Abstract

In this study we report on the dynamic motion of a nano-sized colloidal particle captured in a polarized optical trap. A polystyrene sphere (300nm-diameter) that is electrically charged in solution was trapped with an optical tweezers formed by a linearly polarized TEM00 Gaussian beam, while the Brownian displacements of the trapped particle in x and y directions were measured so that the position of the particle’s mass center can be mapped on the transverse plane and the corss-correlation between x and y displacements can be calculated. We found that the position’s fluctuation of the trapped nano-sized particle in the parallel direction to the laser polarization is significantly larger than that in the normal direction, which suggests that there exists an additional random electric force parallel to the laser polarization direction exerting on the charged particle beside the known radiation forces on the dielectric particle. This asymmetry in dynamic motion is significant when the particle size is well less than the wavelength of the trapping laser. However, in an optical trap formed by a circularly polarized beam, this asymmetry in dynamic motion was observed to disappear. We present both the experimental results and a theoretical analysis.

© 2005 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. T. Weber, J. Herbig, M. Mark, H. C. Nagerl, and R. Grimm, “Bose-Einstein condensation of cesium,” Science 299, 232–235 (2003).
    [Crossref]
  3. K. Svoboda and S.M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struc. 23, 247–284 (1994).
    [Crossref]
  4. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809(2004).
    [Crossref]
  5. A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-Molecule Biomechanics with Optical Methods,” Science 283, 1689–1695 (1999).
    [Crossref] [PubMed]
  6. D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
    [Crossref] [PubMed]
  7. B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, “Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme,” Science 299, 1892–1895 (2003).
    [Crossref] [PubMed]
  8. R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, and S.A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
    [Crossref]
  9. Y.Q. Li, C. Christou, X.H. Hu, and M. Dinno, “Quasi-elastic light scattering of laser trapped biological particles,” Conference on Lasers and Electro-Optics, 2000, San Franscisco, CA, p620.
  10. J. Meiners and S.R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
    [Crossref]
  11. J. Meiners and S.R. Quake, “femtonewton force spectroscopy of single extended DNA molecules,” Phys. Rev. Lett. 84, 5014–5017 (2000).
    [Crossref] [PubMed]
  12. K. Visscher, M.J. Schnitzer, and S.M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184–189 (1999).
    [Crossref] [PubMed]
  13. J. Guck, R. Ananthakrishnan, T.J. Moon, C.C. Cunningham, and J. Kas, “Optical Deformability of Soft Biological Dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
    [Crossref] [PubMed]
  14. C. Xie, M. A. Dinno, and Y.Q. Li, “Near-infrared Raman spectroscopy of single optically trapped biological cells,” Opt. Lett. 27,249–251(2002).
    [Crossref]
  15. T. G.M. Van De Ven, Colloidal Hydrodynamics, p.78, Academic Press, London, 1989.
  16. G. M. Keppler and S. Fradem, “Attractive potential between confined colloids at low ionic strength,” Phys. Rev. Lett. 73, 356–359 (1994).
    [Crossref]
  17. J.C. Crocker and D.G. Grier, “Microscopic measurement of the pair interaction potential of charge-stabilized colloid,” Phys. Rev. Lett. 73, 352–355 (1994).
    [Crossref] [PubMed]

2004 (1)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809(2004).
[Crossref]

2003 (3)

T. Weber, J. Herbig, M. Mark, H. C. Nagerl, and R. Grimm, “Bose-Einstein condensation of cesium,” Science 299, 232–235 (2003).
[Crossref]

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, “Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme,” Science 299, 1892–1895 (2003).
[Crossref] [PubMed]

2002 (1)

2000 (2)

J. Meiners and S.R. Quake, “femtonewton force spectroscopy of single extended DNA molecules,” Phys. Rev. Lett. 84, 5014–5017 (2000).
[Crossref] [PubMed]

J. Guck, R. Ananthakrishnan, T.J. Moon, C.C. Cunningham, and J. Kas, “Optical Deformability of Soft Biological Dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
[Crossref] [PubMed]

1999 (3)

K. Visscher, M.J. Schnitzer, and S.M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184–189 (1999).
[Crossref] [PubMed]

J. Meiners and S.R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[Crossref]

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-Molecule Biomechanics with Optical Methods,” Science 283, 1689–1695 (1999).
[Crossref] [PubMed]

1997 (1)

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, and S.A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[Crossref]

1994 (3)

K. Svoboda and S.M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struc. 23, 247–284 (1994).
[Crossref]

G. M. Keppler and S. Fradem, “Attractive potential between confined colloids at low ionic strength,” Phys. Rev. Lett. 73, 356–359 (1994).
[Crossref]

J.C. Crocker and D.G. Grier, “Microscopic measurement of the pair interaction potential of charge-stabilized colloid,” Phys. Rev. Lett. 73, 352–355 (1994).
[Crossref] [PubMed]

1986 (1)

Ananthakrishnan, R.

J. Guck, R. Ananthakrishnan, T.J. Moon, C.C. Cunningham, and J. Kas, “Optical Deformability of Soft Biological Dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
[Crossref] [PubMed]

Ashkin, A.

Bar-Ziv, R.

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, and S.A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[Crossref]

Bjorkholm, J.E.

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809(2004).
[Crossref]

Block, S.M.

K. Visscher, M.J. Schnitzer, and S.M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184–189 (1999).
[Crossref] [PubMed]

K. Svoboda and S.M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struc. 23, 247–284 (1994).
[Crossref]

Bustamante, C.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, “Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme,” Science 299, 1892–1895 (2003).
[Crossref] [PubMed]

Christou, C.

Y.Q. Li, C. Christou, X.H. Hu, and M. Dinno, “Quasi-elastic light scattering of laser trapped biological particles,” Conference on Lasers and Electro-Optics, 2000, San Franscisco, CA, p620.

Chu, S.

Crocker, J.C.

J.C. Crocker and D.G. Grier, “Microscopic measurement of the pair interaction potential of charge-stabilized colloid,” Phys. Rev. Lett. 73, 352–355 (1994).
[Crossref] [PubMed]

Cunningham, C.C.

J. Guck, R. Ananthakrishnan, T.J. Moon, C.C. Cunningham, and J. Kas, “Optical Deformability of Soft Biological Dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
[Crossref] [PubMed]

Dinno, M.

Y.Q. Li, C. Christou, X.H. Hu, and M. Dinno, “Quasi-elastic light scattering of laser trapped biological particles,” Conference on Lasers and Electro-Optics, 2000, San Franscisco, CA, p620.

Dinno, M. A.

Dumont, S.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, “Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme,” Science 299, 1892–1895 (2003).
[Crossref] [PubMed]

Dziedzic, J.M.

Fradem, S.

G. M. Keppler and S. Fradem, “Attractive potential between confined colloids at low ionic strength,” Phys. Rev. Lett. 73, 356–359 (1994).
[Crossref]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

Grier, D.G.

J.C. Crocker and D.G. Grier, “Microscopic measurement of the pair interaction potential of charge-stabilized colloid,” Phys. Rev. Lett. 73, 352–355 (1994).
[Crossref] [PubMed]

Grimm, R.

T. Weber, J. Herbig, M. Mark, H. C. Nagerl, and R. Grimm, “Bose-Einstein condensation of cesium,” Science 299, 232–235 (2003).
[Crossref]

Guck, J.

J. Guck, R. Ananthakrishnan, T.J. Moon, C.C. Cunningham, and J. Kas, “Optical Deformability of Soft Biological Dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
[Crossref] [PubMed]

Herbig, J.

T. Weber, J. Herbig, M. Mark, H. C. Nagerl, and R. Grimm, “Bose-Einstein condensation of cesium,” Science 299, 232–235 (2003).
[Crossref]

Hu, X.H.

Y.Q. Li, C. Christou, X.H. Hu, and M. Dinno, “Quasi-elastic light scattering of laser trapped biological particles,” Conference on Lasers and Electro-Optics, 2000, San Franscisco, CA, p620.

Kas, J.

J. Guck, R. Ananthakrishnan, T.J. Moon, C.C. Cunningham, and J. Kas, “Optical Deformability of Soft Biological Dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
[Crossref] [PubMed]

Keppler, G. M.

G. M. Keppler and S. Fradem, “Attractive potential between confined colloids at low ionic strength,” Phys. Rev. Lett. 73, 356–359 (1994).
[Crossref]

Li, Y.Q.

C. Xie, M. A. Dinno, and Y.Q. Li, “Near-infrared Raman spectroscopy of single optically trapped biological cells,” Opt. Lett. 27,249–251(2002).
[Crossref]

Y.Q. Li, C. Christou, X.H. Hu, and M. Dinno, “Quasi-elastic light scattering of laser trapped biological particles,” Conference on Lasers and Electro-Optics, 2000, San Franscisco, CA, p620.

Liphardt, J.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, “Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme,” Science 299, 1892–1895 (2003).
[Crossref] [PubMed]

Mark, M.

T. Weber, J. Herbig, M. Mark, H. C. Nagerl, and R. Grimm, “Bose-Einstein condensation of cesium,” Science 299, 232–235 (2003).
[Crossref]

Mehta, A. D.

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-Molecule Biomechanics with Optical Methods,” Science 283, 1689–1695 (1999).
[Crossref] [PubMed]

Meiners, J.

J. Meiners and S.R. Quake, “femtonewton force spectroscopy of single extended DNA molecules,” Phys. Rev. Lett. 84, 5014–5017 (2000).
[Crossref] [PubMed]

J. Meiners and S.R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[Crossref]

Meller, A.

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, and S.A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[Crossref]

Moon, T.J.

J. Guck, R. Ananthakrishnan, T.J. Moon, C.C. Cunningham, and J. Kas, “Optical Deformability of Soft Biological Dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
[Crossref] [PubMed]

Moses, E.

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, and S.A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[Crossref]

Nagerl, H. C.

T. Weber, J. Herbig, M. Mark, H. C. Nagerl, and R. Grimm, “Bose-Einstein condensation of cesium,” Science 299, 232–235 (2003).
[Crossref]

Neuman, K. C.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809(2004).
[Crossref]

Onoa, B.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, “Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme,” Science 299, 1892–1895 (2003).
[Crossref] [PubMed]

Quake, S.R.

J. Meiners and S.R. Quake, “femtonewton force spectroscopy of single extended DNA molecules,” Phys. Rev. Lett. 84, 5014–5017 (2000).
[Crossref] [PubMed]

J. Meiners and S.R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[Crossref]

Rief, M.

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-Molecule Biomechanics with Optical Methods,” Science 283, 1689–1695 (1999).
[Crossref] [PubMed]

Safran, S.A.

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, and S.A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[Crossref]

Schnitzer, M.J.

K. Visscher, M.J. Schnitzer, and S.M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184–189 (1999).
[Crossref] [PubMed]

Simmons, R. M.

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-Molecule Biomechanics with Optical Methods,” Science 283, 1689–1695 (1999).
[Crossref] [PubMed]

Smith, D. A.

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-Molecule Biomechanics with Optical Methods,” Science 283, 1689–1695 (1999).
[Crossref] [PubMed]

Smith, S. B.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, “Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme,” Science 299, 1892–1895 (2003).
[Crossref] [PubMed]

Spudich, J. A.

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-Molecule Biomechanics with Optical Methods,” Science 283, 1689–1695 (1999).
[Crossref] [PubMed]

Stavans, J.

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, and S.A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[Crossref]

Svoboda, K.

K. Svoboda and S.M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struc. 23, 247–284 (1994).
[Crossref]

Tinoco, I.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, “Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme,” Science 299, 1892–1895 (2003).
[Crossref] [PubMed]

Tlusty, T.

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, and S.A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[Crossref]

Van De Ven, T. G.M.

T. G.M. Van De Ven, Colloidal Hydrodynamics, p.78, Academic Press, London, 1989.

Visscher, K.

K. Visscher, M.J. Schnitzer, and S.M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184–189 (1999).
[Crossref] [PubMed]

Weber, T.

T. Weber, J. Herbig, M. Mark, H. C. Nagerl, and R. Grimm, “Bose-Einstein condensation of cesium,” Science 299, 232–235 (2003).
[Crossref]

Xie, C.

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

K. Svoboda and S.M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struc. 23, 247–284 (1994).
[Crossref]

Nature (2)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

K. Visscher, M.J. Schnitzer, and S.M. Block, “Single kinesin molecules studied with a molecular force clamp,” Nature 400, 184–189 (1999).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. Lett. (6)

R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, and S.A. Safran, “Localized dynamic light scattering: probing single particle dynamics at the nanoscale,” Phys. Rev. Lett. 78, 154–157 (1997).
[Crossref]

G. M. Keppler and S. Fradem, “Attractive potential between confined colloids at low ionic strength,” Phys. Rev. Lett. 73, 356–359 (1994).
[Crossref]

J.C. Crocker and D.G. Grier, “Microscopic measurement of the pair interaction potential of charge-stabilized colloid,” Phys. Rev. Lett. 73, 352–355 (1994).
[Crossref] [PubMed]

J. Guck, R. Ananthakrishnan, T.J. Moon, C.C. Cunningham, and J. Kas, “Optical Deformability of Soft Biological Dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
[Crossref] [PubMed]

J. Meiners and S.R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[Crossref]

J. Meiners and S.R. Quake, “femtonewton force spectroscopy of single extended DNA molecules,” Phys. Rev. Lett. 84, 5014–5017 (2000).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809(2004).
[Crossref]

Science (3)

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-Molecule Biomechanics with Optical Methods,” Science 283, 1689–1695 (1999).
[Crossref] [PubMed]

T. Weber, J. Herbig, M. Mark, H. C. Nagerl, and R. Grimm, “Bose-Einstein condensation of cesium,” Science 299, 232–235 (2003).
[Crossref]

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, “Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme,” Science 299, 1892–1895 (2003).
[Crossref] [PubMed]

Other (2)

Y.Q. Li, C. Christou, X.H. Hu, and M. Dinno, “Quasi-elastic light scattering of laser trapped biological particles,” Conference on Lasers and Electro-Optics, 2000, San Franscisco, CA, p620.

T. G.M. Van De Ven, Colloidal Hydrodynamics, p.78, Academic Press, London, 1989.

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setup. A Gaussian beam from a Nd:YAG laser source is expanded (5 x) and introduced into an inverted microscope with a high NA objective (obj.). The polarization of the laser beam can be changed with a λ/2 waveplate. The backscattered light from the trapped particle is imaged onto a quadrant detector (QD). The inserted picture is the image of the backscattered light from a 0.3-µm polystyrene sphere on the QD surface. BE — beam expander, BS — beam splitter, DM — dichroic mirror, Obj — objective, λ/2 —half wavelength plate.

Fig. 2.
Fig. 2.

The position fluctuations of 300nm-diameter polystyrene sphere (a) and (b), and correlation functions (c) and (d) in an optical trap with linear polarization and circular polarization, respectively.

Fig. 3.
Fig. 3.

The mass center position fluctuations of a 300nm-diameter sphere in a linear-polarized trap as the laser polarization direction is rotated at (a) 00, (b) 450, (c) 900, and (d) 1350. The laser power was kept at 25 mW.

Equations (4)

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

γ x · + k x = f 1 ( t ) + f c ( t )
γ y · + k y = f 2 ( t ) ,
< f 1 ( t ) f 1 ( t ) > = < f 2 ( t ) f 2 ( t ) > = 2 γ K B T δ ( t t ) ,
< f 1 ( t ) f 2 ( t ) > = 0 .

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