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Chin. Phys. B, 2009, Vol. 18(7): 2779-2784    DOI: 10.1088/1674-1056/18/7/026
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Fractional Fourier transform of Lorentz beams

Zhou Guo-Quan(周国泉)
School of Sciences, Zhejiang Forestry University, Lin'an 311300, China
Abstract  This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz beam passing through a FRFT system has been derived. By using the derived formula, the properties of a Lorentz beam in the FRFT plane are illustrated numerically.
Keywords:  Lorentz beam      fractional Fourier transform      propagation properties  
Received:  05 November 2008      Revised:  02 December 2008      Accepted manuscript online: 
PACS:  42.60.Jf (Beam characteristics: profile, intensity, and power; spatial pattern formation)  
  02.30.Nw (Fourier analysis)  
  02.30.Uu (Integral transforms)  
Fund: Project supported by the Scientific Research Fund of Zhejiang Provincial Education Department of China.

Cite this article: 

Zhou Guo-Quan(周国泉) Fractional Fourier transform of Lorentz beams 2009 Chin. Phys. B 18 2779

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