{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T19:14:14Z","timestamp":1773947654014,"version":"3.50.1"},"reference-count":51,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,1,28]],"date-time":"2020-01-28T00:00:00Z","timestamp":1580169600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A universal multi-parameter sensing scheme based on a self-interference micro-ring resonator (SIMRR) is proposed. Benefit from the special intensity sensing mechanism, the SIMRR allows multimode sensing in a wide range of wavelengths but immune from frequency noise. To process the multiple mode spectra that are dependent on multiple parameters, we adopt the machine learning algorithm instead of massive asymptotic solutions of resonators. Employing the proposed multi-mode sensing approach, a two-parameter SIMRR sensor is designed. Assuming that two gases have different wavelength dependence of refractive indices, the feasibility and effectiveness of the two-parameter sensing strategy are verified numerically. Moreover, the dependence of parameter estimation accuracy on the laser intensity noises is also investigated. The numerical results indicate that our scheme of multi-parameter sensing in a multimode SIMRR holds great potential for practical high-sensitive sensing platforms compared with the single-mode sensing based on whispering gallery mode (WGM) resonators.<\/jats:p>","DOI":"10.3390\/s20030709","type":"journal-article","created":{"date-parts":[[2020,1,28]],"date-time":"2020-01-28T09:37:09Z","timestamp":1580204229000},"page":"709","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Multi-Parameter Sensing in a Multimode Self-Interference Micro-Ring Resonator by Machine Learning"],"prefix":"10.3390","volume":"20","author":[{"given":"Dong","family":"Hu","sequence":"first","affiliation":[{"name":"College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2484-7292","authenticated-orcid":false,"given":"Chang-ling","family":"Zou","sequence":"additional","affiliation":[{"name":"Key Lab of Quantum Information, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongliang","family":"Ren","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jin","family":"Lu","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zichun","family":"Le","sequence":"additional","affiliation":[{"name":"College of Science, Zhejiang University of Technology, Hangzhou 310023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yali","family":"Qin","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shunqin","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunhua","family":"Dong","sequence":"additional","affiliation":[{"name":"Key Lab of Quantum Information, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6168-2688","authenticated-orcid":false,"given":"Weisheng","family":"Hu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,28]]},"reference":[{"key":"ref_1","unstructured":"Jiang, X., Qavi, A.J., Huang, S.H., and Yang, L. (2018, April 30). Whispering Gallery Microsensors: A Review. Available online: https:\/\/arxiv.org\/pdf\/1805.00062."},{"key":"ref_2","first-page":"074231","article-title":"Emerging opportunities for ultra-high Q whispering gallery mode microcavities","volume":"62","author":"Song","year":"2019","journal-title":"Sci. Chi."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"13832","DOI":"10.1039\/C8NR03709D","article-title":"Optical bio-chemical sensors based on whispering gallery mode resonators","volume":"10","author":"Zhang","year":"2018","journal-title":"Nanoscale"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1038\/nature23281","article-title":"Exceptional points enhance sensing in an optical microcavity","volume":"548","author":"Chen","year":"2017","journal-title":"Nature"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1364\/AOP.7.000168","article-title":"Whispering gallery mode sensors","volume":"7","author":"Foreman","year":"2015","journal-title":"Adv. Opt. Photonics"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1063\/1.3263726","article-title":"Dual-microring-resonator interference sensor","volume":"95","author":"Yi","year":"2009","journal-title":"Appl. Phys. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5199","DOI":"10.1364\/OL.37.005199","article-title":"High performance Vernier racetrack resonators","volume":"37","author":"Boeck","year":"2012","journal-title":"Opt. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1128","DOI":"10.1364\/OL.36.001128","article-title":"Optical waveguide double-ring sensor using intensity interrogation with a low-cost broadband source","volume":"36","author":"Jin","year":"2011","journal-title":"Opt. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3320","DOI":"10.1364\/OL.36.003320","article-title":"Vernier-cascade label-free biosensor with integrated arrayed waveguide grating for wavelength interrogation low-cost broadband source","volume":"36","author":"Claes","year":"2011","journal-title":"Opt. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4831","DOI":"10.3390\/s140304831","article-title":"Recent advances in gas and chemical detection by vernier effect-based photonic sensors","volume":"14","author":"Troia","year":"2014","journal-title":"Sensors"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4653","DOI":"10.1364\/OE.21.004653","article-title":"Thermo-optomechanical oscillator for sensing applications","volume":"21","author":"Deng","year":"2013","journal-title":"Opt. Express"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"8896","DOI":"10.1038\/s41598-017-08875-1","article-title":"Polymer encapsulated microcavity optomechanical magnetometer","volume":"7","author":"Zhu","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1604920","DOI":"10.1002\/adma.201604920","article-title":"Single nanoparticle detection using optical microcavities","volume":"29","author":"Zhi","year":"2017","journal-title":"Adv. Mate."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1190","DOI":"10.1039\/C6LC01595F","article-title":"Towards next-generation label-free biosensors: Recent advances in whispering gallery mode sensors","volume":"17","author":"Kim","year":"2017","journal-title":"Lab Chip"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Su, J. (2017). Label-free biological and chemical sensing using whispering gallery mode optical resonators: Past, present, and future. Sensors, 17.","DOI":"10.3390\/s17030540"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"024011","DOI":"10.1103\/PhysRevApplied.5.024011","article-title":"Detection of single nanoparticles using the dissipativeinteraction in a high-Q microcavity","volume":"5","author":"Shen","year":"2016","journal-title":"Phys. Rev. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"063808","DOI":"10.1103\/PhysRevA.85.063808","article-title":"Statistical theory of nanoparticle sensing using a whispering-gallery-mode resonator","volume":"85","author":"Shen","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"013801","DOI":"10.1103\/PhysRevA.85.013801","article-title":"Nanoparticle sensing using whispering-gallery-mode resonators: Plasmonic and Rayleigh scatterers","volume":"85","author":"Shen","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"073030","DOI":"10.1088\/1367-2630\/15\/7\/073030","article-title":"Statistics of multiple-scatterer-induced frequency splitting in whispering gallery microresonators and microlasers","volume":"15","author":"He","year":"2013","journal-title":"New J. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s00340-016-6565-y","article-title":"Chormaic, Cavity ring-up spectroscopy for dissipative and dispersive sensing in a whispering gallery mode resonator","volume":"122","author":"Yang","year":"2016","journal-title":"Appl. Phys. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"023803","DOI":"10.1103\/PhysRevA.83.023803","article-title":"Multiple-Rayleigh-scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator","volume":"83","author":"Yi","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"085803","DOI":"10.1088\/2040-8986\/aad267","article-title":"Spectral analysis of a four-port DBR micro-ring resonator for spectral sensing applications","volume":"20","author":"Cicek","year":"2018","journal-title":"J. Opt."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"34997","DOI":"10.1364\/OE.27.034997","article-title":"Portable microresonator-based label-free detector: Monotonous resonance splitting with particle adsorption","volume":"27","author":"Acharyya","year":"2019","journal-title":"Opt. Express"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"043847","DOI":"10.1103\/PhysRevA.90.043847","article-title":"Mode broadening induced by nanoparticles in an optical whispering-gallery microcavity","volume":"90","author":"Hu","year":"2014","journal-title":"Phys. Rev. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"034029","DOI":"10.1103\/PhysRevApplied.8.034029","article-title":"Multiple critical couplings and sensing in a microresonator-waveguide system","volume":"8","author":"Acharyya","year":"2017","journal-title":"Phys. Rev. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1469","DOI":"10.1109\/LPT.2016.2531901","article-title":"Highly-sensitive intensity detection by a self-interference micro-ring resonator","volume":"28","author":"Ren","year":"2016","journal-title":"IEEE Photon. Tech. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1364\/PRJ.6.000681","article-title":"Experimental demonstration of dissipative sensing in a self-interference microring resonator","volume":"6","author":"Wan","year":"2018","journal-title":"Photon. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"942","DOI":"10.1364\/JOSAB.36.000942","article-title":"Dissipative sensing with low detection limit in a self-interference microring resonator","volume":"36","author":"Ren","year":"2019","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"18197","DOI":"10.1364\/OE.24.018197","article-title":"Performance and noise analysis of optical microresonator-based biochemical sensors using intensity detection","volume":"24","author":"Zhou","year":"2016","journal-title":"Opt. Express"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2974","DOI":"10.1038\/srep02974","article-title":"Back-scatter based whispering gallery mode sensing","volume":"3","author":"Knittel","year":"2013","journal-title":"Sci. Rep."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1109\/LPT.2011.2136430","article-title":"Cascaded-ring optical sensor with enhanced sensitivity by using suspended Si-nanowires","volume":"23","author":"Hu","year":"2011","journal-title":"IEEE Photon. Tech. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1364\/JOSAB.21.000697","article-title":"Fundamental thermal fluctuations in microspheres","volume":"21","author":"Gorodetsky","year":"2004","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1324","DOI":"10.1364\/JOSAB.24.001324","article-title":"Whispering-gallery-mode resonators as frequency references. I. Fundamental limitations","volume":"24","author":"Matsko","year":"2007","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1038\/s41377-018-0063-4","article-title":"Wireless whispering-gallery-mode sensor for thermal sensing and aerial mapping","volume":"7","author":"Xu","year":"2018","journal-title":"Light-Sci. Appl."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"25905","DOI":"10.1364\/OE.24.025905","article-title":"Phone-sized whispering-gallery microresonator sensing system","volume":"24","author":"Xu","year":"2016","journal-title":"Opt. Express"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1038\/s41928-019-0284-4","article-title":"Sensitive readout of implantable microsensors using a wireless system locked to an exceptional point","volume":"2","author":"Dong","year":"2019","journal-title":"Nature Electro."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2771","DOI":"10.1364\/OL.35.002771","article-title":"Label-free biosensor array based on silicon-on-insulator ring resonators addressed using a WDM approach","volume":"35","author":"Xu","year":"2010","journal-title":"Opt. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1021\/ac902451b","article-title":"Quantitative, label-free detection of five protein biomarkers using muliplexed arrays of silicon photonic microring resonators","volume":"82","author":"Washburn","year":"2010","journal-title":"Anal. Chem."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"654","DOI":"10.1109\/JSTQE.2009.2032510","article-title":"Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation","volume":"16","author":"Iqbal","year":"2010","journal-title":"IEEE J. Sel. Top. Quantum Electron."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"5358","DOI":"10.1039\/C6AN01076H","article-title":"Multiplexed cancer biomarker detection using chip-integrated silicon photonic sensor arrays","volume":"141","author":"Washburn","year":"2016","journal-title":"Analyst"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"31829","DOI":"10.1364\/OE.26.031829","article-title":"Whispering gallery mode micro resonators for multi-parameter sensing applications","volume":"26","author":"Mallik","year":"2019","journal-title":"Opt. Express"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.yofte.2019.02.012","article-title":"Packaged inline cascaded optical micro-resonators for multi-parameter sensing","volume":"50","author":"Kavungal","year":"2019","journal-title":"Opt. Fiber Technol."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Saetchnikov, V.A., Tcherniavskaia, E.A., Schweiger, G., and Ostendorf, A. (2012, January 30). Classification of antibiotics by neural network analysis of optical resonance data of whispering gallery modes in dielectric microspheres. Proceedings of the SPIE photonics Europe, Brussels, Belgium.","DOI":"10.1117\/12.920397"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s10812-011-9486-x","article-title":"Application of neural networks for classification of biological compounds from the characteristics of whispering-gallery-mode optical resonance","volume":"78","author":"Tcherniavskaia","year":"2011","journal-title":"J. Appl. Spectrosc."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/S0925-4005(97)00132-9","article-title":"Quantification of H2S and NO2 using gas sensor arrays and an artificial neural network","volume":"43","author":"Yang","year":"1997","journal-title":"Sens. Actuators B"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1364\/OPTICA.5.000666","article-title":"Deep learning reconstruction of ultrashort pulses","volume":"5","author":"Zahavy","year":"2018","journal-title":"Optica"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Bishop, C.M. (1996). Neural Networks for Pattern Recognition, Oxford University Press.","DOI":"10.1201\/9781420050646.ptb6"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2530","DOI":"10.1364\/OE.27.002530","article-title":"Deep neural networks assisted BOTDA for simultaneous temperature and strain measurement with enhanced accuracy","volume":"27","author":"Wang","year":"2019","journal-title":"Opt. Express"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"6769","DOI":"10.1364\/OE.24.006769","article-title":"Signal processing using artificial neural network for BOTDA sensor system","volume":"24","author":"Azad","year":"2016","journal-title":"Opt. Express"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"2741","DOI":"10.3390\/s7112741","article-title":"Ammonia optical sensing by microring resonators","volume":"7","author":"Vittorio","year":"2007","journal-title":"Sensors"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"5491","DOI":"10.1364\/OE.22.005491","article-title":"Optimizing detection limits in whispering gallery mode biosensing","volume":"22","author":"Foreman","year":"2014","journal-title":"Opt. 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