Bulk-edge correspondence in open photonic systems

Tetsuyuki Ochiai

doi:10.1080/17455030.2021.1923858

Article Bulk-edge correspondence in open photonic systems

Tetsuyuki Ochiai (National Institute for Materials Science)

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Tetsuyuki Ochiai. Bulk-edge correspondence in open photonic systems. Waves in Random and Complex Media. 2024, 34 (2), 951-968. https://doi.org/10.1080/17455030.2021.1923858

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We study the bulk-edge correspondence in topological photonic crystals with open boundary. If boundary is open, edge states become leaky inside the light cone, but still exhibit a chiral and gapless property taking into account the blurring of their band structure due to the leakage. The so-called bulk-edge correspondence is thus verified.
On the other hand, in closed boundaries, edge states exhibit the well-defined band structure without the blurring and show clearly the bulk-edge correspondence.
To demonstrate these results, we employ the transfer-matrix formalism and derive reflection matrices of semi-infinite systems. Optical density of states for the system with open boundaries is available via the Krein-Friedel-Lloyd formula for the reflection matrices.
The leaky photonic band structure of the edge states is obtained by following the peaks and widths of the density of states as a function of momentum parallel to the boundary.
Our derivation of the leaky band structure does not rely on possible effective non-hermitian hamiltonians, but relies on a first-principles calculation of the Maxwell equation.

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Creative Commons BY-NC Attribution-NonCommercial 4.0 International

This is an Accepted Manuscript version of the following article, accepted for publication in Waves in Random and Complex Media. Ochiai, T. (2024). Bulk-edge correspondence in open photonic systems. Waves in Random and Complex Media, 34(2), 951–968. https://doi.org/10.1080/17455030.2021.1923858. It is deposited under the terms of the Creative Commons Attribution-NonCommercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited.