Abstract

We analyze the generation of radiation forces in the various internal reflections that occur when a tightly focused, unpolarized Gaussian beam interacts with a dielectric microsphere. The Euler transformation is used to compute the relevant axial-force vectors that are associated with the internal reflections rapidly. The net force is computed as the average of the forces generated by the s- and p-polarization components of the electric-field vector. The force characteristics are strongly dependent on the algebraic value of the index mismatch Δn at the sphere interface. For the two cases of Δn = 0.65, 0.32 with a sphere index n2 = 1.65, the inclusion of the contributions from the second and third internal reflections after the magnitude of the effective force by at least 10%. For Δn < 0, the individual force contributions from internal reflections beyond the first are at least 4 orders of magnitude less than those of the first interaction. The caustic structures produced by the internal reflections are also profiled for both cases of Δn = ±0.32.

© 1995 Optical Society of America

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  1. J. Barton, D. Alexander, S. 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]
  2. W. Wright, G. Sonek, Y. Tadir, M. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
    [CrossRef]
  3. T. Bakker Schut, G. Hesselink, B. de Grooth, J. Greve, “Experimental and theoretical investigations on the validity of the geometric optics model for calculating the stability of optical traps,” Cytometry 12, 479–485 (1991).
    [CrossRef]
  4. R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. A 9, 1922–1930 (1992).
    [CrossRef]
  5. 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]
  6. W. Wright, G. Sonek, M. Berns, “Radiation-trapping forces in microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
    [CrossRef]
  7. C. Saloma, X. Mei, “The dielectric microsphere in a single-plane polarized Gaussian beam: characteristics of the radiation force,” Optik (Stuttgart) 94, (4) 173–176 (1993).
  8. W. Wright, G. Sonek, M. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
    [CrossRef] [PubMed]
  9. D. Chowdhury, P. Barber, S. Hill, “Energy-density distribution inside large nonabsorbing spheres by using Mie theory and geometrical optics,” Appl. Opt. 31, 3518–3523 (1992).
    [CrossRef] [PubMed]
  10. J. Lock, E. Hovenac, “Internal caustic structure of illuminated liquid droplets,” J. Opt. Soc. Am. A 8, 1541–1552 (1991).
    [CrossRef]
  11. J. Marion, M. Heald, Classical Electromagnetic Radiation2nd ed. (Academic, New York, 1990), pp. 168–169.
  12. A. Seigman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 17.
  13. J. Marion, S. Thornton, Classical Dynamics of Particles and Systems, 3rd ed. (Harcourt Brace Jovanovitch, San Diego, Calif., 1988) pp. 351–394.
  14. Turbo-Pascal Reference Guide, Version 6.0 (Borland-Osborne/McGraw-Hill, Calif., 1991).

1994

1993

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

C. Saloma, X. Mei, “The dielectric microsphere in a single-plane polarized Gaussian beam: characteristics of the radiation force,” Optik (Stuttgart) 94, (4) 173–176 (1993).

1992

D. Chowdhury, P. Barber, S. Hill, “Energy-density distribution inside large nonabsorbing spheres by using Mie theory and geometrical optics,” Appl. Opt. 31, 3518–3523 (1992).
[CrossRef] [PubMed]

R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. A 9, 1922–1930 (1992).
[CrossRef]

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

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

J. Lock, E. Hovenac, “Internal caustic structure of illuminated liquid droplets,” J. Opt. Soc. Am. A 8, 1541–1552 (1991).
[CrossRef]

1990

W. Wright, G. Sonek, Y. Tadir, M. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

1989

J. Barton, D. Alexander, S. 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]

Alexander, D.

J. Barton, D. Alexander, S. 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]

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]

Bakker Schut, T.

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

Barber, P.

Barton, J.

J. Barton, D. Alexander, S. 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. Wright, G. Sonek, M. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

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

W. Wright, G. Sonek, Y. Tadir, M. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Brevik, I.

R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. A 9, 1922–1930 (1992).
[CrossRef]

Chowdhury, D.

de Grooth, B.

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

Greve, J.

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

Gussgard, R.

R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. A 9, 1922–1930 (1992).
[CrossRef]

Heald, M.

J. Marion, M. Heald, Classical Electromagnetic Radiation2nd ed. (Academic, New York, 1990), pp. 168–169.

Hesselink, G.

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

Hill, S.

Hovenac, E.

Lindmo, T.

R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. A 9, 1922–1930 (1992).
[CrossRef]

Lock, J.

Marion, J.

J. Marion, M. Heald, Classical Electromagnetic Radiation2nd ed. (Academic, New York, 1990), pp. 168–169.

J. Marion, S. Thornton, Classical Dynamics of Particles and Systems, 3rd ed. (Harcourt Brace Jovanovitch, San Diego, Calif., 1988) pp. 351–394.

Mei, X.

C. Saloma, X. Mei, “The dielectric microsphere in a single-plane polarized Gaussian beam: characteristics of the radiation force,” Optik (Stuttgart) 94, (4) 173–176 (1993).

Saloma, C.

C. Saloma, X. Mei, “The dielectric microsphere in a single-plane polarized Gaussian beam: characteristics of the radiation force,” Optik (Stuttgart) 94, (4) 173–176 (1993).

Schaub, S.

J. Barton, D. Alexander, S. 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]

Seigman, A.

A. Seigman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 17.

Sonek, G.

W. Wright, G. Sonek, M. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

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

W. Wright, G. Sonek, Y. Tadir, M. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Tadir, Y.

W. Wright, G. Sonek, Y. Tadir, M. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Thornton, S.

J. Marion, S. Thornton, Classical Dynamics of Particles and Systems, 3rd ed. (Harcourt Brace Jovanovitch, San Diego, Calif., 1988) pp. 351–394.

Wright, W.

W. Wright, G. Sonek, M. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

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

W. Wright, G. Sonek, Y. Tadir, M. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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

Cytometry

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

IEEE J. Quantum Electron.

W. Wright, G. Sonek, Y. Tadir, M. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

J. Appl. Phys.

J. Barton, D. Alexander, S. 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. A

R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. A 9, 1922–1930 (1992).
[CrossRef]

J. Lock, E. Hovenac, “Internal caustic structure of illuminated liquid droplets,” J. Opt. Soc. Am. A 8, 1541–1552 (1991).
[CrossRef]

Optik (Stuttgart)

C. Saloma, X. Mei, “The dielectric microsphere in a single-plane polarized Gaussian beam: characteristics of the radiation force,” Optik (Stuttgart) 94, (4) 173–176 (1993).

Other

J. Marion, M. Heald, Classical Electromagnetic Radiation2nd ed. (Academic, New York, 1990), pp. 168–169.

A. Seigman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 17.

J. Marion, S. Thornton, Classical Dynamics of Particles and Systems, 3rd ed. (Harcourt Brace Jovanovitch, San Diego, Calif., 1988) pp. 351–394.

Turbo-Pascal Reference Guide, Version 6.0 (Borland-Osborne/McGraw-Hill, Calif., 1991).

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