Abstract

Based on the vectorial Rayleigh–Sommerfeld diffraction integrals, an analytical propagation equation of vectorial, nonparaxial, elliptical Gaussian beams through a rectangular aperture is derived. Unlike in previous work, the aperture effect and nonrotational symmetry of the beam and aperture are considered in our theoretical model. The results of the far-field and paraxial approximation for the apertured case are treated as special cases of our general expression. It is found that two f parameters fx, fy and two truncation parameters δxy in the x and y directions, respectively, have to be introduced that affect the beam nonparaxial evolution behavior in both the near field and the far field.

© 2004 Optical Society of America

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2004 (1)

2003 (1)

2001 (1)

1999 (2)

H. Laabs, A. T. Friberg, “Nonparaxial eigenmodes of stable resonators,” IEEE J. Quantum Electron. 35, 198–207 (1999).
[CrossRef]

X. Zeng, C. Liang, Y. An, “Far-field propagation of an off-axis Gaussian wave,” Appl. Opt. 38, 6253–6256 (1999).
[CrossRef]

1998 (1)

H. Laabs, “Propagation of Hermite–Gaussian beams beyond the paraxial approximation,” Opt. Commun. 147, 1–4 (1998).
[CrossRef]

1992 (1)

1990 (1)

1985 (1)

1979 (1)

1975 (1)

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

1972 (1)

1966 (1)

Agrawal, G. P.

An, Y.

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999).

Carter, W. H.

Ciattoni, A.

Crosignani, B.

Duan, K.

Friberg, A. T.

H. Laabs, A. T. Friberg, “Nonparaxial eigenmodes of stable resonators,” IEEE J. Quantum Electron. 35, 198–207 (1999).
[CrossRef]

Fukumitsu, O.

Laabs, H.

H. Laabs, A. T. Friberg, “Nonparaxial eigenmodes of stable resonators,” IEEE J. Quantum Electron. 35, 198–207 (1999).
[CrossRef]

H. Laabs, “Propagation of Hermite–Gaussian beams beyond the paraxial approximation,” Opt. Commun. 147, 1–4 (1998).
[CrossRef]

Lax, M.

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Liang, C.

Louisell, W. H.

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Lu, B.

Luneberg, R. K.

R. K. Luneberg, Mathematical Theory of Optics (University of California, Berkeley, Calif., 1964).

Marchand, E. W.

McKnight, W. B.

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Nemoto, S.

Pattanayak, D. N.

Porto, P. D.

Seshadri, S. R. S.

Siegman, A. E.

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

Takenaka, T.

Wolf, E.

Wünsche, A.

Yokota, M.

Zeng, X.

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

H. Laabs, A. T. Friberg, “Nonparaxial eigenmodes of stable resonators,” IEEE J. Quantum Electron. 35, 198–207 (1999).
[CrossRef]

J. Opt. Soc. Am. (3)

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

Opt. Commun. (1)

H. Laabs, “Propagation of Hermite–Gaussian beams beyond the paraxial approximation,” Opt. Commun. 147, 1–4 (1998).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Other (4)

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

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999).

R. K. Luneberg, Mathematical Theory of Optics (University of California, Berkeley, Calif., 1964).

K. Duan, B. B. Lu, “Nonparaxial analysis of far-field properties of Gaussian beams diffracted by an aperture,” Opt. Express11, 1474–1480 (2003); www.opticsexpress.org .

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