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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. 23, Iss. 9 — Sep. 1, 2006
  • pp: 2278–2282

Generation of an elliptic hollow beam using Mathieu and Bessel functions

Rijuparna Chakraborty and Ajay Ghosh  »View Author Affiliations


JOSA A, Vol. 23, Issue 9, pp. 2278-2282 (2006)
http://dx.doi.org/10.1364/JOSAA.23.002278


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Abstract

A new (to our knowledge) technique for the generation of a propagation-invariant elliptic hollow beam is reported. It avoids the use of the radial Mathieu function and hence is mathematically simpler. Bessel functions with their arguments having elliptic locus are used to generate the mask, which is then recorded using holographic technique. To generate such an elliptic beam, both the angular Mathieu function, i.e., elliptic vortex term, and the expression for the circular vortex are used separately. The resultant mask is illuminated with a plane beam, and the proper filtering of its Fourier transform generates the expected elliptic beam. Results with both vortex terms are satisfactory. It has been observed that even for higher ellipticity the vortices do not separate.

© 2006 Optical Society of America

OCIS Codes
(090.0090) Holography : Holography
(090.1760) Holography : Computer holography
(140.0140) Lasers and laser optics : Lasers and laser optics
(140.3300) Lasers and laser optics : Laser beam shaping

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: January 12, 2006
Revised Manuscript: March 8, 2006
Manuscript Accepted: March 9, 2006

Citation
Rijuparna Chakraborty and Ajay Ghosh, "Generation of an elliptic hollow beam using Mathieu and Bessel functions," J. Opt. Soc. Am. A 23, 2278-2282 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-9-2278


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References

  1. P. Coullet, L. Gil, and F. Rocca, "Optical vortices," Opt. Commun. 73, 403-408 (1989). [CrossRef]
  2. M. P. McDonald, L. Patterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 169-175 (2002).
  3. Y. Song, D. Milan, and W. T. Hill III, "Long, narrow all-light atom guide," Opt. Lett. 24, 1805-1807 (1999). [CrossRef]
  4. J. Yin, W. Gao, and Y. Zhu, "Generation of dark hollow beams and their applications," in Progress in Optics XLV, E.Wolf, ed. (Elsevier, 2003). [CrossRef]
  5. S. Chavez Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutierrez Vega, A. T. O'Neil, I. MacVicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B: Quantum Semiclassical Opt. 4, S52-S57 (2002). [CrossRef]
  6. J. C. Gutierrez Vega, M. D. Iturbe-Castillo, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez Cerda, and G. H. C. New, "Experimental demonstration of optical Mathieu beams," Opt. Commun. 195, 35-40 (2001). [CrossRef]
  7. Z. Mei and D. Zhao, "Controllable dark-hollow beams and their propagation characteristics," J. Opt. Soc. Am. A 22, 1898-1902 (2005). [CrossRef]
  8. Z. Mei and D. Zhao, "Decentered controllable elliptical dark-hollow beams," Opt. Commun. 259, 415-423 (2006). [CrossRef]
  9. J. C. Gutiérrez Vega, "Formal analysis of the propagation of invariant optical fields in elliptic corrdinates," Ph.D. thesis (National Institute of Astrophysics and Optics, Mexico, 2000), Chaps. 3 and 4.
  10. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, 1964).
  11. J. Durnin, "Exact solutions for nondiffracting beams," J. Opt. Soc. Am. A 4, 651-654 (1987). [CrossRef]
  12. M. W. Maclachlan, Theory and Application of Mathieu Functions (Dover, 1964).
  13. N. Toyama and K. Shogen, "Computation of the value of the even and odd Mathieu functions of order N for a given parameter S and an argument X," IEEE Trans. Antennas Propag. AP-32, 537-539 (1984). [CrossRef]
  14. M. Schneider and J. Marquardt, "Fast computation of modified Mathieu functions applied to elliptical waveguide problems," IEEE Trans. Microwave Theory Tech. 47, 513-516 (1999). [CrossRef]
  15. G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, 1985).

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