{
  "id": "1805.00722",
  "version": "v1",
  "published": "2018-05-02T10:48:34.000Z",
  "updated": "2018-05-02T10:48:34.000Z",
  "title": "Reflection and refraction problems for metasurfaces related to Monge-Ampère equations",
  "authors": [
    "Cristian E. Gutierrez",
    "Luca Pallucchini"
  ],
  "comment": "20 pages, 4 figures",
  "categories": [
    "math.AP",
    "physics.optics"
  ],
  "abstract": "A metasurface is a surface, tipically a plane, on which a function called phase discontinuity is chosen so that the metasurface produces a desired reflection or refraction job. We derive the equations that the phase discontinuity function must satisfy, they are Monge-Amp\\`ere partial differential equations, and we prove existence of solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-02T10:48:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monge-ampère equations",
      "refraction problems",
      "partial differential equations",
      "phase discontinuity function",
      "metasurface produces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}