Incomplete Airy beams: finite-energy from a sharp spectral cutoff
Incomplete Airy beams: finite-energy from a sharp spectral cutoff
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.
1639-1641
Ring, James D.
a2566643-e341-4966-8c8d-27e61b06e354
Howls, Christopher J.
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Dennis, Mark R.
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15 May 2013
Ring, James D.
a2566643-e341-4966-8c8d-27e61b06e354
Howls, Christopher J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Dennis, Mark R.
8b00c8a0-30e2-4690-bfde-02916f80de2f
Ring, James D., Howls, Christopher J. and Dennis, Mark R.
(2013)
Incomplete Airy beams: finite-energy from a sharp spectral cutoff.
Optics Letters, 38 (10), .
(doi:10.1364/OL.38.001639).
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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Published date: 15 May 2013
Organisations:
Applied Mathematics
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Local EPrints ID: 351437
URI: http://eprints.soton.ac.uk/id/eprint/351437
ISSN: 0146-9592
PURE UUID: 59e7a2a3-08fd-4cc1-9e82-ddf878d04a85
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Date deposited: 22 Apr 2013 11:37
Last modified: 15 Mar 2024 03:05
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Author:
James D. Ring
Author:
Mark R. Dennis
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