{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:32:02Z","timestamp":1760243522976,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2013,8,12]],"date-time":"2013-08-12T00:00:00Z","timestamp":1376265600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In the last years, mid-infrared radiation emitted by CO2 lasers has become increasing popular as a tool in the development of long-period fiber gratings. However, although the development and characterization of the resulting sensing devices have progressed quickly, further research is still necessary to consolidate functional models, especially regarding the interaction between laser radiation and the fiber\u2019s material. In this paper, a 3D finite element model is presented to simulate the interaction between laser radiation and an optical fiber and to determine the resulting refractive index change. Dependence with temperature of the main parameters of the optical fiber materials  (with special focus on the absorption of incident laser radiation) is considered, as well as convection and radiation losses. Thermal and residual stress analyses are made for a standard single mode fiber, and experimental results are presented.<\/jats:p>","DOI":"10.3390\/s130810333","type":"journal-article","created":{"date-parts":[[2013,8,12]],"date-time":"2013-08-12T11:44:25Z","timestamp":1376307865000},"page":"10333-10347","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["3D Finite Element Model for Writing Long-Period Fiber Gratings by CO2 Laser Radiation"],"prefix":"10.3390","volume":"13","author":[{"given":"Jo\u00e3o","family":"Coelho","sequence":"first","affiliation":[{"name":"Laboratory of Optics, Lasers and Systems, Faculty of Sciences, University of Lisbon,  Campus do Lumiar, Estrada do Pa\u00e7o do Lumiar, 22, Building D, 1649-038 Lisboa, Portugal"},{"name":"Institute of Biophysics and Biomedical Engineering, Faculty of Sciences, University of Lisbon, Faculdade de Ci\u00eancias da Universidade de Lisboa, Campo Grande, Lisboa 1749-016, Portugal"}]},{"given":"Marta","family":"Nespereira","sequence":"additional","affiliation":[{"name":"Laboratory of Optics, Lasers and Systems, Faculty of Sciences, University of Lisbon,  Campus do Lumiar, Estrada do Pa\u00e7o do Lumiar, 22, Building D, 1649-038 Lisboa, Portugal"}]},{"given":"Manuel","family":"Abreu","sequence":"additional","affiliation":[{"name":"Laboratory of Optics, Lasers and Systems, Faculty of Sciences, University of Lisbon,  Campus do Lumiar, Estrada do Pa\u00e7o do Lumiar, 22, Building D, 1649-038 Lisboa, Portugal"}]},{"given":"Jos\u00e9","family":"Rebord\u00e3o","sequence":"additional","affiliation":[{"name":"Laboratory of Optics, Lasers and Systems, Faculty of Sciences, University of Lisbon,  Campus do Lumiar, Estrada do Pa\u00e7o do Lumiar, 22, Building D, 1649-038 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2013,8,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1773","DOI":"10.1049\/el:19981237","article-title":"Long period fiber gratings for structural bending sensing","volume":"34","author":"Patrick","year":"1998","journal-title":"Electron. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1364\/OE.4.000457","article-title":"Applications of long-period gratings to single and multi-parameter sensing","volume":"4","author":"Bhatia","year":"1999","journal-title":"Opt. Express"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/S0925-4005(00)00714-0","article-title":"Long period gratings as solution concentration sensors","volume":"74","author":"Falciai","year":"2001","journal-title":"Sens. Actuators B Chem."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"R49","DOI":"10.1088\/0957-0233\/14\/5\/201","article-title":"Optical fibre long-period grating sensors: Characteristics and application","volume":"14","author":"James","year":"2003","journal-title":"Meas. Sci. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"729212","DOI":"10.1117\/12.817715","article-title":"Novel long-period fiber grating optical sensor for large strain measurement","volume":"7292","author":"Chen","year":"2009","journal-title":"Proc. SPIE"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"10105","DOI":"10.3390\/s101110105","article-title":"Feasibility of fiber bragg grating and long-period fiber grating sensors under different environmental conditions","volume":"10","author":"Wang","year":"2010","journal-title":"Sensors"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Yasin, M., Harun, S., and Arof, H. (2012). Fiber Optic Sensors, InTech.","DOI":"10.5772\/1379"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1442","DOI":"10.1109\/50.618377","article-title":"Fiber grating sensors","volume":"15","author":"Kersey","year":"1997","journal-title":"J. Lightwave Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1364\/OL.25.000710","article-title":"Tunable mechanically induced long-period fiber gratings","volume":"25","author":"Savin","year":"2000","journal-title":"Opt. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1109\/50.557563","article-title":"An etched two-mode fiber modal coupling element","volume":"15","author":"Vaziri","year":"1997","journal-title":"J. Lightwave Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/50.476137","article-title":"Long-period fiber gratings as band-rejection filters","volume":"14","author":"Vengsarkar","year":"1996","journal-title":"J. Lightwave Technol."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Yasin, M., Harun, S., and Arof, H. (2012). Fiber Optic Sensors, InTech.","DOI":"10.5772\/1379"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1049\/el:19980239","article-title":"Long period fiber grating fabrication with focused CO2 laser pulses","volume":"34","author":"Davis","year":"1998","journal-title":"Electron. Lett."},{"key":"ref_14","unstructured":"Akiyama, M., Nishide, K., Shima, K., Wada, A., and Yamauchi, R. (2008, January 22\u201327). A Novel Long-Period Fiber Grating Using Periodically Releases Residual Stress of Pure-Silica Core Fiber. San Jos\u00e9, CA, USA."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Harun, W., and Arof, H. (2013). Current Developments in Optical Fiber Technology, InTech.","DOI":"10.5772\/46191"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1109\/JSTQE.2004.826570","article-title":"Optical and mechanical effects of frozen-in stresses and strains in optical fibers","volume":"10","author":"Yablon","year":"2004","journal-title":"IEEE J. Sel. Topics Quantum Electron."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1063\/1.1638883","article-title":"Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity","volume":"84","author":"Yablon","year":"2004","journal-title":"Appl. Phys. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.pmatsci.2011.05.002","article-title":"Fictive temperature in silica-based glasses and its application to optical fiber manufacturing","volume":"57","author":"Lancry","year":"2012","journal-title":"Progr. Mater. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3809","DOI":"10.1364\/AO.41.003809","article-title":"Effect of CO2 laser irradiation on the refractive-index change in optical fibers","volume":"41","author":"Kim","year":"2002","journal-title":"Appl. Opt."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5296","DOI":"10.1364\/AO.47.005296","article-title":"Measurement of CO2-laser-irradiation-induced refractive index modulation in single-mode fiber toward long-period fiber grating design and fabrication","volume":"47","author":"Li","year":"2008","journal-title":"Appl. Opt."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6179","DOI":"10.1364\/AO.51.006179","article-title":"Residual-stress relaxation and densification in CO2-laser-induced long-period fiber gratings","volume":"51","author":"Hutsel","year":"2012","journal-title":"Appl. Opt."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/S0030-4018(98)00164-3","article-title":"Heat transfer modelling in CO2 laser processing of optical fibres","volume":"152","author":"Grellier","year":"1998","journal-title":"Opt. Commun."},{"key":"ref_23","first-page":"1","article-title":"Modeling refractive index change in writing long-period fiber gratings using mid-infrared laser radiation","volume":"2","author":"Coelho","year":"2012","journal-title":"Photonic Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.optlaseng.2007.07.001","article-title":"Modelling the spot shape influence on high-speed transmission lap welding of thermoplastics films","volume":"46","author":"Coelho","year":"2008","journal-title":"J. Opt. Lasers Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1016\/j.jmatprotec.2010.02.006","article-title":"3D finite element modeling of the thermally induced residual stress in the hybrid laser\/arc welding of lap joint","volume":"210","author":"Kong","year":"2010","journal-title":"J. Mater. Process. Technol."},{"key":"ref_26","unstructured":"Timoshenko, S.P., and Goodier, J.N. (1951). Theory of Elasticity, McGraw-Hill. [2nd ed.]."},{"key":"ref_27","unstructured":"Rego, G.M. (2006). Arc-Induced Long-Period Fibre Gratings. Fabrication and Their Application in Communications and Sensing. [Ph.D. Thesis, Department Electrical Computer Engineering, University of Porto]."},{"key":"ref_28","unstructured":"Corning Inc. Available online: http:\/\/www.corning.com\/WorkArea\/showcontent.aspx?id=41261."},{"key":"ref_29","unstructured":"Bernardes, M.A.S. (2011). Developments in Heat Transfer, InTech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1109\/68.681509","article-title":"Pressure sensitivity of side-hole optical fiber sensors","volume":"10","author":"Clowes","year":"2009","journal-title":"IEEE Photon. Technol. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Yang, S., Matthews, M., Elhadj, S., Draggoo, V., and Bisson, S. (2009). Thermal transport in CO2laser irradiated fused silica: In situ measurements and analysis. J. Appl. Phys., 106.","DOI":"10.1063\/1.3259419"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1728","DOI":"10.1364\/AO.26.001728","article-title":"Temperature dependence of the extinction coefficient of fused silica for CO2 laser wavelengths","volume":"26","author":"McLachlan","year":"1987","journal-title":"Appl. Opt."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1098","DOI":"10.1109\/3.83346","article-title":"Choice of clip level for beam width measurements using knife-edge techniques","volume":"27","author":"Siegman","year":"1991","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_34","unstructured":"Baptista, F.D.V. (2009). Simula\u00e7\u00e3o do Comportamento Espectral de Redes de Per\u00edodo Longo em Fibra \u00d3ptica. [M.Sc. Thesis, Centro de Ci\u00eancias Exactas e da Engenharia, University of Madeira]."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1760","DOI":"10.1364\/JOSAA.14.001760","article-title":"Cladding-mode resonances in short- and long-period fiber grating filters","volume":"14","author":"Erdogan","year":"1997","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Erdogan, T. (2000). Cladding-mode resonances in short- and long-period fiber grating filters: Errata. J. Opt. Soc. Am. A, 17.","DOI":"10.1364\/JOSAA.17.002113"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Nespereira, M., Coelho, J.M.P., Monteiro, F., Abreu, M., and Rebord\u00e3o, J.M. (2013). Optical fiber tapers produced by near-infrared laser radiation. Proc. SPIE, 8785.","DOI":"10.1117\/12.2026258"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/8\/10333\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:48:33Z","timestamp":1760219313000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/8\/10333"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,12]]},"references-count":37,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2013,8]]}},"alternative-id":["s130810333"],"URL":"https:\/\/doi.org\/10.3390\/s130810333","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2013,8,12]]}}}