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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 21 — Jul. 20, 2006
  • pp: 5118–5131

Laser beam shaping profiles and propagation

David L. Shealy and John A. Hoffnagle  »View Author Affiliations

Applied Optics, Vol. 45, Issue 21, pp. 5118-5131 (2006)

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We consider four families of functions—the super-Gaussian, flattened Gaussian, Fermi–Dirac, and super-Lorentzian—that have been used to describe flattened irradiance profiles. We determine the shape and width parameters of the different distributions, when each flattened profile has the same radius and slope of the irradiance at its half-height point, and then we evaluate the implicit functional relationship between the shape and width parameters for matched profiles, which provides a quantitative way to compare profiles described by different families of functions. We conclude from an analysis of each profile with matched parameters using Kirchhoff–Fresnel diffraction theory and M 2 analysis that the diffraction patterns as they propagate differ by small amounts, which may not be distinguished experimentally. Thus, beam shaping optics is designed to produce either of these four flattened output irradiance distributions with matched parameters will yield similar irradiance distributions as the beam propagates.

© 2006 Optical Society of America

OCIS Codes
(140.3300) Lasers and laser optics : Laser beam shaping
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

ToC Category:
Lasers and Laser Optics

Original Manuscript: December 12, 2005
Revised Manuscript: March 12, 2006
Manuscript Accepted: March 15, 2006

David L. Shealy and John A. Hoffnagle, "Laser beam shaping profiles and propagation," Appl. Opt. 45, 5118-5131 (2006)

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