{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T07:21:13Z","timestamp":1782372073134,"version":"3.54.5"},"reference-count":21,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2021,10,30]],"date-time":"2021-10-30T00:00:00Z","timestamp":1635552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Outstanding Youth Science Fund Project of Hunan Province Natural Science Foundation","award":["2019JJ20023"],"award-info":[{"award-number":["2019JJ20023"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11974427, 12004431"],"award-info":[{"award-number":["11974427, 12004431"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"State Key Laboratory of Pulsed Power Laser","award":["SKL-2020-ZR05, SKL2021ZR01"],"award-info":[{"award-number":["SKL-2020-ZR05, SKL2021ZR01"]}]},{"name":"Postgraduate Scientific Research Innovation Project of Hunan Province","award":["CX20200046, CX20190027"],"award-info":[{"award-number":["CX20200046, CX20190027"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Line-by-line direct writing by femtosecond laser has been proved to be a simple and effective method for the fabrication of low-loss fiber Bragg gratings (FBGs), and is more flexible compared with the traditional ultraviolet exposure method. In this paper, the line-position-dependent characteristics of cladding modes coupling in line-by-line FBGs have been studied, to the best of our knowledge, for the first time. Both theoretical and experimental results show that off-center inscribing could compress the bandwidth of the Bragg resonance and excite more abundant cladding mode coupling, in which the core-guided fundamental mode would couple to the cladding-guided LP0n and LP1n simultaneously. By aligning the line positions across the core region, the first apodized line-by-line FBG was achieved. This work enriches the theories of line-by-line FBGs and provides an inscription guidance to meet different application requirements.<\/jats:p>","DOI":"10.3390\/s21217231","type":"journal-article","created":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T22:24:22Z","timestamp":1635805462000},"page":"7231","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Line Position-Dependent Effect in Line-by-Line Inscribed Fiber Bragg Gratings"],"prefix":"10.3390","volume":"21","author":[{"given":"Hongye","family":"Li","sequence":"first","affiliation":[{"name":"College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China"},{"name":"State Key Laboratory of Pulsed Power Laser Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaofan","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China"},{"name":"Hunan Provincial Key Laboratory of High Energy Laser Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Binyu","family":"Rao","sequence":"additional","affiliation":[{"name":"College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China"},{"name":"Hunan Provincial Key Laboratory of High Energy Laser Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Meng","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China"},{"name":"State Key Laboratory of Pulsed Power Laser Technology, Changsha 410073, China"},{"name":"Hunan Provincial Key Laboratory of High Energy Laser Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baiyi","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China"},{"name":"State Key Laboratory of Pulsed Power Laser Technology, Changsha 410073, China"},{"name":"Hunan Provincial Key Laboratory of High Energy Laser Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zefeng","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China"},{"name":"State Key Laboratory of Pulsed Power Laser Technology, Changsha 410073, China"},{"name":"Hunan Provincial Key Laboratory of High Energy Laser Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1364\/OL.28.000995","article-title":"Fiber Bragg gratings made with a phase mask and 800-nm femtosecond radiation","volume":"28","author":"Mihailov","year":"2003","journal-title":"Opt. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1864","DOI":"10.1109\/LPT.2004.831239","article-title":"Fiber Bragg gratings with suppressed cladding modes made in SMF-28 with a femtosecond IR laser and a phase mask","volume":"16","author":"Grobnic","year":"2004","journal-title":"IEEE Photon. Technol. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2185","DOI":"10.1109\/JLT.2019.2899585","article-title":"Parallel-Integrated Fiber Bragg Gratings Inscribed by Femtosecond Laser Point-by-Point Technology","volume":"37","author":"Wang","year":"2019","journal-title":"J. Light. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1109\/JLT.2017.2750490","article-title":"Plane-by-Plane Inscription of Grating Structures in Optical Fibers","volume":"36","author":"Lu","year":"2018","journal-title":"J. Light. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1049\/el:20046050","article-title":"Direct writing of fibre Bragg gratings by femtosecond laser","volume":"40","author":"Martinez","year":"2004","journal-title":"Electron. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1364\/OE.19.000325","article-title":"Cladding mode coupling in highly localized fiber Bragg gratings: Modal properties and transmission spectra","volume":"19","author":"Thomas","year":"2011","journal-title":"Opt. Express"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"13451","DOI":"10.1364\/OE.20.013451","article-title":"Optimizing the net reflectivity of point-by-point fiber Bragg gratings: The role of scattering loss","volume":"20","author":"Williams","year":"2012","journal-title":"Opt. Express"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5121","DOI":"10.1364\/OL.44.005121","article-title":"Low short-wavelength loss fiber Bragg gratings inscribed in a small-core fiber by femtosecond laser point-by-point technology","volume":"44","author":"Liu","year":"2019","journal-title":"Opt. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1190","DOI":"10.1109\/LPT.2010.2050877","article-title":"Line-by-Line Fiber Bragg Grating Made by Femtosecond Laser","volume":"22","author":"Zhou","year":"2010","journal-title":"IEEE Photon. Technol. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1364\/OL.38.000594","article-title":"Femtosecond-laser-induced highly birefringent Bragg gratings in standard optical fiber","volume":"38","author":"Chah","year":"2013","journal-title":"Opt. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"17670","DOI":"10.1364\/OE.24.017670","article-title":"Ultra-compact strain- and temperature-insensitive torsion sensor based on a line-by-line inscribed phase-shifted FBG","volume":"24","author":"Huang","year":"2016","journal-title":"Opt. Express"},{"key":"ref_12","first-page":"1","article-title":"Taper Embedded Phase-Shifted Fiber Bragg Grating Fabricated by Femtosecond Laser Line-by-Line Inscription","volume":"10","author":"Zhu","year":"2018","journal-title":"IEEE Photonics J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"12987","DOI":"10.1364\/OE.27.012987","article-title":"Stable and low-threshold random fiber laser via Anderson localization","volume":"27","author":"Deng","year":"2019","journal-title":"Opt. Express"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1474","DOI":"10.1109\/JLT.2019.2956178","article-title":"Optical Fiber Tag Based on an Encoded Fiber Bragg Grating Fabricated by Femtosecond Laser","volume":"38","author":"Yang","year":"2020","journal-title":"J. Light. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4562","DOI":"10.1364\/OL.43.004562","article-title":"Sapphire fiber Bragg gratings inscribed with a femtosecond laser line-by-line scanning technique","volume":"43","author":"Xu","year":"2018","journal-title":"Opt. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7314","DOI":"10.1364\/AO.57.007314","article-title":"Fabrication of a laser cavity mirror in a large mode area fiber by an ultrashort pulse laser","volume":"57","author":"Hasegawa","year":"2018","journal-title":"Appl. Opt."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6679","DOI":"10.1364\/OL.410277","article-title":"High purity optical vortex generation in a fiber Bragg grating inscribed by a femtosecond laser","volume":"45","author":"Li","year":"2020","journal-title":"Opt. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2950","DOI":"10.1364\/OL.393242","article-title":"Dual interference effects in a line-by-line inscribed fiber Bragg grating","volume":"45","author":"Huang","year":"2020","journal-title":"Opt. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"075704","DOI":"10.1088\/2040-8986\/ab92b7","article-title":"Building-up and suppression of cladding mode coupling in fiber Bragg gratings","volume":"22","author":"Li","year":"2020","journal-title":"J. Opt."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1364\/OL.41.001201","article-title":"Off-axis ultraviolet-written fiber Bragg gratings for directional bending measurements","volume":"41","author":"Feng","year":"2016","journal-title":"Opt. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2988","DOI":"10.1364\/OL.36.002988","article-title":"Point-by-point inscription of apodized fiber Bragg gratings","volume":"36","author":"Williams","year":"2011","journal-title":"Opt. Lett."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/21\/7231\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:23:28Z","timestamp":1760167408000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/21\/7231"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,30]]},"references-count":21,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["s21217231"],"URL":"https:\/\/doi.org\/10.3390\/s21217231","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,30]]}}}