Incomplete Airy beams: finite energy from a sharp spectral cutoff

James D. Ring*, Christopher J. Howls, Mark R. Dennis

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

30 Citations (Scopus)
401 Downloads (Pure)


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. (C) 2013 Optical Society of America

Original languageEnglish
Pages (from-to)1639-1641
Number of pages3
JournalOptics Letters
Issue number10
Publication statusPublished - 9 May 2013


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