Abstract

The force equations describing the radiation forces on a microsphere in an arbitrary refractive index profile are derived here by using the photon-stream method in a ray-optics regime. A loosely focused Gaussian beam was employed as the radiating illumination beam. The radiation forces on a spherical microsphere were calculated in a time-varying refractive index profile. The refractive index profile of the surrounding medium was evaluated according to the concentration distribution obtained from the diffusion equation. The scattering and gradient forces on a microsphere were calculated for different refractive indices (1.22, 1.33, 1.43, and 1.59), and the radiation forces on a perfectly reflecting microsphere were calculated. The results were compared with previous results to validate the derivation.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
    [CrossRef]
  2. 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, 288–289 (1986).
    [CrossRef]
  3. J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometer steps,” Nature 368, 113–119 (1994).
    [CrossRef]
  4. A. Ashkin, “Trapping of atoms by resonance radiation pressure,” Phys. Rev. Lett. 40, 729–732 (1978).
    [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]
  6. S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998).
    [CrossRef]
  7. K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
    [CrossRef]
  8. S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83, 5316–5318 (2003).
    [CrossRef]
  9. T. Vestad, J. Oakey, and D. W. M. Marr, “Optical trapping, manipulation, and sorting of cells and colloids in microfluidic systems with diode laser bars,” Opt. Express 12, 4390–4398 (2004).
    [CrossRef]
  10. S. B. Kim, S. Y. Yoon, H. J. Sung, and S. S. Kim, “Cross-type optical particle separation in a microchannel,” Anal. Chem. 80, 2628–2630 (2008).
    [CrossRef]
  11. T. Kaneta, Y. Ishidzu, N. Mishima, and T. Imasaka, “Theory of optical chromatography,” Anal. Chem. 69, 2701–2710 (1997).
    [CrossRef]
  12. J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
    [CrossRef]
  13. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
    [CrossRef]
  14. K. T. Gahagan and G. A. Swartzlander, “Trapping of low-index microparticles in an optical vortex,” J. Opt. Soc. Am. B 15, 524–534 (1998).
    [CrossRef]
  15. H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155, 169–179 (1998).
    [CrossRef]
  16. G. Gouesbet, B. Maheu, and G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
    [CrossRef]
  17. K. F. Ren, G. Gréhan, 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]
  18. K. F. Ren, G. Gréhan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
    [CrossRef]
  19. J. A. Lock, “Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration,” Appl. Opt. 43, 2532–2544 (2004).
    [CrossRef]
  20. J. A. Lock, “Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. II. On-axis trapping force,” Appl. Opt. 43, 2545–2554 (2004).
    [CrossRef]
  21. 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]
  22. R. Li, X. Han, and K. F. Ren, “Debye series analysis of radiation pressure force exerted on a multilayered sphere,” Appl. Opt. 49, 955–963 (2010).
    [CrossRef]
  23. 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]
  24. R. C. Gauthier and S. Wallace, “Optical levitation of spheres: analytical development and numerical computations of the force equations,” J. Opt. Soc. Am. B 12, 1680–1686(1995).
    [CrossRef]
  25. R. C. Gauthier, “Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects,” J. Opt. Soc. Am. B 14, 3323–3333 (1997).
    [CrossRef]
  26. R. C. Gauthier, “Trapping model for the low-index ring-shaped micro-object in a focused, lowest-order Gaussian laser-beam profile,” J. Opt. Soc. Am. B 14, 782–789 (1997).
    [CrossRef]
  27. S. B. Kim and S. S. Kim, “Radiation forces on spheres in loosely focused Gaussian beam: ray-optics regime,” J. Opt. Soc. Am. B 23, 897–903 (2006).
    [CrossRef]
  28. S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. P. Grover, “Automated single-cell sorting system based on optical trapping,” J. Biomed. Opt. 6, 14–22 (2001).
    [CrossRef]
  29. W. Wang, A. E. Chiou, G. J. Sonek, and M. W. Berns, “Self-aligned dual-beam optical laser trap using photorefractive phase conjugation,” J. Opt. Soc. Am. B 14, 697–704 (1997).
    [CrossRef]
  30. K. S. Lee, S. B. Kim, K. H. Lee, H. J. Sung, and S. S. Kim, “Three-dimensional microfluidic liquid-core/liquid-cladding waveguide,” Appl. Phys. Lett. 97, 021109 (2010).
    [CrossRef]

2010

K. S. Lee, S. B. Kim, K. H. Lee, H. J. Sung, and S. S. Kim, “Three-dimensional microfluidic liquid-core/liquid-cladding waveguide,” Appl. Phys. Lett. 97, 021109 (2010).
[CrossRef]

R. Li, X. Han, and K. F. Ren, “Debye series analysis of radiation pressure force exerted on a multilayered sphere,” Appl. Opt. 49, 955–963 (2010).
[CrossRef]

2008

S. B. Kim, S. Y. Yoon, H. J. Sung, and S. S. Kim, “Cross-type optical particle separation in a microchannel,” Anal. Chem. 80, 2628–2630 (2008).
[CrossRef]

2006

2004

2003

S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83, 5316–5318 (2003).
[CrossRef]

2001

S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. P. Grover, “Automated single-cell sorting system based on optical trapping,” J. Biomed. Opt. 6, 14–22 (2001).
[CrossRef]

2000

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

1999

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]

1998

S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998).
[CrossRef]

H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155, 169–179 (1998).
[CrossRef]

K. T. Gahagan and G. A. Swartzlander, “Trapping of low-index microparticles in an optical vortex,” J. Opt. Soc. Am. B 15, 524–534 (1998).
[CrossRef]

1997

1996

1995

1994

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

K. F. Ren, G. Gréhan, 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

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (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]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[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]

1988

1986

1978

A. Ashkin, “Trapping of atoms by resonance radiation pressure,” Phys. Rev. Lett. 40, 729–732 (1978).
[CrossRef]

1970

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

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]

Arlt, J.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[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]

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, 288–289 (1986).
[CrossRef]

A. Ashkin, “Trapping of atoms by resonance radiation pressure,” Phys. Rev. Lett. 40, 729–732 (1978).
[CrossRef]

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

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.

Bjorkholm, J. E.

Block, S. M.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[CrossRef]

Chiou, A. E.

Chu, S.

Dholakia, K.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

Dziedzic, J. M.

Finer, J. T.

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

Gahagan, K. T.

Gauthier, R. C.

Gouesbet, G.

H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155, 169–179 (1998).
[CrossRef]

K. F. Ren, G. Gréhan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef]

K. F. Ren, G. Gréhan, 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]

G. Gouesbet, B. Maheu, and G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

Gréhan, G.

H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155, 169–179 (1998).
[CrossRef]

K. F. Ren, G. Gréhan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef]

K. F. Ren, G. Gréhan, 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]

G. Gouesbet, B. Maheu, and G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

Grover, C. P.

S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. P. Grover, “Automated single-cell sorting system based on optical trapping,” J. Biomed. Opt. 6, 14–22 (2001).
[CrossRef]

Grover, S. C.

S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. P. Grover, “Automated single-cell sorting system based on optical trapping,” J. Biomed. Opt. 6, 14–22 (2001).
[CrossRef]

Han, X.

Hart, S. J.

S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83, 5316–5318 (2003).
[CrossRef]

Heckenberg, N. R.

Imasaka, T.

T. Kaneta, Y. Ishidzu, N. Mishima, and T. Imasaka, “Theory of optical chromatography,” Anal. Chem. 69, 2701–2710 (1997).
[CrossRef]

Ishidzu, Y.

T. Kaneta, Y. Ishidzu, N. Mishima, and T. Imasaka, “Theory of optical chromatography,” Anal. Chem. 69, 2701–2710 (1997).
[CrossRef]

Kaneta, T.

T. Kaneta, Y. Ishidzu, N. Mishima, and T. Imasaka, “Theory of optical chromatography,” Anal. Chem. 69, 2701–2710 (1997).
[CrossRef]

Kim, S. B.

K. S. Lee, S. B. Kim, K. H. Lee, H. J. Sung, and S. S. Kim, “Three-dimensional microfluidic liquid-core/liquid-cladding waveguide,” Appl. Phys. Lett. 97, 021109 (2010).
[CrossRef]

S. B. Kim, S. Y. Yoon, H. J. Sung, and S. S. Kim, “Cross-type optical particle separation in a microchannel,” Anal. Chem. 80, 2628–2630 (2008).
[CrossRef]

S. B. Kim and S. S. Kim, “Radiation forces on spheres in loosely focused Gaussian beam: ray-optics regime,” J. Opt. Soc. Am. B 23, 897–903 (2006).
[CrossRef]

Kim, S. S.

K. S. Lee, S. B. Kim, K. H. Lee, H. J. Sung, and S. S. Kim, “Three-dimensional microfluidic liquid-core/liquid-cladding waveguide,” Appl. Phys. Lett. 97, 021109 (2010).
[CrossRef]

S. B. Kim, S. Y. Yoon, H. J. Sung, and S. S. Kim, “Cross-type optical particle separation in a microchannel,” Anal. Chem. 80, 2628–2630 (2008).
[CrossRef]

S. B. Kim and S. S. Kim, “Radiation forces on spheres in loosely focused Gaussian beam: ray-optics regime,” J. Opt. Soc. Am. B 23, 897–903 (2006).
[CrossRef]

Lee, K. H.

K. S. Lee, S. B. Kim, K. H. Lee, H. J. Sung, and S. S. Kim, “Three-dimensional microfluidic liquid-core/liquid-cladding waveguide,” Appl. Phys. Lett. 97, 021109 (2010).
[CrossRef]

Lee, K. S.

K. S. Lee, S. B. Kim, K. H. Lee, H. J. Sung, and S. S. Kim, “Three-dimensional microfluidic liquid-core/liquid-cladding waveguide,” Appl. Phys. Lett. 97, 021109 (2010).
[CrossRef]

Li, R.

Lock, J. A.

Maheu, B.

Marr, D. W. M.

McDuff, R.

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]

Mishima, N.

T. Kaneta, Y. Ishidzu, N. Mishima, and T. Imasaka, “Theory of optical chromatography,” Anal. Chem. 69, 2701–2710 (1997).
[CrossRef]

Oakey, J.

Polaert, H.

H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155, 169–179 (1998).
[CrossRef]

Ren, K. F.

R. Li, X. Han, and K. F. Ren, “Debye series analysis of radiation pressure force exerted on a multilayered sphere,” Appl. Opt. 49, 955–963 (2010).
[CrossRef]

K. F. Ren, G. Gréhan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef]

K. F. Ren, G. Gréhan, 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]

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]

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]

Schmidt, C. F.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[CrossRef]

Schnapp, B. J.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[CrossRef]

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]

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

Skirtach, A. G.

S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. P. Grover, “Automated single-cell sorting system based on optical trapping,” J. Biomed. Opt. 6, 14–22 (2001).
[CrossRef]

Smith, C. P.

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]

Sonek, G. J.

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]

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

Sung, H. J.

K. S. Lee, S. B. Kim, K. H. Lee, H. J. Sung, and S. S. Kim, “Three-dimensional microfluidic liquid-core/liquid-cladding waveguide,” Appl. Phys. Lett. 97, 021109 (2010).
[CrossRef]

S. B. Kim, S. Y. Yoon, H. J. Sung, and S. S. Kim, “Cross-type optical particle separation in a microchannel,” Anal. Chem. 80, 2628–2630 (2008).
[CrossRef]

Svoboda, K.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[CrossRef]

Swartzlander, G. A.

Terray, A. V.

S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83, 5316–5318 (2003).
[CrossRef]

Vestad, T.

Wallace, S.

Wang, W.

White, A. G.

Yoon, S. Y.

S. B. Kim, S. Y. Yoon, H. J. Sung, and S. S. Kim, “Cross-type optical particle separation in a microchannel,” Anal. Chem. 80, 2628–2630 (2008).
[CrossRef]

Anal. Chem.

S. B. Kim, S. Y. Yoon, H. J. Sung, and S. S. Kim, “Cross-type optical particle separation in a microchannel,” Anal. Chem. 80, 2628–2630 (2008).
[CrossRef]

T. Kaneta, Y. Ishidzu, N. Mishima, and T. Imasaka, “Theory of optical chromatography,” Anal. Chem. 69, 2701–2710 (1997).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83, 5316–5318 (2003).
[CrossRef]

K. S. Lee, S. B. Kim, K. H. Lee, H. J. Sung, and S. S. Kim, “Three-dimensional microfluidic liquid-core/liquid-cladding waveguide,” Appl. Phys. Lett. 97, 021109 (2010).
[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]

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. Biomed. Opt.

S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. P. Grover, “Automated single-cell sorting system based on optical trapping,” J. Biomed. Opt. 6, 14–22 (2001).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nature

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

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[CrossRef]

Opt. Commun.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155, 169–179 (1998).
[CrossRef]

K. F. Ren, G. Gréhan, 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]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

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

A. Ashkin, “Trapping of atoms by resonance radiation pressure,” Phys. Rev. Lett. 40, 729–732 (1978).
[CrossRef]

Rev. Mod. Phys.

S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998).
[CrossRef]

Science

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]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1.
Fig. 1.

Schematic diagram showing the photon-stream method. The initial Nk photons deviate from a Gaussian beam center axis, pass through a microsphere, and divide into Nk,1, Nk,2, and so forth, when the photons encounter the interface between the microsphere and the surrounding medium.

Fig. 2.
Fig. 2.

Geometry used to calculate the ρk value for a given ρk. A Gaussian beam propagates along the z-directional axis. The x and y directions indicate the radial offset from the Gaussian beam center axis: (a) yz plane and (b) xy plane.

Fig. 3.
Fig. 3.

Gradient force as a function of the dimensionless radial offset for different rp/ωo values in a homogeneous refractive index profile. The refractive index of the surrounding medium is assumed to be 1.33, that of DI water.

Fig. 4.
Fig. 4.

Scattering force as a function of the dimensionless radial offset for different rp/ωo values in a homogeneous refractive index profile.

Fig. 5.
Fig. 5.

Results of the diffusion equation for various time points, and the calculated refractive index profile. The refractive index can be calculated according to the following equation, n=1.33547+0.00232·[CaCl2], where [CaCl2] denotes the concentration of CaCl2 in the solvent. The inset shows the refractive index profile as a function of the spatial domain. The refractive index profile is conserved along the z direction (beam propagation direction).

Fig. 6.
Fig. 6.

Gradient force as a function of the dimensionless radial offset for different particle refractive indices. The refractive indices correspond to a hollow glass microsphere (1.22), a DI water droplet (1.33), a silica microsphere (1.43), and a PSL particle (1.59).

Fig. 7.
Fig. 7.

Scattering force as a function of the dimensionless radial offset for each particle refractive index.

Fig. 8.
Fig. 8.

Gradient force as a function of the dimensionless radial offset for different refractive index profiles of the surrounding medium. The refractive index profile can vary according to diffusion of the solvent from the core.

Fig. 9.
Fig. 9.

Scattering force as a function of the dimensionless radial offset for different refractive index profiles of the surrounding medium.

Fig. 10.
Fig. 10.

Optical intensity distribution for various refractive index profiles of the surrounding medium. The total power (watts) was assumed to be constant in the three different cases.

Fig. 11.
Fig. 11.

Gradient force as a function of the dimensionless radial offset for a perfectly reflecting microsphere and for two particles with different refractive indices.

Fig. 12.
Fig. 12.

Scattering force as a function of the dimensionless radial offset for a perfectly reflecting microsphere and two particles with different refractive indices.

Equations (30)

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

F=ΔpΔt=dpdt,
p=n(ρk)hλ,
Nk=λhcI(ρk,z)dAdt,
I(ρk,z)=2Pπω(z)2exp[2ρk2ω(z)2],
ω(z)=ωo[1+(λzπωo2)2]1/2.
N=k=1Nk=k=1n=1Nk,n.
Δpz=hλNk[n(ρk){1+Nk,1Nkcos2θ1}n(ρk)Nk,2Nkcosα],
Δpy=hλNk[n(ρk)Nk,1Nksin2θ1n(ρk)Nk,2Nksinα]cosφ,
α=θ12θ2+θ3,
n(ρk)sinθ1=nssinθ2=n(ρk)sinθ3,
ρk2=a2+(rpsinθ12rpcosθ2sin(θ1θ2))22a(rpsinθ12rpcosθ2sin(θ1θ2))cosφ.
Nk,1=NkR(ρk),
Nk,2=NkT(ρk)T(ρk),
R=RTE+RTM2,
R(ρk)=12[sin2(θ1θ2)sin2(θ1+θ2)+tan2(θ1θ2)tan2(θ1+θ2)],
R(ρk)=12[sin2(θ2θ3)sin2(θ2+θ3)+tan2(θ2θ3)tan2(θ2+θ3)],
T(ρk)=1R(ρk),
T(ρk)=1R(ρk),
Δpz=hλNk[n(ρk){1+R(ρk)cos2θ1}n(ρk)T(ρk)T(ρk)cosα],
Δpy=hλNk[n(ρk)R(ρk)sin2θ1n(ρk)T(ρk)T(ρk)sinα]cosφ.
dFz=I(ρ,z)c[n(ρ){1+R(ρ)cos2θ1}n(ρ)T(ρ)T(ρ)cosα]dA,
dFy=I(ρ,z)c[n(ρ)R(ρ)sin2θ1n(ρ)T(ρ)T(ρ)sinα]cosφdA.
ρ2=a2+rp2sin2θ12arpsinθ1cosφ,
Fs=12c02π0π/2I(ρ,z)[n(ρ){1+R(ρ)cos2θ1}n(ρ)T(ρk)T(ρ)cosα]rp2sin2θ1dθ1dφ,
Fg=12c02π0π/2I(ρ,z)[n(ρ)R(ρ)sin2θ1n(ρ)T(ρ)T(ρ)sinα]rp2sin2θ1cosφdθ1dφ,
Ct=Drr(rCr),
C(r,0)=C0,0rωo,
C(r,0)=0,r>ωo,
C(r,t)=0,r=w,
n=1.33547+0.00232·[CaCl2],

Metrics