OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 5 — May. 1, 2002
  • pp: 1025–1034

Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave

Pavel Zemánek, Alexandr Jonáš, and Miroslav Liška  »View Author Affiliations

JOSA A, Vol. 19, Issue 5, pp. 1025-1034 (2002)

View Full Text Article

Enhanced HTML    Acrobat PDF (822 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We study the axial force acting on dielectric spherical particles smaller than the trapping wavelength that are placed in the Gaussian standing wave. We derive analytical formulas for immersed particles with relative refractive indices close to unity and compare them with the numerical results obtained by generalized Lorenz–Mie theory (GLMT). We show that the axial optical force depends periodically on the particle size and that the equilibrium position of the particle alternates between the standing-wave antinodes and nodes. For certain particle sizes, gradient forces from the neighboring antinodes cancel each other and disable particle confinement. Using the GLMT we compare maximum axial trapping forces provided by the Gaussian standing-wave trap (SWT) and single-beam trap (SBT) as a function of particle size, refractive index, and beam waist size. We show that the SWT produces axial forces at least ten times stronger and permits particle confinement in a wider range of refractive indices and beam waists compared with those of the SBT.

© 2002 Optical Society of America

OCIS Codes
(140.7010) Lasers and laser optics : Laser trapping
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation
(260.2110) Physical optics : Electromagnetic optics
(260.3160) Physical optics : Interference
(290.4020) Scattering : Mie theory
(290.5850) Scattering : Scattering, particles

Original Manuscript: March 23, 2001
Revised Manuscript: October 16, 2001
Manuscript Accepted: October 16, 2001
Published: May 1, 2002

Pavel Zemánek, Alexandr Jonáš, and Miroslav Liška, "Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave," J. Opt. Soc. Am. A 19, 1025-1034 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986). [CrossRef] [PubMed]
  2. K. Svoboda, S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19, 930–932 (1994). [CrossRef] [PubMed]
  3. A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987). [CrossRef] [PubMed]
  4. S. M. Block, L. S. B. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348, 348–352 (1990). [CrossRef] [PubMed]
  5. K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993). [CrossRef] [PubMed]
  6. T. T. Perkins, S. R. Quake, D. E. Smith, S. Chu, “Relaxation of a single DNA molecule observed by optical microscopy,” Science 264, 822–825 (1994). [CrossRef] [PubMed]
  7. G. J. L. Wulte, S. B. Smith, M. Young, D. Keller, C. Bustamante, “Single-molecule studies of the effect of template tension on T7 DNA polymerase activity,” Nature 404, 103–106 (2000). [CrossRef]
  8. M. E. J. Friese, A. G. Truscott, H. Rubinstein-Dunlop, “Three-dimensional imaging with optical tweezers,” Appl. Opt. 38, 6597–6603 (1999). [CrossRef]
  9. S. Kawata, Y. Inouye, T. Sugiura, “Near-field scanning optical microscope with a laser trapped probe,” Jpn. J. Appl. Phys., Part 2 33, L1725–L1727 (1994). [CrossRef]
  10. K. Sasaki, H. Fujiwara, H. Masuhara, “Optical manipulation of lasing microparticle and its application to near-field microspectroscopy,” J. Vac. Sci. Technol. B 15, 2786–2790 (1997). [CrossRef]
  11. E.-L. Florin, A. Pralle, J. K. H. Hörber, E. H. K. Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202–211 (1997). [CrossRef] [PubMed]
  12. A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133, 7–10 (1997). [CrossRef]
  13. W. Wang, A. E. Chiou, G. J. Sonek, M. W. Berns, “Self-aligned dual-beam optical laser trap using photorefractive phase conjugation,” J. Opt. Soc. Am. B 14, 697–704 (1997). [CrossRef]
  14. A. Constable, J. Kim, “Demonstration of a fiber-optical light-force trap,” Opt. Lett. 18, 1867–1867 (1993). [CrossRef] [PubMed]
  15. S. D. Collins, R. J. Baskin, D. G. Howitt, “Microinstrument gradient-force optical trap,” Appl. Opt. 38, 6068–6074 (1999). [CrossRef]
  16. K. Visscher, S. P. Gross, S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066–1076 (1996). [CrossRef]
  17. E. Fällman, O. Axner, “Design for fully steerable dual-trap optical tweezers,” Appl. Opt. 36, 2107–2113 (1997). [CrossRef] [PubMed]
  18. E. R. Dufresne, D. G. Grier, “Optical tweezers arrays and optical substrates created with diffractive optics,” Rev. Sci. Instrum. 69, 1974–1977 (1998). [CrossRef]
  19. K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, H. Masuhara, “Pattern formation and flow control of fine particles by laser-scanning micromanipulation,” Opt. Lett. 16, 1463–1465 (1991). [CrossRef] [PubMed]
  20. P. Zemánek, A. Jonáš, L. Šrámek, M. Liška, “Optical trapping of nanoparticles and microparticles using Gaussian standing wave,” Opt. Lett. 24, 1448–1450 (1999). [CrossRef]
  21. Y. Harada, T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996). [CrossRef]
  22. P. Zemánek, A. Jonáš, L. Šrámek, M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998). [CrossRef]
  23. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  24. G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Physik 25, 377–445 (1908). [CrossRef]
  25. G. Gouesbet, G. Grehan, “Generalized Lorenz–Mie theories, from past to future,” Atomization Sprays 10, 277–333 (2000).
  26. J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989). [CrossRef]
  27. J. P. Barton, D. R. Alexander, 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]
  28. T. Tlusty, A. Meller, R. Bar-Ziv, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998). [CrossRef]
  29. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999).
  30. A. Rohrbach, E. H. K. Stelzer, “Optical trapping of dielectric particles in arbitrary fields,” J. Opt. Soc. Am. A 18, 839–853 (2000). [CrossRef]
  31. J. P. Barton, D. R. Alexander, 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]
  32. G. Gouesbet, “Higher-order descriptions of Gaussian beams,” J. Opt. 27, 35–50 (1996). [CrossRef]
  33. S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989). [CrossRef]
  34. A. Jonáš, P. Zemánek, E. L. Florin, “Single beam trapping in front of reflective surfaces,” Opt. Lett. 26, 1466–1468 (2001). [CrossRef]
  35. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999), Chap. VIII.

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited