Optical Bloch oscillation and Zener tunneling in the fractional Schrödinger equation

We demonstrate optical Bloch oscillation (OBO) and optical Zener tunneling (OZT) in the fractional Schrödinger equation (FSE) with periodic and linear potentials, numerically and theoretically. We investigate in parallel the regular Schrödinger equation and the FSE, by adjusting the Lévy index, and...

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Autores principales: Zhang, Yiqi, Wang, Rong, Zhong, Hua, Zhang, Jingwen, Belić, Milivoj R., Zhang, Yanpeng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2017
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5736706/
https://www.ncbi.nlm.nih.gov/pubmed/29259234
http://dx.doi.org/10.1038/s41598-017-17995-7
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author Zhang, Yiqi
Wang, Rong
Zhong, Hua
Zhang, Jingwen
Belić, Milivoj R.
Zhang, Yanpeng
author_facet Zhang, Yiqi
Wang, Rong
Zhong, Hua
Zhang, Jingwen
Belić, Milivoj R.
Zhang, Yanpeng
author_sort Zhang, Yiqi
collection PubMed
description We demonstrate optical Bloch oscillation (OBO) and optical Zener tunneling (OZT) in the fractional Schrödinger equation (FSE) with periodic and linear potentials, numerically and theoretically. We investigate in parallel the regular Schrödinger equation and the FSE, by adjusting the Lévy index, and expound the differences between the two. We find that the spreading of the OBO decreases in the fractional case, due to the diminishing band width. Increasing the transverse force, due to the linear potential, leads to the appearance of OZT, but this process is suppressed in the FSE. Our results indicate that the adjustment of the Lévy index can effectively control the emergence of OBO and OZT, which can inspire new ideas in the design of optical switches and interconnects.
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spelling pubmed-57367062017-12-21 Optical Bloch oscillation and Zener tunneling in the fractional Schrödinger equation Zhang, Yiqi Wang, Rong Zhong, Hua Zhang, Jingwen Belić, Milivoj R. Zhang, Yanpeng Sci Rep Article We demonstrate optical Bloch oscillation (OBO) and optical Zener tunneling (OZT) in the fractional Schrödinger equation (FSE) with periodic and linear potentials, numerically and theoretically. We investigate in parallel the regular Schrödinger equation and the FSE, by adjusting the Lévy index, and expound the differences between the two. We find that the spreading of the OBO decreases in the fractional case, due to the diminishing band width. Increasing the transverse force, due to the linear potential, leads to the appearance of OZT, but this process is suppressed in the FSE. Our results indicate that the adjustment of the Lévy index can effectively control the emergence of OBO and OZT, which can inspire new ideas in the design of optical switches and interconnects. Nature Publishing Group UK 2017-12-19 /pmc/articles/PMC5736706/ /pubmed/29259234 http://dx.doi.org/10.1038/s41598-017-17995-7 Text en © The Author(s) 2017 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Zhang, Yiqi
Wang, Rong
Zhong, Hua
Zhang, Jingwen
Belić, Milivoj R.
Zhang, Yanpeng
Optical Bloch oscillation and Zener tunneling in the fractional Schrödinger equation
title Optical Bloch oscillation and Zener tunneling in the fractional Schrödinger equation
title_full Optical Bloch oscillation and Zener tunneling in the fractional Schrödinger equation
title_fullStr Optical Bloch oscillation and Zener tunneling in the fractional Schrödinger equation
title_full_unstemmed Optical Bloch oscillation and Zener tunneling in the fractional Schrödinger equation
title_short Optical Bloch oscillation and Zener tunneling in the fractional Schrödinger equation
title_sort optical bloch oscillation and zener tunneling in the fractional schrödinger equation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5736706/
https://www.ncbi.nlm.nih.gov/pubmed/29259234
http://dx.doi.org/10.1038/s41598-017-17995-7
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