Abstract

We show, through analytical theory and rigorous numerical calculations, that optical binding can organize a collection of particles into extended, periodic one-dimensional lattices. These lattices, as well as other optically bound structures, are shown to exhibit spatially localized vibrational eigenmodes. The origin of localization here is distinct from the usual mechanisms such as disorder, defect, or nonlinearity but is a consequence of the long-ranged nature of optical binding. For an array of particles trapped by an interference pattern, the stable configuration is often dictated by the external light source, but we observed that interparticle optical binding forces can have a profound influence on the dynamics.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
    [Crossref]
  2. See e.g., D. G. Grier, Nature 424, 810 (2003).
    [PubMed]
  3. M. M. Burns, J. M. Fournier, and J. A. Golovchenko, Science 249, 749 (1990).
    [Crossref] [PubMed]
  4. J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Phys. Rev. B 72, 085130 (2005).
    [Crossref]
  5. J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Opt. Lett. 30, 1956 (2005).
    [Crossref] [PubMed]
  6. P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 035422 (2001).
    [Crossref]
  7. D. K. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today 57(1), 43 (2004).
    [Crossref]
  8. S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, Phys. Rev. Lett. 89, 283901 (2002).
    [Crossref]
  9. W. Singer, M. Frick, S. Bernet, and M. Ritsch-Marte, J. Opt. Soc. Am. B 20, 1568 (2003).
    [Crossref]
  10. N. K. Metzger, K. Dholakia, and E. M. Wright, Phys. Rev. Lett. 96, 068102 (2006).
    [Crossref] [PubMed]
  11. V. Garces-Chavez and K. Dholakia, Appl. Phys. Lett. 86, 031106 (2005).
    [Crossref]
  12. C. D. Mellor and C. D. Bain, ChemPhysChem 7, 329 (2006).
    [Crossref]
  13. The stable configurations calculated by the MS-MST formalism deviate from Eq. by less than 0.003 lambda.
  14. A. Chowdhury and B. Ackerson, Phys. Rev. Lett. 55, 833 (1985).
    [Crossref] [PubMed]
  15. N. E. Cusack, The Physics of Structurally Disordered Matter: An Introduction (A. Hilger, 1987), p. 239.
  16. The finite coherent length of a real laser will effectively set an upper limit on N. In the unrealistic case where N-->∞, the modes for Eq. become extended modes, whereas Eq. diverges.
  17. M. I. Antonoyiannakis and J. B. Pendry, Phys. Rev. B 60, 613 (1997).
  18. A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
    [Crossref] [PubMed]

2006 (2)

N. K. Metzger, K. Dholakia, and E. M. Wright, Phys. Rev. Lett. 96, 068102 (2006).
[Crossref] [PubMed]

C. D. Mellor and C. D. Bain, ChemPhysChem 7, 329 (2006).
[Crossref]

2005 (4)

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[Crossref] [PubMed]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Opt. Lett. 30, 1956 (2005).
[Crossref] [PubMed]

V. Garces-Chavez and K. Dholakia, Appl. Phys. Lett. 86, 031106 (2005).
[Crossref]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Phys. Rev. B 72, 085130 (2005).
[Crossref]

2004 (1)

D. K. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today 57(1), 43 (2004).
[Crossref]

2003 (2)

2002 (1)

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

2001 (1)

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

1997 (1)

M. I. Antonoyiannakis and J. B. Pendry, Phys. Rev. B 60, 613 (1997).

1990 (1)

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

1985 (1)

A. Chowdhury and B. Ackerson, Phys. Rev. Lett. 55, 833 (1985).
[Crossref] [PubMed]

1970 (1)

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[Crossref]

Ackerson, B.

A. Chowdhury and B. Ackerson, Phys. Rev. Lett. 55, 833 (1985).
[Crossref] [PubMed]

Antonoyiannakis, M. I.

M. I. Antonoyiannakis and J. B. Pendry, Phys. Rev. B 60, 613 (1997).

Ashkin, A.

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[Crossref]

Bain, C. D.

C. D. Mellor and C. D. Bain, ChemPhysChem 7, 329 (2006).
[Crossref]

Bernet, S.

Burns, M. M.

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

Campbell, D. K.

D. K. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today 57(1), 43 (2004).
[Crossref]

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, Phys. Rev. B 72, 085130 (2005).
[Crossref]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Opt. Lett. 30, 1956 (2005).
[Crossref] [PubMed]

Chaumet, P. C.

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

Chowdhury, A.

A. Chowdhury and B. Ackerson, Phys. Rev. Lett. 55, 833 (1985).
[Crossref] [PubMed]

Cusack, N. E.

N. E. Cusack, The Physics of Structurally Disordered Matter: An Introduction (A. Hilger, 1987), p. 239.

Dholakia, K.

N. K. Metzger, K. Dholakia, and E. M. Wright, Phys. Rev. Lett. 96, 068102 (2006).
[Crossref] [PubMed]

V. Garces-Chavez and K. Dholakia, Appl. Phys. Lett. 86, 031106 (2005).
[Crossref]

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

Flach, S.

D. K. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today 57(1), 43 (2004).
[Crossref]

Fournier, J. M.

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

Frick, M.

Garces-Chavez, V.

V. Garces-Chavez and K. Dholakia, Appl. Phys. Lett. 86, 031106 (2005).
[Crossref]

Golovchenko, J. A.

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

Grier, D. G.

See e.g., D. G. Grier, Nature 424, 810 (2003).
[PubMed]

Kivshar, Y. S.

D. K. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today 57(1), 43 (2004).
[Crossref]

Lin, Z. F.

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Phys. Rev. B 72, 085130 (2005).
[Crossref]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Opt. Lett. 30, 1956 (2005).
[Crossref] [PubMed]

Mellor, C. D.

C. D. Mellor and C. D. Bain, ChemPhysChem 7, 329 (2006).
[Crossref]

Metzger, N. K.

N. K. Metzger, K. Dholakia, and E. M. Wright, Phys. Rev. Lett. 96, 068102 (2006).
[Crossref] [PubMed]

Ng, J.

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Phys. Rev. B 72, 085130 (2005).
[Crossref]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Opt. Lett. 30, 1956 (2005).
[Crossref] [PubMed]

Nieto-Vesperinas, M.

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

Pendry, J. B.

M. I. Antonoyiannakis and J. B. Pendry, Phys. Rev. B 60, 613 (1997).

Ritsch-Marte, M.

Rohrbach, A.

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[Crossref] [PubMed]

Sheng, P.

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Phys. Rev. B 72, 085130 (2005).
[Crossref]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Opt. Lett. 30, 1956 (2005).
[Crossref] [PubMed]

Singer, W.

Tatarkova, S. A.

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

Wright, E. M.

N. K. Metzger, K. Dholakia, and E. M. Wright, Phys. Rev. Lett. 96, 068102 (2006).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

V. Garces-Chavez and K. Dholakia, Appl. Phys. Lett. 86, 031106 (2005).
[Crossref]

ChemPhysChem (1)

C. D. Mellor and C. D. Bain, ChemPhysChem 7, 329 (2006).
[Crossref]

J. Opt. Soc. Am. B (1)

Nature (1)

See e.g., D. G. Grier, Nature 424, 810 (2003).
[PubMed]

Opt. Lett. (1)

Phys. Rev. B (3)

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

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, Phys. Rev. B 72, 085130 (2005).
[Crossref]

M. I. Antonoyiannakis and J. B. Pendry, Phys. Rev. B 60, 613 (1997).

Phys. Rev. Lett. (5)

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[Crossref] [PubMed]

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

A. Chowdhury and B. Ackerson, Phys. Rev. Lett. 55, 833 (1985).
[Crossref] [PubMed]

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[Crossref]

N. K. Metzger, K. Dholakia, and E. M. Wright, Phys. Rev. Lett. 96, 068102 (2006).
[Crossref] [PubMed]

Phys. Today (1)

D. K. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today 57(1), 43 (2004).
[Crossref]

Science (1)

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

Other (3)

N. E. Cusack, The Physics of Structurally Disordered Matter: An Introduction (A. Hilger, 1987), p. 239.

The finite coherent length of a real laser will effectively set an upper limit on N. In the unrealistic case where N-->∞, the modes for Eq. become extended modes, whereas Eq. diverges.

The stable configurations calculated by the MS-MST formalism deviate from Eq. by less than 0.003 lambda.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Natural vibration frequencies Ω 0 i versus the inverse participation ratio, for the 1D lattice with N = 100 . (a), (b), and (c) correspond, respectively, to the k branch, ( k × E ) branch, and E branch. The open circles are obtained by the rigorous MS-MST formalism, and the dotted curve is that of the P.E. model, Eq. (4). (d) shows the I.P.R. for the ball and spring model. (e) shows schematically the direction of the particles’ displacements for the three branches.

Fig. 2
Fig. 2

Profiles of a few selected VEMs in the k branch (not to scale). Dashed lines show the equilibrium positions. (a)–(c) The highest-frequency mode for a lattice containing (a) N = 10 , (b) N = 50 , and (c) N = 100 particles. (c)–(f) VEMs for N = 100 , with (c) showing the highest-frequency mode. (d)–(e) correspond to two intermediate frequencies; (f) shows the lowest-frequency mode. (g) shows Ω intrinsic with N = 100 ; see Eq. (7).

Equations (7)

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

E i n ( r ) = 2 E 0 cos ( k z ) x ̂ ,
R n = ( 0 , 0 , n λ 2 ) , n = 1 , 2 , N ,
( I.P.R ) i = [ n = 1 N ( Δ X n ( i ) , Δ Y n ( i ) , Δ Z n ( i ) ) 4 ] 1 .
U = n = 1 N ( α 4 ) E i n ( r n ) 2 α 2 2 × n = 1 N m < n E i n ( r m ) Re { G ( r n r m ) } E i n ( r n ) ,
( K k branch ) l q = { K local ( l ) β n = 1 , n l N ξ ln 1 ( l = q ) , β ξ lq 1 ( l q )
( K u ) l q = { β n = 1 , n l N [ 2 u ξ ln 3 3 u ξ ln 5 ] ( l = q ) , β [ 2 u ξ lq 3 3 u ξ lq 5 ] ( l q )
Ω intrinsic ( l ) = K local ( l ) m ,

Metrics