Abstract

Beam profiles that consist of a sum of complex-Gaussian functions, a sum of polynomial-Gaussian functions and a sum of multi-Gaussian functions offset by some fixed amount are proposed as three types of model for a hard-aperture function. By expanding an aperture function into these models, approximate analytical propagation equations for a Gaussian beam through an apertured ABCD optical system are obtained. Comparison among these models themselves and among propagation characteristics of a Gaussian beam through these models are made. It is shown that the first and third types of model for a hard-aperture function are more suitable than the second type, in terms of calculation efficiency and simulation results, for application to such diffraction problems. Moreover, there are some differences in the applicability of the first and the third models.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2004 (2)

D. Zhao, H. Mao, M. Shen, H. Liu, F. Jing, Q. Zhu, X. Wei, “Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems,” J. Opt. A, Pure Appl. Opt. 6, 148–154 (2004).
[CrossRef]

Z. Mei, D. Zhao, “Propagation of Laguerre–Gaussian and elegant Laguerre–Gaussian beams in apertured fractional Hankel transforming systems,” J. Opt. Soc. Am. A 21, 2375–2381 (2004).
[CrossRef]

2003 (1)

D. Zhao, H. Mao, W. Zhang, S. Wang, “Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system,” Opt. Commun. 224, 5–12 (2003).
[CrossRef]

2002 (1)

2001 (1)

1995 (1)

C. Palma, V. Bagini, “Expansions of general beams in gaussian beams,” Opt. Commun. 116, 1–7 (1995).
[CrossRef]

1994 (1)

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

1992 (1)

A. Parent, M. Morin, P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quantum Electron. 24, S1071–S1079 (1992).
[CrossRef]

1988 (1)

J. J. Wen, M. A. Breazeale, “A diffraction beam field expressed as a superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).

1970 (1)

Bagini, V.

C. Palma, V. Bagini, “Expansions of general beams in gaussian beams,” Opt. Commun. 116, 1–7 (1995).
[CrossRef]

Breazeale, M. A.

J. J. Wen, M. A. Breazeale, “A diffraction beam field expressed as a superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).

Collins, S. A.

Erdelyi, A.

A. Erdelyi, Tables of Integral Transforms (McGraw-Hill, New York, 1954).

Gori, F.

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

Jing, F.

D. Zhao, H. Mao, M. Shen, H. Liu, F. Jing, Q. Zhu, X. Wei, “Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems,” J. Opt. A, Pure Appl. Opt. 6, 148–154 (2004).
[CrossRef]

Lavigne, P.

A. Parent, M. Morin, P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quantum Electron. 24, S1071–S1079 (1992).
[CrossRef]

Li, Y.

Liu, H.

D. Zhao, H. Mao, M. Shen, H. Liu, F. Jing, Q. Zhu, X. Wei, “Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems,” J. Opt. A, Pure Appl. Opt. 6, 148–154 (2004).
[CrossRef]

Mao, H.

D. Zhao, H. Mao, M. Shen, H. Liu, F. Jing, Q. Zhu, X. Wei, “Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems,” J. Opt. A, Pure Appl. Opt. 6, 148–154 (2004).
[CrossRef]

D. Zhao, H. Mao, W. Zhang, S. Wang, “Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system,” Opt. Commun. 224, 5–12 (2003).
[CrossRef]

Mei, Z.

Morin, M.

A. Parent, M. Morin, P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quantum Electron. 24, S1071–S1079 (1992).
[CrossRef]

Palma, C.

C. Palma, V. Bagini, “Expansions of general beams in gaussian beams,” Opt. Commun. 116, 1–7 (1995).
[CrossRef]

Parent, A.

A. Parent, M. Morin, P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quantum Electron. 24, S1071–S1079 (1992).
[CrossRef]

Shen, M.

D. Zhao, H. Mao, M. Shen, H. Liu, F. Jing, Q. Zhu, X. Wei, “Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems,” J. Opt. A, Pure Appl. Opt. 6, 148–154 (2004).
[CrossRef]

Tovar, A. A.

Wang, S.

D. Zhao, H. Mao, W. Zhang, S. Wang, “Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system,” Opt. Commun. 224, 5–12 (2003).
[CrossRef]

S. Wang, D. Zhao, Matrix Optics (CHEP-Springer, Beijing, 2000).

Wei, X.

D. Zhao, H. Mao, M. Shen, H. Liu, F. Jing, Q. Zhu, X. Wei, “Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems,” J. Opt. A, Pure Appl. Opt. 6, 148–154 (2004).
[CrossRef]

Wen, J. J.

J. J. Wen, M. A. Breazeale, “A diffraction beam field expressed as a superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).

Zhang, W.

D. Zhao, H. Mao, W. Zhang, S. Wang, “Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system,” Opt. Commun. 224, 5–12 (2003).
[CrossRef]

Zhao, D.

D. Zhao, H. Mao, M. Shen, H. Liu, F. Jing, Q. Zhu, X. Wei, “Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems,” J. Opt. A, Pure Appl. Opt. 6, 148–154 (2004).
[CrossRef]

Z. Mei, D. Zhao, “Propagation of Laguerre–Gaussian and elegant Laguerre–Gaussian beams in apertured fractional Hankel transforming systems,” J. Opt. Soc. Am. A 21, 2375–2381 (2004).
[CrossRef]

D. Zhao, H. Mao, W. Zhang, S. Wang, “Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system,” Opt. Commun. 224, 5–12 (2003).
[CrossRef]

S. Wang, D. Zhao, Matrix Optics (CHEP-Springer, Beijing, 2000).

Zhu, Q.

D. Zhao, H. Mao, M. Shen, H. Liu, F. Jing, Q. Zhu, X. Wei, “Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems,” J. Opt. A, Pure Appl. Opt. 6, 148–154 (2004).
[CrossRef]

J. Acoust. Soc. Am. (1)

J. J. Wen, M. A. Breazeale, “A diffraction beam field expressed as a superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).

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

D. Zhao, H. Mao, M. Shen, H. Liu, F. Jing, Q. Zhu, X. Wei, “Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems,” J. Opt. A, Pure Appl. Opt. 6, 148–154 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (3)

C. Palma, V. Bagini, “Expansions of general beams in gaussian beams,” Opt. Commun. 116, 1–7 (1995).
[CrossRef]

D. Zhao, H. Mao, W. Zhang, S. Wang, “Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system,” Opt. Commun. 224, 5–12 (2003).
[CrossRef]

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

A. Parent, M. Morin, P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quantum Electron. 24, S1071–S1079 (1992).
[CrossRef]

Other (2)

S. Wang, D. Zhao, Matrix Optics (CHEP-Springer, Beijing, 2000).

A. Erdelyi, Tables of Integral Transforms (McGraw-Hill, New York, 1954).

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