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Diffraction-free beams in fractional Schrödinger equation

We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrödinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D...

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Detalles Bibliográficos
Autores principales: Zhang, Yiqi, Zhong, Hua, Belić, Milivoj R., Ahmed, Noor, Zhang, Yanpeng, Xiao, Min
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2016
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4838869/
https://www.ncbi.nlm.nih.gov/pubmed/27097656
http://dx.doi.org/10.1038/srep23645
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author Zhang, Yiqi
Zhong, Hua
Belić, Milivoj R.
Ahmed, Noor
Zhang, Yanpeng
Xiao, Min
author_facet Zhang, Yiqi
Zhong, Hua
Belić, Milivoj R.
Ahmed, Noor
Zhang, Yanpeng
Xiao, Min
author_sort Zhang, Yiqi
collection PubMed
description We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrödinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D beam deflects along the trajectories z = ±2(x − x(0)), which are independent of the chirp. In the case of 2D Gaussian beam, the propagation is also deflected, but the trajectories align along the diffraction cone [Image: see text] and the direction is determined by the chirp. Both 1D and 2D Gaussian beams are diffractionless and display uniform propagation. The nondiffracting property discovered in this model applies to other beams as well. Based on the nondiffracting and splitting properties, we introduce the Talbot effect of diffractionless beams in FSE.
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spelling pubmed-48388692016-04-27 Diffraction-free beams in fractional Schrödinger equation Zhang, Yiqi Zhong, Hua Belić, Milivoj R. Ahmed, Noor Zhang, Yanpeng Xiao, Min Sci Rep Article We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrödinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D beam deflects along the trajectories z = ±2(x − x(0)), which are independent of the chirp. In the case of 2D Gaussian beam, the propagation is also deflected, but the trajectories align along the diffraction cone [Image: see text] and the direction is determined by the chirp. Both 1D and 2D Gaussian beams are diffractionless and display uniform propagation. The nondiffracting property discovered in this model applies to other beams as well. Based on the nondiffracting and splitting properties, we introduce the Talbot effect of diffractionless beams in FSE. Nature Publishing Group 2016-04-21 /pmc/articles/PMC4838869/ /pubmed/27097656 http://dx.doi.org/10.1038/srep23645 Text en Copyright © 2016, Macmillan Publishers Limited http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
spellingShingle Article
Zhang, Yiqi
Zhong, Hua
Belić, Milivoj R.
Ahmed, Noor
Zhang, Yanpeng
Xiao, Min
Diffraction-free beams in fractional Schrödinger equation
title Diffraction-free beams in fractional Schrödinger equation
title_full Diffraction-free beams in fractional Schrödinger equation
title_fullStr Diffraction-free beams in fractional Schrödinger equation
title_full_unstemmed Diffraction-free beams in fractional Schrödinger equation
title_short Diffraction-free beams in fractional Schrödinger equation
title_sort diffraction-free beams in fractional schrödinger equation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4838869/
https://www.ncbi.nlm.nih.gov/pubmed/27097656
http://dx.doi.org/10.1038/srep23645
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