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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 11 — Nov. 1, 2009
  • pp: 2373–2382

Adaptive Laguerre–Gaussian variant of the Gaussian beam expansion method

Emmanuel Cagniot, Michael Fromager, and Kamel Ait-Ameur  »View Author Affiliations


JOSA A, Vol. 26, Issue 11, pp. 2373-2382 (2009)
http://dx.doi.org/10.1364/JOSAA.26.002373


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Abstract

A variant of the Gaussian beam expansion method consists in expanding the Bessel function J 0 appearing in the Fresnel–Kirchhoff integral into a finite sum of complex Gaussian functions to derive an analytical expression for a Laguerre–Gaussian beam diffracted through a hard-edge aperture. However, the validity range of the approximation depends on the number of expansion coefficients that are obtained by optimization–computation directly. We propose another solution consisting in expanding J 0 onto a set of collimated Laguerre–Gaussian functions whose waist depends on their number and then, depending on its argument, predicting the suitable number of expansion functions to calculate the integral recursively.

© 2009 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1220) Diffraction and gratings : Apertures
(050.1380) Diffraction and gratings : Binary optics

ToC Category:
Diffraction and Gratings

History
Original Manuscript: July 8, 2009
Revised Manuscript: September 17, 2009
Manuscript Accepted: September 17, 2009
Published: October 15, 2009

Citation
Emmanuel Cagniot, Michael Fromager, and Kamel Ait-Ameur, "Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method," J. Opt. Soc. Am. A 26, 2373-2382 (2009)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-11-2373

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