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      Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform

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      Author(s)
      Mendlovic, D.
      Özaktaş, Haldun M.
      Lohmann, A. W.
      Date
      1994
      Source Title
      Applied Optics
      Print ISSN
      0003-6935
      Publisher
      Optical Society of America
      Volume
      33
      Issue
      26
      Pages
      6188 - 6193
      Language
      English
      Type
      Article
      Item Usage Stats
      219
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      241
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      Abstract
      Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a wave field rotates as the wave field propagates through a quadratic graded-index medium. The relation with ray-optics phase space is discussed.
      Keywords
      Fourier optics
      Optical information processing
      Fractional fourier transforms
      Wignerdistribution functions
      Graded-index media
      Spatial filtering
      Permalink
      http://hdl.handle.net/11693/13641
      Published Version (Please cite this version)
      http://dx.doi.org/10.1364/AO.33.006188
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      • Department of Electrical and Electronics Engineering 4011
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