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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 19 — Jul. 1, 2011
  • pp: 3128–3134

Generalized Bessel beams in modified axially symmetric graded index structures

Ashraf Fathallah and Mohamed Shalaby  »View Author Affiliations

Applied Optics, Vol. 50, Issue 19, pp. 3128-3134 (2011)

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We explore a general type of stable Bessel beams in graded index media. The proposed axially symmetric medium is characterized by an “α” index profile. Explicit solutions for the radial envelope of the field E ( r ) are derived in terms of generalized Bessel functions. Emphasis is given on illustrating how far the conditions of the proposed modified structure permit only a Bessel function of the first kind to be uniquely retained in the solution. This paper considers both the optical and mathematical aspects. Some numerical examples corroborating our theoretical results are included, showing the stability, propagation, and diffraction of such Bessel beams.

© 2011 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1940) Diffraction and gratings : Diffraction
(230.0230) Optical devices : Optical devices
(230.7370) Optical devices : Waveguides

ToC Category:
Diffraction and Gratings

Original Manuscript: November 15, 2010
Revised Manuscript: May 18, 2011
Manuscript Accepted: May 19, 2011
Published: June 21, 2011

Ashraf Fathallah and Mohamed Shalaby, "Generalized Bessel beams in modified axially symmetric graded index structures," Appl. Opt. 50, 3128-3134 (2011)

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