English

Interface conditions for Maxwell's equations by homogenization of thin inclusions: transmission, reflection or polarization

Analysis of PDEs 2025-01-30 v1

Abstract

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\eta>0 and the typical scale of the inclusion is η\eta, but we allow also the presence of even smaller scales, e.g. when thin wires are analyzed. We are interested in the limit η0\eta\to 0 and in effective equations. Depending on geometric properties of the inclusions, the effective system can imply perfect transmission, perfect reflection or polarization.

Keywords

Cite

@article{arxiv.2501.17713,
  title  = {Interface conditions for Maxwell's equations by homogenization of thin inclusions: transmission, reflection or polarization},
  author = {Ben Schweizer and David Wiedemann},
  journal= {arXiv preprint arXiv:2501.17713},
  year   = {2025}
}

Comments

28 pages, 7 figures