Revealing topology with transformation optics

Lizhen Lu, Kun Ding (), Emanuele Galiffi, Xikui Ma, Tianyu Dong and J. B. Pendry ()
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Lizhen Lu: Xi’an Jiaotong University
Kun Ding: Imperial College London
Emanuele Galiffi: Imperial College London
Xikui Ma: Xi’an Jiaotong University
Tianyu Dong: Xi’an Jiaotong University
J. B. Pendry: Imperial College London

Nature Communications, 2021, vol. 12, issue 1, 1-7

Abstract: Abstract 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.

Date: 2021
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DOI: 10.1038/s41467-021-27008-x

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