Abstract

We acknowledge the helpful comment by Chaumet [Appl. Opt. 43, 1825 (2004)] on a recent study [Appl. Opt. 41, 2494 (2002)] in which we used a mathematical expression for the optical scattering and gradient forces, which had been introduced in an earlier paper [J. Opt. Soc. Am. A 18, 839 (2001)]. Our reply to the comment gives us the chance to clarify interesting points and to present a novel, to our knowledge, derivation of the two force components from the basic electromagnetic force density on a small polarizable particle. Our final expression [Appl. Opt. 41, 2494 (2002)] for the optical trapping force on particles in the Rayleigh-Gans regime (diameter ≤ λmedium) in a diffraction-limited, vectorial focus remains correctly published.

© 2004 Optical Society of America

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References

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  1. P. C. Chaumet, “Comment on: ‘Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations,’” Appl. Opt. 43, 1825–1826 (2004).
    [CrossRef] [PubMed]
  2. A. Rohrbach, E. H. K. Stelzer, “Optical trapping of dielectric particles in arbitrary fields,” J. Opt. Soc. Am. A 18, 839–853 (2001).
    [CrossRef]
  3. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  4. C. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998).
    [CrossRef]
  5. J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
    [CrossRef]
  6. Y. Harada, T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
    [CrossRef]
  7. P. C. Chaumet, M. Nieto-Vesperinas, “Time-averaged total force on a dipolar sphere in an electromagnetic field,” Opt. Lett. 25, 1065–1067 (2000).
    [CrossRef]
  8. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, New York, 1999), pp. 716–724.
  9. A. Rohrbach, E. H. K. Stelzer, “Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations,” Appl. Opt. 41, 2494–2507 (2002).
    [CrossRef] [PubMed]
  10. A. Rohrbach, H. Kress, E. H. K. Stelzer, “Three-dimensional tracking of small spheres in focused laser beams: influence of the detection angular aperture,” Opt. Lett. 28, 411–413 (2003).
    [CrossRef] [PubMed]

2004 (1)

2003 (1)

2002 (1)

2001 (1)

2000 (1)

1996 (1)

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

1988 (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

1973 (1)

J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
[CrossRef]

Asakura, T.

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

Bohren, C.

C. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, New York, 1999), pp. 716–724.

Chaumet, P. C.

Draine, B. T.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Gordon, J. P.

J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
[CrossRef]

Harada, Y.

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

Huffman, D. R.

C. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998).
[CrossRef]

Kress, H.

Nieto-Vesperinas, M.

Rohrbach, A.

Stelzer, E. H. K.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, New York, 1999), pp. 716–724.

Appl. Opt. (2)

Astrophys. J. (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

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

Opt. Lett. (2)

Phys. Rev. A (1)

J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
[CrossRef]

Other (2)

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, New York, 1999), pp. 716–724.

C. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998).
[CrossRef]

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Equations (8)

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frp, t=12V α0εEr, t · Er, t+1V α0ε tEr, t×Br, t,
α=α01+i2k3α0/3/1+2k3α0/32
F=Vfgradr+fscardV =Vα0nm2cV I0rdV+nmc I0Cextcos θi-Cscacos θsk/|k|.
F=14VRe V α0ε|E|2dV=14VRe A α0εn|E|2dA,
F=14VRe V α0ε|Ei|2+|Es|2+EiEs*+EsEi*dV.
Fz=14VV α0εz|Ei|2dV+14VRe A α0εnz|Es|2+nzEiEs*+EsEi*dA.
F=14VRe  α0εnEs*Ei+Ei*Esr2 sin θdθdφ,
F=ezε/2|E0|21/6πk4α02=ezI0/cCext,

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