Defective States of Structured Light for High-Capacity Information Transmission

Defective States of Structured Light for High-Capacity Information Transmission | 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 Defective States of Structured Light for High-Capacity Information Transmission Zilong Zhang, Yuqi Wang, Lianghaoyue Zhang, Hongzhi Yang, Suyi Zhao, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5562627/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Aug, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Structured light brings a breakthrough in information capacity carried by the laser field, finding an ideal utility in optical information transmission. Advancements in optical intensity-based imaging have facilitated the use of structured light for simple information decoding. However, the practicality of available structured-light-based encoding methods is limited by the scarcity of easily distinguishable beam structures. What’s more, currently the structured light is confined to digital bits encoding or channel distinguishing that needs the decoding process, due to a single structured pattern still lacking of effective information. Here, in response to these limitations, we propose a method for extremely high-capacity information encoding, as well as image direct transmission, by modulating the structured light to defective states. Hermite-Gaussian (HG) eigenmode in defect states are designed and generated to achieve a large quantity of easily distinguishable patterns. With well-designed two-dimensional binary hologram gratings to generate different defects in a single HG mode, we achieve over 10 n ( n > 10) of varying laser states for encoding, corresponding to information capacity being tens of bits. These defect states are recognized by image processing method for quick decoding. What’s more, various image patterns can also be generated and are possible to achieve long-distance transmission with high fidelity. It means that the images can be directly transmitted without Fourier lens imaging, which paves a new way for information transmission. Free propagation and atmospheric turbulence performance of the defective mode are investigated to prove the defective mode has a similar performance to the standard eigenmode and is practical for information transmission. Physical sciences/Optics and photonics/Lasers, LEDs and light sources Physical sciences/Optics and photonics/Optical techniques Full Text Additional Declarations There is NO Competing Interest. Supplementary Files SupplementarymaterialNC.docx Supplementary material Chinesecharactersv2.mp4 Defective mode for Chinese characters v2 DecodingofdefectiveHG77mode.mp4 Decoding of defective HG 77 mode HGdefectmodegeneration.avi HG defect mode generation Chinesecharatersv1.mp4 Defective mode for Chinese characters v1 digitsletters.mp4 Defective mode for digits and letters Cite Share Download PDF Status: Published Journal Publication published 22 Aug, 2025 Read the published version in Nature Communications → 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-5562627","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":400553245,"identity":"7348b10f-2bbd-4841-b239-938112891b6c","order_by":0,"name":"Zilong Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1UlEQVRIiWNgGAWjYDACdgY2ECVnwAyi2IjRwgxRZmzAzEyilsQNDMRqkW9mf/bg547a9O3s/AcYPpQdZuCf3YBfC2MzQ7ph75njuTubmRkYZ5w7zCBx5wABdzEzHJPgbTuWu+EwMwMzb9thBgOJBPxa2JgZ2yT/th1LNwBp+UuMFh5mZjZp3raaBLAWRmK0SDCzsUnLth0wBPrF4GDPuXQeiRsEtMi3tz+TfNtWJ2/Of/Dhgx9l1nL8MwhogYLDYPIAyKVEqQeCOmIVjoJRMApGwUgEAChjOZqf1xgHAAAAAElFTkSuQmCC","orcid":"","institution":"Beijing Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Zilong","middleName":"","lastName":"Zhang","suffix":""},{"id":400553246,"identity":"78c2290c-46f8-4b98-8f23-b8db563e9107","order_by":1,"name":"Yuqi Wang","email":"","orcid":"","institution":"Beijing Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Yuqi","middleName":"","lastName":"Wang","suffix":""},{"id":400553247,"identity":"14f44d76-9f56-4be4-b35d-bf7be0865977","order_by":2,"name":"Lianghaoyue Zhang","email":"","orcid":"","institution":"Beijing Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Lianghaoyue","middleName":"","lastName":"Zhang","suffix":""},{"id":400553248,"identity":"878e92ea-520c-41c9-b5ca-04a45455f924","order_by":3,"name":"Hongzhi Yang","email":"","orcid":"","institution":"China Academy of Aerospace Science and Innovation","correspondingAuthor":false,"prefix":"","firstName":"Hongzhi","middleName":"","lastName":"Yang","suffix":""},{"id":400553249,"identity":"7b707f69-86ae-46f2-a18d-0d75fab9f01f","order_by":4,"name":"Suyi Zhao","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Suyi","middleName":"","lastName":"Zhao","suffix":""},{"id":400553250,"identity":"3a407c17-f48c-4910-9b6a-0ab935a148e1","order_by":5,"name":"Xiangyang Pan","email":"","orcid":"","institution":"Beijing Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Xiangyang","middleName":"","lastName":"Pan","suffix":""},{"id":400553251,"identity":"cd37fa43-7c9f-483f-a005-5e3d71fc1dc0","order_by":6,"name":"Wei He","email":"","orcid":"","institution":"Beijing Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Wei","middleName":"","lastName":"He","suffix":""},{"id":400553252,"identity":"80dbf6f2-d8a2-46a8-a905-87ca5a83a761","order_by":7,"name":"Yunfei Ma","email":"","orcid":"","institution":"Beijing Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Yunfei","middleName":"","lastName":"Ma","suffix":""},{"id":400553253,"identity":"b254948a-50a2-492a-9b8c-1f282f8038f6","order_by":8,"name":"Lingyu Kong","email":"","orcid":"","institution":"Beijing Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Lingyu","middleName":"","lastName":"Kong","suffix":""},{"id":400553254,"identity":"d3577938-d13e-4b31-83da-684d98ac7e27","order_by":9,"name":"Lin Xiao","email":"","orcid":"","institution":"China Academy of Aerospace Science and Innovation","correspondingAuthor":false,"prefix":"","firstName":"Lin","middleName":"","lastName":"Xiao","suffix":""},{"id":400553255,"identity":"d5a07928-3bf7-47ce-9a83-91e510616743","order_by":10,"name":"Changming Zhao","email":"","orcid":"","institution":"Beijing Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Changming","middleName":"","lastName":"Zhao","suffix":""}],"badges":[],"createdAt":"2024-12-02 08:20:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5562627/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5562627/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-025-63100-2","type":"published","date":"2025-08-22T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":89716847,"identity":"2ebd6353-cd8c-48d2-b54f-6e62f54f3c1a","added_by":"auto","created_at":"2025-08-23 07:07:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":987726,"visible":true,"origin":"","legend":"","description":"","filename":"DefectSLforinformationtransmissionNC.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5562627/v1_covered_8589eb5f-d0ee-4602-adaf-7eceab08c5f2.pdf"},{"id":73613464,"identity":"87a6609d-c4bf-4444-ba72-718c7b00711b","added_by":"auto","created_at":"2025-01-13 02:19:39","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":2945213,"visible":true,"origin":"","legend":"Supplementary material","description":"","filename":"SupplementarymaterialNC.docx","url":"https://assets-eu.researchsquare.com/files/rs-5562627/v1/0a68c8c432d53600d15c8fb0.docx"},{"id":73613467,"identity":"52740c80-a2c2-4735-8dc0-5416f0fcbbf3","added_by":"auto","created_at":"2025-01-13 02:19:40","extension":"mp4","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":6835206,"visible":true,"origin":"","legend":"Defective mode for Chinese characters v2","description":"","filename":"Chinesecharactersv2.mp4","url":"https://assets-eu.researchsquare.com/files/rs-5562627/v1/cbd65f80278beb12cddf3411.mp4"},{"id":73614355,"identity":"eb70e3da-7af8-4328-a5e1-ff10b45312e2","added_by":"auto","created_at":"2025-01-13 02:27:40","extension":"mp4","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":8060021,"visible":true,"origin":"","legend":"\u003cp\u003eDecoding of defective HG\u003csup\u003e\u003csub\u003e77\u003c/sub\u003e\u003c/sup\u003e mode\u003c/p\u003e","description":"","filename":"DecodingofdefectiveHG77mode.mp4","url":"https://assets-eu.researchsquare.com/files/rs-5562627/v1/f385be7bd3e70b96c513af84.mp4"},{"id":73613476,"identity":"124dd975-411f-4d10-b284-62aaa5546938","added_by":"auto","created_at":"2025-01-13 02:19:40","extension":"avi","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":10722462,"visible":true,"origin":"","legend":"HG defect mode generation","description":"","filename":"HGdefectmodegeneration.avi","url":"https://assets-eu.researchsquare.com/files/rs-5562627/v1/eb151ee08bcd2501eb3681f1.avi"},{"id":73613481,"identity":"683bcb4f-559c-4528-91b7-d7c7ae786f94","added_by":"auto","created_at":"2025-01-13 02:19:40","extension":"mp4","order_by":5,"title":"","display":"","copyAsset":false,"role":"supplement","size":19590758,"visible":true,"origin":"","legend":"Defective mode for Chinese characters v1","description":"","filename":"Chinesecharatersv1.mp4","url":"https://assets-eu.researchsquare.com/files/rs-5562627/v1/00f324997c6b920b1d386b3c.mp4"},{"id":73613484,"identity":"95e6ab1c-6619-42d0-9ffb-5278f0f2c345","added_by":"auto","created_at":"2025-01-13 02:19:41","extension":"mp4","order_by":6,"title":"","display":"","copyAsset":false,"role":"supplement","size":42159688,"visible":true,"origin":"","legend":"Defective mode for digits and letters","description":"","filename":"digitsletters.mp4","url":"https://assets-eu.researchsquare.com/files/rs-5562627/v1/ce391b41a0912cec171d0896.mp4"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Defective States of Structured Light for High-Capacity Information Transmission","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"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-5562627/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5562627/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eStructured light brings a breakthrough in information capacity carried by the laser field, finding an ideal utility in optical information transmission. Advancements in optical intensity-based imaging have facilitated the use of structured light for simple information decoding. However, the practicality of available structured-light-based encoding methods is limited by the scarcity of easily distinguishable beam structures. What\u0026rsquo;s more, currently the structured light is confined to digital bits encoding or channel distinguishing that needs the decoding process, due to a single structured pattern still lacking of effective information. Here, in response to these limitations, we propose a method for extremely high-capacity information encoding, as well as image direct transmission, by modulating the structured light to defective states. Hermite-Gaussian (HG) eigenmode in defect states are designed and generated to achieve a large quantity of easily distinguishable patterns. With well-designed two-dimensional binary hologram gratings to generate different defects in a single HG mode, we achieve over 10\u003csup\u003e\u003cem\u003en\u003c/em\u003e\u003c/sup\u003e (\u003cem\u003en\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;10) of varying laser states for encoding, corresponding to information capacity being tens of bits. These defect states are recognized by image processing method for quick decoding. What\u0026rsquo;s more, various image patterns can also be generated and are possible to achieve long-distance transmission with high fidelity. It means that the images can be directly transmitted without Fourier lens imaging, which paves a new way for information transmission. Free propagation and atmospheric turbulence performance of the defective mode are investigated to prove the defective mode has a similar performance to the standard eigenmode and is practical for information transmission.\u003c/p\u003e","manuscriptTitle":"Defective States of Structured Light for High-Capacity Information Transmission","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-13 02:19:35","doi":"10.21203/rs.3.rs-5562627/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":"b0d169f3-f5d9-4991-9580-c39fa7cef9bb","owner":[],"postedDate":"January 13th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":42693308,"name":"Physical sciences/Optics and photonics/Lasers, LEDs and light sources"},{"id":42693309,"name":"Physical sciences/Optics and photonics/Optical techniques"}],"tags":[],"updatedAt":"2025-08-23T07:07:25+00:00","versionOfRecord":{"articleIdentity":"rs-5562627","link":"https://doi.org/10.1038/s41467-025-63100-2","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2025-08-22 04:00:00","publishedOnDateReadable":"August 22nd, 2025"},"versionCreatedAt":"2025-01-13 02:19:35","video":"","vorDoi":"10.1038/s41467-025-63100-2","vorDoiUrl":"https://doi.org/10.1038/s41467-025-63100-2","workflowStages":[]},"version":"v1","identity":"rs-5562627","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5562627","identity":"rs-5562627","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}