{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T08:36:21Z","timestamp":1777365381453,"version":"3.51.4"},"reference-count":22,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2020,11,10]],"date-time":"2020-11-10T00:00:00Z","timestamp":1604966400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["MCTechs (POCI-01-0145-FEDER-029282)"],"award-info":[{"award-number":["MCTechs (POCI-01-0145-FEDER-029282)"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Long period gratings (LPGs) inscribed in single mode fibers (SMFs) using CO2 laser irradiation were modelled numerically using the coupled mode method. The model considers the specifications of the inscription technique, such as the shape of the refractive index modulation that mimics the circularly symmetric point-to-point laser irradiation profile. A simple expression for predicting the resonant wavelength was obtained assuming a two-mode coupling model. However, to explain the spectra of the experimental LPGs, it was necessary to assume a reasonably high refractive index change and a multimode coupling model. Furthermore, using the developed model and a genetic algorithm to fit experimental resonances to simulated ones, we were able to estimate the maximum refractive index change, obtaining a value of 2.2 \u00d7 10\u22123, confirming the high refractive index change. The proposed model also predicts a second order resonance for this high value of refractive index change that was confirmed experimentally. Hence, with this model, we found some significant differences in the LPGs behavior when compared with conventional ones, namely, the emergence of coupling between different cladding modes and the competition of first and second order resonances which change the LPG transmission spectrum.<\/jats:p>","DOI":"10.3390\/s20226409","type":"journal-article","created":{"date-parts":[[2020,11,10]],"date-time":"2020-11-10T14:10:41Z","timestamp":1605017441000},"page":"6409","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Analysis of Long Period Gratings Inscribed by CO2 Laser Irradiation and Estimation of the Refractive Index Modulation"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6528-9034","authenticated-orcid":false,"given":"Ana M.","family":"Rocha","sequence":"first","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es and University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]},{"given":"Ana I.","family":"Machado","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es and University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"},{"name":"Department of Physics and I3N, University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]},{"given":"Telmo","family":"Almeida","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es and University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]},{"given":"Joana","family":"Vieira","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es and University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]},{"given":"Margarida","family":"Fac\u00e3o","sequence":"additional","affiliation":[{"name":"Department of Physics and I3N, University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1277","DOI":"10.1109\/50.618322","article-title":"Fiber grating spectra","volume":"15","author":"Erdogan","year":"1997","journal-title":"J. Lightwave Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"081101","DOI":"10.1063\/1.3493111","article-title":"Review of long period fiber gratings written by CO2 laser","volume":"108","author":"Wang","year":"2010","journal-title":"J. Appl. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1789","DOI":"10.1364\/AO.43.001789","article-title":"Prototype CO2 laser-induced long-period fiber grating variable optical attenuators and optical tunable filters","volume":"43","author":"Braiwish","year":"2004","journal-title":"Appl. Opt."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1364\/OL.21.000336","article-title":"Long-period fiber-grating-based gain equalizers","volume":"21","author":"Vengsarkar","year":"1996","journal-title":"Opt. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1109\/50.983240","article-title":"Sensitivity characteristics of long-period fiber gratings","volume":"20","author":"Shu","year":"2002","journal-title":"J. Lightwave Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2240","DOI":"10.1109\/JLT.2018.2790434","article-title":"Optimized strain long-period fiber grating (LPFG) sensors operating at the dispersion turning point","volume":"36","author":"Fuentes","year":"2018","journal-title":"J. Lightwave Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"015201","DOI":"10.1088\/0957-0233\/22\/1\/015201","article-title":"Increasing sensitivity of arc-induced long-period gratings\u2014Pushing the fabrication technique toward its limits","volume":"22","author":"Smietana","year":"2010","journal-title":"Meas. Sci. Technol."},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1109\/JLT.2017.2776599","article-title":"Single-Ended Long Period Fiber Grating Coated with Polystyrene Thin Film for Butane Gas Sensing","volume":"36","author":"Esposito","year":"2018","journal-title":"J. Lightwave Technol."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Janczuk-Richter, M., Gromadzka, B., Richter, \u0141., Panasiuk, M., Zimmer, K., Mikulic, P., Bock, W.J., Ma\u0107kowski, S., \u015amietana, M., and Niedzi\u00f3\u0142ka J\u00f6nsson, J. (2020). Immunosensor Based on Long-Period Fiber Gratings for Detection of Viruses Causing Gastroenteritis. Sensors, 20.","DOI":"10.3390\/s20030813"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1416","DOI":"10.1049\/el:19980978","article-title":"CO2 laser-induced long-period fibre gratings: Spectral characteristics, cladding modes and polarisation independence","volume":"34","author":"Davis","year":"1998","journal-title":"Electron. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/JPHOT.2014.2337875","article-title":"Long Period Fiber Gratings Inscribed With an Improved Two-Dimensional Scanning Technique","volume":"6","author":"Zhong","year":"2014","journal-title":"IEEE Photonics J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1994","DOI":"10.1364\/OL.42.001994","article-title":"Automated technique to inscribe reproducible long-period gratings using a CO2 laser splicer","volume":"42","author":"Almeida","year":"2017","journal-title":"Opt. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1657","DOI":"10.1364\/OL.26.001657","article-title":"Residual stress relaxation in the core of optical fiber by CO2 laser irradiation","volume":"26","author":"Kim","year":"2001","journal-title":"Opt. Lett."},{"key":"ref_15","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_16","doi-asserted-by":"crossref","first-page":"1187","DOI":"10.1049\/el:20081489","article-title":"Mid-infrared spectroscopic detection of refractive index in CO2 laser-written long-period fibre grating","volume":"44","author":"Hirose","year":"2008","journal-title":"Electron. Lett."},{"key":"ref_17","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_18","doi-asserted-by":"crossref","first-page":"1872","DOI":"10.1117\/1.601379","article-title":"Temperature-insensitive and strain-insensitive long-period grating sensors for smart structures","volume":"36","author":"Bhatia","year":"1997","journal-title":"Opt. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1109\/JQE.1973.1077767","article-title":"Coupled-mode theory for guided-wave optics","volume":"9","author":"Yariv","year":"1973","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/S0030-4018(02)01185-9","article-title":"Fabrication and characterisation of ultra-long-period fibre gratings","volume":"203","author":"Shu","year":"2002","journal-title":"Opt. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4486","DOI":"10.1364\/AO.23.004486","article-title":"Dispersion in GeO2-SiO2 glasses","volume":"23","author":"Fleming","year":"1984","journal-title":"Appl. Opt."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1364\/OL.40.000292","article-title":"Analysis of power transfer on multicore fibers with long-period gratings","volume":"40","author":"Rocha","year":"2015","journal-title":"Opt. Lett."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/22\/6409\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:31:26Z","timestamp":1760178686000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/22\/6409"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,10]]},"references-count":22,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["s20226409"],"URL":"https:\/\/doi.org\/10.3390\/s20226409","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,10]]}}}