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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 12 — Dec. 1, 1998
  • pp: 3028–3038

Partial-wave description of shaped beams in elliptical-cylinder coordinates

G. Gouesbet, L. Mees, and G. Gréhan  »View Author Affiliations

JOSA A, Vol. 15, Issue 12, pp. 3028-3038 (1998)

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We present the most general framework, in terms of distributions, for describing a shaped electromagnetic beam in elliptical-cylinder coordinates. This framework is illustrated by investigating the case of a first-order Gaussian beam.

© 1998 Optical Society of America

OCIS Codes
(260.2110) Physical optics : Electromagnetic optics
(290.0290) Scattering : Scattering
(290.4020) Scattering : Mie theory
(350.7420) Other areas of optics : Waves

G. Gouesbet, L. Mees, and G. Gréhan, "Partial-wave description of shaped beams in elliptical-cylinder coordinates," J. Opt. Soc. Am. A 15, 3028-3038 (1998)

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  1. G. Gouesbet, B. Maheu, and 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. G. Gouesbet, G. Gréhan, and B. Maheu, “Generalized Lorenz–Mie theory and applications to optical sizing,” in Combustion Measurements, N. Chigier, ed. (Hemisphere, New York, 1991), pp. 339–384.
  3. F. Onofri, G. Gréhan, and G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
  4. G. Gouesbet, “Scattering of higher-order Gaussian beams by an infinite cylinder,” J. Opt. (Paris) 28, 45–65 (1997).
  5. G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary-shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
  6. G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. (Paris) 26, 225–239 (1995).
  7. G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Charact. 12, 242–256 (1995).
  8. E. Lenglart, G. Gouesbet, “The separability theorem in terms of distributions with discussion of electromagnetic scattering theory,” J. Math. Phys. (New York) 37, 4705–4710 (1996).
  9. F. Roddier, Distributions et transformation de Fourier (McGraw-Hill, Paris, 1992).
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  11. E. Butkov, Mathematical Physics (Addison-Wesley, Reading, Mass., 1968).
  12. Information on theory of distributions and its application to light scattering can be obtained from G. Gouesbet on request.
  13. C. Yeh, “The diffraction of waves by a penetrable ribbon,” J. Math. Phys. (New York) 4, 65–71 (1963).
  14. C. Yeh, “Backscattering cross section of a dielectric elliptical cylinder,” J. Opt. Soc. Am. 55, 309–314 (1965).
  15. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part I (McGraw-Hill, New York, 1953).
  16. T. J. Bromwich, “Electromagnetic waves,” Philos. Mag. 38, 143–164 (1919).
  17. F. E. Borgnis, “Elektromagnetische Eigenschwingungen dielektrischer Raüme,” Ann. Phys. (Leipzig) 35, 359–384 (1939).
  18. Information on electromagnetic scattering of shaped beams (generalized Lorenz–Mie theory) can be obtained from G. Gouesbet on request.
  19. R. Campbell, Théorie générale de l’équation de Mathieu (Masson, Paris, 1955).
  20. N. W. McLachlan, Theory and Application of Mathieu Functions (Clarendon, Oxford, UK, 1951).
  21. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), pp. 723–745.
  22. G. Gouesbet, “Exact description of arbitrary-shaped beams for use in light-scattering theories,” J. Opt. Soc. Am. A 13, 2434–2440 (1996).
  23. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. 19, 1177–1179 (1979).
  24. J. P. Barton and D. R. Alexander, “Fifth-order corrected electromagnetic field components for fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
  25. G. Gouesbet, J. A. Lock, and G. Gréhan, “Partial-wave representations of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
  26. J. A. Lock and G. Gouesbet, “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, 2503–2515 (1994).
  27. 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, 2516–2525 (1994).
  28. G. Gouesbet, “Higher-order descriptions of Gaussian beams,” J. Opt. (Paris) 27, 35–50 (1996).
  29. G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1976).

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