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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 20 — Oct. 2, 2006
  • pp: 9071–9076

Fourier relationship between angular position and optical orbital angular momentum

Eric Yao, Sonja Franke-Arnold, Johannes Courtial, Stephen Barnett, and Miles Padgett  »View Author Affiliations

Optics Express, Vol. 14, Issue 20, pp. 9071-9076 (2006)

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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.

© 2006 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(230.6120) Optical devices : Spatial light modulators

ToC Category:
Fourier Optics and Optical Signal Processing

Original Manuscript: August 1, 2006
Manuscript Accepted: September 8, 2006
Published: October 2, 2006

Eric Yao, Sonja Franke-Arnold, Johannes Courtial, Stephen Barnett, and Miles Padgett, "Fourier relationship between angular position and optical orbital angular momentum," Opt. Express 14, 9071-9076 (2006)

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