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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 2, Iss. 7 — Jul. 1, 2011
  • pp: 1893–1906

Integral localized approximation description of ordinary Bessel beams and application to optical trapping forces

Leonardo A. Ambrosio and Hugo E. Hernández-Figueroa  »View Author Affiliations


Biomedical Optics Express, Vol. 2, Issue 7, pp. 1893-1906 (2011)
http://dx.doi.org/10.1364/BOE.2.001893


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Abstract

Ordinary Bessel beams are described in terms of the generalized Lorenz-Mie theory (GLMT) by adopting, for what is to our knowledge the first time in the literature, the integral localized approximation for computing their beam shape coefficients (BSCs) in the expansion of the electromagnetic fields. Numerical results reveal that the beam shape coefficients calculated in this way can adequately describe a zero-order Bessel beam with insignificant difference when compared to other relative time-consuming methods involving numerical integration over the spherical coordinates of the GLMT coordinate system, or quadratures. We show that this fast and efficient new numerical description of zero-order Bessel beams can be used with advantage, for example, in the analysis of optical forces in optical trapping systems for arbitrary optical regimes.

© 2011 OSA

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation
(290.4020) Scattering : Mie theory
(350.4855) Other areas of optics : Optical tweezers or optical manipulation
(290.5825) Scattering : Scattering theory

ToC Category:
Optical Traps, Manipulation, and Tracking

History
Original Manuscript: April 4, 2011
Revised Manuscript: June 7, 2011
Manuscript Accepted: June 7, 2011
Published: June 9, 2011

Citation
Leonardo A. Ambrosio and Hugo E. Hernández-Figueroa, "Integral localized approximation description of ordinary Bessel beams and application to optical trapping forces," Biomed. Opt. Express 2, 1893-1906 (2011)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-2-7-1893


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References

  1. G. Mie, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. 330(3), 377–452 (1908). [CrossRef]
  2. G. Gouesbet and G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).
  3. B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
  4. G. Gouesbet, G. Gréhan, and B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz-Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
  5. G. Gouesbet, G. Gréhan, and B. Maheu, “On the generalized Lorenz-Mie theory: first attempt to design a localized approximation to the computation of the coefficients gnm,” J. Opt. (Paris) 20, 31–43 (1989).
  6. G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 7(6), 998–1007 (1990). [CrossRef]
  7. K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized lorenz-mie theory,” Appl. Opt. 37(19), 4218–4225 (1998). [CrossRef] [PubMed]
  8. J. A. Lock and G. Gouesbet, “Generalized Lorenz-Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 800–807 (2009). [CrossRef]
  9. G. Gouesbet, “Generalized Lorenz-Mie theories, the third decade: A perspective,” J. Quant. Spectrosc. Radiat. Transf. 110(14-16), 1223–1238 (2009). [CrossRef]
  10. G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz-Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 1–27 (2011). [CrossRef]
  11. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  12. G. Gouesbet and J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. I. On-axis beams,” J. Opt. Soc. Am. A 11(9), 2503–2515 (1994). [CrossRef]
  13. G. Gouesbet and J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11(9), 2516–2525 (1994). [CrossRef]
  14. K. F. Ren, G. Gréhan, and G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108(4-6), 343–354 (1994). [CrossRef]
  15. H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155(1-3), 169–179 (1998). [CrossRef]
  16. L. A. Ambrosio and H. E. Hernández-Figueroa, “Fundamentals of negative refractive index optical trapping: forces and radiation pressures exerted by focused Gaussian beams using the generalized Lorenz-Mie theory,” Biomed. Opt. Express 1(5), 1284–1301 (2010). [CrossRef] [PubMed]
  17. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001). [CrossRef]
  18. V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002). [CrossRef] [PubMed]
  19. V. Garcés-Chávez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85(18), 4001–4003 (2004). [CrossRef]
  20. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004). [CrossRef] [PubMed]
  21. A. N. Rubinov, A. A. Afanas’ev, I. E. Ermolaev, Y. A. Kurochkin, and S. Y. Mikhnevich, “Localization of spherical particles under the action of gradient forces in the field of a zero-order Bessel beam. Rayleigh-Gans approximation,” J. Appl. Spectrosc. 70(4), 565–572 (2003). [CrossRef]
  22. G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemánek, “Transverse particle dynamics in a Bessel beam,” Opt. Express 15(21), 13972–13987 (2007). [CrossRef] [PubMed]
  23. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [CrossRef] [PubMed]
  24. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge, University Press, 1944), p. 358.
  25. K. R. Fen, “Diffusion des Faisceaux Feuille Laser par une Particule Sphérique et Applications aux Ecoulements Diphasiques,” Ph.D thesis (Faculté des Sciences de L’Université de Rouen, 1995).
  26. C. F. Bohren and D. R. Huffmann, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).
  27. K. F. Ren, G. Gréhan, and G. Gouesbet, “Symmetry relations in generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 11(6), 1812–1817 (1994). [CrossRef]
  28. F. Corbin, G. Gréhan, and G. Gouesbet, “Top-hat beam technique: improvements and application to bubble measurements,” Part. Part. Sys. Characterization. 8(1-4), 222–228 (1991). [CrossRef]
  29. G. Gouesbet, J. A. Lock, and G. Gréhan, “Partial-wave representations of laser beams for use in light-scattering calculations,” Appl. Opt. 34(12), 2133–2143 (1995). [CrossRef] [PubMed]
  30. G. Gouesbet, “Validity of the localized approximations for arbitrary shaped beams in the generalized Lorenz-Mie theory for spheres,” J. Opt. Soc. Am. A 16(7), 1641–1650 (1999). [CrossRef]

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