Graded-index fibers, wigner-distribution functions, and the fractional fourier transform

David Mendlovic, Haldun M. Ozaktas, Adolf W. Lohmann

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)6188-6193
Number of pages6
JournalApplied Optics
Issue number26
StatePublished - 10 Sep 1994


  • Fourier optics
  • Fractional fourier transforms
  • Graded-index media
  • Optical information processing
  • Spatial filtering
  • Wignerdistribution functions


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