Abstract

The fractional Fourier transform (FRFT) of the flat-topped multi-Gaussian beam (FMGB) is investigated based on the three kinds of FRFT optical systems: Lohmann I, Lohmann II, and quadratic graded-index systems. The analytical expressions for the FRFT of the FMGB are derived based on the propagation of the FMGB through the three systems. By introducing a hard-edge aperture function, the analytical expressions for the FRFT of the FMGB carried out by the apertured FRFT optical systems are presented. The FRFT characteristics of the FMGB for the three kinds of FRFT optical systems with and without apertures are discussed in detail. Results show that the three types of FRFT optical systems have the same function when the apertures are ignored but that significantly different characteristics are exhibited when the apertures appear.

© 2010 Optical Society of America

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2009 (6)

2008 (1)

2007 (4)

2005 (1)

2002 (1)

2001 (1)

1995 (1)

1994 (4)

1993 (3)

1988 (2)

S. D. Silvestri, P. Laporta, V. Magni, O. Svelto, and B. Majocchi, “Unstable laser resonators with super-Gaussian mirrors,” Opt. Lett. 13, 201-203 (1988).
[CrossRef]

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

1986 (1)

1980 (1)

V. Namias, “The fractional order Fourier transform and its applications to quantum mechanics,” J. Inst. Math. Appl. 25, 241-265 (1980).
[CrossRef]

1970 (1)

Alieva, T.

Bandres, M. A.

Breazeale, M. A.

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

Cai, Y. J.

Calvo, M. L.

Chen, J. N.

Collins, S. A.

Cui, Y. F.

Gao, Q.

Gao, Y. Q

Gao, Y. Q.

Gori, F.

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

Gutierrez-Vaga, J. C.

Laporta, P.

Li, Y.

Liao, T. H.

Lin, Z. Q.

Liu, D. Z.

Liu, S. T.

Liu, Z. J.

Lohmann, A. W.

Magni, V.

Majocchi, B.

Mao, H.

McMullin, J. N.

Mendlovic, D.

Namias, V.

V. Namias, “The fractional order Fourier transform and its applications to quantum mechanics,” J. Inst. Math. Appl. 25, 241-265 (1980).
[CrossRef]

Ozaktas, H. M.

Pellat-Finet, P.

Rodrigo, J. A.

Silvestri, S. D.

Svelto, O.

Tang, B.

B.Tang and M. H. Xu, “Fractional Fourier transform for beams generated by Gaussian mirror resonator,” J. Mod. Opt. 56, 1276-1282 (2009).
[CrossRef]

Tovar, A. A.

Wang, F.

Wen, J. J.

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

Xu, M. H.

B.Tang and M. H. Xu, “Fractional Fourier transform for beams generated by Gaussian mirror resonator,” J. Mod. Opt. 56, 1276-1282 (2009).
[CrossRef]

Zhao, D.

Zhou, G. Q.

G. Q. Zhou, “Fractional Fourier transform of a higher-order cosh-Gaussian beam,” J. Mod. Opt. 2009. 56, 886-892 (2009).
[CrossRef]

G. Q. Zhou, “Fractional Fourier transform of Lorentz-Gauss beams,” J. Opt. Soc. Am. A 26, 350-355 (2009).
[CrossRef]

Zhu, B. Q.

Appl. Opt. (2)

J. Acoust. Soc. Am. (1)

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

J. Inst. Math. Appl. (1)

V. Namias, “The fractional order Fourier transform and its applications to quantum mechanics,” J. Inst. Math. Appl. 25, 241-265 (1980).
[CrossRef]

J. Mod. Opt. (2)

G. Q. Zhou, “Fractional Fourier transform of a higher-order cosh-Gaussian beam,” J. Mod. Opt. 2009. 56, 886-892 (2009).
[CrossRef]

B.Tang and M. H. Xu, “Fractional Fourier transform for beams generated by Gaussian mirror resonator,” J. Mod. Opt. 56, 1276-1282 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (10)

A. A. Tovar, “Propagation of flat-topped multi-Gaussian laser beams,” J. Opt. Soc. Am. A 18, 1897-1904 (2001).
[CrossRef]

H. M. Ozaktas and D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743-751 (1995).
[CrossRef]

D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am. A 10, 1875-1881 (1993).
[CrossRef]

A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181-2186 (1993).
[CrossRef]

H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II,” J. Opt. Soc. Am. A 10, 2522-2531 (1993).
[CrossRef]

Y. Q. Gao, B. Q. Zhu, D. Z. Liu, and Z. Q. Lin, “Propagation of flat-topped multi-Gaussian beams through an apertured ABCD optical system,” J. Opt. Soc. Am. A 26, 2139-2146 (2009).
[CrossRef]

H. Mao and D. Zhao, “Different models for a hard-aperture function and corresponding approximate analytical propagation equations of a Gaussian beam through an apertured optical system,” J. Opt. Soc. Am. A 22, 647-653 (2005).
[CrossRef]

J. N. Chen, “Propagation and transformation of flat-topped multi-Gaussian beams in a general nonsymmetrical apertured double-lens system,” J. Opt. Soc. Am. A 24, 84-92 (2007).
[CrossRef]

F. Wang and Y. J. Cai, “Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics,” J. Opt. Soc. Am. A 24, 1937-1944 (2007).
[CrossRef]

G. Q. Zhou, “Fractional Fourier transform of Lorentz-Gauss beams,” J. Opt. Soc. Am. A 26, 350-355 (2009).
[CrossRef]

Opt. Commun. (1)

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

Opt. Express (3)

Opt. Lett. (6)

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