Abstract

Analytic expressions for radiation force on a sphere in a loosely focused Gaussian beam are derived in suitable form for applications by the photon stream method in the ray-optics regime. For perfect reflecting spheres, an analytic solution for the scattering force and a simplified expression for the gradient force are obtained. The computation results presented are consistent with those of previous theoretical studies and reported experimental results.

© 2006 Optical Society of America

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References

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  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] [PubMed]
  3. T. N. Buican, M. J. Smith, H. A. Crissman, G. C. Salzeman,C. C. Stewart, and J. C. Martin, "Automated single-cell manipulation and sorting by light trapping," Appl. Opt. 26, 5311-5316 (1987).
    [CrossRef] [PubMed]
  4. R. Steubing, S. Chang, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser-cell fusion trap," Cytometry 12, 505-510 (1991).
    [CrossRef] [PubMed]
  5. 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] [PubMed]
  6. S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
    [CrossRef] [PubMed]
  7. A. Ashkin, "Trapping of atoms by resonance radiation pressure," Phys. Rev. Lett. 40, 729-732 (1978).
    [CrossRef]
  8. W. D. Phillips, "Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
    [CrossRef]
  9. S. Chu, "The manipulation of neutral particles," Rev. Mod. Phys. 70, 685-706 (1998).
    [CrossRef]
  10. J. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, and J. Dalibard, "Stopping atoms with laser light," Phys. Rev. Lett. 54, 992-995 (1985).
    [CrossRef] [PubMed]
  11. J. Makihara, T. Kaneta, and T. Imasaka, "Optical chromatography size determination by eluting particles," Talanta 48, 551-557 (1999).
    [CrossRef]
  12. 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]
  13. T. Kaneta, Y. Ishidzu, N. Mishima, and T. Imasaka, "Theory of optical chromatography," Anal. Chem. 69, 2701-2710 (1997).
    [CrossRef] [PubMed]
  14. R. C. Gauthier, "Optical trapping: a tool to assist optical machining," Opt. Laser Technol. 29, 389-399 (1997).
    [CrossRef]
  15. D. R. Koehler, "Optical actuation of micromechanical components," J. Opt. Soc. Am. B 14, 2197-2203 (1997).
    [CrossRef]
  16. J. P. Barton, D. R. Alexander, and S. A. Schaub, "Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam," J. Appl. Phys. 64, 1632-1639 (1988).
    [CrossRef]
  17. 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]
  18. J. S. Kim and S. S. Lee, "Scattering of laser beams and the optical potential well for a homogeneous sphere," J. Opt. Soc. Am. 73, 303-312 (1983).
    [CrossRef]
  19. S. Chang and S. S. Lee, "Optical torque on a homogeneous sphere levitated in circularly polarized fundamental-mode laser beam," J. Opt. Soc. Am. B 2, 1853-1860 (1985).
    [CrossRef]
  20. A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 12, 569-582 (1992).
    [CrossRef]
  21. A. Ashkin and J. M. Dziedzic, "Feedback stabilization of optically levitated particles," Appl. Phys. Lett. 30, 202-204 (1977).
    [CrossRef]
  22. G. Roll, T. Kaiser, and G. Schweiger, "Optical trap sedimentation cell-a new technique for the sizing of microparticles," J. Aerosol Sci. 27, 105-117 (1996).
    [CrossRef]
  23. A. Ashkin and J. M. Dziedzic, "Observation of optical resonances of dielectric spheres by light scattering," Appl. Opt. 20, 1803-1814 (1981).
    [CrossRef] [PubMed]
  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, "Ray optics model and numerical computations for the radiation pressure micromotor," Appl. Phys. Lett. 67, 2269-2271 (1995).
    [CrossRef]
  26. R. C. Gauthier, "Theoretical model for an improved radiation pressure micromotor," Appl. Phys. Lett. 69, 2015-2017 (1996).
    [CrossRef]
  27. 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]
  28. 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]
  29. R. C. Gauthier, "Simulated dynamic behavior of single and multiple spheres in the trap region of focused laser beams," Appl. Opt. 37, 6421-6431 (1998).
    [CrossRef]

2003 (1)

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]

1999 (1)

J. Makihara, T. Kaneta, and T. Imasaka, "Optical chromatography size determination by eluting particles," Talanta 48, 551-557 (1999).
[CrossRef]

1998 (3)

W. D. Phillips, "Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
[CrossRef]

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

R. C. Gauthier, "Simulated dynamic behavior of single and multiple spheres in the trap region of focused laser beams," Appl. Opt. 37, 6421-6431 (1998).
[CrossRef]

1997 (5)

1996 (2)

G. Roll, T. Kaiser, and G. Schweiger, "Optical trap sedimentation cell-a new technique for the sizing of microparticles," J. Aerosol Sci. 27, 105-117 (1996).
[CrossRef]

R. C. Gauthier, "Theoretical model for an improved radiation pressure micromotor," Appl. Phys. Lett. 69, 2015-2017 (1996).
[CrossRef]

1995 (2)

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]

R. C. Gauthier, "Ray optics model and numerical computations for the radiation pressure micromotor," Appl. Phys. Lett. 67, 2269-2271 (1995).
[CrossRef]

1994 (1)

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] [PubMed]

1992 (1)

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 12, 569-582 (1992).
[CrossRef]

1991 (1)

R. Steubing, S. Chang, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser-cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

1989 (1)

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 (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam," J. Appl. Phys. 64, 1632-1639 (1988).
[CrossRef]

1987 (1)

1986 (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] [PubMed]

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

1985 (2)

J. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, and J. Dalibard, "Stopping atoms with laser light," Phys. Rev. Lett. 54, 992-995 (1985).
[CrossRef] [PubMed]

S. Chang and S. S. Lee, "Optical torque on a homogeneous sphere levitated in circularly polarized fundamental-mode laser beam," J. Opt. Soc. Am. B 2, 1853-1860 (1985).
[CrossRef]

1983 (1)

1981 (1)

1978 (1)

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

1977 (1)

A. Ashkin and J. M. Dziedzic, "Feedback stabilization of optically levitated particles," Appl. Phys. Lett. 30, 202-204 (1977).
[CrossRef]

1970 (1)

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]

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam," J. Appl. Phys. 64, 1632-1639 (1988).
[CrossRef]

Ashkin, A.

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 12, 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] [PubMed]

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, "Observation of optical resonances of dielectric spheres by light scattering," Appl. Opt. 20, 1803-1814 (1981).
[CrossRef] [PubMed]

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

A. Ashkin and J. M. Dziedzic, "Feedback stabilization of optically levitated particles," Appl. Phys. Lett. 30, 202-204 (1977).
[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]

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam," J. Appl. Phys. 64, 1632-1639 (1988).
[CrossRef]

Berns, M. W.

R. Steubing, S. Chang, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser-cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

Bjorkholm, J. E.

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] [PubMed]

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

Buican, T. N.

Calbe, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

Chang, S.

R. Steubing, S. Chang, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser-cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

S. Chang and S. S. Lee, "Optical torque on a homogeneous sphere levitated in circularly polarized fundamental-mode laser beam," J. Opt. Soc. Am. B 2, 1853-1860 (1985).
[CrossRef]

Chu, S.

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

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

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] [PubMed]

Crissman, H. A.

Dalibard, J.

J. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, and J. Dalibard, "Stopping atoms with laser light," Phys. Rev. Lett. 54, 992-995 (1985).
[CrossRef] [PubMed]

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] [PubMed]

Gauthier, R. C.

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]

Imasaka, T.

J. Makihara, T. Kaneta, and T. Imasaka, "Optical chromatography size determination by eluting particles," Talanta 48, 551-557 (1999).
[CrossRef]

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

Ishidzu, Y.

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

Kaiser, T.

G. Roll, T. Kaiser, and G. Schweiger, "Optical trap sedimentation cell-a new technique for the sizing of microparticles," J. Aerosol Sci. 27, 105-117 (1996).
[CrossRef]

Kaneta, T.

J. Makihara, T. Kaneta, and T. Imasaka, "Optical chromatography size determination by eluting particles," Talanta 48, 551-557 (1999).
[CrossRef]

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

Kim, J. S.

Koehler, D. R.

Lee, S. S.

Makihara, J.

J. Makihara, T. Kaneta, and T. Imasaka, "Optical chromatography size determination by eluting particles," Talanta 48, 551-557 (1999).
[CrossRef]

Martin, J. C.

Metcalf, H.

J. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, and J. Dalibard, "Stopping atoms with laser light," Phys. Rev. Lett. 54, 992-995 (1985).
[CrossRef] [PubMed]

Migdall, A.

J. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, and J. Dalibard, "Stopping atoms with laser light," Phys. Rev. Lett. 54, 992-995 (1985).
[CrossRef] [PubMed]

Mishima, N.

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

Numajiri, Y.

R. Steubing, S. Chang, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser-cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

Phillips, W. D.

W. D. Phillips, "Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
[CrossRef]

J. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, and J. Dalibard, "Stopping atoms with laser light," Phys. Rev. Lett. 54, 992-995 (1985).
[CrossRef] [PubMed]

Prodan, J.

J. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, and J. Dalibard, "Stopping atoms with laser light," Phys. Rev. Lett. 54, 992-995 (1985).
[CrossRef] [PubMed]

Roll, G.

G. Roll, T. Kaiser, and G. Schweiger, "Optical trap sedimentation cell-a new technique for the sizing of microparticles," J. Aerosol Sci. 27, 105-117 (1996).
[CrossRef]

Salzeman, G. C.

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]

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam," J. Appl. Phys. 64, 1632-1639 (1988).
[CrossRef]

Schweiger, G.

G. Roll, T. Kaiser, and G. Schweiger, "Optical trap sedimentation cell-a new technique for the sizing of microparticles," J. Aerosol Sci. 27, 105-117 (1996).
[CrossRef]

Simmons, R. M.

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] [PubMed]

Smith, M. J.

So, I.

J. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, and J. Dalibard, "Stopping atoms with laser light," Phys. Rev. Lett. 54, 992-995 (1985).
[CrossRef] [PubMed]

Spudich, J. A.

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] [PubMed]

Steubing, R.

R. Steubing, S. Chang, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser-cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

Stewart, C. C.

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]

Wallace, S.

Wright, W. H.

R. Steubing, S. Chang, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser-cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

Anal. Chem. (1)

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

Appl. Opt. (3)

Appl. Phys. Lett. (4)

A. Ashkin and J. M. Dziedzic, "Feedback stabilization of optically levitated particles," Appl. Phys. Lett. 30, 202-204 (1977).
[CrossRef]

R. C. Gauthier, "Ray optics model and numerical computations for the radiation pressure micromotor," Appl. Phys. Lett. 67, 2269-2271 (1995).
[CrossRef]

R. C. Gauthier, "Theoretical model for an improved radiation pressure micromotor," Appl. Phys. Lett. 69, 2015-2017 (1996).
[CrossRef]

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]

Biophys. J. (1)

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 12, 569-582 (1992).
[CrossRef]

Cytometry (1)

R. Steubing, S. Chang, W. H. Wright, Y. Numajiri, and M. W. Berns, "Laser induced cell fusion in combination with optical tweezers: the laser-cell fusion trap," Cytometry 12, 505-510 (1991).
[CrossRef] [PubMed]

J. Aerosol Sci. (1)

G. Roll, T. Kaiser, and G. Schweiger, "Optical trap sedimentation cell-a new technique for the sizing of microparticles," J. Aerosol Sci. 27, 105-117 (1996).
[CrossRef]

J. Appl. Phys. (2)

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam," J. Appl. Phys. 64, 1632-1639 (1988).
[CrossRef]

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. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (5)

Nature (1)

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] [PubMed]

Opt. Laser Technol. (1)

R. C. Gauthier, "Optical trapping: a tool to assist optical machining," Opt. Laser Technol. 29, 389-399 (1997).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (4)

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

J. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, and J. Dalibard, "Stopping atoms with laser light," Phys. Rev. Lett. 54, 992-995 (1985).
[CrossRef] [PubMed]

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Calbe, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

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

Rev. Mod. Phys. (2)

W. D. Phillips, "Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
[CrossRef]

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

Talanta (1)

J. Makihara, T. Kaneta, and T. Imasaka, "Optical chromatography size determination by eluting particles," Talanta 48, 551-557 (1999).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Geometry of a photon-stream path, apart from a Gaussian beam center axis, passing through a sphere. Initial N k photons are divided into N k , 1 , N k , 2 and so on, through N k , 1 path, N k , 2 path….

Fig. 2
Fig. 2

Geometry of a sphere at an arbitrary position in the Gaussian beam. φ is the polar angle, θ 1 is the incident angle, and a is the radial distance from the Gaussian beam center axis to the sphere center axis.

Fig. 3
Fig. 3

Scattering force versus axial distance. For r p ω 0 < 1 , there is no dip, but dip exists for r p ω 0 > 1 . The maximum force increases as r p ω 0 increases but remains unchanged when r p ω 0 > 1 .

Fig. 4
Fig. 4

Dimensionless scattering coefficient versus incident angle. For different relative indexes of refraction, the coefficient has different distributions.

Fig. 5
Fig. 5

For θ > 70 ° , ρ θ can be greater than ω 0 when the sphere has a radius larger than the minimum beam waist.

Fig. 6
Fig. 6

Gradient force versus dimensionless radial offset for different r p ω 0 values sizes. The gradient force is zero when spheres are located at the center of the Gaussian beam. The maximum gradient force increases steeply as r p ω 0 increases.

Fig. 7
Fig. 7

Scattering force versus radial offset and axial distance. r p = 2 μ m , ω 0 = 3 μ m , P = 50 mW , n 0 = 1.33 , n s = 1.59 , λ 0 = 0.488 μ m .

Fig. 8
Fig. 8

Gradient force versus radial offset and axial distance. r p = 2 μ m , ω 0 = 3 μ m , P = 50 mW , n 0 = 1.33 , n s = 1.59 , λ 0 = 0.488 μ m .

Fig. 9
Fig. 9

Comparison with a previous study[12] and Eq. (17) for application to optical chromatography. Equation (17) gives more accurate predictions than the previous study. The experimental and theoretical conditions were the same as in the referenced paper.

Fig. 10
Fig. 10

Scattering force versus axial distance for a perfect reflecting sphere and a sphere that has a high index of refraction. Although the sphere radius is greater than the minimum beam waist, there is no dip in the scattering force distribution for the perfect reflecting sphere and the sphere that has a high index of refraction.

Fig. 11
Fig. 11

Gradient force versus axial distance for a perfect reflecting sphere and a sphere that has a high index of refraction. The gradient force has negative value for the perfect reflecting sphere and the sphere that has a high index of refraction. Therefore the trapping of spheres that have a high index of refraction is unstable, as is trapping perfect reflecting spheres.

Equations (24)

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

p = n 0 h λ ,
I ( ρ k , z ) = 2 P π ω ( z ) 2 exp [ 2 ρ k 2 ω ( z ) 2 ] ,
ω ( z ) = ω 0 [ 1 + ( λ z π ω 0 2 ) 2 ] 1 2 .
N k = λ h c I ( ρ k , z ) d A Δ t ,
N k = n = 1 N k , n .
N = k = 1 N k = k = 1 n = 1 N k , n .
Δ p z = n 0 h λ N k [ 1 + N k , 1 N k cos 2 θ 1 n = 2 N k , n N k cos ( α + n β ) ] ,
Δ p r = n 0 h λ N k [ N 1 , 1 N k sin 2 θ 1 n = 2 N 1 , n N k sin ( α + n β ) ] cos φ ,
N k , I = N k R , N k , n = N k R n 2 T 2 for n 2 .
R = 1 2 [ sin 2 ( θ 1 θ 2 ) sin 2 ( θ 1 + θ 2 ) + tan 2 ( θ 1 θ 2 ) tan 2 ( θ 1 + θ 2 ) ] .
Δ p z = n 0 h λ N k [ 1 + R cos 2 θ 1 T 2 cos ( 2 θ 1 2 θ 2 ) + R cos 2 θ 1 1 + R 2 + 2 R cos 2 θ 2 ] = n 0 h λ N k Q z ,
Δ p r = n 0 h λ N k [ R sin 2 θ 1 T 2 sin ( 2 θ 1 2 θ 2 ) + R sin 2 θ 1 1 + R 2 + 2 R cos 2 θ 2 ] cos φ = n 0 h λ N k Q r ,
F = Δ p Δ t .
d F z = n 0 c I ( ρ , z ) [ 1 + R cos 2 θ 1 T 2 cos ( 2 θ 1 2 θ 2 ) + R cos 2 θ 1 1 + R 2 + 2 R cos 2 θ 2 ] d A ,
d F r = n 0 c I ( ρ , z ) [ R sin 2 θ 1 T 2 sin ( 2 θ 1 2 θ 2 ) + R sin 2 θ 1 1 + R 2 + 2 R cos 2 θ 2 ] cos φ d A ,
ρ 2 = a 2 + r p 2 sin 2 θ 1 2 a r p sin θ 1 cos φ ,
F s = n 0 2 c 0 2 π 0 π 2 I ( ρ , z ) [ 1 + R cos 2 θ 1 T 2 cos 2 ( θ 1 θ 2 ) + R cos 2 θ 1 1 + R 2 + 2 R cos 2 θ 2 ] r p 2 sin 2 θ 1 d θ 1 d φ ,
F g = n 0 2 c 0 2 π 0 π 2 I ( ρ , z ) [ R sin 2 θ 1 T 2 sin 2 ( θ 1 θ 2 ) + R sin 2 θ 1 1 + R 2 + 2 R cos 2 θ 2 ] r p 2 sin 2 θ 1 cos φ d θ 1 d φ ,
N θ = λ h c 2 P π ω ( z ) 2 exp [ 2 ρ θ ω ( z ) 2 ] ,
N k , l = N k , N k , n = 0 for n 2 .
F s , perfect = 0 π 2 2 n 0 P c ω ( z ) 2 exp [ 2 r p 2 sin 2 θ 1 ω ( z ) 2 ] ( 1 + cos 2 θ 1 ) r p 2 sin 2 θ 1 d θ 1 .
F s , perfect = 2 n 0 P C ( 1 + ω ( z ) 2 2 r p 2 { exp [ 2 r p 2 ω ( z ) 2 ] 1 } ) .
F g , perfect = 0 2 π 0 π 2 n 0 P c π ω ( z ) 2 exp [ 2 ρ 2 ω ( z ) 2 ] r p 2 sin 2 2 θ 1 cos φ d θ 1 d φ .
F g , perfect = 2 n 0 P c ω ( z ) exp [ 2 a 2 ω ( z ) 2 ] 0 π 2 I 1 [ 4 a r p sin θ 1 ω ( z ) 2 ] exp [ 2 r p 2 ω ( z ) 2 ] r p 2 sin 2 2 θ 1 d θ 1 ,

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