{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T14:38:54Z","timestamp":1767969534929,"version":"3.49.0"},"reference-count":44,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T00:00:00Z","timestamp":1767916800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia, I.P.","award":["10.54499\/UID\/50014\/2025"],"award-info":[{"award-number":["10.54499\/UID\/50014\/2025"]}]},{"name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia, I.P.","award":["10.54499\/UIDP\/06121\/2025"],"award-info":[{"award-number":["10.54499\/UIDP\/06121\/2025"]}]},{"name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia, I.P.","award":["10.54499\/UID\/50008\/2025"],"award-info":[{"award-number":["10.54499\/UID\/50008\/2025"]}]},{"name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia, I.P.","award":["10.54499\/2021.01066.CEECIND\/CP1653\/CT0004"],"award-info":[{"award-number":["10.54499\/2021.01066.CEECIND\/CP1653\/CT0004"]}]},{"name":"Generalitat Valenciana, Spain","award":["PROMETEO:CIPROM\/2022\/30"],"award-info":[{"award-number":["PROMETEO:CIPROM\/2022\/30"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Over the past 18 months, we have performed hundreds of temperature characterizations of fiber Bragg gratings inscribed in different germanium-doped silica glass fibers. Under experimental conditions, the main conclusions are as follows: the temperature dependence of the \u201ctemperature gauge factor\u201d or the normalized temperature sensitivity, KT, was found to be quadratic in the \u221250\u2013200 \u00b0C range, while it may be considered linear for the \u221220\u2013100 \u00b0C range; KT values at 20 \u00b0C vary from 5.176 \u00d7 10\u22126 K\u22121, for a B\/Ge co-doped fiber up to 6.724 \u00d7 10\u22126 K\u22121, for a highly Ge-doped fiber; KT does not depend on the hydrogen-loading process or the gratings coupling strength; KT is essentially independent of wavelength in the 1500\u20131600 nm range, its value being accurately determined with a relative error ~0.2%; based on the accurate value of KT = 6.165 \u00d7 10\u22126 K\u22121, at 20 \u00b0C, obtained for gratings inscribed in the SMF-28 fiber, we calculated a value of 19.4 \u00d7 10\u22126 K\u22121 for the thermo-optic coefficient of bulk germanium glass; and gratings produced by femtosecond-laser radiation and UV-laser radiation exhibit comparable values of KT. The previous achievements allow, by having knowledge of KT for a single grating, the accurate determination of the temperature dependence of the Bragg wavelength for any other grating inscribed in the same fiber; the presented methodology enables one to determine the \u201cunknown\u201d gratings\u2019 temperature sensitivity, typically with an error of 0.01 pm\/\u00b0C, being, therefore, very useful in research labs and computer simulations. Thus, expressions for the temperature dependence of KT for gratings inscribed in several fibers are given, as well as an expression for KT as a function of the effective refractive index. We have also fully analyzed the potential sources of error in KT determination.<\/jats:p>","DOI":"10.3390\/s26020435","type":"journal-article","created":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T11:45:33Z","timestamp":1767959133000},"page":"435","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Accurate Determination of the Temperature Sensitivity of UV-Induced Fiber Bragg Gratings"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-4508-453X","authenticated-orcid":false,"given":"Miguel","family":"Cosme","sequence":"first","affiliation":[{"name":"HBK FiberSensing, S. A., 4485-860 Maia, Portugal"}]},{"given":"Marizane","family":"Pota","sequence":"additional","affiliation":[{"name":"Applied Digital Transformation Laboratory (ADiT-LAB), Instituto Polit\u00e9cnico de Viana do Castelo, Rua Escola Industrial e Comercial Nun\u2019\u00c1lvares, 4900-347 Viana do Castelo, Portugal"}]},{"given":"Jo\u00e3o","family":"Preizal","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es, University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3223-9783","authenticated-orcid":false,"given":"Paulo","family":"Caldas","sequence":"additional","affiliation":[{"name":"Center for Applied Photonics, Institute for Systems and Computer Engineering, Technology and Science (INESC TEC), Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"Center for Research and Development in Agrifood Systems and Sustainability (CISAS), Escola Superior de Tecnologia e Gest\u00e3o, Instituto Polit\u00e9cnico de Viana do Castelo, 4900-347 Viana do Castelo, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7973-6891","authenticated-orcid":false,"given":"Ricardo","family":"Oliveira","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es, University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]},{"given":"Rog\u00e9rio","family":"Nogueira","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es, University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]},{"given":"Francisco M.","family":"Ara\u00fajo","sequence":"additional","affiliation":[{"name":"HBK FiberSensing, S. A., 4485-860 Maia, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4360-9989","authenticated-orcid":false,"given":"Jos\u00e9 L.","family":"Cruz","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Universidad de Valencia, Dr. Moliner 50, 46100 Burjassot, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8807-4108","authenticated-orcid":false,"given":"Gaspar M.","family":"Rego","sequence":"additional","affiliation":[{"name":"Applied Digital Transformation Laboratory (ADiT-LAB), Instituto Polit\u00e9cnico de Viana do Castelo, Rua Escola Industrial e Comercial Nun\u2019\u00c1lvares, 4900-347 Viana do Castelo, Portugal"},{"name":"Center for Applied Photonics, Institute for Systems and Computer Engineering, Technology and Science (INESC TEC), Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1364\/OL.14.000823","article-title":"Formation of Bragg gratings in optical fibers by a transverse holographic method","volume":"14","author":"Meltz","year":"1989","journal-title":"Opt. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1109\/50.618320","article-title":"Fiber Bragg grating technology fundamentals and overview","volume":"15","author":"Hill","year":"1997","journal-title":"J. Light. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1442","DOI":"10.1109\/50.618377","article-title":"Fiber grating sensors","volume":"15","author":"Kersey","year":"2002","journal-title":"J. Light. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1063\/1.108786","article-title":"Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask","volume":"62","author":"Hill","year":"1993","journal-title":"Appl. Phys. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1088\/0957-0233\/8\/4\/002","article-title":"In-fibre Bragg grating sensors","volume":"8","author":"Rao","year":"1997","journal-title":"Meas. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1049\/el:19940746","article-title":"Discrimination between strain and temperature effects using dual-wavelength fibre grating sensors","volume":"30","author":"Xu","year":"1994","journal-title":"Electron. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"060901","DOI":"10.1117\/1.OE.59.6.060901","article-title":"Fiber Bragg grating sensors for monitoring of physical parameters: A comprehensive review","volume":"59","author":"Sahota","year":"2020","journal-title":"Opt. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.snb.2006.02.027","article-title":"Self temperature referenced refractive index sensor by non-uniform thinned fiber Bragg gratings","volume":"120","author":"Iadicicco","year":"2006","journal-title":"Sens. Actuators B Chem."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"7288","DOI":"10.1109\/JLT.2021.3112854","article-title":"Plasmonic Fiber Grating Biosensors Demodulated Through Spectral Envelopes Intersection","volume":"39","author":"Lobry","year":"2021","journal-title":"J. Light. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2559","DOI":"10.1109\/JLT.2021.3050153","article-title":"High-Precision Temperature-Compensated Magnetic Field Sensor Based on Optoelectronic Oscillator","volume":"39","author":"Feng","year":"2021","journal-title":"J. Light. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0143-8166(02)00117-3","article-title":"Discrimination methods and demodulation techniques for fiber Bragg grating sensors","volume":"41","author":"Zhao","year":"2004","journal-title":"Opt. Lasers Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7394","DOI":"10.3390\/s140407394","article-title":"Fiber Bragg Grating Sensors toward Structural Health Monitoring in Composite Materials: Challenges and Solutions","volume":"14","author":"Kinet","year":"2014","journal-title":"Sensors"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"171","DOI":"10.3390\/opt4010013","article-title":"Optical Fiber Based Temperature Sensors: A Review","volume":"4","author":"Gangwar","year":"2023","journal-title":"Optics"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"13811","DOI":"10.1109\/JSEN.2022.3181949","article-title":"Optical Fiber Sensors in Extreme Temperature and Radiation Environments: A Review","volume":"22","author":"Deng","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Ma, S., Xu, Y., Pang, Y., Zhao, X., Li, Y., Qin, Z., Liu, Z., Lu, P., and Bao, X. (2022). Optical Fiber Sensors for High-Temperature Monitoring: A Review. Sensors, 22.","DOI":"10.3390\/s22155722"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"090007","DOI":"10.3788\/COL202321.090007","article-title":"Recent advances in optical fiber high-temperature sensors and encapsulation technique [Invited]","volume":"21","author":"Xu","year":"2023","journal-title":"Chin. Opt. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2511","DOI":"10.1109\/JLT.2014.2381236","article-title":"Cryogenic Temperature Response of Reflection-Based Phase-Shifted Long-Period Fiber Gratings","volume":"33","author":"Martins","year":"2015","journal-title":"J. Light. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Ivanov, O.V., Caldas, P., and Rego, G. (2022). High Sensitivity Cryogenic Temperature Sensors Based on Arc-Induced Long-Period Fiber Gratings. Sensors, 22.","DOI":"10.3390\/s22197119"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"085008","DOI":"10.1088\/1361-6668\/adf5f0","article-title":"Cryogenic optical fiber sensors for superconducting system protection in cryo-electric aircraft","volume":"38","author":"Haneef","year":"2025","journal-title":"Supercond. Sci. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4584","DOI":"10.1109\/JLT.2016.2540678","article-title":"Arc-Induced Long-Period Fiber Gratings in the Dispersion Turning Points","volume":"34","author":"Colaco","year":"2016","journal-title":"J. Light. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Rego, G. (2023). Temperature Dependence of the Thermo-Optic Coefficient of SiO2 Glass. Sensors, 23.","DOI":"10.3390\/s23136023"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Leviton, D.B., and Frey, B.J. (2006). Temperature-dependent absolute refractive index measurements of synthetic fused silica. Proceedings of the Optomechanical Technologies for Astronomy, Orlando, FL, USA, 24\u201331 May 2006, SPIE\u2014The International Society for Optical Engineering.","DOI":"10.1117\/12.672853"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Rego, G.M. (2024). Temperature Dependence of the Thermo-Optic Coefficient of GeO2-Doped Silica Glass Fiber. Sensors, 24.","DOI":"10.20944\/preprints202407.0272.v1"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2744","DOI":"10.1364\/AO.43.002744","article-title":"Quadratic behavior of fiber Bragg grating temperature coefficients","volume":"43","author":"Flockhart","year":"2004","journal-title":"Appl. Opt."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Preizal, J., Cosme, M., Pota, M., Caldas, P., Ara\u00fajo, F.M., Oliveira, R., Nogueira, R., and Rego, G.M. (2025, January 25\u201330). Normalized temperature sensitivity of fiber Bragg gratings inscribed under different conditions. Proceedings of the 29th International Conference on Optical Fiber Sensors, Porto, Portugal.","DOI":"10.1117\/12.3061856"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"6859","DOI":"10.1364\/AO.34.006859","article-title":"Passive temperature-compensating package for optical fiber gratings","volume":"34","author":"Yoffe","year":"1995","journal-title":"Appl. Opt."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"E8","DOI":"10.1364\/AO.477573","article-title":"Accurate compensation and prediction of the temperature cross-sensitivity of tilted FBG cladding mode resonances","volume":"62","author":"Imas","year":"2023","journal-title":"Appl. Opt."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"44769","DOI":"10.1364\/OE.470093","article-title":"Generalized and wavelength-dependent temperature calibration function for multipoint regenerated fiber Bragg grating sensors","volume":"30","author":"Buchfellner","year":"2022","journal-title":"Opt. Express"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"110278","DOI":"10.1016\/j.optlastec.2023.110278","article-title":"An intrinsic sensitivity calibration scheme for high temperature measurements using femtosecond point-by-point written fiber Bragg gratings","volume":"170","author":"Lerner","year":"2024","journal-title":"Opt. Laser Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2824","DOI":"10.1364\/AO.418049","article-title":"Measurement of phase and group refractive indices and dispersion of thermo-optic and strain-optic coefficients of optical fibers using weak fiber Bragg gratings","volume":"60","author":"Cruz","year":"2021","journal-title":"Appl. Opt."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Wang, W., Yu, Y., Geng, Y., and Li, X. (2015, January 17\u201319). Measurements of thermo-optic coefficient of standard single mode fiber in large temperature range. Proceedings of the 2015 International Conference on Optical Instruments and Technology: Optical Sensors and Applications, Beijing, China.","DOI":"10.1117\/12.2193091"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1140\/epjb\/s10051-021-00147-2","article-title":"Dependence of the refractive index on density, temperature, and the wavelength of the incident light","volume":"94","author":"Tan","year":"2021","journal-title":"Eur. Phys. J. B"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"5813","DOI":"10.1016\/j.ijleo.2014.07.053","article-title":"Research on the temperature characteristics of optical fiber refractive index","volume":"125","author":"Yang","year":"2014","journal-title":"Optik"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Shen, X., Song, C., Shi, F., Tian, Y., Tie, G., Qiao, S., Peng, X., Zhang, W., and Hou, Z. (2023). Research on Laser-Induced Damage Post-Restoration Morphology of Fused Silica and Optimization of Patterned CO2 Laser Repair Strategy. Micromachines, 14.","DOI":"10.3390\/mi14071359"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1111\/j.1151-2916.1951.tb09128.x","article-title":"Effect of Composition and Temperature on the Specific Heat of Glass","volume":"34","author":"Sharp","year":"1951","journal-title":"J. Am. Ceram. Soc."},{"key":"ref_36","unstructured":"Rego, G.M. (2006). Arc-Induced Long-Period Fibre Gratings: Fabrication and Their Applications in Optical Communications and Sensing. [Ph.D. Thesis, Engineering Faculty, Porto University]."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/S0030-4018(03)01374-9","article-title":"New technique to mechanically induce long-period fibre gratings","volume":"220","author":"Rego","year":"2003","journal-title":"Opt. Commun."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"6082","DOI":"10.1364\/OE.17.006082","article-title":"Polarization-dependent effects in point-by-point fiber Bragg gratings enable simple, linearly polarized fiber lasers","volume":"17","author":"Jovanovic","year":"2009","journal-title":"Opt. Express"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Leviton, D.B., Frey, B.J., and Madison, T.J. (2007). Temperature-dependent refractive index of CaF2 and Infrasil 301. Proceedings of the Cryogenic Optical Systems and Instruments XII, San Diego, CA, USA, 26\u201327 August 2007, SPIE\u2014The International Society for Optical Engineering.","DOI":"10.1117\/12.735594"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Leviton, D.B., Miller, K.H., Quijada, M.A., and Grupp, F.U. (2015). Temperature-dependent refractive index measurements of CaF2, Suprasil 3001, and S-FTM16 for the Euclid near-infrared spectrometer and photometer. Proceedings of the Current Developments in Lens Design and Optical Engineering XVI, San Diego, CA, USA, 10\u201311 August 2015, SPIE\u2014The International Society for Optical Engineering.","DOI":"10.1117\/12.2189024"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Miller, K.H., Quijada, M.A., and Leviton, D.B. (2017). Cryogenic refractive index of Heraeus homosil glass. Proceedings of the Current Developments in Lens Design and Optical Engineering XVIII, San Diego, CA, USA, 7\u20138 August 2017, SPIE\u2014The International Society for Optical Engineering.","DOI":"10.1117\/12.2274423"},{"key":"ref_42","unstructured":"Uhlmann, D.R., and Kreidl, N.J. (1991). Optical Properties of Glass, The American Ceramic Society."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"14774","DOI":"10.1364\/OE.390521","article-title":"Enhancement of spectral response of Bragg gratings written in nanostructured and multi-stepped optical fibers with radially shaped GeO2 concentration","volume":"28","author":"Osuch","year":"2020","journal-title":"Opt. Express"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.sna.2004.01.024","article-title":"Non-linear temperature dependence of Bragg gratings written in different fibres, optimised for sensor applications over a wide range of temperatures","volume":"112","author":"Pal","year":"2004","journal-title":"Sens. Actuators A Phys."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/2\/435\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T11:46:54Z","timestamp":1767959214000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/2\/435"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,9]]},"references-count":44,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["s26020435"],"URL":"https:\/\/doi.org\/10.3390\/s26020435","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,9]]}}}