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Optics Letters

Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Editor: Alan E. Willner
  • Vol. 38, Iss. 10 — May. 15, 2013
  • pp: 1639–1641

Incomplete Airy beams: finite energy from a sharp spectral cutoff

James D. Ring, Christopher J. Howls, and Mark R. Dennis  »View Author Affiliations


Optics Letters, Vol. 38, Issue 10, pp. 1639-1641 (2013)
http://dx.doi.org/10.1364/OL.38.001639


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Abstract

We present a mathematical analysis of the finite-energy Airy beam with a sharply truncated spectrum, which can be generated by a uniformly illuminated, finite-sized spatial light modulator, or windowed cubic phase mask. The resulting “incomplete Airy beam” is tractable mathematically, and differs from an infinite-energy Airy beam by an additional oscillating modulation and the decay of its fringes. Its propagation can be described explicitly using an incomplete Airy function, from which we derive simple expressions for the beam’s total power and mean position. Asymptotic analysis reveals a simple connection between the cutoff and the region of the beam with Airy-like behavior.

© 2013 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(090.0090) Holography : Holography

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: February 7, 2013
Revised Manuscript: April 12, 2013
Manuscript Accepted: April 12, 2013
Published: May 9, 2013

Citation
James D. Ring, Christopher J. Howls, and Mark R. Dennis, "Incomplete Airy beams: finite energy from a sharp spectral cutoff," Opt. Lett. 38, 1639-1641 (2013)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-38-10-1639

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