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Optics Letters

Optics Letters


  • Vol. 25, Iss. 20 — Oct. 15, 2000
  • pp: 1493–1495

Alternative formulation for invariant optical fields: Mathieu beams

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda  »View Author Affiliations

Optics Letters, Vol. 25, Issue 20, pp. 1493-1495 (2000)

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Based on the separability of the Helmholtz equation into elliptical cylindrical coordinates, we present another class of invariant optical fields that may have a highly localized distribution along one of the transverse directions and a sharply peaked quasi-periodic structure along the other. These fields are described by the radial and angular Mathieu functions. We identify the corresponding function in the McCutchen sphere that produces this kind of beam and propose an experimental setup for the realization of an invariant optical field.

© 2000 Optical Society of America

OCIS Codes
(110.6760) Imaging systems : Talbot and self-imaging effects
(140.3300) Lasers and laser optics : Laser beam shaping
(200.4650) Optics in computing : Optical interconnects
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, "Alternative formulation for invariant optical fields: Mathieu beams," Opt. Lett. 25, 1493-1495 (2000)

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  1. J. E. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
  2. E. G. Kalnins and W. Miller, Jr., J. Math. Phys. 17, 331 (1976).
  3. C. W. McCutchen, J. Opt. Soc. Am. 54, 240 (1964).
  4. G. Indebetouw, J. Opt. Soc. Am. A 6, 150 (1989).
  5. Y. Y. Ananev, Opt. Spectrosc. (USSR) 64, 722 (1988).
  6. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  7. A. Vasara, J. Turunen, and A. T. Friberg, J. Opt. Soc. Am. A 6, 1748 (1989).
  8. R. Piestun and J. Shamir, J. Opt. Soc. Am. A 15, 3039 (1998).
  9. Z. Bouchal and J. Wagner, Opt. Commun. 176, 299 (2000).
  10. J. Turunen, A. Vasara, and A. T. Friberg, J. Opt. Soc. Am. A 8, 282 (1991).
  11. N. W. McLachlan, Theory and Applications of Mathieu Functions (Oxford University, London, 1951).
  12. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 5th ed. (Academic, London, 1994).
  13. J. C. Gutiérrez-Vega, “Formal analysis of the propagation of invariant optical fields with elliptical symmetries,” Ph.D. dissertation (Instituto Nacional de Astrofísica, Optica y Electroníca, Puebla, Mexico, 2000); jgutierr@campus.mty.itesm.mx.
  14. M. D. Feit and J. A. Fleck, Jr., J. Opt. Soc. Am. B 5, 633 (1988).

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