{
  "abstract": "Programmable control of individual pulses in a high-repetition-rate (typically MHz) ultrafast pulse train is a long-standing goal for optical arbitrary waveform synthesis. Here, we report a programmable pulse-by-pulse shaper that enables deterministic spectral-temporal control of ultrafast pulses at a repetition rate of $\\sim$ 20~MHz. By synchronizing an FPGA-driven electro-optic modulation on the stretched waveform in a temporal 4$f$ shaping system, the regime writes pulse-index-dependent spectral phase profiles onto individual pulses. We demonstrate three levels of programmable ability: zero-order phase coding that maps pulse-by-pulse phase sequences into double-slit-like spectral-temporal interference; first-order phase programming that produces arbitrary temporal trajectories with deterministic delay; and fractional-order phase engineering that generates programmable temporal breathing. By launching the shaped pulse train into a nonlinear fiber stage, the programmed temporal breathing is converted into one spectral breathing. We further construct a phase-level-dependent regime map of nonlinear spectral breathing, revealing transitions from weak single-envelope breathing to multi-peak spectral splitting and strongly breathing merged-spectrum dynamics, in agreement with numerical simulations. This pulse-by-pulse spectral-temporal synthesis platform establishes pulse index as a programmable degree of freedom for ultrafast pulse shaping and provides a route toward real-time and pulse resolved optical arbitary waveform synthesis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06894",
  "author_total": 5,
  "authors": [
    {
      "name": "Shilong Liu"
    },
    {
      "name": "Gabriel Demontigny"
    },
    {
      "name": "Émile Dessureault"
    },
    {
      "name": "Stéphane Virally"
    },
    {
      "name": "Denis V. Seletskiy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0rnp6b5yfey17.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06894",
  "fulltext_url": null,
  "id": "0rnp6b5yfey17",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06894",
  "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",
      "nlin.PS"
    ],
    [
      "arxiv",
      "physics.optics"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Laser-Matter Interactions and Applications"
    ]
  ],
  "openalex": "W7212011627",
  "pdf_url": "https://arxiv.org/pdf/2609.06894",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0rnp6b5yfey17.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.06894",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06894"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.PS",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Pulse-by-pulse programmable synthesis of ultrafast optical waveforms",
  "title_text": "Pulse-by-pulse programmable synthesis of ultrafast optical waveforms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/0rnp6b5yfey17",
  "venue": "arXiv",
  "versions": []
}