Analysis of splitting direction for coupling WGM resonators | 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 Analysis of splitting direction for coupling WGM resonators Jianwei Wang, Jiapeng Sun, Yeshuai Song, Xulong Yang, Yu Zhang, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4951735/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Jun, 2025 Read the published version in Applied Physics B → Version 1 posted 10 You are reading this latest preprint version Abstract The opposite splitting directions of mode splitting are observed in whispering gallery mode resonators, composed of coupling asymmetrical bispheres. A "virtual ellipsoid" model approximates the bispherical structure, linking the observed optical phenomena in bispheres to those in ellipsoids. The splitting characteristics are investigated theoretically and experimentally, including intensity difference and wavelength separation. The splitting direction is determined by the positions of the fundamental mode and azimuthal mode in the splitting peaks. Experimental results reveal that the resonant wavelength of the splitting peaks exhibits a redshift due to the increased diameter of Sphere D 2 , which is attributed to longer light propagation paths in the whispering gallery mode. The optical barcodes converted from transmission spectra provides potential applications for measuring the sizes of microspheres or ellipsoids, and their uniqueness can also be utilized for optical information identification. Whispering gallery mode Coupling WGM resonators Mode splitting Optical barcodes Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 04 Jun, 2025 Read the published version in Applied Physics B → Version 1 posted Editorial decision: Revision requested 03 Mar, 2025 Reviews received at journal 11 Feb, 2025 Reviews received at journal 11 Feb, 2025 Reviewers agreed at journal 05 Feb, 2025 Reviewers agreed at journal 03 Feb, 2025 Reviewers agreed at journal 29 Oct, 2024 Reviewers invited by journal 09 Oct, 2024 Editor assigned by journal 04 Sep, 2024 Submission checks completed at journal 22 Aug, 2024 First submitted to journal 21 Aug, 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. 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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-4951735","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":353161584,"identity":"cca9cb2b-4964-4bd8-8617-0a737ee962ae","order_by":0,"name":"Jianwei Wang","email":"","orcid":"","institution":"Harbin Engineering University","correspondingAuthor":false,"prefix":"","firstName":"Jianwei","middleName":"","lastName":"Wang","suffix":""},{"id":353161585,"identity":"f3dcc651-c511-49e4-830d-f6536fb7381d","order_by":1,"name":"Jiapeng Sun","email":"","orcid":"","institution":"Harbin Engineering University","correspondingAuthor":false,"prefix":"","firstName":"Jiapeng","middleName":"","lastName":"Sun","suffix":""},{"id":353161586,"identity":"58d86db6-ca43-4040-ba6f-963b04882286","order_by":2,"name":"Yeshuai Song","email":"","orcid":"","institution":"Harbin Engineering University","correspondingAuthor":false,"prefix":"","firstName":"Yeshuai","middleName":"","lastName":"Song","suffix":""},{"id":353161587,"identity":"17792247-b12d-4ddb-bab8-d3501b01b9b7","order_by":3,"name":"Xulong Yang","email":"","orcid":"","institution":"Harbin Engineering University","correspondingAuthor":false,"prefix":"","firstName":"Xulong","middleName":"","lastName":"Yang","suffix":""},{"id":353161588,"identity":"4a4eb3a7-8174-42f6-9a4b-a63dd804192e","order_by":4,"name":"Yu Zhang","email":"","orcid":"","institution":"Harbin Engineering University","correspondingAuthor":false,"prefix":"","firstName":"Yu","middleName":"","lastName":"Zhang","suffix":""},{"id":353161589,"identity":"d7a66b61-5deb-44c5-be11-3013892ec89c","order_by":5,"name":"Zhihai Liu","email":"","orcid":"","institution":"Harbin Engineering University","correspondingAuthor":false,"prefix":"","firstName":"Zhihai","middleName":"","lastName":"Liu","suffix":""},{"id":353161590,"identity":"b659c181-fd18-41e2-b47b-44714260edb9","order_by":6,"name":"Hanyang Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxElEQVRIiWNgGAWjYBACAxiDj5n5AIla2JjZEkjVwsBjgE8hApiznz0m8XNHLQMbO8/HG28Y7OR0GwhosezJS5PsPXMc6DDezZZzGJKNzQ4QctiBHDMJ3rZjIC3bpHkYDiRuI6jl/Bszyb9gLTzPiNRyI8dMmretBqSFjVgtb4ytZdsOgALZ2HKOATF+OZ9jePNtWx0DP//hhzfeVNjJEdQCBCwSDAyH6xuALAlio4b5AwNDHZglwUOcjlEwCkbBKBhhAAAPJDmL0qkjIgAAAABJRU5ErkJggg==","orcid":"","institution":"Harbin Engineering University","correspondingAuthor":true,"prefix":"","firstName":"Hanyang","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2024-08-21 12:51:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4951735/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4951735/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00340-025-08501-3","type":"published","date":"2025-06-04T15:56:51+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":84242328,"identity":"4f9ae922-291c-4ef8-8708-0323db6bca00","added_by":"auto","created_at":"2025-06-09 16:00:22","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":863960,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4951735/v1_covered_a40ac575-3a46-4094-8e2f-b52b5ad5e85c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Analysis of splitting direction for coupling WGM resonators","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":"
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