Abstract

We determine the characteristics of the radiation force that is exerted on a nonresonant nonlinear (Kerr-effect) rigid microsphere by a strongly focused Gaussian beam when diffraction and interference effects are significant (sphere radius a ≤ illumination wavelength λ). The average force is calculated from the surface integral of the energy-momentum tensor consisting of incident, scattered, and internal electromagnetic field vectors, which are expressed as multipole spherical-wave expansions. The refractive index of a Kerr microsphere is proportional to the internal field intensity, which is computed iteratively by the Rytov approximation (residual error of solution, 10-30). The expansion coefficients for the field vectors are calculated from the approximated index value. Compared with that obtained in a dielectric (linear) microsphere in the same illumination conditions, we find that the force magnitude on the Kerr microsphere is larger and increases more rapidly with both a and the numerical aperture of the focusing objective. It also increases nonlinearly with the beam power unlike that of a linear sphere. The Kerr nonlinearity also leads to possible reversals of the force direction. The proposed technique is applicable to other types of weak optical nonlinearity.

© 2002 Optical Society of America

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References

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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. R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. B 9, 1922–1930 (1992).
    [CrossRef]
  3. F. Ren, G. Grehan, G. Gouesbet, “Radiation pressure forces exerted on a particle located arbitrarily in a Gaussian beam by using the generalized Lorentz–Mie theory and associated resonance effects,” Opt. Commun. 108, 343–354 (1993).
    [CrossRef]
  4. 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]
  5. Y. Harada, T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
    [CrossRef]
  6. P. Zemanek, A. Jonas, L. Sramek, M. Liska, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
    [CrossRef]
  7. A. Ashkin, “History of optical trapping and manipulation of small neutral particle, atoms, and molecules,” IEEE J. Sel. Top. Quantum Electron. 6, 841–856 (2000).
    [CrossRef]
  8. M. Lester, M. Nieto-Vesperinas, “Optical forces on microparticles in an evanescent laser field,” Opt. Lett. 24, 936–938 (1999).
    [CrossRef]
  9. A. Rohrbach, E. H. K. Stelzer, “Optical trapping of dielectric particles in arbitrary fields,” J. Opt. Soc. Am. A 18, 839–853 (2001).
    [CrossRef]
  10. M. Lester, J. Arias-Gonzalez, M. Nieto-Vesperinas, “Fundamentals and model of photonic-force microscopy,” Opt. Lett. 26, 707–709 (2001).
    [CrossRef]
  11. T. Lemaire, “Coupled-multipole formulation for the treatment of electromagnetic scattering by a small dielectric particle of arbitrary shape,” J. Opt. Soc. Am. A 14, 470–474 (1997).
    [CrossRef]
  12. W. Inami, Y. Kawata, “Analysis of the scattered light distribution of a tightly focused laser beam by a particle near a substrate,” J. Appl. Phys. 89, 5876–5880 (2001).
    [CrossRef]
  13. L. Chernov, Wave Propagation in a Random Medium (Dover, New York, 1960).
  14. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999).
  15. R. Boyd, Nonlinear Optics (Academic, New York, 1991).
  16. R. Pobre, C. Saloma, “Single Gaussian beam interaction with a Kerr microsphere: characteristics of the radiation force,” Appl. Opt. 36, 3515–3520 (1997).
    [CrossRef] [PubMed]
  17. W. Tomlinson, J. Gordon, P. Smith, A. Kaplan, “Reflection of a Gaussian beam at nonlinear interfaces,” Appl. Opt. 21, 2041–2051 (1982).
    [CrossRef] [PubMed]
  18. P. Smith, W. Tomlinson, “Nonlinear optical interfaces: switching behavior,” IEEE J. Quantum Electron. 20, 30–36 (1984).
    [CrossRef]
  19. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Rider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
    [CrossRef]
  20. P. Prasad, D. Williams, Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley Interscience, New York, 1991).
  21. P. Prasad, “Nonlinear optical effects in organic materials,” in Contemporary Nonlinear Optics, G. Agrawal, R. Boyd, eds. (Academic, New York, 1992), Chap. 9, pp. 367–410.
  22. Ch. Bosshard, P. Gunter, K. Sutter, P. Pretre, J. Hulliger, Organic Nonlinear Optical Materials, Vol. 1 of Advances in Nonlinear Optics (Gordon and Breach, New York, 1995).
  23. G. Gurzadian, V. Dmitriev, D. Nikogosian, D. Nikogoskilan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1999).
  24. P. Gunter, Nonlinear Optical Effects and Materials (Springer-Verlag, Berlin, 2000).
  25. S. Vigil, M. Kuzyk, “Absolute molecular optical Kerr effect spectroscopy of dilute organic solutions and neat organic liquids,” J. Opt. Soc. Am. B 18, 679–691 (2001).
    [CrossRef]
  26. L. Malmqvist, H. Hertz, “Second-harmonic generation in optically trapped nonlinear particles with pulsed lasers,” Appl. Opt. 34, 3392–3397 (1995).
    [CrossRef] [PubMed]
  27. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), pp. 220, 236–240, 739–775.
  28. J. Marion, M. Heald, Classical Electromagnetic Radiation, 2nd ed. (Academic, New York, 1980).
  29. S. Caorsi, A. Massa, M. Pastorino, “Rytov approximation: application to scattering by two-dimensional weakly nonlinear dielectrics,” J. Opt. Soc. Am. A 13, 509–516 (1996).
    [CrossRef]
  30. J. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
    [CrossRef]
  31. F. Lin, M. Fiddy, “Born–Rytov controversy. II. Applications to nonlinear and stochastic scattering problems in one-dimensional half-space media,” J. Opt. Soc. Am. A 10, 1971–1983 (1993).
    [CrossRef]
  32. M. D. Feit, J. A. Fleck, “Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams,” J. Opt. Soc. Am. B 5, 633–644 (1988).
    [CrossRef]

2001 (5)

W. Inami, Y. Kawata, “Analysis of the scattered light distribution of a tightly focused laser beam by a particle near a substrate,” J. Appl. Phys. 89, 5876–5880 (2001).
[CrossRef]

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Rider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef]

A. Rohrbach, E. H. K. Stelzer, “Optical trapping of dielectric particles in arbitrary fields,” J. Opt. Soc. Am. A 18, 839–853 (2001).
[CrossRef]

S. Vigil, M. Kuzyk, “Absolute molecular optical Kerr effect spectroscopy of dilute organic solutions and neat organic liquids,” J. Opt. Soc. Am. B 18, 679–691 (2001).
[CrossRef]

M. Lester, J. Arias-Gonzalez, M. Nieto-Vesperinas, “Fundamentals and model of photonic-force microscopy,” Opt. Lett. 26, 707–709 (2001).
[CrossRef]

2000 (1)

A. Ashkin, “History of optical trapping and manipulation of small neutral particle, atoms, and molecules,” IEEE J. Sel. Top. Quantum Electron. 6, 841–856 (2000).
[CrossRef]

1999 (1)

1998 (1)

P. Zemanek, A. Jonas, L. Sramek, M. Liska, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[CrossRef]

1997 (2)

1996 (2)

S. Caorsi, A. Massa, M. Pastorino, “Rytov approximation: application to scattering by two-dimensional weakly nonlinear dielectrics,” J. Opt. Soc. Am. A 13, 509–516 (1996).
[CrossRef]

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

1995 (1)

1994 (1)

1993 (2)

F. Lin, M. Fiddy, “Born–Rytov controversy. II. Applications to nonlinear and stochastic scattering problems in one-dimensional half-space media,” J. Opt. Soc. Am. A 10, 1971–1983 (1993).
[CrossRef]

F. Ren, G. Grehan, G. Gouesbet, “Radiation pressure forces exerted on a particle located arbitrarily in a Gaussian beam by using the generalized Lorentz–Mie theory and associated resonance effects,” Opt. Commun. 108, 343–354 (1993).
[CrossRef]

1992 (1)

1989 (2)

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. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

1988 (1)

1984 (1)

P. Smith, W. Tomlinson, “Nonlinear optical interfaces: switching behavior,” IEEE J. Quantum Electron. 20, 30–36 (1984).
[CrossRef]

1982 (1)

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]

Alexander, D. R.

J. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

Arias-Gonzalez, J.

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, “History of optical trapping and manipulation of small neutral particle, atoms, and molecules,” IEEE J. Sel. Top. Quantum Electron. 6, 841–856 (2000).
[CrossRef]

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]

J. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

Berns, M.

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999).

Bosshard, Ch.

Ch. Bosshard, P. Gunter, K. Sutter, P. Pretre, J. Hulliger, Organic Nonlinear Optical Materials, Vol. 1 of Advances in Nonlinear Optics (Gordon and Breach, New York, 1995).

Boyd, R.

R. Boyd, Nonlinear Optics (Academic, New York, 1991).

Brabec, T.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Rider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef]

Brevik, I.

Caorsi, S.

Chernov, L.

L. Chernov, Wave Propagation in a Random Medium (Dover, New York, 1960).

Corkum, P.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Rider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef]

Dmitriev, V.

G. Gurzadian, V. Dmitriev, D. Nikogosian, D. Nikogoskilan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1999).

Drescher, M.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Rider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef]

Feit, M. D.

Fiddy, M.

Fleck, J. A.

Gordon, J.

Gouesbet, G.

F. Ren, G. Grehan, G. Gouesbet, “Radiation pressure forces exerted on a particle located arbitrarily in a Gaussian beam by using the generalized Lorentz–Mie theory and associated resonance effects,” Opt. Commun. 108, 343–354 (1993).
[CrossRef]

Grehan, G.

F. Ren, G. Grehan, G. Gouesbet, “Radiation pressure forces exerted on a particle located arbitrarily in a Gaussian beam by using the generalized Lorentz–Mie theory and associated resonance effects,” Opt. Commun. 108, 343–354 (1993).
[CrossRef]

Gunter, P.

P. Gunter, Nonlinear Optical Effects and Materials (Springer-Verlag, Berlin, 2000).

Ch. Bosshard, P. Gunter, K. Sutter, P. Pretre, J. Hulliger, Organic Nonlinear Optical Materials, Vol. 1 of Advances in Nonlinear Optics (Gordon and Breach, New York, 1995).

Gurzadian, G.

G. Gurzadian, V. Dmitriev, D. Nikogosian, D. Nikogoskilan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1999).

Gussgard, R.

Harada, Y.

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

Heald, M.

J. Marion, M. Heald, Classical Electromagnetic Radiation, 2nd ed. (Academic, New York, 1980).

Heinzmann, U.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Rider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef]

Hentschel, M.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Rider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef]

Hertz, H.

Hulliger, J.

Ch. Bosshard, P. Gunter, K. Sutter, P. Pretre, J. Hulliger, Organic Nonlinear Optical Materials, Vol. 1 of Advances in Nonlinear Optics (Gordon and Breach, New York, 1995).

Inami, W.

W. Inami, Y. Kawata, “Analysis of the scattered light distribution of a tightly focused laser beam by a particle near a substrate,” J. Appl. Phys. 89, 5876–5880 (2001).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), pp. 220, 236–240, 739–775.

Jonas, A.

P. Zemanek, A. Jonas, L. Sramek, M. Liska, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[CrossRef]

Kaplan, A.

Kawata, Y.

W. Inami, Y. Kawata, “Analysis of the scattered light distribution of a tightly focused laser beam by a particle near a substrate,” J. Appl. Phys. 89, 5876–5880 (2001).
[CrossRef]

Kienberger, R.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Rider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef]

Krausz, F.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Rider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef]

Kuzyk, M.

Lemaire, T.

Lester, M.

Lin, F.

Lindmo, T.

Liska, M.

P. Zemanek, A. Jonas, L. Sramek, M. Liska, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[CrossRef]

Malmqvist, L.

Marion, J.

J. Marion, M. Heald, Classical Electromagnetic Radiation, 2nd ed. (Academic, New York, 1980).

Massa, A.

Milosevic, N.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Rider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef]

Nieto-Vesperinas, M.

Nikogosian, D.

G. Gurzadian, V. Dmitriev, D. Nikogosian, D. Nikogoskilan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1999).

Nikogoskilan, D.

G. Gurzadian, V. Dmitriev, D. Nikogosian, D. Nikogoskilan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1999).

Pastorino, M.

Pobre, R.

Prasad, P.

P. Prasad, “Nonlinear optical effects in organic materials,” in Contemporary Nonlinear Optics, G. Agrawal, R. Boyd, eds. (Academic, New York, 1992), Chap. 9, pp. 367–410.

P. Prasad, D. Williams, Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley Interscience, New York, 1991).

Pretre, P.

Ch. Bosshard, P. Gunter, K. Sutter, P. Pretre, J. Hulliger, Organic Nonlinear Optical Materials, Vol. 1 of Advances in Nonlinear Optics (Gordon and Breach, New York, 1995).

Ren, F.

F. Ren, G. Grehan, G. Gouesbet, “Radiation pressure forces exerted on a particle located arbitrarily in a Gaussian beam by using the generalized Lorentz–Mie theory and associated resonance effects,” Opt. Commun. 108, 343–354 (1993).
[CrossRef]

Rider, G. A.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Rider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef]

Rohrbach, A.

Saloma, C.

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]

Smith, P.

P. Smith, W. Tomlinson, “Nonlinear optical interfaces: switching behavior,” IEEE J. Quantum Electron. 20, 30–36 (1984).
[CrossRef]

W. Tomlinson, J. Gordon, P. Smith, A. Kaplan, “Reflection of a Gaussian beam at nonlinear interfaces,” Appl. Opt. 21, 2041–2051 (1982).
[CrossRef] [PubMed]

Sonek, G.

Spielmann, Ch.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Rider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef]

Sramek, L.

P. Zemanek, A. Jonas, L. Sramek, M. Liska, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[CrossRef]

Stelzer, E. H. K.

Sutter, K.

Ch. Bosshard, P. Gunter, K. Sutter, P. Pretre, J. Hulliger, Organic Nonlinear Optical Materials, Vol. 1 of Advances in Nonlinear Optics (Gordon and Breach, New York, 1995).

Tomlinson, W.

P. Smith, W. Tomlinson, “Nonlinear optical interfaces: switching behavior,” IEEE J. Quantum Electron. 20, 30–36 (1984).
[CrossRef]

W. Tomlinson, J. Gordon, P. Smith, A. Kaplan, “Reflection of a Gaussian beam at nonlinear interfaces,” Appl. Opt. 21, 2041–2051 (1982).
[CrossRef] [PubMed]

Vigil, S.

Williams, D.

P. Prasad, D. Williams, Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley Interscience, New York, 1991).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999).

Wright, W.

Zemanek, P.

P. Zemanek, A. Jonas, L. Sramek, M. Liska, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[CrossRef]

Appl. Opt. (4)

IEEE J. Quantum Electron. (1)

P. Smith, W. Tomlinson, “Nonlinear optical interfaces: switching behavior,” IEEE J. Quantum Electron. 20, 30–36 (1984).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Ashkin, “History of optical trapping and manipulation of small neutral particle, atoms, and molecules,” IEEE J. Sel. Top. Quantum Electron. 6, 841–856 (2000).
[CrossRef]

J. Appl. Phys. (3)

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]

W. Inami, Y. Kawata, “Analysis of the scattered light distribution of a tightly focused laser beam by a particle near a substrate,” J. Appl. Phys. 89, 5876–5880 (2001).
[CrossRef]

J. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

J. Opt. Soc. Am. A (4)

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

Nature (London) (1)

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Rider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature (London) 414, 509–513 (2001).
[CrossRef]

Opt. Commun. (3)

F. Ren, G. Grehan, G. Gouesbet, “Radiation pressure forces exerted on a particle located arbitrarily in a Gaussian beam by using the generalized Lorentz–Mie theory and associated resonance effects,” Opt. Commun. 108, 343–354 (1993).
[CrossRef]

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

P. Zemanek, A. Jonas, L. Sramek, M. Liska, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[CrossRef]

Opt. Lett. (2)

Other (10)

P. Prasad, D. Williams, Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley Interscience, New York, 1991).

P. Prasad, “Nonlinear optical effects in organic materials,” in Contemporary Nonlinear Optics, G. Agrawal, R. Boyd, eds. (Academic, New York, 1992), Chap. 9, pp. 367–410.

Ch. Bosshard, P. Gunter, K. Sutter, P. Pretre, J. Hulliger, Organic Nonlinear Optical Materials, Vol. 1 of Advances in Nonlinear Optics (Gordon and Breach, New York, 1995).

G. Gurzadian, V. Dmitriev, D. Nikogosian, D. Nikogoskilan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1999).

P. Gunter, Nonlinear Optical Effects and Materials (Springer-Verlag, Berlin, 2000).

L. Chernov, Wave Propagation in a Random Medium (Dover, New York, 1960).

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999).

R. Boyd, Nonlinear Optics (Academic, New York, 1991).

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), pp. 220, 236–240, 739–775.

J. Marion, M. Heald, Classical Electromagnetic Radiation, 2nd ed. (Academic, New York, 1980).

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Figures (4)

Fig. 1
Fig. 1

Nonresonant Kerr microsphere on the path of a tightly focused Gaussian beam of optical frequency ω1= ω/n 1. The sphere center is located a distance z = z c from the geometrical focus at z = 0. The refractive index of the microsphere is n 2 = n 2 (0) + n 2 (1)| E 2*E 2|, while that of the surrounding medium is n 1. Three types of electric (magnetic) vector fields are the relevant: incident field E g (r, θ, ϕ), internal field E 2(r, θ, ϕ), and the scattered field E s (r, θ, ϕ), where the origin of the polar coordinate system is at the center of the microsphere. E g (r, θ, ϕ) is pictured as a spherical wave emanating from the geometrical focus at z = 0, while both E 2(r, θ, ϕ) and E s (r, θ, ϕ) are spherical waves originating from z = z c .

Fig. 2
Fig. 2

Behavior of radiation force for open circles, n 2 (1) = 0 and, solid circles, n 2 (1) = 1.8 × 10-11. (a) 〈F〉 versus z c with a = 1 µm, (b) d〈F〉/dz versus z c with a = 1 µm, (c) 〈F〉 versus a with z c = 1 µm. Other parameters are NA = 1.25, P = 100 mW, λ = 1.06 µm, n 2 (0) = 1.4, n 1 = 1.33. Note that z c > 0 when the sphere is initially located after the beam focus at z = 0. In (c) the best-fit curves (solid curves) are described by 〈F〉 (in 10-10 N units) = -1.065a + 0.707 for the linear case and 〈F〉 (in 10-10 N units) = -8.838a + 5.866, for the nonlinear case.

Fig. 3
Fig. 3

Behavior of radiation force for open circles, n 2 (1) = 0 and, solid circles, n 2 (1) = 1.8 × 10-11. (a) 〈F〉 versus average beam power P where λ = 1.06 µm, (b) 〈F〉 versus λ where P = 100 mW. Other parameters are z c = 1 µm, NA = 1.25, a = 1 µm, n 2 (0) = 1.4, and n 1 = 1.33. (a) The best-fit curves (solid curves) are described by 〈F〉 (in 10-10 N units) = -0.004P for the linear case and 〈F〉 (in 10-10 N units) = -2.15 × 10-4 P 2 - 8.58 × 10-3 P + 8.35 for the nonlinear case. (b) Best-fit curves (solid curves) are described by 〈F〉 (in 10-10 N units) = -0.143λ - 0.203 for the linear case and 〈F〉 (in 10-10 N units) = -0.544λ - 2.36 for the nonlinear case.

Fig. 4
Fig. 4

Behavior of the radiation force for, open circles, n 2 (1) = 0 and, solid circles, n 2 (1) = 1.8 × 10-11: (a) 〈F〉 versus NA where n 2 (0) = 1.4 and n 1 = 1.33 and (b) 〈F〉 versus Δn = n 2 (0) - n 1, where NA = 1.25. Other parameters are n 1 = 1.33, λ = 1.06 µm, z c = 1 µm, NA = 1.25, a = 1 µm. In the linear curves (solid curves) are described by 〈F〉 (in 10-10 N units) = -0.454 NA + 0.195 for the linear case and 〈F〉 (in 10-10 N units) = -03.73 NA + 1.63 for the nonlinear case.

Equations (37)

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n2r, θ, ϕ=n20+n21I2r, θ, ϕ,
Fμ= fμdV= eμTμνdA-ddt gμdV,
Tμν=ε1EμEν+HμHν-12δμνε1E2+H2,
F=Aen·TdA|r>a,
F=02π0πε1E1rE1+H1rH1-12ε1E12+H12err2 sin θdθdϕ|r>a,
Egr, θ, ϕ=l,m-ik1Al,m×jlk1rXl,mθ, ϕ+Bl,mjlk1rXl,mθ, ϕ,
Hgr, θ, ϕ=l,mAl,mjlk1rXl,mθ, ϕ+ik1Bl,m×jlk1rXl,mθ, ϕ,
Al,m=-1j1k1all+1-1/2  Yl,m*θ, ϕr · Eg5×a, θ, ϕdΩ,
Bl,m=1j1k1all+1-1/2  Yl,m*θ, ϕr · Hg5×a, θ, ϕdΩ,
Esr, θ, ϕ=l,m-ik1al,m×hl1k1rXl,mθ, ϕ+bl,mhl1k1rXl,mθ, ϕ,
Hsr, θ, ϕ=l,mal,mhl1k1rXl,mθ, ϕ+ik1bl,m×hl1k1rXl,mθ, ϕ.
al,m=n1jln2αjln1α-n2jln1αjln2αn2hl1n1αjln2α-n1jln2αhl1n2αAl,m,
bl,m=n1jln2αjln1α-n2jln1αjln2αn2hl1n1αjln2α-n1jln2αhl1n1αBl,m,
E2r, θ, ϕ=l,m-ik2cl,m×j1k2rXl,mθ, ϕ+dl,mjlk2rXl,mθ, ϕ,
H2r, θ, ϕ=l,mcl,mj1k2rXl,mθ, ϕ+ik2dl,m×jlk2rXl,mθ, ϕ,
cl,m=n1hl1n1αjln1α-n1jln1αhl1n1αn2hl1n1αjln2α-n1jln2αhl1n1αAl,m,
dl,m=n1hl1n1αjln1α-n1jln1αhl1n1αn1hl1n1αjln2α-n2jln2αhl1n1αBl,m.
Fx+iFyε0E02a2=iα24l=1m=-1l×l+m+2l+m+12l+12l+31/2×ll+22n12al,mal+1,m+1*+n12al,mAl+1,m+1*+n12Al,mal+1,m+1*+2bl,mbl+1,m+1*+bl,mBl+1,m+1*+Bl,mbl+1,m+1*+l-m+1l-m+22l+12l+31/2ll+2×2n12al+1,m-1al,m*+n12al+1,m-1Al,m*+n12Al+1,m-1al,m*+2bl+1,m-1bl,m*+bl+1,m-1Bl,m*+Bl+1,m-1bl,m*-l+m+1l-m1/2×n1-2al,mbl,m+1*+2bl,mal,m+1*-al,mBl,m+1*+bl,mAl,m+1*+Bl,mal,m+1*-Al,mbl,m+1*,
Fzε0E02a2=-α22l=1m=-1l×l+m+2l+m+12l+12l+31/2×ll+2lm2n12al+1,mal,m*+n12al+1,mAl,m*+n12Al+1,mal,m*+2bl+1,mbl+1,m*+bl+1,mBl,m*+Bl+1,mbl,m*+n1m2al,mbl,m*+al,mBl,m*+Al,mbl,m*.
2+k202E2r, θ, ϕ=k22r, θ, ϕ-k202E2r, θ, ϕ,
k22r, θ, ϕ=k102ε20+ε21E2r, θ, ϕ2,
n2r, θ, ϕ=k22r, θ, ϕn1/k12.
E2r, θ, ϕ; p+1E1r, θ, ϕ-i/4×Vk2r, θ, ϕ; p2-k202E2r, θ, ϕ; ph02×k20rr2 sin θdθϕdr,
E2r, θ, ϕ; p=0=expΦ1r, θ, ϕ+Φsr, θ, ϕ,
Φ1r, θ, ϕ=lnE1r, θ, ϕ,
Φsr, θ, ϕ=-i/4|E1r, θ, ϕ|×V |E1r, θ, ϕ|k22r, θ, ϕ-k202h02k20rr2 sin θdθdϕdr.
Ξp=V|E2r, θ, ϕ; p+1|-|E2r, θ, ϕ; p|r2 sin θdθdϕdr.
Eg+Es-E2×en=0,
k1Hg+Hs-k2H2×en=0,
n1[Al,mjln1α+al,mhl1n1α=n2cl,mjln2α,
Al,mjln1α+al,mhl1n1α=cl,mjln2α,
Bl,mjln1α+bl,mhl1n1α=dl,mjln2α,
n1[Bl,mjln1α+bl,mhl1n1α=n2dl,mjln2α.
al,m=Al,mn1jln2αjln1α-n2jln1αjln2α×n2hl1n1αjln2α-n1jln2αhl1n1α-1.
cl,m=Al,mn1hl1n1αjln1α-n1jln1αhl1n1α×n2hl1n1αjln2α-n1jln2αhl1n2α-1.
bl,m=Bl,mn2jln2αjln1α-n1jln1α×jln2αn1hl1n1αjln2α-n2jln2αhl1n1α-1,
dl,m=Bl,mn1hl1n1αjln1α-n1jln1α×hl1n1αn1hl1n1αjln2α-n2jln2αhl1n1α-1.

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