Abstract

Optical traps are routinely used for the manipulation of neutral particles. However, optical trap design is limited by the lack of an accurate theory. The generalized Lorenz-Mie theory (GLMT) solves the scattering problem for arbitrary particle size and predicts radial forces accurately. Here we show that the GLMT predicts the observed radial and axial forces in a variety of optical manipulators. We also present a dimensionless parameter β for the prediction of axial forces. Coupled with our correlation for radial escape forces, we now have a set of two simple correlations for the practical design of radiation-force-based systems.

© 2004 Optical Society of America

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  1. K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
    [CrossRef] [PubMed]
  2. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
    [CrossRef]
  3. A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
    [CrossRef]
  4. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
    [CrossRef] [PubMed]
  5. S. M. Block, L. S. B. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348, 348–352 (1990).
    [CrossRef] [PubMed]
  6. J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics—piconewton forces and nanometer steps,” Nature 368, 113–119 (1994).
    [CrossRef] [PubMed]
  7. M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
    [CrossRef] [PubMed]
  8. B. Schnurr, F. Gittes, F. C. MacKintosh, C. F. Schmidt, “Determining microscopic viscoelasticity in flexible and semiflexible polymer networks from thermal fluctuations,” Macromolecules 30, 7781–7792 (1997).
    [CrossRef]
  9. J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
    [CrossRef] [PubMed]
  10. D. J. Odde, M. J. Renn, “Laser-guided direct writing for applications in biotechnology,” Trends Biotechnol. 17, 385–389 (1999).
    [CrossRef] [PubMed]
  11. D. J. Odde, M. J. Renn, “Laser-guided direct writing of living cells,” Biotechnol. Bioeng. 67, 312–318 (2000).
    [CrossRef] [PubMed]
  12. J. E. Molloy, M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241–258 (2002).
    [CrossRef]
  13. Y. Harada, T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
    [CrossRef]
  14. 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]
  15. G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976).
  16. W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
    [CrossRef]
  17. G. Gouesbet, G. Gréhan, “Generalized Lorenz-Mie theories, from past to future,” Atomization Sprays 10, 277–333 (2000).
  18. G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
    [CrossRef]
  19. K. F. Ren, G. Gouesbet, G. Grehan, “Integral localized approximation in generalized Lorenz-Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
    [CrossRef]
  20. G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beams in the generalized Lorenz-Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641–1650 (1999).
    [CrossRef]
  21. L. Mees, K. F. Ren, G. Grehan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results,” Appl. Opt. 38, 1867–1876 (1999).
    [CrossRef]
  22. Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, G. Grehan, “Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. 36, 5188–5198 (1997).
    [CrossRef] [PubMed]
  23. Y. K. Nahmias, D. J. Odde, “Analysis of radiation forces in laser trapping and laser-guided direct writing applications,” IEEE J. Quantum Electron. 38, 131–141 (2002).
    [CrossRef]
  24. T. C. Bakker-Schut, G. Hesselink, B. G. d. Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
    [CrossRef]
  25. A. C. Dogariu, R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770–2778 (2000).
    [CrossRef]
  26. F. Gittes, C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23, 7–9 (1998).
    [CrossRef]
  27. K. F. Ren, G. Gréhan, 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]
  28. P. Bartlett, D. Henderson, “Three-dimensional force calibration of a single-beam optical gradient trap,” J. Phys. Condens. Matter 14, 7757–7768 (2002).
    [CrossRef]
  29. J. P. Barton, “Effects of surface perturbations on the quality and the focused-beam excitation of microsphere resonance,” J. Opt. Soc. Am. A 16, 1974–1980 (1999).
    [CrossRef]
  30. R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, J. J. Sáenz, “Resonant radiation pressure on neutral particles in a waveguide,” Phys. Rev. Lett. 86, 4275–4277 (2001).
    [CrossRef] [PubMed]
  31. E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1998).
  32. J. N. Fass, D. J. Odde, “Tensile force-dependent neurite elicitation via anti-β1 integrin antibody-coated magnetic beads,” Biophys. J. 85, 623–636 (2003).
    [CrossRef] [PubMed]
  33. Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
    [CrossRef] [PubMed]

2003 (1)

J. N. Fass, D. J. Odde, “Tensile force-dependent neurite elicitation via anti-β1 integrin antibody-coated magnetic beads,” Biophys. J. 85, 623–636 (2003).
[CrossRef] [PubMed]

2002 (4)

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

P. Bartlett, D. Henderson, “Three-dimensional force calibration of a single-beam optical gradient trap,” J. Phys. Condens. Matter 14, 7757–7768 (2002).
[CrossRef]

J. E. Molloy, M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241–258 (2002).
[CrossRef]

Y. K. Nahmias, D. J. Odde, “Analysis of radiation forces in laser trapping and laser-guided direct writing applications,” IEEE J. Quantum Electron. 38, 131–141 (2002).
[CrossRef]

2001 (2)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, J. J. Sáenz, “Resonant radiation pressure on neutral particles in a waveguide,” Phys. Rev. Lett. 86, 4275–4277 (2001).
[CrossRef] [PubMed]

2000 (3)

A. C. Dogariu, R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770–2778 (2000).
[CrossRef]

D. J. Odde, M. J. Renn, “Laser-guided direct writing of living cells,” Biotechnol. Bioeng. 67, 312–318 (2000).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, “Generalized Lorenz-Mie theories, from past to future,” Atomization Sprays 10, 277–333 (2000).

1999 (4)

1998 (3)

1997 (2)

B. Schnurr, F. Gittes, F. C. MacKintosh, C. F. Schmidt, “Determining microscopic viscoelasticity in flexible and semiflexible polymer networks from thermal fluctuations,” Macromolecules 30, 7781–7792 (1997).
[CrossRef]

Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, G. Grehan, “Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. 36, 5188–5198 (1997).
[CrossRef] [PubMed]

1996 (1)

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

1994 (4)

J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics—piconewton forces and nanometer steps,” Nature 368, 113–119 (1994).
[CrossRef] [PubMed]

K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, 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 (1)

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

1992 (1)

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 (1)

T. C. Bakker-Schut, G. Hesselink, B. G. d. Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

1990 (1)

S. M. Block, L. S. B. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348, 348–352 (1990).
[CrossRef] [PubMed]

1986 (1)

1976 (1)

G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976).

1971 (1)

A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
[CrossRef]

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

Aldrich, S.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Ananthakrishnan, R.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

Asakura, T.

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

Ashkin, A.

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]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
[CrossRef]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

Bakker-Schut, T. C.

T. C. Bakker-Schut, G. Hesselink, B. G. d. Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

Bartlett, P.

P. Bartlett, D. Henderson, “Three-dimensional force calibration of a single-beam optical gradient trap,” J. Phys. Condens. Matter 14, 7757–7768 (2002).
[CrossRef]

Barton, J. P.

Berns, M. W.

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

Bjorkholm, J. E.

Blackstad, M.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Block, S. M.

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

S. M. Block, L. S. B. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348, 348–352 (1990).
[CrossRef] [PubMed]

Chu, S.

Cunningham, C. C.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

d. Grooth, B. G.

T. C. Bakker-Schut, G. Hesselink, B. G. d. Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

Dogariu, A. C.

A. C. Dogariu, R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770–2778 (2000).
[CrossRef]

Du, J.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Dziedzic, J. M.

Fass, J. N.

J. N. Fass, D. J. Odde, “Tensile force-dependent neurite elicitation via anti-β1 integrin antibody-coated magnetic beads,” Biophys. J. 85, 623–636 (2003).
[CrossRef] [PubMed]

Finer, J. T.

J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics—piconewton forces and nanometer steps,” Nature 368, 113–119 (1994).
[CrossRef] [PubMed]

García-Martín, A.

R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, J. J. Sáenz, “Resonant radiation pressure on neutral particles in a waveguide,” Phys. Rev. Lett. 86, 4275–4277 (2001).
[CrossRef] [PubMed]

Gelles, J.

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

Gittes, F.

F. Gittes, C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23, 7–9 (1998).
[CrossRef]

B. Schnurr, F. Gittes, F. C. MacKintosh, C. F. Schmidt, “Determining microscopic viscoelasticity in flexible and semiflexible polymer networks from thermal fluctuations,” Macromolecules 30, 7781–7792 (1997).
[CrossRef]

Goldstein, L. S. B.

S. M. Block, L. S. B. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348, 348–352 (1990).
[CrossRef] [PubMed]

Gómez-Medina, R.

R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, J. J. Sáenz, “Resonant radiation pressure on neutral particles in a waveguide,” Phys. Rev. Lett. 86, 4275–4277 (2001).
[CrossRef] [PubMed]

Gouesbet, G.

Grehan, G.

Gréhan, G.

G. Gouesbet, G. Gréhan, “Generalized Lorenz-Mie theories, from past to future,” Atomization Sprays 10, 277–333 (2000).

K. F. Ren, G. Gréhan, 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]

Greve, J.

T. C. Bakker-Schut, G. Hesselink, B. G. d. Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

Guck, J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

Guo, L. X.

Harada, Y.

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

Hecht, E.

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1998).

Henderson, D.

P. Bartlett, D. Henderson, “Three-dimensional force calibration of a single-beam optical gradient trap,” J. Phys. Condens. Matter 14, 7757–7768 (2002).
[CrossRef]

Hesselink, G.

T. C. Bakker-Schut, G. Hesselink, B. G. d. Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

Imbert, C.

G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976).

Jahagirdar, B. N.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Jiang, Y.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Kas, J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

Keenek, C. D.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Landick, R.

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

Largaespada, D. A.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Lenvik, T.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Lester, M.

R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, J. J. Sáenz, “Resonant radiation pressure on neutral particles in a waveguide,” Phys. Rev. Lett. 86, 4275–4277 (2001).
[CrossRef] [PubMed]

Lisberg, A.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Lock, J. A.

Lowk, W. C.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Lund, T.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

MacKintosh, F. C.

B. Schnurr, F. Gittes, F. C. MacKintosh, C. F. Schmidt, “Determining microscopic viscoelasticity in flexible and semiflexible polymer networks from thermal fluctuations,” Macromolecules 30, 7781–7792 (1997).
[CrossRef]

Mahmood, H.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

Mees, L.

Molloy, J. E.

J. E. Molloy, M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241–258 (2002).
[CrossRef]

Moon, T. J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

Nahmias, Y. K.

Y. K. Nahmias, D. J. Odde, “Analysis of radiation forces in laser trapping and laser-guided direct writing applications,” IEEE J. Quantum Electron. 38, 131–141 (2002).
[CrossRef]

Nieto-Vesperinas, M.

R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, J. J. Sáenz, “Resonant radiation pressure on neutral particles in a waveguide,” Phys. Rev. Lett. 86, 4275–4277 (2001).
[CrossRef] [PubMed]

Odde, D. J.

J. N. Fass, D. J. Odde, “Tensile force-dependent neurite elicitation via anti-β1 integrin antibody-coated magnetic beads,” Biophys. J. 85, 623–636 (2003).
[CrossRef] [PubMed]

Y. K. Nahmias, D. J. Odde, “Analysis of radiation forces in laser trapping and laser-guided direct writing applications,” IEEE J. Quantum Electron. 38, 131–141 (2002).
[CrossRef]

D. J. Odde, M. J. Renn, “Laser-guided direct writing of living cells,” Biotechnol. Bioeng. 67, 312–318 (2000).
[CrossRef] [PubMed]

D. J. Odde, M. J. Renn, “Laser-guided direct writing for applications in biotechnology,” Trends Biotechnol. 17, 385–389 (1999).
[CrossRef] [PubMed]

Ortiz-Gonzalezk, X. R.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Padgett, M. J.

J. E. Molloy, M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241–258 (2002).
[CrossRef]

Rajagopalan, R.

A. C. Dogariu, R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770–2778 (2000).
[CrossRef]

Reinhardt, R. L.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Ren, K. F.

Renn, M. J.

D. J. Odde, M. J. Renn, “Laser-guided direct writing of living cells,” Biotechnol. Bioeng. 67, 312–318 (2000).
[CrossRef] [PubMed]

D. J. Odde, M. J. Renn, “Laser-guided direct writing for applications in biotechnology,” Trends Biotechnol. 17, 385–389 (1999).
[CrossRef] [PubMed]

Reyes, M.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Roosen, G.

G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976).

Sáenz, J. J.

R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, J. J. Sáenz, “Resonant radiation pressure on neutral particles in a waveguide,” Phys. Rev. Lett. 86, 4275–4277 (2001).
[CrossRef] [PubMed]

San José, P.

R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, J. J. Sáenz, “Resonant radiation pressure on neutral particles in a waveguide,” Phys. Rev. Lett. 86, 4275–4277 (2001).
[CrossRef] [PubMed]

Schmidt, C. F.

F. Gittes, C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23, 7–9 (1998).
[CrossRef]

B. Schnurr, F. Gittes, F. C. MacKintosh, C. F. Schmidt, “Determining microscopic viscoelasticity in flexible and semiflexible polymer networks from thermal fluctuations,” Macromolecules 30, 7781–7792 (1997).
[CrossRef]

Schnapp, B. J.

S. M. Block, L. S. B. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348, 348–352 (1990).
[CrossRef] [PubMed]

Schnitzer, M. J.

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

Schnurr, B.

B. Schnurr, F. Gittes, F. C. MacKintosh, C. F. Schmidt, “Determining microscopic viscoelasticity in flexible and semiflexible polymer networks from thermal fluctuations,” Macromolecules 30, 7781–7792 (1997).
[CrossRef]

Schwartz, R. E.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Simmons, R. M.

J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics—piconewton forces and nanometer steps,” Nature 368, 113–119 (1994).
[CrossRef] [PubMed]

Sonek, G. J.

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

Spudich, J. A.

J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics—piconewton forces and nanometer steps,” Nature 368, 113–119 (1994).
[CrossRef] [PubMed]

Svoboda, K.

K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

Verfaillie, C. M.

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

Wang, M. D.

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

Wright, W. H.

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

Wu, Z. S.

Yin, H.

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

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

K. Svoboda, S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

Appl. Opt. (3)

Appl. Phys. Lett. (2)

W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
[CrossRef]

Atomization Sprays (1)

G. Gouesbet, G. Gréhan, “Generalized Lorenz-Mie theories, from past to future,” Atomization Sprays 10, 277–333 (2000).

Biophys. J. (3)

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]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

J. N. Fass, D. J. Odde, “Tensile force-dependent neurite elicitation via anti-β1 integrin antibody-coated magnetic beads,” Biophys. J. 85, 623–636 (2003).
[CrossRef] [PubMed]

Biotechnol. Bioeng. (1)

D. J. Odde, M. J. Renn, “Laser-guided direct writing of living cells,” Biotechnol. Bioeng. 67, 312–318 (2000).
[CrossRef] [PubMed]

Contemp. Phys. (1)

J. E. Molloy, M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241–258 (2002).
[CrossRef]

Cytometry (1)

T. C. Bakker-Schut, G. Hesselink, B. G. d. Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. K. Nahmias, D. J. Odde, “Analysis of radiation forces in laser trapping and laser-guided direct writing applications,” IEEE J. Quantum Electron. 38, 131–141 (2002).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Phys. Condens. Matter (1)

P. Bartlett, D. Henderson, “Three-dimensional force calibration of a single-beam optical gradient trap,” J. Phys. Condens. Matter 14, 7757–7768 (2002).
[CrossRef]

Langmuir (1)

A. C. Dogariu, R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770–2778 (2000).
[CrossRef]

Macromolecules (1)

B. Schnurr, F. Gittes, F. C. MacKintosh, C. F. Schmidt, “Determining microscopic viscoelasticity in flexible and semiflexible polymer networks from thermal fluctuations,” Macromolecules 30, 7781–7792 (1997).
[CrossRef]

Nature (3)

Y. Jiang, B. N. Jahagirdar, R. L. Reinhardt, R. E. Schwartz, C. D. Keenek, X. R. Ortiz-Gonzalezk, M. Reyes, T. Lenvik, T. Lund, M. Blackstad, J. Du, S. Aldrich, A. Lisberg, W. C. Lowk, D. A. Largaespada, C. M. Verfaillie, “Pluripotency of mesenchymal stem cells derived from adult marrow,” Nature 418, 41–49 (2002).
[CrossRef] [PubMed]

S. M. Block, L. S. B. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348, 348–352 (1990).
[CrossRef] [PubMed]

J. T. Finer, R. M. Simmons, J. A. Spudich, “Single myosin molecule mechanics—piconewton forces and nanometer steps,” Nature 368, 113–119 (1994).
[CrossRef] [PubMed]

Opt. Commun. (2)

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

K. F. Ren, G. Gréhan, 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]

Opt. Lett. (2)

Phys. Lett. (1)

G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976).

Phys. Rev. Lett. (2)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

R. Gómez-Medina, P. San José, A. García-Martín, M. Lester, M. Nieto-Vesperinas, J. J. Sáenz, “Resonant radiation pressure on neutral particles in a waveguide,” Phys. Rev. Lett. 86, 4275–4277 (2001).
[CrossRef] [PubMed]

Science (1)

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282, 902–907 (1998).
[CrossRef] [PubMed]

Trends Biotechnol. (1)

D. J. Odde, M. J. Renn, “Laser-guided direct writing for applications in biotechnology,” Trends Biotechnol. 17, 385–389 (1999).
[CrossRef] [PubMed]

Other (1)

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1998).

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Figures (10)

Fig. 1
Fig. 1

Schematic of the laser guidance system.

Fig. 2
Fig. 2

Prediction of optical trap stiffness. The BFP detector signal as a function of silica bead displacement for various bead diameters in an actin solution (2-mg/mL F-actin), taken from Schnurr et al.8 Experimental results of Schnurr et al. (thick curves) are compared with GLMT predictions (thin curves). System parameters: 1064-nm wavelength, 0.6-mW power, 1.2-μm beam waist at the focal point (personal communication with C. Schmidt, Division of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam; 9 September 2002), and 1.17 relative refractive index.

Fig. 3
Fig. 3

Prediction of BFP detector sensitivity. Bead-size dependence of detector sensitivity (see Fig. 2), taken from Schnurr et al.8 Experimental results are compared with GLMT predictions. As the photodetector signal is proportional to the scattering cross section and hence the trapping force, the detector response (volts/nanometers) is proportional to the trap stiffness.

Fig. 4
Fig. 4

Prediction of the optical levitation force profile. The axial force profile in an optical levitation experiment as a function of the axial position of the bead from the center of the trap. Experimental results corrected for the shift in focus caused by the dielectric discontinuity, following Dogariu and Rajagopalan.25 System parameters: 488-nm wavelength, 0.1-W power, 1.79-μm beam waist at the focal point, 1.16 relative refractive index, and 3.75-μm particle radius. See Bakker-Schut et al.’s results, Ref. 24.

Fig. 5
Fig. 5

Prediction of the axial force profile in laser guidance. Axial force profiles in a laser guidance experiment as a function of the axial location of 27.4 ± 2.3-μm-diameter polystyrene microspheres relative to the beam’s focal point. System parameters: 810-nm wavelength, 35-mW power, 5-μm beam waist at the focal point, 1.17 relative refractive index, and 13.7-μm particle radius.

Fig. 6
Fig. 6

Resonance effects on variability in the axial force. The resonance peaks are the result of a standing wave created inside the sphere, and their detection requires small changes in the size parameter α = ka. The inset shows the cumulative Gaussian distribution of particle sizes obtained by fitting to the experimentally observed particle sizes. The variability in particle size superimposed on the resonance effect is sufficient to explain the variability in the axial force. Simulation parameters: 810-nm wavelength, 35-mW power, 5-μm beam waist at the focal point, and 1.17 relative refractive index.

Fig. 7
Fig. 7

Prediction of the axial force profile in laser guidance for a bead radius smaller than the beam waist at the focal point. Axial force profiles in a laser guidance experiment are shown as a function of the axial location of 8 ± 0.11-μm-diameter polystyrene microspheres relative to the beam’s focal point. System parameters: 800-nm wavelength, 100-mW power, 5-μm beam waist at the focal point, 1.17 relative refractive index, and 4-μm particle radius.

Fig. 8
Fig. 8

Correlation for predicting the average axial force. The average axial force (1 W of power, n m = 1.33) was computed as a function of the dimensionless parameter β for relative refractive indices m = 1.05 (biological) and m = 1.16 (polystyrene). Axial force was averaged over twice the Rayleigh range of the Gaussian beam. Results for wavelengths varying from 10 nm to 100 μm and appropriate particle sizes and beam waists maintain direct correspondence when β is smaller than unity. Axial force is proportional to [(m 2 - 1)/(m 2 + 2)]2 and can be estimated for arbitrary refractive index.

Fig. 9
Fig. 9

Correlation for predicting radial escape force. Radial escape force (1 W of power, n m = 1.33) was computed as a function of dimensionless radius α̃ for relative refractive indices m = 1.05 (biological), m = 1.16 (polystyrene), and m = 1.20 (silica). Radial force is proportional to [(m 2 - 1)/(m 2 + 2)] and can be estimated for arbitrary refractive index. Reprinted with permission from Nahmias and Odde.23

Fig. 10
Fig. 10

MAPCs patterning by laser-guided direct writing. The system produced sufficient axial and radial forces to create a two-dimensional H pattern of MAPCs when viewed axially. The bright spot at the top right is the location of the beam focal point. System parameters: 830-nm wavelength, 200-mW power, 5-μm beam waist at the focal point, 1.05 relative refractive index, and 6-μm particle radius.

Equations (8)

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

β=a4λω03,
12kω02-kω02kω02 Fzdz=P a6λ4ω02ncm2-1m2+22×832π4 arctan2,
α˜=a/ωz,
Fgradmax=P4ncm2-1m2+2exp-12α˜3,
aF-trap,max=πω0=λ1.6/NA,
Ftrap,max=1.3×10-8m2-1m2+2P,
Faverage,max=3.7×10-8m2-1m2+22P.
Velocity=3.7×10-86πμam2-1m2+22P,

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