Nonparaxial wave analysis of three-dimensional Airy beams

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
Yan Kaganovsky, Ehud Heyman

Abstract

The three-dimensional Airy beam (AiB) is thoroughly explored from a wave-theory point of view. We utilize the exact spectral integral for the AiB to derive local ray-based solutions that do not suffer from the limitations of the conventional parabolic equation (PE) solution and are valid far beyond the paraxial zone and for longer ranges. The ray topology near the main lobe of the AiB delineates a hyperbolic umbilic catastrophe, consisting of a cusped double-layered caustic. In the far zone this caustic is deformed and the field loses its beam shape. The field in the vicinity of this caustic is described uniformly by a hyperbolic umbilic canonical integral, which is structured explicitly on the local geometry of the caustic. In order to accommodate the finite-energy AiB, we also modify the conventional canonical integral by adding a complex loss parameter. The canonical integral is calculated using a series expansion, and the results are used to identify the validity zone of the conventional PE solution. The analysis is performed within the framework of the nondispersive AiB where the aperture field is scaled with frequency such that the ray skeleton is frequency independent. This scaling enables an extension of the theory to t...Continue Reading

References

Mar 22, 2007·Optics Letters·Georgios A Siviloglou, Demetrios N Christodoulides
Feb 1, 2008·Physical Review Letters·G A SiviloglouD N Christodoulides
Feb 5, 2008·Optics Letters·G A SiviloglouD N Christodoulides
Jul 9, 2008·Optics Express·Peeter Saari
Aug 20, 2008·Optics Express·John BrokyDemetrios N Christodoulides
Apr 11, 2009·Science·Pavel PolynkinDemetrios N Christodoulides
Dec 10, 2007·Optics Express·Miguel A Bandres, Julio C Gutiérrez-Vega
Jul 1, 2010·Optics Express·Y Kaganovsky, E Heyman
Oct 23, 2010·Optics Letters·Yalong Gu, Greg Gbur
Dec 2, 2010·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·Sophie VoJannick P Rolland
Jun 7, 2011·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·Yan Kaganovsky, Ehud Heyman
Jun 28, 2011·Physical Review Letters·Elad GreenfieldOren Raz

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Citations

Aug 15, 2014·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·Yi LiangZhigang Chen
Nov 18, 2014·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·R Jáuregui, P A Quinto-Su
Feb 3, 2016·Applied Optics·Yixian Qian, Liangwei Dong
Oct 6, 2012·Optics Express·Michel Zamboni-RachedC A Dartora
Jul 1, 2014·Optics Express·Miguel A Alonso, Miguel A Bandres
Mar 26, 2014·Optics Express·Miguel A Alonso, Miguel A Bandres
May 4, 2016·Optics Express·Yixian Qian, Site Zhang
Sep 24, 2016·Applied Optics·Zhijun RenYile Shi
Jul 19, 2020·Optics Express·Gabriel LasryYaniv Brick
Mar 2, 2017·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·Yixian QianHongxing Mao
Sep 29, 2017·Optics Letters·Timor Melamed, Amir Shlivinski
Dec 14, 2016·Optics Express·Changming LiuJinsong Liu
Dec 12, 2012·Physical Review Letters·Peng ZhangXiang Zhang

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