[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-439479-105":59,"doc-detail-439479-en":129},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":122,"head_meta":124,"extra_data":126,"updated_unix":128},105,"en","physical-interpretation-of-diffractive-optical-networks-for-high-dimensional-vortex-mode-sorting","Physical Interpretation of Diffractive Optical Networks for High-Dimensional Vortex Mode Sorting","","Despite major progress of diffractive optical networks in tasks like mode multiplexing and demultiplexing, layer-by-layer physical meanings remain insufficiently explored. This study reveals physical transformation rules for each layer in trained diffractive networks under well-defined input/output mode relations for high-dimensional vortex mode sorting. A mask-number–dependent transformation partition is observed, linked to saturated sorting performance. The work also demonstrates using physical interpretation to design high-performance parameter-varying networks and guides mode-conversion systems.",{"@graph":69,"@context":121},[70,84,104],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/physical-interpretation-of-diffractive-optical-networks-for-high-dimensional-vortex-mode-sorting/439479/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":98,"encodingFormat":97,"isAccessibleForFree":99,"interactionStatistic":100},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/physical-interpretation-of-diffractive-optical-networks-for-high-dimensional-vortex-mode-sorting/439479.png","ImageObject",300,407,{"name":92,"@type":93},"วิน","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-29",true,{"@type":101,"interactionType":102,"userInteractionCount":4},"InteractionCounter",{"@type":103},"ViewAction",{"@type":105,"mainEntity":106},"FAQPage",[107,113,117],{"name":108,"@type":109,"acceptedAnswer":110},"What problem does the paper address about diffractive optical networks?","Question",{"text":111,"@type":112},"It addresses the lack of clear physical meanings behind complex diffractive networks, especially at the layer level, for mode sorting tasks.","Answer",{"name":114,"@type":109,"acceptedAnswer":115},"How are layer-wise transformation rules obtained in this work?",{"text":116,"@type":112},"The study defines input/output mode relations and shows physical transformation rules for each layer within trained diffractive networks.",{"name":118,"@type":109,"acceptedAnswer":119},"What observation is made when the number of masks increases?",{"text":120,"@type":112},"An intriguing physical transformation division phenomenon appears and is associated with the system’s saturated sorting performance as masks increase.","https://schema.org",{"og:url":83,"og:type":123,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":125,"canonical":83},"index,follow",{"doc_id":127,"site_id":62},439479,1790688852,{"code":4,"msg":5,"data":130},{"doc_id":127,"user_id":131,"nickname":92,"user_avatar":132,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":133,"file_id":134,"file_url":135,"file_type":136,"file_size":137,"view_count":4,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":138,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":139,"faqs":140,"seo_title":141,"seo_description":67,"update_tm":128,"read_time":142},2336475104736,"https://ap-avatar.wpscdn.com/avatar/22000c4c5e0e5b17e70?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786591360781797222","RESEARCH ARTICLE  \n[www.advancedscience.com](www.advancedscience.com)  \nPhysical Interpretation of Diffractive Optical Networks for High-Dimensional Vortex Mode Sorting  \nRuitao Wu, Juncheng Fang, Rui Pan, Rongyi Lin, Kaiyuan Li, Ting Lei,* Luping Du,*  \nand Xiaocong Yuan*  \nDespite the significant progress achieved by diffractive optical networks in diverse computing tasks, such as mode multiplexing and demultiplexing, investigations into the physical meanings behind complex diffractive networks at the layer level have been quite limited. Here, for high-dimensional vortex mode sorting tasks, the physical transformation rules for each layer within trained diffractive networks are shown to be revealed under properly defined input/output mode relations. An intriguing physical transformation division phenomenon, associated with the saturated sorting performance of the system, has been observed with an increasing number of masks. In addition, the use of physical interpretation for efficiently designing parameter-varying networks with high performance is also demonstrated. The physical interpretation of optical networks resolves the contradiction between rigorous physical theorems and operationally vague network structures, paving the way for designing and understanding systems for various mode conversion tasks, and inspiring further interpretation of diffractive networks in advanced tasks and other network structures.  \nlight conversion (MPLC) for the optical device community.[7–9] Perhaps the most interesting and well-known application of DNs/MPLCs is mode multiplexing/demultiplexing, since it directly relates to a crucial application, space-division optical communications. [10,11]  \nIn general, the design of diffractive surfaces for operating modes can be classified into two approaches. In certain scenarios, analytical solutions for the phase distribution have been reported and demonstrated. This approach is typically applied to low-dimensional mode transformations with a small number of masks with clear mathematical operations, such as the manipulation and sorting of orbital angular momentum (OAM) modes through dual-plane optical coordinate transformations. [12–14] In most cases, especially when the dimensionality of the problem increases and no known solutions are  \n1. Introduction  \nOptical diffractive networks (DNs) have been developed to perform computing at the speed of light in a power-efficient manner for diverse tasks or applications, including image classification,[1] optical imaging,[2] and quantum-related problems. [3] From a spatial mode manipulation perspective, the global functionality of a DN can be described by a linear matrix operator that performs input/output mode mapping. [4–6] Such operations are achieved through cascaded diffractive surfaces with spatially varying phase distributions, which are often referred to as multi-plane  \nR. Wu, J. Fang, R. Pan, R. Lin, K. Li, T. Lei, L. Du, X. Yuan Nanophotonics Research Center  \nInstitute of Microscale Optoelectronics & State Key Laboratory of Radio Frequency Heterogeneous Integration  \nShenzhen University  \nShenzhen 518060, China  \nE-mail: [leiting@szu.edu.cn](leiting@szu.edu.cn); [lpdu@szu.edu.cn](lpdu@szu.edu.cn); [xcyuan@szu.edu.cn](xcyuan@szu.edu.cn)  \nThe ORCID identification number(s) for the author(s) of this article  \ncan be found under [https://doi.org/10.1002/advs.202514100](https://doi.org/10.1002/advs.202514100)[ ](https://doi.org/10.1002/advs.202514100)© 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.  \nDOI: 10.1002/advs.202514100  \nfound, it is necessary to apply iterative optimization and inverse design algorithms, such as wave-front matching (WFM),[15,16] orthe machine-learning framework,[1] which have been proven tobe both efficient and flexible.  \nT","cbCaikiSpErie13x","https://ap.wps.com/l/cbCaikiSpErie13x","pdf",4258122,"English","# Introduction\n## Physical transformation and layer-wise interpretation for high-dimensional vortex mode sorting\n## Limitations of current black-box iterative design\n## Motivation and expected impact on mode-conversion device design","[{\"question\":\"What problem does the paper address about diffractive optical networks?\",\"answer\":\"It addresses the lack of clear physical meanings behind complex diffractive networks, especially at the layer level, for mode sorting tasks.\"},{\"question\":\"How are layer-wise transformation rules obtained in this work?\",\"answer\":\"The study defines input/output mode relations and shows physical transformation rules for each layer within trained diffractive networks.\"},{\"question\":\"What observation is made when the number of masks increases?\",\"answer\":\"An intriguing physical transformation division phenomenon appears and is associated with the system’s saturated sorting performance as masks increase.\"}]","Physical Interpretation of Diffractive Optical Networks for High-Dimensional Vortex Mode Sorting | PDF",25]