Bulk-edge correspondence in finite photonic structure
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913859113058304 |
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| author | Qiu, Jiayu Zhang, Hai |
| author_facet | Qiu, Jiayu Zhang, Hai |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_15531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bulk-edge correspondence in finite photonic structure Qiu, Jiayu Zhang, Hai Mathematical Physics Analysis of PDEs Spectral Theory 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. |
| title | Bulk-edge correspondence in finite photonic structure |
| topic | Mathematical Physics Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2501.15531 |