{
  "annotation_id": "12f2cfa2-95c0-4fba-826d-1fb46716784d",
  "date_created": "2026-03-02T18:00:43.214000Z",
  "date_modified": "2026-03-02T18:00:43.214000Z",
  "file_hash": "90cec78895dc9428bd553560a9b3d2239442e354f385fc999224f7ccba7b2545",
  "private": false,
  "record": {
    "abstract": "A new type of perturbative expansion is built in order to give a rigorous\nderivation and to clarify the range of validity of some commonly used model\nequations.\n  This model describes the evolution of the modulation of two short and\nlocalized pulses, fundamental and second harmonic, propagating together in a\nbulk uniaxial crystal with non-vanishing second order susceptibility $\\chi^(2)$\nand interacting through the nonlinear effect known as ``cascading\u0027\u0027 in\nnonlinear optics.\n  The perturbative method mixes a multi-scale expansion with a power series\nexpansion of the susceptibility, and must be carefully adapted to the physical\nsituation. It allows the determination of the physical conditions under which\nthe model is valid: the order of magnitude of the walk-off, phase-mismatch,and\nanisotropy must have determined values.",
    "arxiv_id": "physics/0211078",
    "authors": [
      "Herve Leblond"
    ],
    "categories": [
      "physics.optics"
    ],
    "doi": "10.2991/jnmp.2002.9.2.1",
    "journal_ref": "J. Nonlinear Math. Phys. 9, no. 2 (2002) 126-143",
    "title": "Mixed perturbative expansion: the validity of a model for the cascading",
    "url": "https://arxiv.org/abs/physics/0211078"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5ef2e4a0-91fa-4200-9ca9-158dba881cde",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}