{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T15:21:36Z","timestamp":1785424896029,"version":"3.56.0"},"reference-count":19,"publisher":"Optica Publishing Group","issue":"4","license":[{"start":{"date-parts":[[2025,2,14]],"date-time":"2025-02-14T00:00:00Z","timestamp":1739491200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,2,14]],"date-time":"2025-02-14T00:00:00Z","timestamp":1739491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/V006797\/1"],"award-info":[{"award-number":["EP\/V006797\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/R513295\/1"],"award-info":[{"award-number":["EP\/R513295\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000271","name":"Science and Technology Facilities Council","doi-asserted-by":"publisher","award":["ST\/V001655\/1"],"award-info":[{"award-number":["ST\/V001655\/1"]}],"id":[{"id":"10.13039\/501100000271","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2025,2,24]]},"abstract":"<jats:p>Simultaneous space-time focusing (SSTF) is sometimes claimed to reduce the longitudinal extent of the high-intensity region near the focus, in contradiction to the original work on this topic. Here we seek to address this confusion by using numerical and analytical methods to investigate the degree of localization of the spatio-temporal intensity of an SSTF pulse. The analytical method is found to be in excellent agreement with numerical calculations and yields, for bi-Gaussian input pulses, expressions for the three-dimensional spatio-temporal intensity profile of the SSTF pulse, and for the on-axis bandwidth, pulse duration, and pulse-front tilt (PFT) of the SSTF pulse. To provide further insight, we propose a method for determining the transverse input profile of a non-SSTF pulse with equivalent spatial focusing. We find that the longitudinal variations of the peak axial intensities of the SSTF and spatially equivalent (SE) pulses are the same, apart from a constant factor, and hence that SSTF does not constrain the region of high intensity more than a non-SSTF pulse with equivalent focusing. We demonstrate that a simplistic method for calculating the pulse intensity exaggerates the degree of intensity localization, unless the spatio-temporal couplings inherent to SSTF pulses are accounted for.<\/jats:p>","DOI":"10.1364\/oe.546012","type":"journal-article","created":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T09:00:39Z","timestamp":1738746039000},"page":"7645","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the localization of the high-intensity region of simultaneous space-time foci"],"prefix":"10.1364","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8513-3918","authenticated-orcid":true,"given":"Emily","family":"Archer","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}]},{"id":[{"id":"https:\/\/ror.org\/01js2sh04","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bangshan","family":"Sun","sequence":"additional","affiliation":[{"name":"University of Oxford"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roman","family":"Walczak","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Somerville College"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9525-8981","authenticated-orcid":true,"given":"Martin","family":"Booth","sequence":"additional","affiliation":[{"name":"University of Oxford"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1243-520X","authenticated-orcid":true,"given":"Simon","family":"Hooker","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2025,2,14]]},"reference":[{"key":"oe-33-4-7645-R1","doi-asserted-by":"publisher","first-page":"2153","DOI":"10.1364\/OPEX.13.002153","volume":"13","author":"Zhu","year":"2005","journal-title":"Opt. Express"},{"key":"oe-33-4-7645-R2","doi-asserted-by":"publisher","first-page":"12243","DOI":"10.1364\/OE.14.012243","volume":"14","author":"Durst","year":"2006","journal-title":"Opt. Express"},{"key":"oe-33-4-7645-R3","doi-asserted-by":"publisher","first-page":"1796","DOI":"10.1016\/j.optcom.2007.05.071","volume":"281","author":"Durst","year":"2008","journal-title":"Opt. Commun."},{"key":"oe-33-4-7645-R4","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1364\/JOSAB.33.000292","volume":"33","author":"Lanier","year":"2016","journal-title":"J. Opt. Soc. Am. B"},{"key":"oe-33-4-7645-R5","doi-asserted-by":"publisher","first-page":"17117","DOI":"10.1038\/lsa.2017.117","volume":"7","author":"Sun","year":"2017","journal-title":"Light:Sci. Appl."},{"key":"oe-33-4-7645-R6","doi-asserted-by":"publisher","first-page":"2898","DOI":"10.1016\/j.rinp.2017.08.010","volume":"7","author":"Li","year":"2017","journal-title":"Results Phys."},{"key":"oe-33-4-7645-R7","doi-asserted-by":"publisher","first-page":"14244","DOI":"10.1364\/OE.20.014244","volume":"20","author":"Durfee","year":"2012","journal-title":"Opt. Express"},{"key":"oe-33-4-7645-R8","doi-asserted-by":"publisher","first-page":"1259","DOI":"10.1103\/PhysRevLett.62.1259","volume":"62","author":"Corkum","year":"1989","journal-title":"Phys. Rev. Lett."},{"key":"oe-33-4-7645-R9","doi-asserted-by":"publisher","first-page":"20180182","DOI":"10.1098\/rsta.2018.0182","volume":"377","author":"Manahan","year":"2019","journal-title":"Philos. Trans. R. Soc., A"},{"key":"oe-33-4-7645-R10","doi-asserted-by":"publisher","first-page":"1168","DOI":"10.1364\/JOSA.60.001168","volume":"60","author":"Collins","year":"1970","journal-title":"J. Opt. Soc. Am."},{"key":"oe-33-4-7645-R11","doi-asserted-by":"publisher","first-page":"8642","DOI":"10.1364\/OPEX.13.008642","volume":"13","author":"Akturk","year":"2005","journal-title":"Opt. Express"},{"key":"oe-33-4-7645-R12","doi-asserted-by":"publisher","first-page":"15808","DOI":"10.1364\/OE.17.015808","volume":"17","author":"Coughlan","year":"2009","journal-title":"Opt. Express"},{"key":"oe-33-4-7645-R13","doi-asserted-by":"publisher","first-page":"2437","DOI":"10.1364\/JOSAA.31.002437","volume":"31","author":"Zhang","year":"2014","journal-title":"J. Opt. Soc. Am. A"},{"key":"oe-33-4-7645-R15","doi-asserted-by":"crossref","DOI":"10.1364\/DLAI.1998.MQ1","article-title":"How to (Maybe) Measure Laser Beam Quality","author":"Siegman","year":"1998"},{"key":"oe-33-4-7645-R16","author":"Siegman","year":"2006"},{"key":"oe-33-4-7645-R17","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1021\/acsphotonics.8b01437","volume":"6","author":"Kondakci","year":"2019","journal-title":"ACS Photonics"},{"key":"oe-33-4-7645-R18","doi-asserted-by":"publisher","first-page":"033512","DOI":"10.1103\/PhysRevA.103.033512","volume":"103","author":"Jolly","year":"2021","journal-title":"Phys. Rev. A"},{"key":"oe-33-4-7645-R19","doi-asserted-by":"publisher","first-page":"10237","DOI":"10.1364\/OE.485072","volume":"31","author":"Jolly","year":"2023","journal-title":"Opt. Express"},{"key":"oe-33-4-7645-R20","doi-asserted-by":"publisher","first-page":"5435","DOI":"10.1038\/s41467-024-49819-4","volume":"15","author":"Liu","year":"2024","journal-title":"Nat. Commun."}],"container-title":["Optics Express"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-33-4-7645&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,14]],"date-time":"2025-02-14T11:22:19Z","timestamp":1739532139000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=oe-33-4-7645"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,14]]},"references-count":19,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025]]},"published-print":{"date-parts":[[2025]]}},"URL":"https:\/\/doi.org\/10.1364\/oe.546012","relation":{},"ISSN":["1094-4087"],"issn-type":[{"value":"1094-4087","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,14]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OE.546012","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"research-article","name":"content_type","label":"Article type"},{"value":"Screened by Similarity Check","name":"cross_check","label":"Similarity check"},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"25 October 2024","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"5 February 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"14 February 2025","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article\u2019s title, journal citation, and DOI.","name":"copyright","label":"Copyright"}]}}