{
  "annotation_id": "0a743ffb-4da4-4fd7-aa64-9ab302b7a70b",
  "date_created": "2026-03-02T18:01:07.852000Z",
  "date_modified": "2026-03-02T18:01:07.852000Z",
  "file_hash": "66b2d288b7dba0a8fd62101474201a0333282b556e5cacb66a67ef7b472ed8e3",
  "private": false,
  "record": {
    "abstract": "The equivalent circuit model for artificial magnetic materials based on\nvarious arrangements of split rings is generalized by taking into account\nlosses in the substrate or matrix material. It is shown that a modification is\nneeded to the known macroscopic permeability function in order to correctly\ndescribe these materials. Depending on the dominating loss mechanism\n(conductive losses in metal parts or dielectric losses in the substrate) the\npermeability function has different forms. The proposed circuit model and\npermeability function are experimentally validated. Furthermore, starting from\nthe generalized circuit model we derive an explicit expression for the\nelectromagnetic field energy density in artificial magnetic media. This\nexpression is valid at low frequencies and in the vicinity of the resonance\nalso when dispersion and losses in the material are strong. The presently\nobtained results for the energy density are compared with the results obtained\nusing different methods.",
    "arxiv_id": "physics/0602182",
    "authors": [
      "Pekka Ikonen",
      "Sergei Tretyakov"
    ],
    "categories": [
      "physics.class-ph"
    ],
    "doi": "10.1109/TMTT.2006.886914",
    "journal_ref": "IEEE Trans. Microw. Theory Tech., vol. 55, no. 1, pp. 92-99, Jan.\n  2007.",
    "title": "Generalized Permeability Function and Field Energy Density in Artificial   Magnetics Using the Equivalent Circuit Method",
    "url": "https://arxiv.org/abs/physics/0602182"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "decfa238-695d-4270-ac30-e61af2c284df",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}