Engineering topology in waveguide arrays
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912937190359040 |
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| author | Upreti, Lavi K. |
| author_facet | Upreti, Lavi K. |
| contents | The topological classification of a system depends on the discrete symmetries of its Hamiltonian. In Floquet photonic waveguide arrays, the abstract symmetries of the Altland--Zirnbauer (AZ) scheme -- chiral, particle-hole, and time-reversal (for photonics, $z$-reversal) -- arise from structural properties of the lattice, yet a systematic correspondence has not been established. Here, we illustrate this correspondence for a simpler system of one-dimensional waveguide arrays with real coupling coefficients, showing how bipartite structure and $z$-reflection symmetry alone determine the whole AZ class. We further demonstrate that non-bipartite networks -- lacking conventional particle-hole symmetry, chiral symmetry, and $z$-reversal symmetry -- can nonetheless support topologically protected boundary states at quasienergy $\varepsilon = π$, even in one dimension. The protecting symmetry -- \textit{shifted}-particle-hole symmetry -- applies equally to higher-dimensional Floquet waveguides. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01769 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Engineering topology in waveguide arrays Upreti, Lavi K. Optics Mesoscale and Nanoscale Physics Other Condensed Matter The topological classification of a system depends on the discrete symmetries of its Hamiltonian. In Floquet photonic waveguide arrays, the abstract symmetries of the Altland--Zirnbauer (AZ) scheme -- chiral, particle-hole, and time-reversal (for photonics, $z$-reversal) -- arise from structural properties of the lattice, yet a systematic correspondence has not been established. Here, we illustrate this correspondence for a simpler system of one-dimensional waveguide arrays with real coupling coefficients, showing how bipartite structure and $z$-reflection symmetry alone determine the whole AZ class. We further demonstrate that non-bipartite networks -- lacking conventional particle-hole symmetry, chiral symmetry, and $z$-reversal symmetry -- can nonetheless support topologically protected boundary states at quasienergy $\varepsilon = π$, even in one dimension. The protecting symmetry -- \textit{shifted}-particle-hole symmetry -- applies equally to higher-dimensional Floquet waveguides. |
| title | Engineering topology in waveguide arrays |
| topic | Optics Mesoscale and Nanoscale Physics Other Condensed Matter |
| url | https://arxiv.org/abs/2603.01769 |