General law of refraction

General law of refraction | 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In Submit a Preprint Cite Share Download PDF Article General law of refraction Yuchuan Chen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4783430/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Refraction, accompanied with reflection is involved in all photonic devices, including emerging photonic materials constructed with lossy materials. However, refraction in a lossy medium is still a puzzle up to this day even though the law of refraction for lossless media, Snell’s law, was discovered over a millennium ago. To obtain predictable designs and allow for valuable evaluation of photonic materials, a general law of refraction valid for lossy media becomes indispensable. Here we derive it from the phase continuity of electromagnetic waves by introducing a transition layer of permittivity and permeability with gradual variations between two media, instead of the single physical interface. It well simulates our experimental results of reflectance vs. incident angle and polarization at the interface of glass and indium tin oxide coating at multi wavelengths, which cannot be done by complex Snell’s law. With a real refraction angle in lossy media, it finally solves the millennium puzzle of refraction in a lossy medium. It covers Snell’s law and reveals a new phenomenon of incident angle and polarization independent reflection, some kind of invisibility. It will contribute to the designs of photonic materials, correct the complex permittivity measured by ellipsometry and improve the design of external total reflection of X-ray. Physical sciences/Optics and photonics/Applied optics/Integrated optics Physical sciences/Physics/Optical physics/Sub-wavelength optics Physical sciences/Optics and photonics/Applied optics/Solar energy and photovoltaic technology Physical sciences/Optics and photonics/Optical materials and structures/Metamaterials Physical sciences/Optics and photonics/Optical techniques/Imaging and sensing Full Text Additional Declarations (Not answered) Cite Share Download PDF Status: Posted 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. 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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-4783430","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":331121468,"identity":"f343a5a9-9659-4cd5-a01c-ff74b7cf3834","order_by":0,"name":"Yuchuan Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyElEQVRIiWNgGAWjYHACNiC2kQESjAcSSNCSxgNiHUggUg9Iy2GIFgZitBgcP/zswccd53n4+w8fOPDwh00eA/vhoxvwajmTZm4488xtHokbaQlAh6UVM/Ckpd3Aq+UGD5s0b9ttHoYbPAZALYcTGyR4zAhr+dt2jkf+/BlStDC2HQBakUOkFskzaWaSvW3JPIZgv6SlJbYR8gsfMMQkfrbZycmdP3wQGGA2if3sh4/h1aJwAF2EDZ9yEJBvIKRiFIyCUTAKRgEAGGBOvFIFCboAAAAASUVORK5CYII=","orcid":"","institution":"Lasoliton LLC","correspondingAuthor":true,"prefix":"","firstName":"Yuchuan","middleName":"","lastName":"Chen","suffix":""}],"badges":[],"createdAt":"2024-07-22 16:50:34","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4783430/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4783430/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":61400912,"identity":"175a57b0-be6e-4951-8927-9bb06271bb88","added_by":"auto","created_at":"2024-07-30 09:54:11","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":440777,"visible":true,"origin":"","legend":"","description":"","filename":"GenerallawofrefractionLSAYCChen.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4783430/v1_covered_eebd8628-fdf9-4366-bfaa-bef42f6128d5.pdf"}],"financialInterests":"(Not answered)","formattedTitle":"General law of refraction","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4783430/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4783430/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRefraction, accompanied with reflection is involved in all photonic devices, including emerging photonic materials constructed with lossy materials. However, refraction in a lossy medium is still a puzzle up to this day even though the law of refraction for lossless media, Snell\u0026rsquo;s law, was discovered over a millennium ago. To obtain predictable designs and allow for valuable evaluation of photonic materials, a general law of refraction valid for lossy media becomes indispensable. Here we derive it from the phase continuity of electromagnetic waves by introducing a transition layer of permittivity and permeability with gradual variations between two media, instead of the single physical interface. It well simulates our experimental results of reflectance vs. incident angle and polarization at the interface of glass and indium tin oxide coating at multi wavelengths, which cannot be done by complex Snell\u0026rsquo;s law. With a real refraction angle in lossy media, it finally solves the millennium puzzle of refraction in a lossy medium. It covers Snell\u0026rsquo;s law and reveals a new phenomenon of incident angle and polarization independent reflection, some kind of invisibility. 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