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Incomplete Airy beams: finite energy from a sharp spectral cutoff.

Authors
Type
Published Article
Journal
Optics Letters
1539-4794
Publisher
The Optical Society
Publication Date
Volume
38
Issue
10
Pages
1639–1641
Identifiers
DOI: 10.1364/OL.38.001639
PMID: 23938895
Source
Medline
License
Unknown

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.

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