Abstract

An optimized optical trap is a favorable choice for nanoparticle trapping and micromanipulation of biological tissues. The collimation of laser beam before the objective can have significant influence on the trap by controlling the effective NA of the system. We have shown by both theory and experiment that in the aberration-free condition the filling factor of WD0.67 provides the strongest trap in the lateral directions for a micrometer-size bead. In this condition improvements up to 117% (168%), compared with the previously suggested ratio of WD1 (WD1.25), were achieved in the lateral direction.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. Throughout the Letter the improvements are calculated by comparison to the reference values: Improvement percentage=newvalue-referencevalue∕referencevalue×100, e.g., 168% improvement would be 2.68 as large as the reference value.

2010 (1)

2009 (1)

2008 (2)

B. H. Meng, J. H. Zhou, M. C. Zhong, Y. M. Lee, J. G. Wu, and H. L. Ren, Chin. Phys. Lett. 25, 2300 (2008).
[CrossRef]

A. C. Richardson, S. N. S. Reihani, and L. B. Oddershede, Opt. Express 16, 15709 (2008).
[CrossRef] [PubMed]

2007 (2)

S. N. S. Reihani and L. B. Oddershede, Opt. Lett. 32, 1998 (2007).
[CrossRef] [PubMed]

T. M. Hansen, S. N. S. Reihani, L. Oddershede, and M. Sørensen, Proc. Natl. Acad. Sci. U.S.A. 104, 5830 (2007).
[CrossRef] [PubMed]

2006 (1)

2004 (1)

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

2003 (2)

E. Fällman and O. Axner, Appl. Opt. 42, 3915 (2003).
[CrossRef] [PubMed]

H. I. Kim, I. J. Joo, S. H. Song, P. S. Kim, K. B. Im, and C. H. Oh, J. Korean Phys. Soc. 43, 348 (2003).

2002 (1)

1999 (1)

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, Biophys. J. 77, 2856 (1999).
[CrossRef] [PubMed]

1998 (1)

P. C. Ke and M. Gu, J. Mod. Opt. 45, 2159 (1998).
[CrossRef]

1996 (1)

S. B. Smith, Y. Cui, and C. Bustamante, Science 271, 795 (1996).
[CrossRef] [PubMed]

1992 (1)

A. Ashkin, Biophys. J. 61, 569 (1992).
[CrossRef] [PubMed]

1990 (1)

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, Nature 348, 348 (1990).
[CrossRef] [PubMed]

1989 (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

1986 (1)

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

Ashkin, A.

Axner, O.

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

Bergman, K.

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, Biophys. J. 77, 2856 (1999).
[CrossRef] [PubMed]

Berg-Sørensen, K.

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, Biophys. J. 77, 2856 (1999).
[CrossRef] [PubMed]

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, Nature 348, 348 (1990).
[CrossRef] [PubMed]

Bustamante, C.

S. B. Smith, Y. Cui, and C. Bustamante, Science 271, 795 (1996).
[CrossRef] [PubMed]

Chadd, E. H.

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, Biophys. J. 77, 2856 (1999).
[CrossRef] [PubMed]

Charsooghi, M. A.

Chu, S.

Cui, Y.

S. B. Smith, Y. Cui, and C. Bustamante, Science 271, 795 (1996).
[CrossRef] [PubMed]

Dharmadhikari, A. K.

Dharmadhikari, J. A.

Dziedzic, J. M.

Fällman, E.

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Goldstein, L. S. B.

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, Nature 348, 348 (1990).
[CrossRef] [PubMed]

Golestanian, R.

Gu, M.

P. C. Ke and M. Gu, J. Mod. Opt. 45, 2159 (1998).
[CrossRef]

Hajizadeh, F.

Hansen, T. M.

T. M. Hansen, S. N. S. Reihani, L. Oddershede, and M. Sørensen, Proc. Natl. Acad. Sci. U.S.A. 104, 5830 (2007).
[CrossRef] [PubMed]

Im, K. B.

H. I. Kim, I. J. Joo, S. H. Song, P. S. Kim, K. B. Im, and C. H. Oh, J. Korean Phys. Soc. 43, 348 (2003).

Joo, I. J.

H. I. Kim, I. J. Joo, S. H. Song, P. S. Kim, K. B. Im, and C. H. Oh, J. Korean Phys. Soc. 43, 348 (2003).

Ke, P. C.

P. C. Ke and M. Gu, J. Mod. Opt. 45, 2159 (1998).
[CrossRef]

Khalesifard, H. R.

Kim, H. I.

H. I. Kim, I. J. Joo, S. H. Song, P. S. Kim, K. B. Im, and C. H. Oh, J. Korean Phys. Soc. 43, 348 (2003).

Kim, P. S.

H. I. Kim, I. J. Joo, S. H. Song, P. S. Kim, K. B. Im, and C. H. Oh, J. Korean Phys. Soc. 43, 348 (2003).

Lee, Y. M.

B. H. Meng, J. H. Zhou, M. C. Zhong, Y. M. Lee, J. G. Wu, and H. L. Ren, Chin. Phys. Lett. 25, 2300 (2008).
[CrossRef]

Liou, G. F.

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, Biophys. J. 77, 2856 (1999).
[CrossRef] [PubMed]

Mathur, D.

Meng, B. H.

B. H. Meng, J. H. Zhou, M. C. Zhong, Y. M. Lee, J. G. Wu, and H. L. Ren, Chin. Phys. Lett. 25, 2300 (2008).
[CrossRef]

Neuman, K. C.

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, Biophys. J. 77, 2856 (1999).
[CrossRef] [PubMed]

Oddershede, L.

T. M. Hansen, S. N. S. Reihani, L. Oddershede, and M. Sørensen, Proc. Natl. Acad. Sci. U.S.A. 104, 5830 (2007).
[CrossRef] [PubMed]

Oddershede, L. B.

Oh, C. H.

H. I. Kim, I. J. Joo, S. H. Song, P. S. Kim, K. B. Im, and C. H. Oh, J. Korean Phys. Soc. 43, 348 (2003).

Ramachandran, H.

Ramanandan, G.

Reihani, S. N. S.

Ren, H. L.

B. H. Meng, J. H. Zhou, M. C. Zhong, Y. M. Lee, J. G. Wu, and H. L. Ren, Chin. Phys. Lett. 25, 2300 (2008).
[CrossRef]

Richardson, A. C.

Rohrbach, A.

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

Schnapp, B. J.

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, Nature 348, 348 (1990).
[CrossRef] [PubMed]

Smith, S. B.

S. B. Smith, Y. Cui, and C. Bustamante, Science 271, 795 (1996).
[CrossRef] [PubMed]

Song, S. H.

H. I. Kim, I. J. Joo, S. H. Song, P. S. Kim, K. B. Im, and C. H. Oh, J. Korean Phys. Soc. 43, 348 (2003).

Sørensen, M.

T. M. Hansen, S. N. S. Reihani, L. Oddershede, and M. Sørensen, Proc. Natl. Acad. Sci. U.S.A. 104, 5830 (2007).
[CrossRef] [PubMed]

Stelzer, E. H. K.

Wu, J. G.

B. H. Meng, J. H. Zhou, M. C. Zhong, Y. M. Lee, J. G. Wu, and H. L. Ren, Chin. Phys. Lett. 25, 2300 (2008).
[CrossRef]

Zhong, M. C.

B. H. Meng, J. H. Zhou, M. C. Zhong, Y. M. Lee, J. G. Wu, and H. L. Ren, Chin. Phys. Lett. 25, 2300 (2008).
[CrossRef]

Zhou, J. H.

B. H. Meng, J. H. Zhou, M. C. Zhong, Y. M. Lee, J. G. Wu, and H. L. Ren, Chin. Phys. Lett. 25, 2300 (2008).
[CrossRef]

Appl. Opt. (2)

Biophys. J. (2)

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, Biophys. J. 77, 2856 (1999).
[CrossRef] [PubMed]

A. Ashkin, Biophys. J. 61, 569 (1992).
[CrossRef] [PubMed]

Chin. Phys. Lett. (1)

B. H. Meng, J. H. Zhou, M. C. Zhong, Y. M. Lee, J. G. Wu, and H. L. Ren, Chin. Phys. Lett. 25, 2300 (2008).
[CrossRef]

J. Appl. Phys. (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

J. Korean Phys. Soc. (1)

H. I. Kim, I. J. Joo, S. H. Song, P. S. Kim, K. B. Im, and C. H. Oh, J. Korean Phys. Soc. 43, 348 (2003).

J. Mod. Opt. (1)

P. C. Ke and M. Gu, J. Mod. Opt. 45, 2159 (1998).
[CrossRef]

Nature (1)

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, Nature 348, 348 (1990).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (3)

Proc. Natl. Acad. Sci. U.S.A. (1)

T. M. Hansen, S. N. S. Reihani, L. Oddershede, and M. Sørensen, Proc. Natl. Acad. Sci. U.S.A. 104, 5830 (2007).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Science (1)

S. B. Smith, Y. Cui, and C. Bustamante, Science 271, 795 (1996).
[CrossRef] [PubMed]

Other (1)

Throughout the Letter the improvements are calculated by comparison to the reference values: Improvement percentage=newvalue-referencevalue∕referencevalue×100, e.g., 168% improvement would be 2.68 as large as the reference value.

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Figures (3)

Fig. 1
Fig. 1

Theoretical results. (a) Lateral intensity distribution at focus for different values of W D . (b) Intensity gradient in the radial direction for distributions presented in (a). (c) Area under graphs presented in (b) versus W D for particles with diameters of d b = 0.8 μ m and d b = 1 μ m .

Fig. 2
Fig. 2

Instrumental details. BE, DM, L, and QPD represent beam expander, dichroic mirror, lens, and quadrant photodiode, respectively. The blown-up view shows the definition of W and D. The upper left graph shows a typical variation of trap stiffness by depth using an immersion oil with n = 1.55 . The optimal trap occurs at depth of 17 μ m . The laser power is measured to be 37 mW before the objective.

Fig. 3
Fig. 3

Experimental results. (a) Lateral and axial (inset) trap stiffness for 1 μ m polystyrene beads. (b) Lateral stiffness for 0.8 μ m polystyrene beads. X denotes the polarization direction of the laser beam. The laser power was measured to be (a) 37 mW and (b) 50 mW before the objective and was kept constant throughout the measurements.

Equations (2)

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I ( r , z ) = 0 α exp ( ρ 2 W 2 ) ( cos θ 1 ) 1 2 sin θ 1 exp [ i k 0 ψ ( θ 1 , θ 2 , d ) ] ( τ s + τ p cos θ 2 ) J 0 ( k 0 n 1 r sin θ 1 ) exp ( i k 0 n 2 z cos θ 2 ) d θ 1 ,
ψ ( θ 1 , θ 2 , d ) = d ( n 1 cos θ 1 n 2 cos θ 2 ) ,

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