Interface conditions for Maxwell's equations by homogenization of thin inclusions: transmission, reflection or polarization
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| author | Schweizer, Ben Wiedemann, David |
| author_facet | Schweizer, Ben Wiedemann, David |
| contents | We consider the time-harmonic Maxwell equations in a complex geometry. We are interested in geometries that model polarization filters or Faraday cages. We study the situation that the underlying domain contains perfectly conducting inclusions, the inclusions are distributed in a periodic fashion along a surface. The periodicity is $η>0$ and the typical scale of the inclusion is $η$, but we allow also the presence of even smaller scales, e.g. when thin wires are analyzed. We are interested in the limit $η\to 0$ and in effective equations. Depending on geometric properties of the inclusions, the effective system can imply perfect transmission, perfect reflection or polarization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17713 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interface conditions for Maxwell's equations by homogenization of thin inclusions: transmission, reflection or polarization Schweizer, Ben Wiedemann, David Analysis of PDEs 78M40, 78M35, 35Q61 We consider the time-harmonic Maxwell equations in a complex geometry. We are interested in geometries that model polarization filters or Faraday cages. We study the situation that the underlying domain contains perfectly conducting inclusions, the inclusions are distributed in a periodic fashion along a surface. The periodicity is $η>0$ and the typical scale of the inclusion is $η$, but we allow also the presence of even smaller scales, e.g. when thin wires are analyzed. We are interested in the limit $η\to 0$ and in effective equations. Depending on geometric properties of the inclusions, the effective system can imply perfect transmission, perfect reflection or polarization. |
| title | Interface conditions for Maxwell's equations by homogenization of thin inclusions: transmission, reflection or polarization |
| topic | Analysis of PDEs 78M40, 78M35, 35Q61 |
| url | https://arxiv.org/abs/2501.17713 |