Incomplete Airy beams: finite energy from a sharp spectral cutoff

James D. Ring; Christopher J. Howls; Mark R. Dennis

doi:10.1364/OL.38.001639

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 journal › Article (Academic Journal) › peer-review

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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. (C) 2013 Optical Society of America

Original language	English
Pages (from-to)	1639-1641
Number of pages	3
Journal	Optics Letters
Volume	38
Issue number	10
DOIs	https://doi.org/10.1364/OL.38.001639
Publication status	Published - 9 May 2013

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10.1364/OL.38.001639

OL38 1639
This paper was published in Optics Lettera and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-38-10-1639]. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.
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title = "Incomplete Airy beams: finite energy from a sharp spectral cutoff",

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. (C) 2013 Optical Society of America",

author = "Ring, {James D.} and Howls, {Christopher J.} and Dennis, {Mark R.}",

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T1 - Incomplete Airy beams: finite energy from a sharp spectral cutoff

AU - Ring, James D.

AU - Howls, Christopher J.

AU - Dennis, Mark R.

PY - 2013/5/9

Y1 - 2013/5/9

N2 - 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

AB - 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

U2 - 10.1364/OL.38.001639

DO - 10.1364/OL.38.001639

M3 - Article (Academic Journal)

C2 - 23938895

SN - 0146-9592

VL - 38

SP - 1639

EP - 1641

JO - Optics Letters

JF - Optics Letters

IS - 10

ER -

Incomplete Airy beams: finite energy from a sharp spectral cutoff

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