Abstract

We have studied the transverse and axial equilibrium positions of dielectric micro-spheres trapped in a single-beam gradient optical trap and exposed to an increasing fluid flow transverse to the trapping beam axis. It is demonstrated that the axial equilibrium position of a trapped micro-sphere is a function of its transverse position in the trapping beam. Moreover, although the applied drag-force acts perpendicularly to the beam axis, reaching a certain distance r 0 from the beam axis (r 0/a ≃ 0.6, a being the sphere radius) the particle escapes the trap due to a breaking axial equilibrium before the actual maximum transverse trapping force is reached. The comparison between a theoretical model and the measurements shows that neglecting these axial equilibrium considerations leads to a theoretical overestimation in the maximal optical transverse trapping forces of up to 50%.

© 2006 Optical Society of America

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2005

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

S. L. Neale, M. P. Macdonald, K. Dholakia, and T. F. Krauss, "All-optical control of microfluidic components using form birefringence," Nat. Mater. 4, 530-533 (2005).
[CrossRef] [PubMed]

Y. Roichman, A. Waldron, E. Gardel and D. G. Grier, "Performance of optical traps with geometric aberrations," Appl. Opt., in press (2005).

K. C. Neuman, E. A. Abbondanzieri, and S. M. Block, "Measurement of the effective focal shift in an optical trap," Opt. Lett. 30, 1318-1320 (2005).
[CrossRef] [PubMed]

O. Moine and B. Stout, "Optical force calculations in arbitrary beams by use of the vector addition theorem," J. Opt. Soc. Am. B 22, 1620-1631 (2005).
[CrossRef]

2004

D. Ganic, X. S. Gan, and M. Gu, "Exact radiation trapping force calculation based on vectorial diffraction theory," Opt. Express 12, 2670-2675 (2004).
[CrossRef] [PubMed]

E. Theofanidou, L. Wilson,W. J. Hossack and J. Arlt, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145 (2004).
[CrossRef]

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

J. Enger, M. Goksor, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab. Chip 4, 196-200 (2004).
[CrossRef] [PubMed]

J. Glückstad, "Microfluidics: Sorting particles with light," Nat. Mater. 3, 9-10 (2004).
[CrossRef] [PubMed]

2003

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

M. Ozkan, M. Wang, C. Ozkan, R. Flynn, A. Birkbeck, and S. Esener, "Optical manipulation of objects and biological cells in microfluidic devices," Biomed. Microdevices 5, 61-67 (2003).
[CrossRef]

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. R. Soc. London Ser. A-Math.Phys. Eng. Sci. 459, 3021-3041 (2003).
[CrossRef]

2002

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, "Measurements of trapping efficiency and stiffness in optical tweezers," Opt. Commun. 214, 15-24 (2002).
[CrossRef]

A. Rohrbach and E. H. K. Stelzer, "Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations," Appl. Opt. 41, 2494-2507 (2002).
[CrossRef] [PubMed]

2001

A. T. O’Neill and M. J. Padgett, "Axial and lateral trapping efficiency of Laguerre-Gaussian modes in inverted optical tweezers," Opt. Commun. 193, 45-50 (2001).
[CrossRef]

1998

P. C. Ke and M. Gu, "Characterization of trapping force in the presence of spherical aberration," J. Mod. Opt. 45, 2159-2168 (1998)
[CrossRef]

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

1995

1994

W. H. Wright, G. J. Sonek, and M. W. Berns, "Parametric Study of the Forces on Microspheres Held by Optical Tweezers," Appl. Opt. 33, 1735-1748 (1994).
[CrossRef] [PubMed]

K. F. Ren, G. Greha, and G. Gouesbet, "Radiation Pressure Forces Exerted on a Particle Arbitrarily Located in a Gaussian-Beam by Using the Generalized Lorenz-Mie Theory, and Associated Resonance Effects," Opt. Commun. 108, 343-354 (1994).
[CrossRef]

1993

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in Confocal Fluorescence Microscopy Induced by Mismatches in Refractive-Index," J. Microsc.-Oxford 169, 391-405 (1993).
[CrossRef]

1992

A. Ashkin, "Forces of a Single-Beam Gradient Laser Trap on a Dielectric Sphere in the Ray Optics Regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

1991

S. Sato, M. Ishigure, and H. Inaba, "Optical Trapping and Rotational Manipulation of Microscopic Particles and Biological Cells Using Higher-Order Mode Nd-Yag Laser-Beams," Electron. Lett. 27, 1831-1832 (1991).
[CrossRef]

1989

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

1986

1979

G. Roosen, "La lévitation optique de sphéres," Can. J. Phys. 57, 1260-1279 (1979).
[CrossRef]

Abbondanzieri, E. A.

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

Allen, L.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

Arimondo, E.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, "Measurements of trapping efficiency and stiffness in optical tweezers," Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Arlt, J.

E. Theofanidou, L. Wilson,W. J. Hossack and J. Arlt, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145 (2004).
[CrossRef]

Ashkin, A.

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

Berns, M. W.

Birkbeck, A.

M. Ozkan, M. Wang, C. Ozkan, R. Flynn, A. Birkbeck, and S. Esener, "Optical manipulation of objects and biological cells in microfluidic devices," Biomed. Microdevices 5, 61-67 (2003).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

Booker, G. R.

Butler, W. F.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

Chu, S.

Cremer, C.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in Confocal Fluorescence Microscopy Induced by Mismatches in Refractive-Index," J. Microsc.-Oxford 169, 391-405 (1993).
[CrossRef]

Dees, B.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

Dholakia, K.

S. L. Neale, M. P. Macdonald, K. Dholakia, and T. F. Krauss, "All-optical control of microfluidic components using form birefringence," Nat. Mater. 4, 530-533 (2005).
[CrossRef] [PubMed]

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

Dziedzic, J. M.

Enger, J.

J. Enger, M. Goksor, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab. Chip 4, 196-200 (2004).
[CrossRef] [PubMed]

Esener, S.

M. Ozkan, M. Wang, C. Ozkan, R. Flynn, A. Birkbeck, and S. Esener, "Optical manipulation of objects and biological cells in microfluidic devices," Biomed. Microdevices 5, 61-67 (2003).
[CrossRef]

Felgner, H.

Flynn, R.

M. Ozkan, M. Wang, C. Ozkan, R. Flynn, A. Birkbeck, and S. Esener, "Optical manipulation of objects and biological cells in microfluidic devices," Biomed. Microdevices 5, 61-67 (2003).
[CrossRef]

Forster, A. H.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

Gan, X. S.

Ganic, D.

Gardel, E.

Y. Roichman, A. Waldron, E. Gardel and D. G. Grier, "Performance of optical traps with geometric aberrations," Appl. Opt., in press (2005).

Glückstad, J.

J. Glückstad, "Microfluidics: Sorting particles with light," Nat. Mater. 3, 9-10 (2004).
[CrossRef] [PubMed]

Goksor, M.

J. Enger, M. Goksor, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab. Chip 4, 196-200 (2004).
[CrossRef] [PubMed]

Gouesbet, G.

K. F. Ren, G. Greha, and G. Gouesbet, "Radiation Pressure Forces Exerted on a Particle Arbitrarily Located in a Gaussian-Beam by Using the Generalized Lorenz-Mie Theory, and Associated Resonance Effects," Opt. Commun. 108, 343-354 (1994).
[CrossRef]

Greha, G.

K. F. Ren, G. Greha, and G. Gouesbet, "Radiation Pressure Forces Exerted on a Particle Arbitrarily Located in a Gaussian-Beam by Using the Generalized Lorenz-Mie Theory, and Associated Resonance Effects," Opt. Commun. 108, 343-354 (1994).
[CrossRef]

Grier, D. G.

Y. Roichman, A. Waldron, E. Gardel and D. G. Grier, "Performance of optical traps with geometric aberrations," Appl. Opt., in press (2005).

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

Gu, M.

D. Ganic, X. S. Gan, and M. Gu, "Exact radiation trapping force calculation based on vectorial diffraction theory," Opt. Express 12, 2670-2675 (2004).
[CrossRef] [PubMed]

P. C. Ke and M. Gu, "Characterization of trapping force in the presence of spherical aberration," J. Mod. Opt. 45, 2159-2168 (1998)
[CrossRef]

Hagberg, P.

J. Enger, M. Goksor, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab. Chip 4, 196-200 (2004).
[CrossRef] [PubMed]

Hagen, N.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

Hanstorp, D.

J. Enger, M. Goksor, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab. Chip 4, 196-200 (2004).
[CrossRef] [PubMed]

Hell, S.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in Confocal Fluorescence Microscopy Induced by Mismatches in Refractive-Index," J. Microsc.-Oxford 169, 391-405 (1993).
[CrossRef]

Hossack, W. J.

E. Theofanidou, L. Wilson,W. J. Hossack and J. Arlt, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145 (2004).
[CrossRef]

Inaba, H.

S. Sato, M. Ishigure, and H. Inaba, "Optical Trapping and Rotational Manipulation of Microscopic Particles and Biological Cells Using Higher-Order Mode Nd-Yag Laser-Beams," Electron. Lett. 27, 1831-1832 (1991).
[CrossRef]

Ishigure, M.

S. Sato, M. Ishigure, and H. Inaba, "Optical Trapping and Rotational Manipulation of Microscopic Particles and Biological Cells Using Higher-Order Mode Nd-Yag Laser-Beams," Electron. Lett. 27, 1831-1832 (1991).
[CrossRef]

Kariv, I.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

Ke, P. C.

P. C. Ke and M. Gu, "Characterization of trapping force in the presence of spherical aberration," J. Mod. Opt. 45, 2159-2168 (1998)
[CrossRef]

Krauss, T. F.

S. L. Neale, M. P. Macdonald, K. Dholakia, and T. F. Krauss, "All-optical control of microfluidic components using form birefringence," Nat. Mater. 4, 530-533 (2005).
[CrossRef] [PubMed]

Laczik, Z.

Macdonald, M. P.

S. L. Neale, M. P. Macdonald, K. Dholakia, and T. F. Krauss, "All-optical control of microfluidic components using form birefringence," Nat. Mater. 4, 530-533 (2005).
[CrossRef] [PubMed]

Malagnino, N.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, "Measurements of trapping efficiency and stiffness in optical tweezers," Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Marchand, P. J.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

Mazolli, A.

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. R. Soc. London Ser. A-Math.Phys. Eng. Sci. 459, 3021-3041 (2003).
[CrossRef]

McGloin, D.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

Mercer, E. M.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

Moine, O.

Muller, O.

Neale, S. L.

S. L. Neale, M. P. Macdonald, K. Dholakia, and T. F. Krauss, "All-optical control of microfluidic components using form birefringence," Nat. Mater. 4, 530-533 (2005).
[CrossRef] [PubMed]

Neto, P. A. M.

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. R. Soc. London Ser. A-Math.Phys. Eng. Sci. 459, 3021-3041 (2003).
[CrossRef]

Neuman, K. C.

Nussenzveig, H. M.

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. R. Soc. London Ser. A-Math.Phys. Eng. Sci. 459, 3021-3041 (2003).
[CrossRef]

O’Neill, A. T.

A. T. O’Neill and M. J. Padgett, "Axial and lateral trapping efficiency of Laguerre-Gaussian modes in inverted optical tweezers," Opt. Commun. 193, 45-50 (2001).
[CrossRef]

Ozkan, C.

M. Ozkan, M. Wang, C. Ozkan, R. Flynn, A. Birkbeck, and S. Esener, "Optical manipulation of objects and biological cells in microfluidic devices," Biomed. Microdevices 5, 61-67 (2003).
[CrossRef]

Ozkan, M.

M. Ozkan, M. Wang, C. Ozkan, R. Flynn, A. Birkbeck, and S. Esener, "Optical manipulation of objects and biological cells in microfluidic devices," Biomed. Microdevices 5, 61-67 (2003).
[CrossRef]

Padgett, M. J.

A. T. O’Neill and M. J. Padgett, "Axial and lateral trapping efficiency of Laguerre-Gaussian modes in inverted optical tweezers," Opt. Commun. 193, 45-50 (2001).
[CrossRef]

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

Pesce, G.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, "Measurements of trapping efficiency and stiffness in optical tweezers," Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Ramser, K.

J. Enger, M. Goksor, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab. Chip 4, 196-200 (2004).
[CrossRef] [PubMed]

Raymond, D. E.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

Reiner, G.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in Confocal Fluorescence Microscopy Induced by Mismatches in Refractive-Index," J. Microsc.-Oxford 169, 391-405 (1993).
[CrossRef]

Ren, K. F.

K. F. Ren, G. Greha, and G. Gouesbet, "Radiation Pressure Forces Exerted on a Particle Arbitrarily Located in a Gaussian-Beam by Using the Generalized Lorenz-Mie Theory, and Associated Resonance Effects," Opt. Commun. 108, 343-354 (1994).
[CrossRef]

Rohrbach, A.

Roichman, Y.

Y. Roichman, A. Waldron, E. Gardel and D. G. Grier, "Performance of optical traps with geometric aberrations," Appl. Opt., in press (2005).

Roosen, G.

G. Roosen, "La lévitation optique de sphéres," Can. J. Phys. 57, 1260-1279 (1979).
[CrossRef]

Sasso, A.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, "Measurements of trapping efficiency and stiffness in optical tweezers," Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Sato, S.

S. Sato, M. Ishigure, and H. Inaba, "Optical Trapping and Rotational Manipulation of Microscopic Particles and Biological Cells Using Higher-Order Mode Nd-Yag Laser-Beams," Electron. Lett. 27, 1831-1832 (1991).
[CrossRef]

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

Schliwa, M.

Simpson, N. B.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

Sonek, G. J.

Stelzer, E. H. K.

A. Rohrbach and E. H. K. Stelzer, "Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations," Appl. Opt. 41, 2494-2507 (2002).
[CrossRef] [PubMed]

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in Confocal Fluorescence Microscopy Induced by Mismatches in Refractive-Index," J. Microsc.-Oxford 169, 391-405 (1993).
[CrossRef]

Stout, B.

Theofanidou, E.

E. Theofanidou, L. Wilson,W. J. Hossack and J. Arlt, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145 (2004).
[CrossRef]

Torok, P.

Tu, E.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

Varga, P.

Waldron, A.

Y. Roichman, A. Waldron, E. Gardel and D. G. Grier, "Performance of optical traps with geometric aberrations," Appl. Opt., in press (2005).

Wang, M.

M. Ozkan, M. Wang, C. Ozkan, R. Flynn, A. Birkbeck, and S. Esener, "Optical manipulation of objects and biological cells in microfluidic devices," Biomed. Microdevices 5, 61-67 (2003).
[CrossRef]

Wang, M. M.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

Wilson, L.

E. Theofanidou, L. Wilson,W. J. Hossack and J. Arlt, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145 (2004).
[CrossRef]

Wright, W. H.

Yang, J. M.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

Zhang, H. C.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

Appl. Opt.

Biomed. Microdevices

M. Ozkan, M. Wang, C. Ozkan, R. Flynn, A. Birkbeck, and S. Esener, "Optical manipulation of objects and biological cells in microfluidic devices," Biomed. Microdevices 5, 61-67 (2003).
[CrossRef]

Biophys. J.

A. Ashkin, "Forces of a Single-Beam Gradient Laser Trap on a Dielectric Sphere in the Ray Optics Regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

Can. J. Phys.

G. Roosen, "La lévitation optique de sphéres," Can. J. Phys. 57, 1260-1279 (1979).
[CrossRef]

Electron. Lett.

S. Sato, M. Ishigure, and H. Inaba, "Optical Trapping and Rotational Manipulation of Microscopic Particles and Biological Cells Using Higher-Order Mode Nd-Yag Laser-Beams," Electron. Lett. 27, 1831-1832 (1991).
[CrossRef]

J. Appl. Phys.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

J. Mod. Opt.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, "Optical tweezers with increased axial trapping efficiency," J. Mod. Opt. 45, 1943-1949 (1998).
[CrossRef]

P. C. Ke and M. Gu, "Characterization of trapping force in the presence of spherical aberration," J. Mod. Opt. 45, 2159-2168 (1998)
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Lab. Chip

J. Enger, M. Goksor, K. Ramser, P. Hagberg, and D. Hanstorp, "Optical tweezers applied to a microfluidic system," Lab. Chip 4, 196-200 (2004).
[CrossRef] [PubMed]

Nat. Biotechnol.

M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, "Microfluidic sorting of mammalian cells by optical force switching," Nat. Biotechnol. 23, 83-87 (2005).
[CrossRef]

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S. L. Neale, M. P. Macdonald, K. Dholakia, and T. F. Krauss, "All-optical control of microfluidic components using form birefringence," Nat. Mater. 4, 530-533 (2005).
[CrossRef] [PubMed]

J. Glückstad, "Microfluidics: Sorting particles with light," Nat. Mater. 3, 9-10 (2004).
[CrossRef] [PubMed]

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

Opt. Commun.

K. F. Ren, G. Greha, and G. Gouesbet, "Radiation Pressure Forces Exerted on a Particle Arbitrarily Located in a Gaussian-Beam by Using the Generalized Lorenz-Mie Theory, and Associated Resonance Effects," Opt. Commun. 108, 343-354 (1994).
[CrossRef]

E. Theofanidou, L. Wilson,W. J. Hossack and J. Arlt, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145 (2004).
[CrossRef]

A. T. O’Neill and M. J. Padgett, "Axial and lateral trapping efficiency of Laguerre-Gaussian modes in inverted optical tweezers," Opt. Commun. 193, 45-50 (2001).
[CrossRef]

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, "Measurements of trapping efficiency and stiffness in optical tweezers," Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Oxford

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, "Aberrations in Confocal Fluorescence Microscopy Induced by Mismatches in Refractive-Index," J. Microsc.-Oxford 169, 391-405 (1993).
[CrossRef]

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A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. R. Soc. London Ser. A-Math.Phys. Eng. Sci. 459, 3021-3041 (2003).
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K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

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Supplementary Material (1)

» Media 1: MOV (516 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Focusing light with a high-NA microscope objective, through a planar interface of mismatched index. The azimuth angle θ is not shown due to symmetry.

Fig. 2.
Fig. 2.

Geometry for the calculation of the momentum transfer between the beam and the dielectric sphere. The forces are calculated using a ray-optics approximation in the plane of incidence defined by (y 1, z 1), and then projected onto the (y,z) axes.

Fig. 3.
Fig. 3.

Experimental set-up for optical trapping and video processing based measurement of the polystyrene bead positions, built around an inverted microscope.

Fig. 4.
Fig. 4.

r-z position tracking by video-processing. (a) The trapped bead in its equilibrium position in still water (above) and when submitted to a transverse viscous force Fvis (below). The video processing computes the distance r 0 from the still position, and the axial position was experimentally related to the area of bright spot (A 0, A 1) resulting from the focusing of the white light apical illumination by the trapped bead. (b) Axial position calibration curves for both the 5 μm (diamonds ◇) and the 7 μm beads (circles ○), measured by observing a stuck microbead on the sample cell bottom and by stepwise displacing the MO axially.

Fig. 5.
Fig. 5.

(516 KB) - Movie of the drag-force experiment, showing the image analysis to retrieve the transverse and axial bead positions r 0 and z 0. The resting equilibrium position of the bead (no drag-force applied) is shown by the + marker. [Media 1]

Fig. 6.
Fig. 6.

Numerical results. (a) Pure ray-optics (RO) calculation of equilibrium trajectory [r 0, z0eq (r 0)] (continuous line). The dashed line represents a pure transverse displacement in the focal plane. (b) Displacement-force curves in the RO approximation. Forces calculated along the equilibrium trajectory [r 0, zeq 0 (r 0)] (continuous line) and along [r 0, z 0 =0] (dashed line) are compared. (c) Equilibrium trajectory according to the vectorial diffraction (VD) for the 7 μm beads at two different trapping depths (5μm and 15μm). (d) Displacementforce curves using the VD. Forces on the equilibrium trajectory (continuous lines) and in the focal plane (dashed lines) are compared.

Fig. 7.
Fig. 7.

Experimental results. (a) Measured trajectories in the 4 directions of the viscous drag, for the 5μm beads, compared to the theoretical trajectory (solid line). (b) Measured force-displacement curves corresponding to subfigure (a). Measurements are compared both to the theoretical force along the equilibrium trajectory (solid line - almost hidden by the measurements) and to the force calculated for a purely radial displacement (dashed line). (c) Same as (a), but for the 7μm beads. (d) Same as (b), but for the 7μm beads.

Tables (1)

Tables Icon

Table 1. Experiment parameters

Equations (22)

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r P = [ x P , y P , z P ] = r P [ sin ϕ P cos θ P , sin ϕ P sin θ P , cos ϕ P ]
e x = i K [ I 0 ( e ) + I 2 ( e ) cos ( 2 θ P ) ]
e y = i K I 2 ( e ) sin ( 2 θ P )
e z = 2 K I 1 ( e ) cos ( θ P )
K = π n 1 f λ 0 e 0 n 1
I 0 ( e ) ( r P , z P ) = 0 α exp ( γ 2 sin 2 ϕ 1 ) ( cos ϕ 1 ) 1 2 sin ϕ 1 exp [ i k 0 ψ ( ϕ 1 , ϕ 2 , d ) ] × ( τ s + τ p cos ϕ 2 ) J 0 ( k 1 r P sin ϕ 1 ) exp ( i k 2 z P cos ϕ 2 ) d ϕ 1
I 1 ( e ) ( r P , z P ) = 0 α exp ( γ 2 sin 2 ϕ 1 ) ( cos ϕ 1 ) 1 2 sin ϕ 1 exp [ i k 0 ψ ( ϕ 1 , ϕ 2 , d ) ] × τ p sin ϕ 2 × J 1 ( k 1 r P sin ϕ 1 ) exp ( i k 2 z P cos ϕ 2 ) d ϕ 1
I 2 ( e ) ( r P , z P ) = 0 α exp ( γ 2 sin 2 ϕ 1 ) ( cos ϕ 1 ) 1 2 sin ϕ 1 exp [ i k 0 ψ ( ϕ 1 , ϕ 2 , d ) ] × ( τ s τ p cos ϕ 2 ) × J 2 ( k 1 r P sin ϕ 1 ) exp ( i k 2 z P cos ϕ 2 ) d ϕ 1
ψ ( ϕ 1 , ϕ 2 , d ) = d ( n 1 cos ϕ 1 n 1 cos ϕ 2 )
I = < S > = 1 2 R { e × h * }
z focus = k f d
I = I 0 exp { 2 γ 2 sin 2 ϕ 2 } f 2 cosϕ 2 1 r p 2 ;
dF z 1 = n 2 I c cos i [ cos ( α i θ ) + R cos ( α i + θ ) T 2 cos ( 2 α r α i θ ) + R cos ( α i + θ ) 1 + R 2 + 2 R cos ( 2 α r ) ] d A
dF y 1 = n 2 I c cos i [ sin ( α i θ ) + R sin ( α i + θ ) T 2 sin ( 2 α r α i θ ) + R sin ( α i + θ ) 1 + R 2 + 2 R cos ( 2 α r ) ] d A
m 0 = F r ( r 0 , z 0 ) + β v r
m 0 = F z ( r 0 , z 0 ) ( ρ ρ fluid ) V g
β = 6 π a η 1 9 16 ( a b ) + 1 8 ( a b ) 3 45 256 ( a b ) 4 1 16 ( a b ) 5
F r ( r 0 ( t ) , z 0 ( t ) ) = β a r ( t t 0 ) , t t 0
F z ( r 0 , z 0 ) = 0
Q = c n 2 P F
Q r m a x = c n 2 P β v r max
Δz ' = Δz k f Δz Δz ' Δz = 1 k f

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