Unveiling unique ultrafast nonlinearities in liquid-phase high-order harmonic generation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Unveiling unique ultrafast nonlinearities in liquid-phase high-order harmonic generation Pengfei Lan, Wanchen Tao, Zhuang-Wei Ding, Lixin He, Changlong Xia, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7261581/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract High-order harmonic generation (HHG) provides a powerful optical tool for probing ultrafast dynamics on the attosecond timescale. While its mechanisms in gases and solids are well-established, understanding nonlinear optical responses in liquids remains challenging. The absence of long-range order in liquids questions the applicability of the existing HHG models developed in other media. Through combined experimental and theoretical investigations, we identify unique characters of liquid-phase HHG-spectral redshift and broadening, which are fundamentally distinct from both the gaseous and solid-state counterparts. Quantitative measurements and simulations of HHG in liquids illustrate a near linear dependence of harmonic redshift and broadening on the laser intensity, with the nonlinear response of water exceeding that of ethanol. The simulations reveal that these features arise from delocalized electronic states with energy loss in multiple scatterings and transient Stark shift during their transitions in laser fields. Meanwhile, we find that liquid polarity or hydrogen bond exerts decisive control over the transition dipole momentum distributions of delocalized states. Our findings establish a nonlinear spectral method for probing the internal network in liquids, paving the way for studying its role in chemical and biological processes. Physical sciences/Physics/Optical physics/High-harmonic generation Physical sciences/Physics/Atomic and molecular physics/Attosecond science Full Text Additional Declarations There is NO Competing Interest. Supplementary Files SM0731.pdf Unveiling unique ultrafast nonlinearities in liquid-phase high-order harmonic generation: supplementary information Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7261581","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":500108271,"identity":"67dfe4ff-3fb5-4129-ab92-1043aadfbe79","order_by":0,"name":"Pengfei Lan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/UlEQVRIiWNgGAWjYLCCCgYJGQYG5mNQbgIRWs4wSPAwMLClAZkGRGthAGrhMSNOizl77+EXByosePhn93x7zPPnDwM/e44Bw88duLVY9pxLszhwRoJH4s7Z7ca8bQYMkj1vDBh7z+DWYnAjx8z4YxvQLzdyt0nzNhiARAyYGdvwaLn/xszg4D8JHvkbOc+kef4YMNgT1HKDx/jBwQYJHqDhbNI8bEBbJAhosezJMWM4cEyCx/BGmpnk3DZjHokzzwoO9uLRYs5+xvjDgZo6Obkbyc8k3vyRk+NvT9744Cc+hwGjUAJZgAdEHMCtAayF+QM+BaNgFIyCUTAKGADMLE2qK7FtwwAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-1111-5308","institution":"Huazhong University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Pengfei","middleName":"","lastName":"Lan","suffix":""},{"id":500108272,"identity":"6279f07d-e628-44a4-ad5a-e75ed8eef3a6","order_by":1,"name":"Wanchen Tao","email":"","orcid":"","institution":"Huazhong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Wanchen","middleName":"","lastName":"Tao","suffix":""},{"id":500108273,"identity":"4ab97301-db6d-404b-9acb-6ae13baeb725","order_by":2,"name":"Zhuang-Wei Ding","email":"","orcid":"","institution":"Innovation Academy for Precision Measurement Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Zhuang-Wei","middleName":"","lastName":"Ding","suffix":""},{"id":500108274,"identity":"aab4310b-a382-4afb-a319-e18dd42f6cc1","order_by":3,"name":"Lixin He","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Lixin","middleName":"","lastName":"He","suffix":""},{"id":500108275,"identity":"6a685273-7a8b-4f14-8476-331a7beb8488","order_by":4,"name":"Changlong Xia","email":"","orcid":"","institution":"Shanxi Normal University","correspondingAuthor":false,"prefix":"","firstName":"Changlong","middleName":"","lastName":"Xia","suffix":""},{"id":500108276,"identity":"6c356ceb-bcc3-457d-bb53-8bb561fb8f5d","order_by":5,"name":"Xingdong Guan","email":"","orcid":"","institution":"Huazhong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Xingdong","middleName":"","lastName":"Guan","suffix":""},{"id":500108277,"identity":"18e3622a-23ff-4ba1-aef7-b7e5ba52e5f6","order_by":6,"name":"Xue-Bin Bian","email":"","orcid":"https://orcid.org/0000-0002-5537-833X","institution":"Wuhan Institute of Physics and Mathematics","correspondingAuthor":false,"prefix":"","firstName":"Xue-Bin","middleName":"","lastName":"Bian","suffix":""},{"id":500108278,"identity":"a15de566-7a43-4282-9978-e9d84bdb2f10","order_by":7,"name":"Peixiang Lu","email":"","orcid":"https://orcid.org/0000-0001-6993-8986","institution":"Huazhong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Peixiang","middleName":"","lastName":"Lu","suffix":""}],"badges":[],"createdAt":"2025-07-31 11:16:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7261581/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7261581/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104061492,"identity":"d0b2c1f4-c510-4f84-b35b-4387b6eb2957","added_by":"auto","created_at":"2026-03-06 09:43:29","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2835728,"visible":true,"origin":"","legend":"Article File","description":"","filename":"manuscript0731.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7261581/v1_covered_f954e668-c650-4633-ae0f-e4b19176767f.pdf"},{"id":89291894,"identity":"3c06a31f-1d35-4774-9d63-d3baebf499d0","added_by":"auto","created_at":"2025-08-18 12:34:05","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1926253,"visible":true,"origin":"","legend":"Unveiling unique ultrafast nonlinearities in liquid-phase high-order harmonic generation: supplementary information","description":"","filename":"SM0731.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7261581/v1/306fc17c3ede982ff1e801e4.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Unveiling unique ultrafast nonlinearities in liquid-phase high-order harmonic generation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"
[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7261581/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7261581/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"High-order harmonic generation (HHG) provides a powerful optical tool for probing ultrafast dynamics on the attosecond timescale. While its mechanisms in gases and solids are well-established, understanding nonlinear optical responses in liquids remains challenging. The absence of long-range order in liquids questions the applicability of the existing HHG models developed in other media. Through combined experimental and theoretical investigations, we identify unique characters of liquid-phase HHG-spectral redshift and broadening, which are fundamentally distinct from both the gaseous and solid-state counterparts. Quantitative measurements and simulations of HHG in liquids illustrate a near linear dependence of harmonic redshift and broadening on the laser intensity, with the nonlinear response of water exceeding that of ethanol. The simulations reveal that these features arise from delocalized electronic states with energy loss in multiple scatterings and transient Stark shift during their transitions in laser fields. Meanwhile, we find that liquid polarity or hydrogen bond exerts decisive control over the transition dipole momentum distributions of delocalized states. Our findings establish a nonlinear spectral method for probing the internal network in liquids, paving the way for studying its role in chemical and biological processes.","manuscriptTitle":"Unveiling unique ultrafast nonlinearities in liquid-phase high-order harmonic generation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-18 12:34:00","doi":"10.21203/rs.3.rs-7261581/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"
[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"eb89b404-3f0d-4b29-8bfa-63e010cd60ba","owner":[],"postedDate":"August 18th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":53127379,"name":"Physical sciences/Physics/Optical physics/High-harmonic generation"},{"id":53127380,"name":"Physical sciences/Physics/Atomic and molecular physics/Attosecond science"}],"tags":[],"updatedAt":"2026-03-09T10:48:52+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-18 12:34:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7261581","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7261581","identity":"rs-7261581","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}
Text is read by the "Ask this paper" AI Q&A widget below.
Extraction quality varies by source — PMC NXML preserves structure
cleanly, OA-HTML may include some navigation residue, and OA-PDF can
have broken hyphenation. The publisher copy
(via DOI)
is the canonical version.