Fourier relationship between angular position and optical orbital angular momentum

Eric Yao, Sonja Franke-Arnold, Johannes Courtial, Stephen M. Barnett, Miles Padgett

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We demonstrate the Fourier relationship between angular position and angular momentum for a light mode. In particular we measure the distribution of orbital angular momentum states of light that has passed through an aperture and verify that the orbital angular momentum distribution is given by the complex Fourier-transform of the aperture function. We use spatial light modulators, configured as diffractive optical components, to define the initial orbital angular momentum state of the beam, set the defining aperture, and measure the angular momentum spread of the resulting beam. These measurements clearly confirm the Fourier relationship between angular momentum and angular position, even at light intensities corresponding to the single photon level.
Original languageEnglish
Pages (from-to)9071-9076
Number of pages5
JournalOptics Express
Issue number20
Publication statusPublished - 2 Oct 2006


  • physics
  • optics
  • fourier relationship
  • light
  • photons
  • angular momentum
  • beam
  • aperture

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