Theoretical investigation of slow gain recovery of quantum cascade lasers observed in pump-probe experiment

Theoretical investigation of slow gain recovery of quantum cascade lasers observed in pump-probe experiment | 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 Research Article Theoretical investigation of slow gain recovery of quantum cascade lasers observed in pump-probe experiment Mrinmoy Kundu, Aroni Ghosh, Abdullah Jubair Bin Iqbal, Muhammad Anisuzzaman Talukder This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5332834/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 24 Jun, 2025 Read the published version in Optical and Quantum Electronics → Version 1 posted 9 You are reading this latest preprint version Abstract Time-resolved spectroscopy-based pump-probe experiments performed on quantum cascade lasers (QCLs) exhibit an initial fast gain recovery followed by a slow tail such that the equilibrium gain is not recovered in a cavity round-trip time. This ultra-slow gain recovery or non-recovered gain cannot be explained by only the intersubband carrier dynamics of QCLs. This work shows that the Fabry-Perot cavity dynamics and localized intersubband electron heating of QCLs are essential in ultra-slow and nonrecovered gain recovery. We developed a comprehensive model, coupling cavity dynamics to the intersubband electrons' thermal evolution. We employ a four-level coupled Maxwell-Bloch model that considers temperature-dependent scattering and transport mechanisms in calculating the gain recovery dynamics. If an intense pump pulse electrically pumped close to the threshold propagates in the forward direction after being coupled into the cavity, the reflected pump pulse will significantly deplete the gain medium while propagating in the backward direction. Additionally, we show that the intersubband electron sustains a localized high temperature even after the pump pulse has left, which affects the overall carrier dynamics and leads to an ultra-slow gain recovery process. At near-perfect reflectivity, we observe a gain depletion of 4% for 2 mm QCL. We further demonstrate that an additional 10% gain depletion of probe pulse is seen at a steady state when the laser is pumped at 1.6 times the threshold compared to the case where the hot electron effect is not considered. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 24 Jun, 2025 Read the published version in Optical and Quantum Electronics → Version 1 posted Editorial decision: Revision requested 31 Mar, 2025 Reviews received at journal 31 Mar, 2025 Reviews received at journal 04 Feb, 2025 Reviewers agreed at journal 30 Oct, 2024 Reviewers agreed at journal 28 Oct, 2024 Reviewers invited by journal 28 Oct, 2024 Editor assigned by journal 28 Oct, 2024 Submission checks completed at journal 26 Oct, 2024 First submitted to journal 25 Oct, 2024 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. 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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-5332834","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":373468944,"identity":"10dbe4b6-7c0f-4d5c-8225-deeb92e4014d","order_by":0,"name":"Mrinmoy Kundu","email":"","orcid":"","institution":"Bangladesh University of Engineering and Technology","correspondingAuthor":false,"prefix":"","firstName":"Mrinmoy","middleName":"","lastName":"Kundu","suffix":""},{"id":373468945,"identity":"7563710b-8078-4e04-a594-8c324e2828d8","order_by":1,"name":"Aroni Ghosh","email":"","orcid":"","institution":"Bangladesh University of Engineering and Technology","correspondingAuthor":false,"prefix":"","firstName":"Aroni","middleName":"","lastName":"Ghosh","suffix":""},{"id":373468946,"identity":"541e270b-24ce-49c4-b744-97ed3578a87a","order_by":2,"name":"Abdullah Jubair Bin Iqbal","email":"","orcid":"","institution":"Bangladesh University of Engineering and Technology","correspondingAuthor":false,"prefix":"","firstName":"Abdullah","middleName":"Jubair Bin","lastName":"Iqbal","suffix":""},{"id":373468947,"identity":"6ca989a2-6c12-4b08-96cb-6f49c8afcc68","order_by":3,"name":"Muhammad Anisuzzaman Talukder","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVRIiWNgGAWjYFACxgaGDyBaAiYgwWBAUAvjDJiWA8RpYWBg5iFJC//s5ubPNhU2cgzSPYaPPzDYyTNIN2/Aq0XizsE26ZwzacYMMmeMDQ4wJBs2yBwrwO+qG4ltzLlthxMbJHLMJA4wMCcwSOTgd5j8jcTmz5b//tcDtZj/OMBQT1iLwY3EBmnGhgMglWZA7x8mrMUQ6DDJnmPJhm0yx4olzhgcBzHw+0XuRvrjDz9q7OT5pZs3fqioqAYx8IcYHLBB3AljjIJRMApGwSigCAAA/7VB+9+TIEMAAAAASUVORK5CYII=","orcid":"","institution":"Bangladesh University of Engineering and Technology","correspondingAuthor":true,"prefix":"","firstName":"Muhammad","middleName":"Anisuzzaman","lastName":"Talukder","suffix":""}],"badges":[],"createdAt":"2024-10-25 13:53:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5332834/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5332834/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11082-025-08304-y","type":"published","date":"2025-06-24T15:56:52+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":85686020,"identity":"15c898f9-cd5e-4358-add6-2ba21c37becd","added_by":"auto","created_at":"2025-06-30 15:59:56","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1502914,"visible":true,"origin":"","legend":"","description":"","filename":"ThermalmodelofQCL241025.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5332834/v1_covered_4220b997-955d-4472-ba90-4bd86f97dfe4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Theoretical investigation of slow gain recovery of quantum cascade lasers observed in pump-probe experiment","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"optical-and-quantum-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"oqel","sideBox":"Learn more about [Optical and Quantum Electronics](https://www.springer.com/journal/11082)","snPcode":"11082","submissionUrl":"https://submission.nature.com/new-submission/11082/3","title":"Optical and Quantum Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5332834/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5332834/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Time-resolved spectroscopy-based pump-probe experiments performed on quantum cascade lasers (QCLs) exhibit an initial fast gain recovery followed by a slow tail such that the equilibrium gain is not recovered in a cavity round-trip time. This ultra-slow gain recovery or non-recovered gain cannot be explained by only the intersubband carrier dynamics of QCLs. This work shows that the Fabry-Perot cavity dynamics and localized intersubband electron heating of QCLs are essential in ultra-slow and nonrecovered gain recovery. We developed a comprehensive model, coupling cavity dynamics to the intersubband electrons' thermal evolution. We employ a four-level coupled Maxwell-Bloch model that considers temperature-dependent scattering and transport mechanisms in calculating the gain recovery dynamics. If an intense pump pulse electrically pumped close to the threshold propagates in the forward direction after being coupled into the cavity, the reflected pump pulse will significantly deplete the gain medium while propagating in the backward direction. Additionally, we show that the intersubband electron sustains a localized high temperature even after the pump pulse has left, which affects the overall carrier dynamics and leads to an ultra-slow gain recovery process. At near-perfect reflectivity, we observe a gain depletion of 4\\% for 2 mm QCL. We further demonstrate that an additional 10\\% gain depletion of probe pulse is seen at a steady state when the laser is pumped at 1.6 times the threshold compared to the case where the hot electron effect is not considered. 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