Abstract

It is shown that three-dimensional nonparaxial beams are described by the oblate spheroidal exact solutions of the Helmholtz equation. For what is believed to be the first time, their beam behavior is investigated and their corresponding parameters are defined. Using the fact that the beam width of the family of paraxial Gaussian beams is described by a hyperbola, we formally establish the connection between the physical parameters of nonparaxial spheroidal beam solutions and those of paraxial beams. These results are also helpful for investigating exact vector nonparaxial beams.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  17. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Chap. VII.

2002 (1)

S. R. Seshadri, J. Opt. Soc. Am. 19, 2134 (2002) and references therein.
[CrossRef]

2001 (2)

2000 (2)

Z. Ulanowski and I. K. Ludlow, Opt. Lett. 25, 1792 (2000).
[CrossRef]

A. Ciattoni, B. Crosignani, and P. Di Porto, Opt. Commun. 177, 9 (2000).
[CrossRef]

1999 (1)

S. Chavez-Cerda, J. Mod. Opt. 46, 923 (1999).

1998 (2)

Q. Cao and X. Deng, J. Opt. Soc. Am. A 15, 1144 (1998).
[CrossRef]

C. J. R. Sheppard and S. Saghafi, Phys. Rev. A 57, 2971 (1998).
[CrossRef]

1990 (1)

1988 (1)

1977 (1)

1975 (1)

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

1971 (1)

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

Barrett, H. H.

Cao, Q.

Chavez-Cerda, S.

S. Chavez-Cerda, J. Mod. Opt. 46, 923 (1999).

Ciattoni, A.

A. Ciattoni, B. Crosignani, and P. Di Porto, Opt. Commun. 177, 9 (2000).
[CrossRef]

Crosignani, B.

A. Ciattoni, B. Crosignani, and P. Di Porto, Opt. Commun. 177, 9 (2000).
[CrossRef]

Deng, X.

Deschamps, G. A.

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

Di Porto, P.

A. Ciattoni, B. Crosignani, and P. Di Porto, Opt. Commun. 177, 9 (2000).
[CrossRef]

Felsen, L. B.

Flammer, C.

C. Flammer, Spheroidal Wave Functions (Stanford U. Press, Stanford, Calif., 1957).

Jin, J.

S. Zhang and J. Jin, Computation of Special Functions (Wiley, New York, 1996), Chap. 15.

Kraus, H. G.

Landesman, B. T.

Lax, M.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Lekner, J.

J. Lekner, J. Opt. A Pure Appl. Opt. 3, 407 (2001).
[CrossRef]

Louisell, W. H.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Ludlow, I. K.

McKnight, W. B.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Saari, P.

Saghafi, S.

C. J. R. Sheppard and S. Saghafi, Phys. Rev. A 57, 2971 (1998).
[CrossRef]

Seshadri, S. R.

S. R. Seshadri, J. Opt. Soc. Am. 19, 2134 (2002) and references therein.
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard and S. Saghafi, Phys. Rev. A 57, 2971 (1998).
[CrossRef]

Shin, S. Y.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Stratton, J. A.

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

Ulanowski, Z.

Zhang, S.

S. Zhang and J. Jin, Computation of Special Functions (Wiley, New York, 1996), Chap. 15.

Electron. Lett. (1)

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

J. Mod. Opt. (1)

S. Chavez-Cerda, J. Mod. Opt. 46, 923 (1999).

J. Opt. A Pure Appl. Opt. (1)

J. Lekner, J. Opt. A Pure Appl. Opt. 3, 407 (2001).
[CrossRef]

J. Opt. Soc. Am. (2)

S. R. Seshadri, J. Opt. Soc. Am. 19, 2134 (2002) and references therein.
[CrossRef]

S. Y. Shin and L. B. Felsen, J. Opt. Soc. Am. 67, 699 (1977).

J. Opt. Soc. Am. A (3)

Opt. Commun. (1)

A. Ciattoni, B. Crosignani, and P. Di Porto, Opt. Commun. 177, 9 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (2)

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

C. J. R. Sheppard and S. Saghafi, Phys. Rev. A 57, 2971 (1998).
[CrossRef]

Other (4)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

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

C. Flammer, Spheroidal Wave Functions (Stanford U. Press, Stanford, Calif., 1957).

S. Zhang and J. Jin, Computation of Special Functions (Wiley, New York, 1996), Chap. 15.

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