Reconfigurable topological valley-Hall interfaces: Asymptotics of arrays of Dirichlet and Neumann inclusions for multiple scattering in metamaterials
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arXiv
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| Format: | Preprint |
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2026
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| author | Wiltshaw, Richard Putley, Henry J. Dagher, Christelle Bou Makwana, Mehul P. |
| author_facet | Wiltshaw, Richard Putley, Henry J. Dagher, Christelle Bou Makwana, Mehul P. |
| contents | We study two-dimensional periodic metamaterials in which idealised cylindrical inclusions are modelled by boundary conditions. In the scalar time-harmonic setting, the background field satisfies the Helmholtz equation, and high-contrast inclusion limits reduce to Dirichlet or Neumann conditions, with direct analogues in dielectric and acoustic media. By switching the condition assigned to selected inclusions, we break point-group symmetries of the primitive cell and thereby lift symmetry-induced degeneracies in the Floquet--Bloch spectrum of hexagonal and square lattices, opening valley-type band gaps with Berry curvature localised near opposite valleys.
To analyse infinite and finite structures within a unified framework, we derive matched-asymptotic point-scatterer approximations for mixed Dirichlet--Neumann arrays. For doubly periodic systems, this yields a finite-dimensional generalised eigenvalue problem for the Floquet--Bloch spectrum; for finite arrays, it yields a generalised Foldy multiple-scattering system. In both hexagonal and square lattices, geometrically identical crystals can realise distinct valley-Hall phases solely through boundary-condition assignment while retaining an overlapping bulk gap. Spatially varying this assignment therefore creates and relocates internal interfaces without altering the underlying geometry, enabling the associated valley-Hall interfacial modes to be repositioned within the same crystal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24297 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reconfigurable topological valley-Hall interfaces: Asymptotics of arrays of Dirichlet and Neumann inclusions for multiple scattering in metamaterials Wiltshaw, Richard Putley, Henry J. Dagher, Christelle Bou Makwana, Mehul P. Optics Mathematical Physics Computational Physics We study two-dimensional periodic metamaterials in which idealised cylindrical inclusions are modelled by boundary conditions. In the scalar time-harmonic setting, the background field satisfies the Helmholtz equation, and high-contrast inclusion limits reduce to Dirichlet or Neumann conditions, with direct analogues in dielectric and acoustic media. By switching the condition assigned to selected inclusions, we break point-group symmetries of the primitive cell and thereby lift symmetry-induced degeneracies in the Floquet--Bloch spectrum of hexagonal and square lattices, opening valley-type band gaps with Berry curvature localised near opposite valleys. To analyse infinite and finite structures within a unified framework, we derive matched-asymptotic point-scatterer approximations for mixed Dirichlet--Neumann arrays. For doubly periodic systems, this yields a finite-dimensional generalised eigenvalue problem for the Floquet--Bloch spectrum; for finite arrays, it yields a generalised Foldy multiple-scattering system. In both hexagonal and square lattices, geometrically identical crystals can realise distinct valley-Hall phases solely through boundary-condition assignment while retaining an overlapping bulk gap. Spatially varying this assignment therefore creates and relocates internal interfaces without altering the underlying geometry, enabling the associated valley-Hall interfacial modes to be repositioned within the same crystal. |
| title | Reconfigurable topological valley-Hall interfaces: Asymptotics of arrays of Dirichlet and Neumann inclusions for multiple scattering in metamaterials |
| topic | Optics Mathematical Physics Computational Physics |
| url | https://arxiv.org/abs/2603.24297 |