Abstract

We present the theoretical analysis and the numerical modeling of optical levitation and trapping of the stuck particles with a pulsed optical tweezers. In our model, a pulsed laser was used to generate a large gradient force within a short duration that overcame the adhesive interaction between the stuck particles and the surface; and then a low power continuous-wave (cw) laser was used to capture the levitated particle. We describe the gradient force generated by the pulsed optical tweezers and model the binding interaction between the stuck beads and glass surface by the dominative van der Waals force with a randomly distributed binding strength. We numerically calculate the single pulse levitation efficiency for polystyrene beads as the function of the pulse energy, the axial displacement from the surface to the pulsed laser focus and the pulse duration. The result of our numerical modeling is qualitatively consistent with the experimental result.

© 2005 Optical Society of America

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References

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Annu. Rev. Biophys. Biomol. Struct. (1)

K. Svoboda and S. M. Block, �??Biological applications of optical forces,�?? Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

C. A. Xie, and Y. Q. Li, �??Raman spectra and optical trapping of highly refractive and nontransparent particles,�?? Appl. Phys. Lett. 81, 951-953 (2002).
[CrossRef]

J. Appl. Phys. (1)

C. A. Xie, and Y. Q. Li, �??Confocal micro-Raman spectroscopy of single biological cells using optical trapping and shifted excitation difference techniques,�?? J. Appl. Phys. 93, 2982-2986 (2003)
[CrossRef]

J. Raman Spectrosc. (1)

J. L. Deng, Q. Wei, M. H. Zhang, Y. Z. Wang, and Y. Q. Li, �??Study of the effect of alcohol on single human red blood cells using near-infrared laser tweezers Raman spectroscopy,�?? J. Raman Spectrosc. 36, 257-261 (2005).
[CrossRef]

Methods in Cell Biology (1)

A. Ashkin, �??Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optical regime,�?? in Methods in Cell Biology, vol.55, M.P. Sheetz, ed. (Academic Press, San Diego, 1998), pp.1-27.
[CrossRef]

Nature (3)

D. G. Grier, �??A revolution in optical manipulation�??, Nature (London), 424, 810-816 (2003).
[CrossRef]

A. Ashkin, J. M. Dziedzic and T. Yamane, �??Optical trapping and manipulation of single cells using infrared laser beams,�?? Nature, 330, 769-771 (1987)
[CrossRef] [PubMed]

C. Bustamante, Z. Bryant, and S.B. Smith, �??Ten years of tension: single-molecule DNA mechanics�??, Nature (London), 421, 423-427 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

P.T. Korda, M.B. Taylor, D.G. Grier, �??Kinetically Locked-In Colloidal Transport in an Array of Optical Tweezers�??, Phys. Rev. Lett. 89, 128301-1 (2002).
[CrossRef]

Rev. Sci. Instrum. (1)

K.C. Neuman and S.M. Block, �??Optical trapping�??, Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Science (5)

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, R. M. Simmons, �??Single-molecule biomechanics with optical methods�??, Science, 283, 1689-1695 (1999).
[CrossRef] [PubMed]

A. Ashkin, and J. M. Dziedzic, �??Optical trapping and manipulation of viruses and bacteria,�?? Science, 235, 1517-1520 (1987)
[CrossRef] [PubMed]

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, C. Bustamante, �??Identifying kinetic barriers to mechanical unfolding of the T-thermophila ribozyme�??, Science, 292, 1892-1895 (2003).
[CrossRef]

L. Paterson, M.P. MacDonald, J. Arlt, P.E. Bryant and K. Dholakia, �??Controlled rotation of optically trapped microscopic particles,�?? Science, 292, 912-914 (2001).
[CrossRef] [PubMed]

M.P. MacDonald, L. Peterson, K.Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, �??Creation and manipulation of three-dimensional optically trapped structures,�?? Science, 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Other (2)

T. G. M. van de Ven. Colloidal Hydrodynamics, (Academic Press, San Diego, 1989).

J. Happel, and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1965).

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Figures (6)

Fig. 1.
Fig. 1.

Schematics of the pulsed optical tweezers

Fig. 2.
Fig. 2.

(a) The beads were stuck on the surface. (b) The marked bead was levitated with a pulse and moved to the focus.

Fig. 3.
Fig. 3.

The position h of the bead versus time at the different pulse energy. Curve a is for E=1.1×10-5Ns/m; b for E=7×10-7Ns/m; c for E=0.

Fig. 4.
Fig. 4.

The levitation efficiency versus the E with a fixed z0=6µm andτ=45µs.

Fig. 5.
Fig. 5.

The dependence of the levitation efficiency on the displacement z0 with the fixed E=1.1×10-6Ns/m and τ=45µs.

Fig. 6.
Fig. 6.

The dependence of the levitation efficiency on the pulse duration τ with the fixed E=1.1×10-6Ns/m and z0=6µm.

Equations (12)

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I ( x , y , z , t ) = I 0 ω 0 2 ω ( z ) 2 exp ( 2 ( x 2 + y 2 ) ω ( z ) 2 )
+ 2 U τ π ω 0 2 ω ( z ) 2 exp ( ( t τ ) 2 ) exp ( 2 ( x 2 + y 2 ) ω ( z ) 2 ) ,
ω ( z ) = ω 0 ( 1 + ( z z s ) 2 ) 1 2 ,
F cw = k z z ( 1 + ( z z s ) 2 ) 2 ,
F cw = k z z ( 1 + ( z z s ) 2 ) 2 exp ( ( z z s ) 4 )
F pulse = 2 E τ π z ( 1 + ( z z s ) 2 ) 2 exp ( ( t τ ) 2 ) exp ( ( z z s ) 4 )
m z ̈ = F cw + F pulse + F S + F V ,
F V = Aa 6 h 2 f ( p ) ,
F S = 6 π a η λ z ˙ = D z ˙
λ = 1 1 9 8 ( a h + a ) + 1 2 ( a h + a ) 3 .
p { A } = 1 2 π σ e ( A ζ ) 2 2 σ 2 ,
P { A } = 1 2 π σ A e ( t ζ ) 2 2 σ 2 dt = Φ ( A ζ σ ) ,

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