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arXiv · 2501.15531

Bulk-edge correspondence in finite photonic structure

Jiayu Qiu·Hai Zhang
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Abstract

In this work, we establish the bulk-edge correspondence principle for finite two-dimensional photonic structures. Specifically, we focus on the divergence-form operator with periodic coefficients and prove the equality between the well-known gap Chern number (the bulk invariant) and an edge index defined via a trace formula for the operator restricted to a finite domain with Dirichlet boundary conditions. We demonstrate that the edge index characterizes the circulation of electromagnetic energy along the system's boundary, and the BEC principle is a consequence of energy conservation. The proof leverages Green function techniques and can be extended to other systems. These results provide a rigorous theoretical foundation for designing robust topological photonic devices with finite geometries, complementing recent advances in discrete models.

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Jiayu Qiu, Hai Zhang. 2025-01-26. Bulk-edge correspondence in finite photonic structure. https://arxiv.org/abs/2501.15531

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