Abstract

We investigate the dynamics of an array of polystyrene micron-sized spheres in a dual-beam fiber-optic trap. Experimental results show non-uniform equilibrium particle spacing and spontaneous self-sustained oscillation for large particle numbers. Results are analyzed with a Maxwell-Stress Tensor method using the Generalized Multipole Technique, where hydrodynamic interactions between particles are included. The theoretical analysis matches well with the experimentally observed equilibrium particle spacing. The theory shows that an offset in the trapping beams is the underlying mechanism for the oscillations and influences both the oscillation frequency and the damping rate for oscillations. The theory presented is of general interest to other systems involving multi-particle optical interactions.

© 2008 Optical Society of America

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References

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  1. D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-878 (2004).
    [CrossRef]
  2. A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
    [CrossRef]
  3. A. Constable, J. Kim, J. Mervis, F. Zarinetchi, and M. Prentiss, "Demonstration of a fiber-optical light-force trap," Opt. Lett. 18, 1867-1869 (1993).
    [CrossRef] [PubMed]
  4. E. R. Lyons and G. J. Sonek, "Confinement and bistability in a tapered hemispherically lensed optical fiber trap," Appl. Phys. Lett. 66, 1584-1586 (1995).
    [CrossRef]
  5. S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-Dimensional Optically Bound Arrays of Microscopic Particles," Phys. Rev. Lett. 89, 283901 (2002).
    [CrossRef]
  6. W. Singer, M. Frick, S. Bernet, and M. Ritsch-Marte, "Self-organized array of regularly spaced microbeads in a fiber-optical trap," J. Opt. Soc. Am. B 20, 1568-1574 (2003).
    [CrossRef]
  7. D. McGloin, A. E. Carruthers, K. Dholakia, and M. Wright, "Optically bound microscopic particles in one dimension," Phys. Rev. E 69, 021403 (2004).
    [CrossRef]
  8. N. K. Metzger, K. Dholakia, and E. M. Wright, "Observation of Bistability and Hysteresis in Optical Binding of Two Dielectric Sphere," Phys. Rev. Lett. 96, 068102 (2006).
    [CrossRef] [PubMed]
  9. N. K. Metzger, E. M. Wright, W. Sibbett, and K. Dholakia, "Visualization of optical of microparticles using a femtosecond fiber optical trap," Opt. Express 14, 3677-3687 (2006).
    [CrossRef] [PubMed]
  10. M. Guillon, O. Moine, and B. Stout, "Longitudinal optical binding of high optical contrast microdroplets in air," Phys. Rev. Lett. 96, 143902 (2006).
    [CrossRef] [PubMed]
  11. N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, "Measurement of the Restoring Forces Acting on Two Optically Bound Particles from Normal Mode Correlations," Phys. Rev. Lett. 98, 068102 (2007).
    [CrossRef] [PubMed]
  12. H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt- Kaler, and R. Blatt, "Ion strings for quantum gates," Appl. Phys. B 66, 603-608 (1998).
    [CrossRef]
  13. V. Karasek, K. Dholakia, and P. Zemanek, "Analysis of optical binding in one dimension," Appl. Phys. B 84, 149-156 (2006).
    [CrossRef]
  14. J. Ng, C. T. Chan, and P. Sheng, "Strong optical force induced by morphology-dependent resonance," Opt. Lett. 30, 1956-1958 (2005).
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  15. T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field," J. Opt. Soc. Am. A 23, 2324-2330 (2006).
    [CrossRef]
  16. C. Hafner, The Generalized Multiple Multipole Technique for Computational Electromagnetics, (Boston: Artech, 1990).
  17. K. Koba, H. Ikuno, and M. Kawano, "Numerical analysis of electromagnetic scattering from 3-D dielectric objects using the Yasuura method," Electrical Engineering in Japan, 148 (2), 39-45, New York:Wiley (2004).
    [CrossRef]
  18. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Oxford Press, Oxford, 1994).
  19. D. C. Duffy, J. C. McDonald, O. J. Schueller and G. M. Whitesides, "Rapid prototyping of Microfluidic Systems in Poly(dimethylsiloxane)," Anal. Chem. 70, 4974-4984 (1998).
    [CrossRef] [PubMed]
  20. X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang and X. Hu, "Determination of complex refractive index of polystyrene microsphere from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
    [CrossRef]
  21. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  22. J. A. Stratton, Electromagnetic Theory, (McGraw-Hill, 1941).
  23. J. P. Barton and D. R. Alexander, "Fifth order corrected electromagnetic field components for a fundamental Gaussian beam," J. Appl. Phys. 66, 2800-2802 (1989).
    [CrossRef]
  24. FDTD Solutions, from Lumerical Solutions Inc., http://www.lumerical.com.
  25. I. H. Shames, Mechanics of Fluids, (McGraw-Hill, 2002).
  26. A. Ashkin, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
    [CrossRef] [PubMed]
  27. F. J. Garcia de Abajo, "Collective oscillations in optical matter," Opt. Express 15, 11082-11094 (2007).
    [CrossRef]

2007 (2)

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, "Measurement of the Restoring Forces Acting on Two Optically Bound Particles from Normal Mode Correlations," Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

F. J. Garcia de Abajo, "Collective oscillations in optical matter," Opt. Express 15, 11082-11094 (2007).
[CrossRef]

2006 (5)

N. K. Metzger, E. M. Wright, W. Sibbett, and K. Dholakia, "Visualization of optical of microparticles using a femtosecond fiber optical trap," Opt. Express 14, 3677-3687 (2006).
[CrossRef] [PubMed]

T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field," J. Opt. Soc. Am. A 23, 2324-2330 (2006).
[CrossRef]

V. Karasek, K. Dholakia, and P. Zemanek, "Analysis of optical binding in one dimension," Appl. Phys. B 84, 149-156 (2006).
[CrossRef]

M. Guillon, O. Moine, and B. Stout, "Longitudinal optical binding of high optical contrast microdroplets in air," Phys. Rev. Lett. 96, 143902 (2006).
[CrossRef] [PubMed]

N. K. Metzger, K. Dholakia, and E. M. Wright, "Observation of Bistability and Hysteresis in Optical Binding of Two Dielectric Sphere," Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (2)

D. McGloin, A. E. Carruthers, K. Dholakia, and M. Wright, "Optically bound microscopic particles in one dimension," Phys. Rev. E 69, 021403 (2004).
[CrossRef]

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-878 (2004).
[CrossRef]

2003 (2)

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang and X. Hu, "Determination of complex refractive index of polystyrene microsphere from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

W. Singer, M. Frick, S. Bernet, and M. Ritsch-Marte, "Self-organized array of regularly spaced microbeads in a fiber-optical trap," J. Opt. Soc. Am. B 20, 1568-1574 (2003).
[CrossRef]

2002 (1)

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-Dimensional Optically Bound Arrays of Microscopic Particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

1998 (2)

D. C. Duffy, J. C. McDonald, O. J. Schueller and G. M. Whitesides, "Rapid prototyping of Microfluidic Systems in Poly(dimethylsiloxane)," Anal. Chem. 70, 4974-4984 (1998).
[CrossRef] [PubMed]

H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt- Kaler, and R. Blatt, "Ion strings for quantum gates," Appl. Phys. B 66, 603-608 (1998).
[CrossRef]

1995 (1)

E. R. Lyons and G. J. Sonek, "Confinement and bistability in a tapered hemispherically lensed optical fiber trap," Appl. Phys. Lett. 66, 1584-1586 (1995).
[CrossRef]

1993 (1)

1989 (1)

J. P. Barton and D. R. Alexander, "Fifth order corrected electromagnetic field components for a fundamental Gaussian beam," J. Appl. Phys. 66, 2800-2802 (1989).
[CrossRef]

1986 (1)

1970 (1)

A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

Alexander, D. R.

J. P. Barton and D. R. Alexander, "Fifth order corrected electromagnetic field components for a fundamental Gaussian beam," J. Appl. Phys. 66, 2800-2802 (1989).
[CrossRef]

Ashkin, A.

A. Ashkin, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

Barton, J. P.

J. P. Barton and D. R. Alexander, "Fifth order corrected electromagnetic field components for a fundamental Gaussian beam," J. Appl. Phys. 66, 2800-2802 (1989).
[CrossRef]

Bechter, W.

H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt- Kaler, and R. Blatt, "Ion strings for quantum gates," Appl. Phys. B 66, 603-608 (1998).
[CrossRef]

Bernet, S.

Brock, R. S.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang and X. Hu, "Determination of complex refractive index of polystyrene microsphere from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Carruthers, A. E.

D. McGloin, A. E. Carruthers, K. Dholakia, and M. Wright, "Optically bound microscopic particles in one dimension," Phys. Rev. E 69, 021403 (2004).
[CrossRef]

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-Dimensional Optically Bound Arrays of Microscopic Particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Chan, C. T.

Constable, A.

Dholakia, K.

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, "Measurement of the Restoring Forces Acting on Two Optically Bound Particles from Normal Mode Correlations," Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

N. K. Metzger, K. Dholakia, and E. M. Wright, "Observation of Bistability and Hysteresis in Optical Binding of Two Dielectric Sphere," Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

V. Karasek, K. Dholakia, and P. Zemanek, "Analysis of optical binding in one dimension," Appl. Phys. B 84, 149-156 (2006).
[CrossRef]

N. K. Metzger, E. M. Wright, W. Sibbett, and K. Dholakia, "Visualization of optical of microparticles using a femtosecond fiber optical trap," Opt. Express 14, 3677-3687 (2006).
[CrossRef] [PubMed]

D. McGloin, A. E. Carruthers, K. Dholakia, and M. Wright, "Optically bound microscopic particles in one dimension," Phys. Rev. E 69, 021403 (2004).
[CrossRef]

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-Dimensional Optically Bound Arrays of Microscopic Particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Duffy, D. C.

D. C. Duffy, J. C. McDonald, O. J. Schueller and G. M. Whitesides, "Rapid prototyping of Microfluidic Systems in Poly(dimethylsiloxane)," Anal. Chem. 70, 4974-4984 (1998).
[CrossRef] [PubMed]

Eschner, J.

H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt- Kaler, and R. Blatt, "Ion strings for quantum gates," Appl. Phys. B 66, 603-608 (1998).
[CrossRef]

Frick, M.

Garcia de Abajo, F. J.

Grier, D. G.

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-878 (2004).
[CrossRef]

Grzegorczyk, T. M.

Guillon, M.

M. Guillon, O. Moine, and B. Stout, "Longitudinal optical binding of high optical contrast microdroplets in air," Phys. Rev. Lett. 96, 143902 (2006).
[CrossRef] [PubMed]

Hu, X.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang and X. Hu, "Determination of complex refractive index of polystyrene microsphere from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Jacobs, K. M.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang and X. Hu, "Determination of complex refractive index of polystyrene microsphere from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Karasek, V.

V. Karasek, K. Dholakia, and P. Zemanek, "Analysis of optical binding in one dimension," Appl. Phys. B 84, 149-156 (2006).
[CrossRef]

Kemp, B. A.

Kim, J.

Kong, J. A.

Lu, J. Q.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang and X. Hu, "Determination of complex refractive index of polystyrene microsphere from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Lyons, E. R.

E. R. Lyons and G. J. Sonek, "Confinement and bistability in a tapered hemispherically lensed optical fiber trap," Appl. Phys. Lett. 66, 1584-1586 (1995).
[CrossRef]

Ma, X.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang and X. Hu, "Determination of complex refractive index of polystyrene microsphere from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Marchington, R. F.

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, "Measurement of the Restoring Forces Acting on Two Optically Bound Particles from Normal Mode Correlations," Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

Mazilu, M.

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, "Measurement of the Restoring Forces Acting on Two Optically Bound Particles from Normal Mode Correlations," Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

McDonald, J. C.

D. C. Duffy, J. C. McDonald, O. J. Schueller and G. M. Whitesides, "Rapid prototyping of Microfluidic Systems in Poly(dimethylsiloxane)," Anal. Chem. 70, 4974-4984 (1998).
[CrossRef] [PubMed]

McGloin, D.

D. McGloin, A. E. Carruthers, K. Dholakia, and M. Wright, "Optically bound microscopic particles in one dimension," Phys. Rev. E 69, 021403 (2004).
[CrossRef]

Mervis, J.

Metzger, N. K.

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, "Measurement of the Restoring Forces Acting on Two Optically Bound Particles from Normal Mode Correlations," Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

N. K. Metzger, K. Dholakia, and E. M. Wright, "Observation of Bistability and Hysteresis in Optical Binding of Two Dielectric Sphere," Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

N. K. Metzger, E. M. Wright, W. Sibbett, and K. Dholakia, "Visualization of optical of microparticles using a femtosecond fiber optical trap," Opt. Express 14, 3677-3687 (2006).
[CrossRef] [PubMed]

Moine, O.

M. Guillon, O. Moine, and B. Stout, "Longitudinal optical binding of high optical contrast microdroplets in air," Phys. Rev. Lett. 96, 143902 (2006).
[CrossRef] [PubMed]

Nagerl, H. C.

H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt- Kaler, and R. Blatt, "Ion strings for quantum gates," Appl. Phys. B 66, 603-608 (1998).
[CrossRef]

Ng, J.

Prentiss, M.

Ritsch-Marte, M.

Schueller, O. J.

D. C. Duffy, J. C. McDonald, O. J. Schueller and G. M. Whitesides, "Rapid prototyping of Microfluidic Systems in Poly(dimethylsiloxane)," Anal. Chem. 70, 4974-4984 (1998).
[CrossRef] [PubMed]

Sheng, P.

Sibbett, W.

Singer, W.

Smith, R. L.

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, "Measurement of the Restoring Forces Acting on Two Optically Bound Particles from Normal Mode Correlations," Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

Sonek, G. J.

E. R. Lyons and G. J. Sonek, "Confinement and bistability in a tapered hemispherically lensed optical fiber trap," Appl. Phys. Lett. 66, 1584-1586 (1995).
[CrossRef]

Stout, B.

M. Guillon, O. Moine, and B. Stout, "Longitudinal optical binding of high optical contrast microdroplets in air," Phys. Rev. Lett. 96, 143902 (2006).
[CrossRef] [PubMed]

Tatarkova, S. A.

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-Dimensional Optically Bound Arrays of Microscopic Particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Whitesides, G. M.

D. C. Duffy, J. C. McDonald, O. J. Schueller and G. M. Whitesides, "Rapid prototyping of Microfluidic Systems in Poly(dimethylsiloxane)," Anal. Chem. 70, 4974-4984 (1998).
[CrossRef] [PubMed]

Wright, E. M.

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, "Measurement of the Restoring Forces Acting on Two Optically Bound Particles from Normal Mode Correlations," Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

N. K. Metzger, K. Dholakia, and E. M. Wright, "Observation of Bistability and Hysteresis in Optical Binding of Two Dielectric Sphere," Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

N. K. Metzger, E. M. Wright, W. Sibbett, and K. Dholakia, "Visualization of optical of microparticles using a femtosecond fiber optical trap," Opt. Express 14, 3677-3687 (2006).
[CrossRef] [PubMed]

Wright, M.

D. McGloin, A. E. Carruthers, K. Dholakia, and M. Wright, "Optically bound microscopic particles in one dimension," Phys. Rev. E 69, 021403 (2004).
[CrossRef]

Yang, P.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang and X. Hu, "Determination of complex refractive index of polystyrene microsphere from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Zarinetchi, F.

Zemanek, P.

V. Karasek, K. Dholakia, and P. Zemanek, "Analysis of optical binding in one dimension," Appl. Phys. B 84, 149-156 (2006).
[CrossRef]

Anal. Chem. (1)

D. C. Duffy, J. C. McDonald, O. J. Schueller and G. M. Whitesides, "Rapid prototyping of Microfluidic Systems in Poly(dimethylsiloxane)," Anal. Chem. 70, 4974-4984 (1998).
[CrossRef] [PubMed]

Appl. Phys. B (2)

H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt- Kaler, and R. Blatt, "Ion strings for quantum gates," Appl. Phys. B 66, 603-608 (1998).
[CrossRef]

V. Karasek, K. Dholakia, and P. Zemanek, "Analysis of optical binding in one dimension," Appl. Phys. B 84, 149-156 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

E. R. Lyons and G. J. Sonek, "Confinement and bistability in a tapered hemispherically lensed optical fiber trap," Appl. Phys. Lett. 66, 1584-1586 (1995).
[CrossRef]

J. Appl. Phys. (1)

J. P. Barton and D. R. Alexander, "Fifth order corrected electromagnetic field components for a fundamental Gaussian beam," J. Appl. Phys. 66, 2800-2802 (1989).
[CrossRef]

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

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

Nature (1)

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-878 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Med. Biol. (1)

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang and X. Hu, "Determination of complex refractive index of polystyrene microsphere from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Phys. Rev. E (1)

D. McGloin, A. E. Carruthers, K. Dholakia, and M. Wright, "Optically bound microscopic particles in one dimension," Phys. Rev. E 69, 021403 (2004).
[CrossRef]

Phys. Rev. Lett. (5)

N. K. Metzger, K. Dholakia, and E. M. Wright, "Observation of Bistability and Hysteresis in Optical Binding of Two Dielectric Sphere," Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-Dimensional Optically Bound Arrays of Microscopic Particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

M. Guillon, O. Moine, and B. Stout, "Longitudinal optical binding of high optical contrast microdroplets in air," Phys. Rev. Lett. 96, 143902 (2006).
[CrossRef] [PubMed]

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, "Measurement of the Restoring Forces Acting on Two Optically Bound Particles from Normal Mode Correlations," Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

Other (7)

C. Hafner, The Generalized Multiple Multipole Technique for Computational Electromagnetics, (Boston: Artech, 1990).

K. Koba, H. Ikuno, and M. Kawano, "Numerical analysis of electromagnetic scattering from 3-D dielectric objects using the Yasuura method," Electrical Engineering in Japan, 148 (2), 39-45, New York:Wiley (2004).
[CrossRef]

M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Oxford Press, Oxford, 1994).

FDTD Solutions, from Lumerical Solutions Inc., http://www.lumerical.com.

I. H. Shames, Mechanics of Fluids, (McGraw-Hill, 2002).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

J. A. Stratton, Electromagnetic Theory, (McGraw-Hill, 1941).

Supplementary Material (3)

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Figures (7)

Fig. 1.
Fig. 1.

Fluorescence microscopy images of a stably trapped 10-particle array containing 1-micron fluorescent polystyrene spheres and a 13-particle oscillating array. A video demonstrating the transition from a 10- to 13-particle array is also provided.

Fig. 2.
Fig. 2.

Schematic used to model of the dual-beam fiber trap.

Fig. 3.
Fig. 3.

Optical forces acting on trapped particles as a function of distance between neighboring particles. Solid lines and blue dots are results obtained using MST-GMT and MST-FDTD, respectively. (a) Two-particle array. (b) Three-particle array.

Fig. 4.
Fig. 4.

Trajectories of particles obtained by the dynamic simulation. Red and blue lines are the results with and without HDI, respectively. (a) From two- to four- particle array. (b) Thirteenparticle array.

Fig. 5.
Fig. 5.

Inhomogeneous properties of inter-particle spacing. (a) Averaged inter-particle spacing d av as a function of the number of particles I. A standard deviation plot is applied to the experimental results. (b) The inner most inter-particle spacing d inn and the outer most inter-particle spacing d out, as a function of I. Green and red positions denote theoretical and experimental results, respectively.

Fig. 6.
Fig. 6.

Simulation results for a 7-particle array. (a) Introduction of a 7th particle into a system where the beam axes are offset by 4 µm. The arrow indicates the trajectory of the 7th particle. (b) Final equilibrium positions for the 7 particles after undergoing damped oscillation induced by the introduction of the 7th particle. (c) The resulting self-sustained oscillation after increasing the beam offset to 5 µm. A video demonstrating these results is also provided. [Video 2][Video 3]

Fig. 7.
Fig. 7.

Oscillation frequency and damping as a function of a number of the particles I for various offsets D off. Squares and crosses represent results for D off=5 µm and 4 µm, respectively, and red and blue lines represent results with and without HDI, respectively. (a) Frequency Ω, (b) Damping coefficient Λ.

Equations (14)

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F i = S M , i T · v M d S
T = 1 2 Re [ ε E ( r ) E * ( r ) + μ H ( r ) H * ( r ) 1 2 { ε E ( r ) 2 + μ H ( r ) 2 } I ]
E = E in + E sc and H = H in + H sc
E N sc ( r ) = i = 1 I E i , N sc ( r i )
E i , N sc ( r i ) = n = 1 N m = n n a nm i ( N ) m nm ( 4 ) ( k r i ) + b nm i ( N ) n nm ( 4 ) ( k r i )
E i , N tr ( r i ) = n = 1 N m = n n c nm i ( N ) m nm ( 1 ) ( k i r i ) + d nm i ( N ) n nm ( 1 ) ( k i r i )
H i , N sc ( r i ) = 1 Z out n = 1 N m = n n a nm i ( N ) n nm ( 4 ) ( k r i ) + b nm i ( N ) m nm ( 4 ) ( k r i )
H i , N tr ( r i ) = 1 Z in n = 1 N m = n n c nm i ( N ) n nm ( 1 ) ( k i r i ) + d nm i ( N ) m nm ( 1 ) ( k i r i )
Ω ( N ) = j = 1 I S P , j v p ( r j ) × { i = 1 I E i , N sc ( r j ) + E in ( r j ) E j , N tr ( r j ) } 2 d S S P , j v P ( r j ) × E in ( r j ) 2 d S
+ S P , j v p ( r j ) × { i = 1 I H i , N sc ( r j ) + H in ( r j ) H j , N tr ( r j ) } 2 d S S P , j v P ( r j ) × H in ( r j ) 2 d S
d R i d t = v i
v i = j = 1 I H i , j F j
H i , j = I ζ δ ij + 3 a 4 ζ r ij ( 1 δ ij ) [ I + r ij r ij r ij 2 ] .
R i m + 1 = R i m + v i m Δ t , ( m = 0 , 1 , 2 , 3 · · · )

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