers, A. E.

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

Chan, C. T.

J. Ng, Z. F Lin, C. T. Chan, and P. Sheng, “Photonic clusters,” http://arXiv.org/abs/cond-mat/0501733.

Connolly, T. M.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Dholakia, K.

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

Donegan, J. F.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Fournier, J.-M.

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

Fraysse, V.

V. Fraysse, L. Giraud, S. Gratton, and J. Langou, (European Centre for Research and Advanced Training in Scientific Computation, Toulouse, France, 2003).

Fuller, K. A.

Gaponik, N.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Gerlach, M.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Giraud, L.

V. Fraysse, L. Giraud, S. Gratton, and J. Langou, (European Centre for Research and Advanced Training in Scientific Computation, Toulouse, France, 2003).

Golovchenko, J. A.

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

Gratton, S.

V. Fraysse, L. Giraud, S. Gratton, and J. Langou, (European Centre for Research and Advanced Training in Scientific Computation, Toulouse, France, 2003).

Hara, Y.

Israelachvili, J.

See, e.g., J. Israelachvili, Intermolecular and Surface Forces, 2nd ed. (Academic, 1991).

Jimba, Y.

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

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Kall, M.

H. Xu and M. Kall, Phys. Rev. Lett. 89, 246802 (2002).
[CrossRef]

Kuwata-Gonokami, M.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Opt. Lett. 28, 2437 (2003).
[CrossRef] [PubMed]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Langou, J.

V. Fraysse, L. Giraud, S. Gratton, and J. Langou, (European Centre for Research and Advanced Training in Scientific Computation, Toulouse, France, 2003).

Lin, Z. F

J. Ng, Z. F Lin, C. T. Chan, and P. Sheng, “Photonic clusters,” http://arXiv.org/abs/cond-mat/0501733.

Miyazaki, H.

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

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Mukaiyama, T.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Opt. Lett. 28, 2437 (2003).
[CrossRef] [PubMed]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Ng, J.

J. Ng, Z. F Lin, C. T. Chan, and P. Sheng, “Photonic clusters,” http://arXiv.org/abs/cond-mat/0501733.

Pendry, J. B.

M. I. Antonoyiannakis and J. B. Pendry, Europhys. Lett. 40, 613 (1997).
[CrossRef]

Rakovich, Y. P.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Rogach, A.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Sheng, P.

J. Ng, Z. F Lin, C. T. Chan, and P. Sheng, “Photonic clusters,” http://arXiv.org/abs/cond-mat/0501733.

Takeda, K.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Opt. Lett. 28, 2437 (2003).
[CrossRef] [PubMed]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Tatarkova, S. A.

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

Xu, H.

H. Xu and M. Kall, Phys. Rev. Lett. 89, 246802 (2002).
[CrossRef]

Xu, Y. L.

Appl. Opt. (2)

Europhys. Lett. (1)

M. I. Antonoyiannakis and J. B. Pendry, Europhys. Lett. 40, 613 (1997).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Phys. Rev. B (1)

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

Phys. Rev. Lett. (4)

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

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

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

H. Xu and M. Kall, Phys. Rev. Lett. 89, 246802 (2002).
[CrossRef]

Other (3)

V. Fraysse, L. Giraud, S. Gratton, and J. Langou, (European Centre for Research and Advanced Training in Scientific Computation, Toulouse, France, 2003).

See, e.g., J. Israelachvili, Intermolecular and Surface Forces, 2nd ed. (Academic, 1991).

J. Ng, Z. F Lin, C. T. Chan, and P. Sheng, “Photonic clusters,” http://arXiv.org/abs/cond-mat/0501733.

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Figures (4)

Fig. 1
Fig. 1

(a) Radiation pressure for a sphere with ϵ = 2.5281 . (b), (c) Optical forces acting on two contiguous microspheres ( ϵ = 2.5281 + 10 4 i ) , with the configuration depicted in (d), with (b) for the upper sphere and (c) for the lower sphere. (d) Pair of contiguous spheres illuminated by a linearly polarized plane wave propagating along the bisphere’s axis (z axis).

Fig. 2
Fig. 2

Optical forces acting on a pair of spheres with the configuration shown in Fig. 1(d). The horizontal axis is the size parameter of the bottom sphere. Solid curve, both spheres have radii of 2.5 μ m . Dashed curve, the bottom sphere has a radius of 2.5 μ m and the top sphere has a radius of 2.45 μ m .

Fig. 3
Fig. 3

Optical forces as a function of the size parameter acting on two contiguous spheres as depicted in Fig. 1(d). ϵ = 2.5281 + 10 4 i . Only the force acting on the top sphere is plotted.

Fig. 4
Fig. 4

Optical force acting on a pair of spheres plotted as a function of D, the separation between the closest points on the spheres. The forces acting on the spheres are equal and opposite by symmetry; the positive force represents repulsion and vice versa. The positions of the spheres are (0, 0, D 2 R ) and (0, 0, D 2 + R ). The incident wave has the form E in = x ̂ E 0 sin ( k z ) . The 39TE1 resonance of a single sphere is at λ = 558.6 nm . F v d w is an upper bound of the magnitude of the van der Waals force. (a) Ideal case with no absorption, i.e. ϵ = 2.5281 . (b) ϵ = 2.5281 + 10 4 i . The stable equilibrium separations (optical force equals zero and stable against perturbation) for different incident wavelengths are marked by arrows.

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