Topological photonics of generalized and nonlinear eigenvalue equations
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918021355798528 |
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| author | Isobe, Takuma Yoshida, Tsuneya Hatsugai, Yasuhiro |
| author_facet | Isobe, Takuma Yoshida, Tsuneya Hatsugai, Yasuhiro |
| contents | Topological photonics is developed based on the analogy of Schrödinger equation which is mathematically reduced to a standard eigenvalue equation. Notably, several photonic systems are beyond the standard topological band theory as they are described by generalized or nonlinear eigenvalue equations. In this article, we review the topological band theory of this category. In the first part, we discuss topological photonics of generalized eigenvalue equations where the band structure may take complex values even when the involved matrices are Hermitian. These complex bands explain the characteristic dispersion relation of hyperbolic metamaterials. In addition, our numerical analysis predicts the emergence of symmetry-protected exceptional points in a photonic crystal composed of negative index media. In the second part, by introducing auxiliary bands, we establish the nonlinear bulk-edge correspondence under ``weak" nonlinearity of eigenvalues. The nonlinear bulk-edge correspondence elucidates the robustness of chiral edge modes in photonic systems where the permittivity and permeability are frequency dependent. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_09876 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological photonics of generalized and nonlinear eigenvalue equations Isobe, Takuma Yoshida, Tsuneya Hatsugai, Yasuhiro Optics Mesoscale and Nanoscale Physics Other Condensed Matter Topological photonics is developed based on the analogy of Schrödinger equation which is mathematically reduced to a standard eigenvalue equation. Notably, several photonic systems are beyond the standard topological band theory as they are described by generalized or nonlinear eigenvalue equations. In this article, we review the topological band theory of this category. In the first part, we discuss topological photonics of generalized eigenvalue equations where the band structure may take complex values even when the involved matrices are Hermitian. These complex bands explain the characteristic dispersion relation of hyperbolic metamaterials. In addition, our numerical analysis predicts the emergence of symmetry-protected exceptional points in a photonic crystal composed of negative index media. In the second part, by introducing auxiliary bands, we establish the nonlinear bulk-edge correspondence under ``weak" nonlinearity of eigenvalues. The nonlinear bulk-edge correspondence elucidates the robustness of chiral edge modes in photonic systems where the permittivity and permeability are frequency dependent. |
| title | Topological photonics of generalized and nonlinear eigenvalue equations |
| topic | Optics Mesoscale and Nanoscale Physics Other Condensed Matter |
| url | https://arxiv.org/abs/2505.09876 |