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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 35, Iss. 9 — Mar. 20, 1996
  • pp: 1537–1542

Discussion of two quadrature methods of evaluating beam-shape coefficients in generalized Lorenz–Mie theory

G. Gouesbet, C. Letellier, K. F. Ren, and G. Gréhan  »View Author Affiliations


Applied Optics, Vol. 35, Issue 9, pp. 1537-1542 (1996)
http://dx.doi.org/10.1364/AO.35.001537


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Abstract

A comparison between two quadrature methods of evaluating beam-shape coefficients in generalized Lorenz–Mie theory, in the case of incident Gaussian beams, is carried out. It is shown that, when the electromagnetic description of the Gaussian beams does not perfectly satisfy Maxwell's equations, both quadrature methods are basically flawed. These flaws do not prevent an accurate evaluation of beam-shape coefficients when their nature is correctly identified, because they produce artifacts that can easily be identified and removed.

© 1996 Optical Society of America

History
Original Manuscript: January 30, 1995
Published: March 20, 1996

Citation
G. Gouesbet, C. Letellier, K. F. Ren, and G. Gréhan, "Discussion of two quadrature methods of evaluating beam-shape coefficients in generalized Lorenz–Mie theory," Appl. Opt. 35, 1537-1542 (1996)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-35-9-1537


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References

  1. G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A. 5, 1427–1443 (1988).
  2. B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
  3. G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–34 (1994).
  4. L. Lorenz, “Lysbevaegelsen i og uden for en haf plane lysbolger belyst kulge,” Vidensk. Selk. Skr. 6, 1–62 (1890).
  5. L. Lorenz, “Sur la lumière réfractée par une sphère transparente,” in Oeuvres Scientifiques de L. Lorenz, Revues et Annotées par H. Valentiner (Libraire Lehmann et Stage, Copenhagen, 1898), pp. 405–529.
  6. G. Mie, “Beitrage zur optik truber medien, speziell kolloidaler metallosungen,” Ann. Phys. 25, 377–452 (1908).
  7. G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the coefficients gn in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
  8. G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory using finite series,” J. Opt. (Paris) 19, 35–48 (1988).
  9. G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
  10. G. Gouesbet, G. Gréhan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
  11. J. A. Lock, G. Gouesbet, “Rigorous justification of the localized approximation to the beam-shape coefficients in the generalized Lorenz–Mie theory. I. On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
  12. G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in the generalized Lorenz–Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
  13. G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. (Paris) 13, 97–103 (1982).
  14. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. 19, 1177–1179 (1979).
  15. G. Gouesbet, J.A. Lock, G. Gréhan, “Do you know what a laser beam is?’’ in Proceedings of the Seventh Workshop on Two-Phase Flows (to be published).
  16. G. Gouesbet, J. A. Lock, G. Gréhan, “Partial-wave representations of laser beams for use in light-scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
  17. S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficients for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989).
  18. J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
  19. G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1966).
  20. J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle illuminated by a focussed laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
  21. J. A. Lock, “Contribution of high-order rainbows to the scattering of a Gaussian laser beam by a spherical particle,” J. Opt. Soc. Am. A 10, 693–706 (1993).
  22. G. Gouesbet, G. Gréhan, B. Maheu, “Electromagnetic scattering of shaped beams,” is in preparation. A rather polished draft is available on request.
  23. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (New York, Academic, 1980).
  24. B. Maheu, G. Gréhan, G. Gouesbet, “Generalized Lorenz–Mie theory: first exact values and comparisons with the localized approximation,” Appl. Opt. 26, 23–26 (1987).
  25. B. Maheu, G. Gréhan, G. Gouesbet, “Diffusion de la lumière par une sphère dans le cas d’un faisceau d’extension finie. lere partie: théorie de Lorenz–Mie généralisée, les coefficients gn et leur calcul numérique,” presented at the 3éme Journées d’ Etudes sur les Aérosols, Paris, 9–10 Décembre, 1986 [published in J. Aerosol Sci.19, 47–53 (1988).]
  26. B. Maheu, G. Gréhan, G. Gouesbet, “Laser beam scattering by individual spherical particles: theoretical progress and applications to optical sizing,” presented at the International Symposium: Optical Particle Sizing: Theory and Practice, Rouen, France, 12–15 May 1987 [published in J. Part. Charact.4, 141–146 (1987).]
  27. B. Maheu, G. Gréhan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).

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