Topological invariants and topological charges in photonic systems
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arXiv
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| Format: | Preprint |
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2025
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| author | Arjas, Kristian Salerno, Grazia Törmä, Päivi |
| author_facet | Arjas, Kristian Salerno, Grazia Törmä, Päivi |
| contents | Topology in photonics comes in two distinct flavors: global and local. Global topology considers invariants that are obtained by integrating over the energy band, whereas local topology considers defects, typically vortices, in the far-field emission. These topologies are described by a wide range of models built in both real and momentum space, which are connected only by computationally expensive numerical methods that lack physical intuition. Here we propose a general framework based on a real-space Hamiltonian capable of describing electric field as a vector in both near- and far fields, allowing us to bridge between topological defects in the far-field and global topological invariants. The proposed Hamiltonian is constructed from the symmetry-representations of the lattice, is deformable to both atomic localized-mode (tight-binding) and photonic delocalized-mode (long-range) limits, and allows for independent control over the energies of eigenmodes of different symmetries at high-symmetry points of the Brillouin zone. This symmetry-based approach enables the design of structures with almost arbitrary topological properties and is not limited to photonic systems, but could apply to any system with engineered real-space couplings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological invariants and topological charges in photonic systems Arjas, Kristian Salerno, Grazia Törmä, Päivi Optics Mesoscale and Nanoscale Physics Topology in photonics comes in two distinct flavors: global and local. Global topology considers invariants that are obtained by integrating over the energy band, whereas local topology considers defects, typically vortices, in the far-field emission. These topologies are described by a wide range of models built in both real and momentum space, which are connected only by computationally expensive numerical methods that lack physical intuition. Here we propose a general framework based on a real-space Hamiltonian capable of describing electric field as a vector in both near- and far fields, allowing us to bridge between topological defects in the far-field and global topological invariants. The proposed Hamiltonian is constructed from the symmetry-representations of the lattice, is deformable to both atomic localized-mode (tight-binding) and photonic delocalized-mode (long-range) limits, and allows for independent control over the energies of eigenmodes of different symmetries at high-symmetry points of the Brillouin zone. This symmetry-based approach enables the design of structures with almost arbitrary topological properties and is not limited to photonic systems, but could apply to any system with engineered real-space couplings. |
| title | Topological invariants and topological charges in photonic systems |
| topic | Optics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2508.03302 |