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Revealing topology with transformation optics
Symmetry deepens our insight into a physical system and its interplay with topology enables the discovery of topological phases. Symmetry analysis is conventionally performed either in the physical space of interest, or in the corresponding reciprocal space. Here we borrow the concept of virtual spa...
Autores principales: | , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8617177/ https://www.ncbi.nlm.nih.gov/pubmed/34824222 http://dx.doi.org/10.1038/s41467-021-27008-x |
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author | Lu, Lizhen Ding, Kun Galiffi, Emanuele Ma, Xikui Dong, Tianyu Pendry, J. B. |
author_facet | Lu, Lizhen Ding, Kun Galiffi, Emanuele Ma, Xikui Dong, Tianyu Pendry, J. B. |
author_sort | Lu, Lizhen |
collection | PubMed |
description | Symmetry deepens our insight into a physical system and its interplay with topology enables the discovery of topological phases. Symmetry analysis is conventionally performed either in the physical space of interest, or in the corresponding reciprocal space. Here we borrow the concept of virtual space from transformation optics to demonstrate how a certain class of symmetries can be visualised in a transformed, spectrally related coordinate space, illuminating the underlying topological transitions. By projecting a plasmonic system in a higher-dimensional virtual space onto a lower-dimensional system in real space, we show how transformation optics allows us to construct a topologically non-trivial system by inspecting its modes in the virtual space. Interestingly, we find that the topological invariant can be controlled via the singularities in the conformal mapping, enabling the intuitive engineering of edge states. The confluence of transformation optics and topology here can be generalized to other wave realms beyond photonics. |
format | Online Article Text |
id | pubmed-8617177 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-86171772021-12-10 Revealing topology with transformation optics Lu, Lizhen Ding, Kun Galiffi, Emanuele Ma, Xikui Dong, Tianyu Pendry, J. B. Nat Commun Article Symmetry deepens our insight into a physical system and its interplay with topology enables the discovery of topological phases. Symmetry analysis is conventionally performed either in the physical space of interest, or in the corresponding reciprocal space. Here we borrow the concept of virtual space from transformation optics to demonstrate how a certain class of symmetries can be visualised in a transformed, spectrally related coordinate space, illuminating the underlying topological transitions. By projecting a plasmonic system in a higher-dimensional virtual space onto a lower-dimensional system in real space, we show how transformation optics allows us to construct a topologically non-trivial system by inspecting its modes in the virtual space. Interestingly, we find that the topological invariant can be controlled via the singularities in the conformal mapping, enabling the intuitive engineering of edge states. The confluence of transformation optics and topology here can be generalized to other wave realms beyond photonics. Nature Publishing Group UK 2021-11-25 /pmc/articles/PMC8617177/ /pubmed/34824222 http://dx.doi.org/10.1038/s41467-021-27008-x Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/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/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Lu, Lizhen Ding, Kun Galiffi, Emanuele Ma, Xikui Dong, Tianyu Pendry, J. B. Revealing topology with transformation optics |
title | Revealing topology with transformation optics |
title_full | Revealing topology with transformation optics |
title_fullStr | Revealing topology with transformation optics |
title_full_unstemmed | Revealing topology with transformation optics |
title_short | Revealing topology with transformation optics |
title_sort | revealing topology with transformation optics |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8617177/ https://www.ncbi.nlm.nih.gov/pubmed/34824222 http://dx.doi.org/10.1038/s41467-021-27008-x |
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