Abstract

A variant of the Gaussian beam expansion method consists in expanding the Bessel function J₀ 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 J₀ 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

» View Full Text: Acrobat PDF (353 KB)

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

References

Please [login to View References]

Author Affiliations

Emmanuel Cagniot, Michael Fromager, Kamel Ait-Ameur

Centre de recherche sur les Ions, les Matériaux et la Photonique, Unité Mixte de Recherche 6252, Commissariat à l'Énergie Atomique, Centre National de la Recherche Scientifique, École Nationale Supérieure d'Ingénieurs de Caen, Université de Caen, 6 Bd Maréchal Juin, F-14050 Caen, France

Cited By

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Advanced Search

Recent ToC Categories (Beta)

• Oct 08 2009 : See the latest ISP articles in the Applied Optics feature on Digital Holography in 3-D Imaging.
• Sep 25 2009 : Energy Express: Optics Express announces a special bi-monthly supplement dedicated to rapid developments in optics for sustainable energy.
• Sep 21 2009 : The 2009 Education and Training in Optics and Photonics papers are now available.

More News

• Invisibility Visualized
  Nov 12, 2009 - Scientists and curiosity seekers who want to know what a partially or... more
• Diamonds are a Laser's Best Friend
  Sep 18, 2009 - Tomorrow’s lasers may come with a bit of bling, thanks to a new... more
• Open Wide and Say ‘Zap’
  Aug 19, 2009 - A group of researchers in Australia and Taiwan has developed a new... more