Abstract

Based on the principle that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, propagation characteristics of a Gaussian beam or a plane wave passing through apertured fractional Fourier transforming systems are analyzed and corresponding analytical formulae are obtained. Analytical formulae in different fractional orders are numerically simulated and compared with the diffraction integral formulae, the applicable range and exactness of analytical formulae are confirmed. It is shown that the calculating speed of using the obtained approximate analytical formulae, is several hundred times faster than that of using diffraction integral directly. Meanwhile, by using analytical formulae the effect of different aperture sizes on Gaussian beam propagation characteristics is numerically simulated, it is shown that the diffraction effect can be neglected when the aperture size is 5 times larger than the beam waist size.

© 2005 Chinese Optics Letters

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D. Zhao, H. Mao, and H. Liu, J. Opt. A: Pure and Appl. Opt. 6, 77 (2004).

2002 (2)

Y. S. Zeng, Y. X. Zhang, F. H. Gao, F. Gao, and Y. K. Guo, Acta Opt. Sin. (in Chinese) 22, 947 (2002).

Y. S. Zeng, Y. X. Zhang, J. L. Du, and Y. K. Guo, Chin. J. Lasers (in Chinese) 29, 743 (2002).

1999 (1)

Y. K. Guo, Q. Z. Huang, and J. L. Du, Acta Opt. Sin. (in Chinese) 19, 821 (1999).

1998 (2)

1997 (1)

J. W. Hua, L. R. Liu, and G. Q. Li, Acta Opt. Sin. (in Chinese) 17, 1040 (1997).

1995 (1)

S. T. Liu, J. D. Xu, R. Zhang, and C. Li, Acta Opt. Sin. (in Chinese) 15, 1404 (1995).

1994 (2)

1993 (2)

1988 (1)

J. J. Wen and M. A. Breazeale, J. Acoust. Soc. Am. 83, 1752 (1988).

1970 (1)

Almeida, L. B.

L. B. Almeida, IEEE Trans. Signal Proc. 42, 3084 (1994).

Barshan, B.

Breazeale, M. A.

J. J. Wen and M. A. Breazeale, J. Acoust. Soc. Am. 83, 1752 (1988).

Chen, N.

Collins, S. A.

Cong, W.

Dong, B.

Du, J. L.

Y. S. Zeng, Y. X. Zhang, J. L. Du, and Y. K. Guo, Chin. J. Lasers (in Chinese) 29, 743 (2002).

Y. K. Guo, Q. Z. Huang, and J. L. Du, Acta Opt. Sin. (in Chinese) 19, 821 (1999).

Gao, F.

Y. S. Zeng, Y. X. Zhang, F. H. Gao, F. Gao, and Y. K. Guo, Acta Opt. Sin. (in Chinese) 22, 947 (2002).

Gao, F. H.

Y. S. Zeng, Y. X. Zhang, F. H. Gao, F. Gao, and Y. K. Guo, Acta Opt. Sin. (in Chinese) 22, 947 (2002).

Gu, B.

Guo, Y. K.

Y. S. Zeng, Y. X. Zhang, J. L. Du, and Y. K. Guo, Chin. J. Lasers (in Chinese) 29, 743 (2002).

Y. S. Zeng, Y. X. Zhang, F. H. Gao, F. Gao, and Y. K. Guo, Acta Opt. Sin. (in Chinese) 22, 947 (2002).

Y. K. Guo, Q. Z. Huang, and J. L. Du, Acta Opt. Sin. (in Chinese) 19, 821 (1999).

Hua, J. W.

J. W. Hua, L. R. Liu, and G. Q. Li, Acta Opt. Sin. (in Chinese) 17, 1040 (1997).

Huang, Q. Z.

Y. K. Guo, Q. Z. Huang, and J. L. Du, Acta Opt. Sin. (in Chinese) 19, 821 (1999).

Li, C.

S. T. Liu, J. D. Xu, R. Zhang, and C. Li, Acta Opt. Sin. (in Chinese) 15, 1404 (1995).

Li, G. Q.

J. W. Hua, L. R. Liu, and G. Q. Li, Acta Opt. Sin. (in Chinese) 17, 1040 (1997).

Liu, H.

D. Zhao, H. Mao, and H. Liu, J. Opt. A: Pure and Appl. Opt. 6, 77 (2004).

Liu, L. R.

J. W. Hua, L. R. Liu, and G. Q. Li, Acta Opt. Sin. (in Chinese) 17, 1040 (1997).

Liu, S. T.

S. T. Liu, J. D. Xu, R. Zhang, and C. Li, Acta Opt. Sin. (in Chinese) 15, 1404 (1995).

Lohmann, A. W.

Mao, H.

D. Zhao, H. Mao, and H. Liu, J. Opt. A: Pure and Appl. Opt. 6, 77 (2004).

Mendlovic, D.

Onural, L.

Ozaktas, H. M.

Wen, J. J.

J. J. Wen and M. A. Breazeale, J. Acoust. Soc. Am. 83, 1752 (1988).

Xu, J. D.

S. T. Liu, J. D. Xu, R. Zhang, and C. Li, Acta Opt. Sin. (in Chinese) 15, 1404 (1995).

Yang, G.

Zeng, Y. S.

Y. S. Zeng, Y. X. Zhang, J. L. Du, and Y. K. Guo, Chin. J. Lasers (in Chinese) 29, 743 (2002).

Y. S. Zeng, Y. X. Zhang, F. H. Gao, F. Gao, and Y. K. Guo, Acta Opt. Sin. (in Chinese) 22, 947 (2002).

Zhang, R.

S. T. Liu, J. D. Xu, R. Zhang, and C. Li, Acta Opt. Sin. (in Chinese) 15, 1404 (1995).

Zhang, Y.

Zhang, Y. X.

Y. S. Zeng, Y. X. Zhang, J. L. Du, and Y. K. Guo, Chin. J. Lasers (in Chinese) 29, 743 (2002).

Y. S. Zeng, Y. X. Zhang, F. H. Gao, F. Gao, and Y. K. Guo, Acta Opt. Sin. (in Chinese) 22, 947 (2002).

Zhao, D.

D. Zhao, H. Mao, and H. Liu, J. Opt. A: Pure and Appl. Opt. 6, 77 (2004).

Acta Opt. Sin. (in Chinese) (4)

S. T. Liu, J. D. Xu, R. Zhang, and C. Li, Acta Opt. Sin. (in Chinese) 15, 1404 (1995).

J. W. Hua, L. R. Liu, and G. Q. Li, Acta Opt. Sin. (in Chinese) 17, 1040 (1997).

Y. S. Zeng, Y. X. Zhang, F. H. Gao, F. Gao, and Y. K. Guo, Acta Opt. Sin. (in Chinese) 22, 947 (2002).

Y. K. Guo, Q. Z. Huang, and J. L. Du, Acta Opt. Sin. (in Chinese) 19, 821 (1999).

Appl. Opt. (1)

Chin. J. Lasers (in Chinese) (1)

Y. S. Zeng, Y. X. Zhang, J. L. Du, and Y. K. Guo, Chin. J. Lasers (in Chinese) 29, 743 (2002).

IEEE Trans. Signal Proc. (1)

L. B. Almeida, IEEE Trans. Signal Proc. 42, 3084 (1994).

J. Acoust. Soc. Am. (1)

J. J. Wen and M. A. Breazeale, J. Acoust. Soc. Am. 83, 1752 (1988).

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

D. Zhao, H. Mao, and H. Liu, J. Opt. A: Pure and Appl. Opt. 6, 77 (2004).

J. Opt. Soc. Am. (1)

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

Other (3)

A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, in Progress in Optics, E. Wolf ed. (Elsevier, Amsterdam, 1998).

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transforming with Applications in Optics and Signal Processing (Wiley, New York, 2000).

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

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