{
  "abstract": "A time-domain representation for ultrabroadband optical pulses that includes chirp, stretching, and absolute phase is presented. This is accomplished by holomorphic Fourier transform of a class of spectra that include spectral phase up to second order, resulting in derivatives of the Faddeeva function $w(ζ)$. Relating the real part of this pulse to physical quantities, its shape is investigated. The derivative order $η$ is shown to dictate relative spectral bandwidth. The absolute phase determines the mixing of more localized (Gaussian decay) and less localized (algebraic decay) components of $w(ζ)$. Second order spectral phase accounts for linear dispersion and is shown to cause a sheering of the Wigner-Ville distribution of the pulse, akin to the linear chirp that would be seen in the quasi-monochromatic case. Along with $η$ it determines the pulse length and number of oscillations. A correspondence with the slowly varying envelope approximation is derived for large order $η$, although the algebraic decay persists.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30040",
  "author_total": 1,
  "authors": [
    {
      "name": "George A. Hine"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8awcmc0nydmj4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30040",
  "fulltext_url": null,
  "id": "8awcmc0nydmj4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30040",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.optics"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.30040",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8awcmc0nydmj4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.30040",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30040"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "Ultrabroadband Optical Pulses with Quadratic Spectral Phase Part I: Temporal Form",
  "title_text": "Ultrabroadband Optical Pulses with Quadratic Spectral Phase Part I: Temporal Form",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/8awcmc0nydmj4",
  "venue": "arXiv",
  "versions": []
}