Abstract

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

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    [CrossRef]

2000 (1)

Z. Bouchal and J. Wagner, Opt. Commun. 176, 299 (2000).
[CrossRef]

1998 (1)

1991 (1)

1989 (2)

1988 (2)

Y. Y. Ananev, Opt. Spectrosc. (USSR) 64, 722 (1988).

M. D. Feit and J. A. Fleck, J. Opt. Soc. Am. B 5, 633 (1988).
[CrossRef]

1987 (1)

J. E. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

1976 (1)

E. G. Kalnins and W. Miller, J. Math. Phys. 17, 331 (1976).
[CrossRef]

1964 (1)

Ananev, Y. Y.

Y. Y. Ananev, Opt. Spectrosc. (USSR) 64, 722 (1988).

Bouchal, Z.

Z. Bouchal and J. Wagner, Opt. Commun. 176, 299 (2000).
[CrossRef]

Durnin, J. E.

J. E. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. E. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Feit, M. D.

Fleck, J. A.

Friberg, A. T.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 5th ed. (Academic, London, 1994).

Gutiérrez-Vega, J. C.

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.

Indebetouw, G.

Kalnins, E. G.

E. G. Kalnins and W. Miller, J. Math. Phys. 17, 331 (1976).
[CrossRef]

McCutchen, C. W.

McLachlan, N. W.

N. W. McLachlan, Theory and Applications of Mathieu Functions (Oxford University, London, 1951).

Miceli, J. J.

J. E. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Miller, W.

E. G. Kalnins and W. Miller, J. Math. Phys. 17, 331 (1976).
[CrossRef]

Piestun, R.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 5th ed. (Academic, London, 1994).

Shamir, J.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Turunen, J.

Vasara, A.

Wagner, J.

Z. Bouchal and J. Wagner, Opt. Commun. 176, 299 (2000).
[CrossRef]

J. Math. Phys. (1)

E. G. Kalnins and W. Miller, J. Math. Phys. 17, 331 (1976).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

Z. Bouchal and J. Wagner, Opt. Commun. 176, 299 (2000).
[CrossRef]

Opt. Spectrosc. (USSR) (1)

Y. Y. Ananev, Opt. Spectrosc. (USSR) 64, 722 (1988).

Phys. Rev. Lett. (1)

J. E. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Other (4)

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

N. W. McLachlan, Theory and Applications of Mathieu Functions (Oxford University, London, 1951).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 5th ed. (Academic, London, 1994).

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.

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