[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120503-en":3,"doc-seo-120503-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120503,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Machine learning assisted inverse design of microresonators - Research Article","High demand for fabricating microresonators with target optical properties drives methods to optimize geometry, mode structures, nonlinearities, and dispersion. Application-dependent dispersion can counter nonlinear effects and reshape intracavity optical dynamics. This paper uses a machine learning algorithm to infer microresonator geometry directly from dispersion profiles. A training set of about 460 finite-element simulations is created and validated experimentally with integrated silicon nitride microresonators. Two ML approaches are compared; Random Forest performs best with simulated average error below 15%.","Research Article  \nVol. 31, No. 5/27 Feb 2023/Optics Express  \n8020  \nMachine learning assisted inverse design of microresonators  \nARGHADEEP PAL , 1,2 ALEKHYA GHOSH , 1,2 SHUANGYOU ZHANG , 1 TOBY BI , 1,2  AND PASCAL DEL’HAYE1,2,*  \n1 Max Planck Institute for the Science of Light, 91058 Erlangen, Germany  \n2 Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany  \n*  \npascal.delhaye@mpl.mpg.de  \nAbstract: The high demand for fabricating microresonators with desired optical properties has led to various techniques to optimize geometries, mode structures, nonlinearities, and dispersion. Depending on applications, the dispersion in such resonators counters their optical nonlinearities and influences the intracavity optical dynamics. In this paper, we demonstrate the use of a machine learning (ML) algorithm as a tool to determine the geometry of microresonators from their dispersion profiles. The training dataset with ∼460 samples is generated by finite element simulations and the model is experimentally verified using integrated silicon nitride microresonators. Two ML algorithms are compared along with suitable hyperparameter tuning, out of which Random Forest yields the best results. The average error on the simulated data is well below 15% .  \n© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement  \n1. Introduction  \nThe small mode volumes and high quality (Q) factors of microresonators have made them excellent tools to confine light and steer up high nonlinear effects with low input power threshold [1] . One example is four-wave mixing (FWM), which leads to the formation of optical frequency combs [2] . These combs have shown great applications [3], mainly in the fields of spectroscopy [4], sensing [5], telecommunications [6], and waveform generation [7], due to their broad spectrum with uniform spacings. Sufficiently good overlaps of the equidistant FWM generated sidebands and the respective resonance frequencies of the microresonator are needed to generate broadband frequency combs. Thus, the comb formation is strongly influenced by dispersion, which leads to uneven spacings between the resonance frequencies. These deviations in resonances from the equidistant positions are evaluated via the integrated dispersion Dint, which can be written as  \nDint (m) = ωm − ω0 − D1 × (m − m0 ) . (1)  \nHere, ωm is the angular resonance frequency of the mth mode with respect to the pump modem0 at angular pump frequency ω0 . D 1/2π is the free spectral range (FSR) around the pump mode. Resonator dispersion also plays an important role in the temporal intracavity soliton dynamics. Out of many applications, the generation of bright Kerr frequency combs occurs in presence of anomalous dispersion [8], whereas, normal dispersion [9] favors the formation of dark pulsesolitons as shown in Fig. 1(a), where Dint has been plotted as a function of wavelength for silicon nitride (Si3N4 ) ring resonators with similar radii but different core heights and widths. Recently, it has been demonstrated that dark-bright soliton bound states can be generated in a microresonator crossing different dispersion regimes [10], leading to light states with close to constant output power but resembling a comb in the frequency domain. In addition, resonators with zero dispersion not only exhibit different soliton dynamics, but also are desirable for ultra-broadband comb generation [11, 12] . Therefore, proper engineering of the dispersion becomes vital [13, 14] . Dispersion calculations can be carried out via simulations and experiments. A quick analysis of dispersion is not possible by the conventional simulation techniques due to their iterative  \n\\#479899 [https://doi.org/10.1364/OE.479899](https://doi.org/10.1364/OE.479899)  \nJournal © 2023 Received 8 Nov 2022; revised 16 Jan 2023; accepted 16 Jan 2023; published 17 Feb 2023  \nResearch Article  \nVol. 31, No. 5/27 Feb 2023/Optics Express","cbCaiaNR1pqcPWie","https://ap.wps.com/l/cbCaiaNR1pqcPWie","pdf",2904833,1,9,"English","en",105,"# Introduction\n## Microresonators, dispersion, and optical combs\n## Inverse design and its computational challenges\n## Motivation for machine learning approaches","[{\"question\":\"How does the proposed method determine microresonator geometry?\",\"answer\":\"It uses a machine learning model trained on dispersion profiles so that geometry can be inferred from measured or simulated dispersion data.\"},{\"question\":\"What data is used to train and evaluate the machine learning model?\",\"answer\":\"The training dataset of roughly 460 samples is generated via finite element simulations, and the experimentally realized integrated silicon nitride microresonators are used for experimental verification.\"},{\"question\":\"Which machine learning algorithm performs best, and what accuracy is achieved?\",\"answer\":\"Random Forest yields the best results after hyperparameter tuning, achieving an average error on simulated data well below 15%.\"}]","Machine learning assisted inverse design of microresonators - Research Article | PDF",1785730393,23,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"machine-learning-assisted-inverse-design-of-microresonators-research-article","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-assisted-inverse-design-of-microresonators-research-article/120503/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"How does the proposed method determine microresonator geometry?","Question",{"text":75,"@type":76},"It uses a machine learning model trained on dispersion profiles so that geometry can be inferred from measured or simulated dispersion data.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What data is used to train and evaluate the machine learning model?",{"text":80,"@type":76},"The training dataset of roughly 460 samples is generated via finite element simulations, and the experimentally realized integrated silicon nitride microresonators are used for experimental verification.",{"name":82,"@type":73,"acceptedAnswer":83},"Which machine learning algorithm performs best, and what accuracy is achieved?",{"text":84,"@type":76},"Random Forest yields the best results after hyperparameter tuning, achieving an average error on simulated data well below 15%.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]