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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2603.07855 |
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| _version_ | 1866917385053667328 |
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| author | Morozov, Gregory V |
| author_facet | Morozov, Gregory V |
| contents | For the Hill equation describing one-dimensional periodic systems, a constructive formulation is developed for generating Floquet-Bloch states directly from arbitrary pairs of linearly independent solutions. One-dimensional photonic crystals are used as a concrete illustration. Explicit closed-form formulas map an arbitrary fundamental system to the corresponding Floquet-Bloch basis via the monodromy matrix, including the generic Jordan band-edge case, without reliance on canonically normalized solutions. The construction can be expressed directly in terms of the transfer matrix, making the residual representation freedom transparent and providing an implementation-ready framework for analytical and numerical studies of periodic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07855 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Explicit Construction of Floquet-Bloch States from Arbitrary Solution Bases of the Hill Equation Morozov, Gregory V Optics Mesoscale and Nanoscale Physics Mathematical Physics For the Hill equation describing one-dimensional periodic systems, a constructive formulation is developed for generating Floquet-Bloch states directly from arbitrary pairs of linearly independent solutions. One-dimensional photonic crystals are used as a concrete illustration. Explicit closed-form formulas map an arbitrary fundamental system to the corresponding Floquet-Bloch basis via the monodromy matrix, including the generic Jordan band-edge case, without reliance on canonically normalized solutions. The construction can be expressed directly in terms of the transfer matrix, making the residual representation freedom transparent and providing an implementation-ready framework for analytical and numerical studies of periodic systems. |
| title | Explicit Construction of Floquet-Bloch States from Arbitrary Solution Bases of the Hill Equation |
| topic | Optics Mesoscale and Nanoscale Physics Mathematical Physics |
| url | https://arxiv.org/abs/2603.07855 |