{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T10:38:15Z","timestamp":1770892695445,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T00:00:00Z","timestamp":1689033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["23-21-00169"],"award-info":[{"award-number":["23-21-00169"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This work focuses on the methods of creating in-fiber devices, such as sensors, filters, and scatterers, using the fiber fuse effect. The effect allows for the creation of structures in a fiber core. However, it is necessary to know exactly how this process works, when the plasma spark occurs, what size it reaches, and how it depends on external parameters such as power and wavelength of radiation. Thus, this present study aims to create the possibility of predicting the consequences of optical breakdown. This paper describes a mathematical model of the optical breakdown initiation in a fiber core based on the thermal conductivity equation. The breakdown generates a plasma spark, which subsequently moves along the fiber. The problem is solved in the axisymmetric formulation. The computational domain consists of four elements with different thermophysical properties at the boundaries of which conjugation conditions are fulfilled. The term describing the heat source in the model is determined by the wavelength of radiation and the refractive indices of the core and the shell and also includes the radiation absorption on the released electrons during the thermal ionization of the quartz glass. The temperature field distributions in the optical fiber are obtained. Based on the calculations, it is possible to estimate the occurrence times of various phase states inside the fiber, in particular, the plasma spark occurrence time.<\/jats:p>","DOI":"10.3390\/a16070331","type":"journal-article","created":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T01:01:41Z","timestamp":1689123701000},"page":"331","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Mathematical Model of Fuse Effect Initiation in Fiber Core"],"prefix":"10.3390","volume":"16","author":[{"given":"Victoria A.","family":"Starikova","sequence":"first","affiliation":[{"name":"Applied Mathematics and Mechanics Faculty, Perm National Research Polytechnic University, 614990 Perm, Russia"}]},{"given":"Yuri A.","family":"Konin","sequence":"additional","affiliation":[{"name":"Applied Mathematics and Mechanics Faculty, Perm National Research Polytechnic University, 614990 Perm, Russia"},{"name":"Institute of Laser Technologies, ITMO University, 197101 St. Petersburg, Russia"}]},{"given":"Alexandra Yu.","family":"Petukhova","sequence":"additional","affiliation":[{"name":"Applied Mathematics and Mechanics Faculty, Perm National Research Polytechnic University, 614990 Perm, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5943-0457","authenticated-orcid":false,"given":"Svetlana S.","family":"Aleshkina","sequence":"additional","affiliation":[{"name":"Dianov Fiber Optics Research Center, Prokhorov General Physics Institute of the Russian Academy of Sciences, 119333 Moscow, Russia"}]},{"given":"Andrey A.","family":"Petrov","sequence":"additional","affiliation":[{"name":"Institute of Laser Technologies, ITMO University, 197101 St. Petersburg, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1927-2949","authenticated-orcid":false,"given":"Anatolii V.","family":"Perminov","sequence":"additional","affiliation":[{"name":"Applied Mathematics and Mechanics Faculty, Perm National Research Polytechnic University, 614990 Perm, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,11]]},"reference":[{"key":"ref_1","unstructured":"Kashyap, R. (1987, January 7\u201311). Self-propelled self-focusing damage in optical fibers. Proceedings of the Tenth International Conference on Lasers and Applications, Lake Tahoe, NV, USA."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1049\/el:19880032","article-title":"Observation of catastrophic self-propelled self-focusing in optical fibres","volume":"24","author":"Kashyap","year":"1988","journal-title":"Electron. Lett."},{"key":"ref_3","first-page":"586","article-title":"Heat flow modeling and visualization of catastrophic self-propagating damage in single-mode optical fibres at low powers","volume":"2966","author":"Kashyap","year":"1996","journal-title":"Proc. Soc. Photo-Opt. Instrum. Eng."},{"key":"ref_4","first-page":"100","article-title":"Optical discharge in fiber light guides","volume":"175","author":"Bufetov","year":"2005","journal-title":"Adv. Phys. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Bufetov, I.A., Frolov, A.A., Dianov, M., Fortov, V.E., and Efremov, V.P. (2005, January 6). Dynamics of fiber fuse propagation. Proceedings of the Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, Anaheim, CA, USA.","DOI":"10.1109\/OFC.2005.192998"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1070\/QE2008v038n05ABEH013751","article-title":"Propagation of an optical discharge through optical fibres upon interference of modes","volume":"38","author":"Bufetov","year":"2008","journal-title":"Quantum Electron."},{"key":"ref_7","unstructured":"Shuto, Y. (2023). Elements of Fiber Fuse Phenomena, Design Egg, Inc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1109\/JQE.2004.831635","article-title":"Fiber Fuse Phenomenon in Step-Index Single-Mode Optical Fibers","volume":"40","author":"Shuto","year":"2004","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_9","first-page":"271","article-title":"Cavity pattern formation and its dynamics of fiber fuse in single-mode optical fibers","volume":"12","author":"Shuto","year":"2020","journal-title":"J. Inform. Math. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Todoroki, S. (2015, January 22\u201326). Quantitative evaluation of fiber fuse initiation probability in typical single-mode fibers. Proceedings of the 2015 Optical Fiber Communications Conference and Exhibition (OFC), Los Angeles, CA, USA.","DOI":"10.1364\/OFC.2015.W2A.33"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2781392","DOI":"10.1155\/2016\/2781392","article-title":"End face damage and fiber fuse phenomena in single mode fiber optic connectors","volume":"2016","author":"Shuto","year":"2016","journal-title":"J. Photon."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"25366","DOI":"10.1038\/srep25366","article-title":"Quantitative evaluation of fiber fuse initiation with exposure to arc discharge provided by a fusion splicer","volume":"6","author":"Todoroki","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_13","first-page":"243","article-title":"Modes and threshold power of fiber fuse propagation","volume":"J96-B","author":"Todoroki","year":"2013","journal-title":"IEICE Trans. Commun. B"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Todoroki, S. (2013, January 17\u201321). Fiber Fuse Propagation Modes in Typical Single-mode Fibers. Proceedings of the Optical Fiber Communication Conference\/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (online), Anaheim, CA, USA.","DOI":"10.1364\/NFOEC.2013.JW2A.11"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Hanzawa, N., Kurokawa, K., Tsujikawa, K., Mori, T., Wada, M., and Yamamoto, F. (2015, January 6\u201311). Fiber fuse propagation in LP11 mode in few-mode fiber. Proceedings of the Optical Fiber Communication Conference, OSA Technical Digest (online), Anaheim, CA, USA.","DOI":"10.1364\/OFC.2015.W4I.5"},{"key":"ref_16","unstructured":"Domingues, F., and Radwan, A. (2004). Optical Fiber Sensors for loT and Smart Devices, Springer."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5654","DOI":"10.1109\/JSEN.2015.2446534","article-title":"Liquid Hydrostatic Pressure Optical Sensor Based on Micro-Cavity Produced by the Catastrophic Fuse Effect","volume":"15","author":"Domingues","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1364\/JOT.88.000672","article-title":"Structural characteristics of internal microcavities produced in optical fiber via the fuse effect","volume":"88","author":"Konin","year":"2021","journal-title":"J. Opt. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7174","DOI":"10.1038\/s41598-020-63969-7","article-title":"High-order mode suppression in double-clad optical fibers by adding absorbing inclusions","volume":"10","author":"Aleshkina","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_20","unstructured":"Carslaw, H.S., and Jaeger, J.C. (1959). Conduction of Heat in Solids, Oxford University Press. [2nd ed.]."},{"key":"ref_21","unstructured":"Davis, D.D., Mettler, S.C., and DiGiovanni, D.J. (November, January 30). Experimental data on the fiber fuse. Proceedings of the SPIE, Boulder, CO, USA."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1356","DOI":"10.1063\/1.336107","article-title":"Formation mechanism of drawing-induced E centers in silica optical fibers","volume":"58","author":"Hanafusa","year":"1985","journal-title":"J. Appl. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1002\/j.1538-7305.1977.tb00534.x","article-title":"Loss analysis of single-mode fiber splices","volume":"56","author":"Marcuse","year":"1977","journal-title":"Bell Syst. Tech. J."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Pervadchuk, V., Vladimirova, D., and Derevyankina, A. (2023). Mathematical Modeling of Capillary Drawing Stability for Hollow Optical Fibers. Algorithms, 16.","DOI":"10.3390\/a16020083"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Agliullin, T., Anfinogentov, V., Morozov, O., Sakhabutdinov, A., Valeev, B., Niyazgulyeva, A., and Garovov, Y. (2023). Comparative Analysis of the Methods for Fiber Bragg Structures Spectrum Modeling. Algorithms, 16.","DOI":"10.3390\/a16020101"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Turov, A., Konstantinov, Y., Barkov, F., Korobko, D., Zolotovskii, I., Lopez-Mercado, C., and Fotiadi, A. (2023). Enhancing the Distributed Acoustic Sensors\u2019 (DAS) Performance by the Simple Noise Reduction Algorithms Sequential Application. Algorithms, 16.","DOI":"10.3390\/a16050217"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Reddy, G.M.M., Seitenfuss, A.B., Medeiros, D.d.O., Meacci, L., Assun\u00e7\u00e3o, M., and Vynnycky, M. (2020). A Compact FEM Implementation for Parabolic Integro-Differential Equations in 2D. Algorithms, 13.","DOI":"10.3390\/a13100242"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/7\/331\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:10:55Z","timestamp":1760127055000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/7\/331"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,11]]},"references-count":27,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["a16070331"],"URL":"https:\/\/doi.org\/10.3390\/a16070331","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,11]]}}}