OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN 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)
http://dx.doi.org/10.1364/AO.50.003128


View Full Text Article

Enhanced HTML    Acrobat PDF (933 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

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

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

Citation
Ashraf Fathallah and Mohamed Shalaby, "Generalized Bessel beams in modified axially symmetric graded index structures," Appl. Opt. 50, 3128-3134 (2011)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-50-19-3128


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. C. Zapata-Rodriguez and J. J. Miret, “Diffraction-free beams in thin films,” J. Opt. Soc. Am. A 27, 663–670 (2010). [CrossRef]
  2. A. P. Sergey, W. Huang and M. Cada, “Dark and anti-dark diffraction free beams,” Opt. Lett. 32, 2508–2510 (2007). [CrossRef]
  3. Y. Z. Yu and W. B. Dou, “Vector analyses of nondiffracting Bessel beams,” Progr. Electromagn. Res. Lett. 5, 57–71 (2008). [CrossRef]
  4. J. Canning, “Diffraction free mode generation and propagation in optical waveguides,” Opt. Commun. 207, 35–39 (2002). [CrossRef]
  5. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Elsevier, 2005).
  6. F. E. Relton, Applied Bessel Functions (Blackie & Son, 1946).
  7. R. E. Collin, Field Theory of Guided Waves, 2nd ed. (IEEE, 1991).
  8. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, 1982).
  9. M. Bronstein and S. Lafaille, “Solutions of linear ordinary differential equations in terms of special functions,” Proceedings of the International Symposium on Algorithms and Computation, ISAAC ’2002 (ACM, 2002), pp. 23–28.
  10. R. Debeerst, M. Hoeij, and W. Koepf, Solving Differential Equations in Terms of Bessel Functions (ACM, 2008).
  11. Z. X. Wang and D. R. Guo, Special Functions (World Scientific, 1989).
  12. F. Bowman, Introduction to Bessel Functions (Dover, 1958).
  13. M. Shalaby, “Transformation of the three dimensional beam propagation method to two dimensions for cylindrically symmetric structures based on the Hankel transform,” Pure Appl. Opt. 5, 997–1004 (1996). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited