OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 41, Iss. 36 — Dec. 20, 2002
  • pp: 7694–7701

Radiation force on a nonlinear microsphere by a tightly focused Gaussian beam

Romeric Pobre and Caesar Saloma  »View Author Affiliations

Applied Optics, Vol. 41, Issue 36, pp. 7694-7701 (2002)

View Full Text Article

Enhanced HTML    Acrobat PDF (139 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(190.3270) Nonlinear optics : Kerr effect
(260.1960) Physical optics : Diffraction theory
(290.5850) Scattering : Scattering, particles

Original Manuscript: April 22, 2002
Revised Manuscript: September 12, 2002
Published: December 20, 2002

Romeric Pobre and Caesar Saloma, "Radiation force on a nonlinear microsphere by a tightly focused Gaussian beam," Appl. Opt. 41, 7694-7701 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited