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Chinese Physics, 2005, Vol. 14(6): 1130-1135    DOI: 10.1088/1009-1963/14/6/013
CLASSICAL AREAS OF PHENOMENOLOGY Prev   Next  

Fractional Fourier transform of flat-topped multi-Gaussian beams based on the Wigner distribution function

Wu Ping (吴平)a, Lü Bai-Da (吕百达)b, Chen Tian-Lu (陈天禄)a
a Deptartment of Applied Physics, Southwest Jiaotong University, Chengdu 610031, China; b Institute of Laser Physics&Chemistry, Sichuan University, Chengdu 610064, China
Abstract  By using the Wigner distribution function (WDF), the fractional Fourier transform (FRFT) of flat-topped multi-Gaussian(FTMG) beams is studied. Analytical expressions for the intensity distribution, beam width, far-field divergence angle, M2 factor and K parameter of FTMG beams are derived. The influence of fractional order on transformation properties of FTMG beams in the FRFT plane is illustrated with numerical examples.
Keywords:  Wigner distribution function      flat-topped multi-Gaussian beam      fraction Fourier transform  
Received:  03 September 2004      Revised:  08 January 2005      Accepted manuscript online: 
PACS:  42.60.Jf (Beam characteristics: profile, intensity, and power; spatial pattern formation)  
  42.30.Kq (Fourier optics)  
  02.50.Ng (Distribution theory and Monte Carlo studies)  
Fund: This work is supported by the Foundation of Sichuan Provincial Applied Basic Research (grant 03JY029-063-1) and the Foundation of Science and Technology Research of Southwest Jiaotong University.

Cite this article: 

Wu Ping (吴平), Lü Bai-Da (吕百达), Chen Tian-Lu (陈天禄) Fractional Fourier transform of flat-topped multi-Gaussian beams based on the Wigner distribution function 2005 Chinese Physics 14 1130

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