Abstract

Recently, Stilgoe, et al., [Opt. Express 16, 15039 (2008)] reported calculations of the force on an optically trapped sphere performed using the “optical tweezers toolbox”. This software suffers from numerical inaccuracies that lead to qualitative errors in the state diagram for stable trapping, particularly for spheres smaller than the wavelength of light.

© 2009 Optical Society of America

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References

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  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
    [CrossRef] [PubMed]
  2. A. B. Stilgoe, T. A. Nieminen, G. Knoner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "The effect of Mie resonances on trapping in optical tweezers," Opt. Express 16, 15039-15051 (2008).
    [CrossRef] [PubMed]
  3. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1983).
  4. B. Sun, Y. Roichman, and D. G. Grier, "Theory of holographic optical trapping," Opt. Express 16, 765-776 (2008).
    [CrossRef] [PubMed]
  5. T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A.M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical tweezers computational toolbox," J. Opt. A 9, S196-S203 (2007).
    [CrossRef]
  6. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, Cambridge, 2001).
  7. T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, Y. Hu, G. Knoener, and A. M. Branczyk, "Optical tweezers toolbox 1.1," University of Queensland (2007), http://www.physics.uq.edu.au/people/nieminen/software.html.
  8. T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Multipole expansion of strongly focussed laser beams," J. Quant. Spec. Rad. Transfer 79-80, 1005-1017 (2003).
    [CrossRef]
  9. J. H. Crichton and P. L. Marston, "The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation," Electron. J. Differ. Equations Conf. 04, 37-50 (2000).
  10. Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
    [CrossRef]

2007 (1)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A.M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical tweezers computational toolbox," J. Opt. A 9, S196-S203 (2007).
[CrossRef]

2003 (1)

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Multipole expansion of strongly focussed laser beams," J. Quant. Spec. Rad. Transfer 79-80, 1005-1017 (2003).
[CrossRef]

2000 (1)

J. H. Crichton and P. L. Marston, "The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation," Electron. J. Differ. Equations Conf. 04, 37-50 (2000).

1996 (1)

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

1986 (1)

Asakura, T.

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

Ashkin, A.

Bjorkholm, J. E.

Branczyk, A.M.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A.M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical tweezers computational toolbox," J. Opt. A 9, S196-S203 (2007).
[CrossRef]

Chu, S.

Crichton, J. H.

J. H. Crichton and P. L. Marston, "The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation," Electron. J. Differ. Equations Conf. 04, 37-50 (2000).

Dziedzic, J. M.

Harada, Y.

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

Heckenberg, N. R.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A.M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical tweezers computational toolbox," J. Opt. A 9, S196-S203 (2007).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Multipole expansion of strongly focussed laser beams," J. Quant. Spec. Rad. Transfer 79-80, 1005-1017 (2003).
[CrossRef]

Knöner, G.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A.M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical tweezers computational toolbox," J. Opt. A 9, S196-S203 (2007).
[CrossRef]

Loke, V. L. Y.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A.M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical tweezers computational toolbox," J. Opt. A 9, S196-S203 (2007).
[CrossRef]

Marston, P. L.

J. H. Crichton and P. L. Marston, "The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation," Electron. J. Differ. Equations Conf. 04, 37-50 (2000).

Nieminen, T. A.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A.M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical tweezers computational toolbox," J. Opt. A 9, S196-S203 (2007).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Multipole expansion of strongly focussed laser beams," J. Quant. Spec. Rad. Transfer 79-80, 1005-1017 (2003).
[CrossRef]

Rubinsztein-Dunlop, H.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A.M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical tweezers computational toolbox," J. Opt. A 9, S196-S203 (2007).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Multipole expansion of strongly focussed laser beams," J. Quant. Spec. Rad. Transfer 79-80, 1005-1017 (2003).
[CrossRef]

Stilgoe, A. B.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A.M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical tweezers computational toolbox," J. Opt. A 9, S196-S203 (2007).
[CrossRef]

Conf. (1)

J. H. Crichton and P. L. Marston, "The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation," Electron. J. Differ. Equations Conf. 04, 37-50 (2000).

J. Opt. A (1)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A.M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical tweezers computational toolbox," J. Opt. A 9, S196-S203 (2007).
[CrossRef]

J. Quant. Spec. Rad. Transfer (1)

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Multipole expansion of strongly focussed laser beams," J. Quant. Spec. Rad. Transfer 79-80, 1005-1017 (2003).
[CrossRef]

Opt. Commun. (1)

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

Opt. Lett. (1)

Other (5)

A. B. Stilgoe, T. A. Nieminen, G. Knoner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "The effect of Mie resonances on trapping in optical tweezers," Opt. Express 16, 15039-15051 (2008).
[CrossRef] [PubMed]

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1983).

B. Sun, Y. Roichman, and D. G. Grier, "Theory of holographic optical trapping," Opt. Express 16, 765-776 (2008).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, Cambridge, 2001).

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, Y. Hu, G. Knoener, and A. M. Branczyk, "Optical tweezers toolbox 1.1," University of Queensland (2007), http://www.physics.uq.edu.au/people/nieminen/software.html.

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Figures (1)

Fig. 1.
Fig. 1.

State diagram for dielectric spheres in an optical tweezer of numerical aperture 1.3. Colors in the main diagram correspond to the maximum axial trapping efficiency at each set of conditions, computed on a 144×60 grid. White regions denote conditions for which particles are not stably trapped. Images (a) and (b) show the magnitude of normalized surface fields for the particular conditions indicated on the diagram. (a) corresponds to an unstable point. The sphere at (b) is stably trapped.

Equations (8)

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E 0 ( r ) = n = 1 m = n n a n m M n m ( 2 ) ( k r ) + b n m N n m ( 2 ) ( k r ) ,
E s ( r ) = n = 1 m = n n P n m M n m ( 1 ) ( k r ) + q n m N n m ( 2 ) ( k r ) ,
E i ( r ) = n = 1 m = n n C n m ( M n m ( 1 ) ( m p k r ) + M n m ( 2 ) ( m p k r ) ) + d n m ( N n m ( 1 ) ( m p k r ) + N n m ( 2 ) ( m p k r ) ) ,
C n m = i m p α m n ξ n ' ( x ) ψ n ( m p x ) m p ξ n ( x ) ψ n ( m p x ) and
d n m = i m p b m n m p ξ n ' ( x ) ψ n ( m p x ) ξ n ( x ) ψ n ' ( m p x ) ,
Q = 2 P n = 1 1 n + 1 m = n n ( m n { a n m * b n m P n m * q n m } +
[ n ( n + 2 ) ( n + 1 m ) ( n + 1 + m ) ( 2 n + 1 ) ( 2 n + 3 ) ] 1 2 ×
{ P n m P n + 1 , m * + q n m q n + 1 , m * a n m a n + 1 , m * b n m b n + 1 , m * } ) .

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