{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T05:21:10Z","timestamp":1766726470978,"version":"3.48.0"},"reference-count":19,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T00:00:00Z","timestamp":1766534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Photonics"],"abstract":"<jats:p>The m-lines spectroscopy is a precise, non-destructive and contactless method, and one of its main applications is the determination of the geometric-optical parameters of a thin film deposited over a substrate, namely the refractive index and the thickness of the film under analysis. The method was first described in 1969 with the seminal work of Tien, more than half a century ago, and, since then, it has been reported in the literature that at least two modal indices of the same polarization are required to unequivocally determine a given film\u2019s refractive index and thickness. This constraint imposes a limit on the waveguide\u2019s thickness, for it leaves out the possibility of determining the geometric-optical parameters of all films where only single-mode propagation is feasible. In this work, we propose and validate a strategy that extends the applicability of the method to single-mode operation, enlarging its operational thickness detection range. Moreover, the results obtained demonstrate that restricting the parameter extraction to fundamental modes leads to a measurable increase in precision. This improvement is attributed to the lower susceptibility to experimental uncertainties, lower sensitivity to surface roughness and nearby structures, and higher confinement that characterize fundamental modes as opposed to higher-order ones.<\/jats:p>","DOI":"10.3390\/photonics13010015","type":"journal-article","created":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T16:41:19Z","timestamp":1766594479000},"page":"15","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["M-Lines Spectroscopy for Thin Films: A New Perspective"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8785-445X","authenticated-orcid":false,"given":"Paulo","family":"Louren\u00e7o","sequence":"first","affiliation":[{"name":"Lisbon School of Engineering (ISEL\/IPL), Rua Conselheiro Em\u00eddio Navarro, No. 1, 1959-007 Lisboa, Portugal"},{"name":"CTS-Centre of Technology and Systems and Associated Lab of Intelligent Systems (LASI), 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9938-0351","authenticated-orcid":false,"given":"Alessandro","family":"Fantoni","sequence":"additional","affiliation":[{"name":"Lisbon School of Engineering (ISEL\/IPL), Rua Conselheiro Em\u00eddio Navarro, No. 1, 1959-007 Lisboa, Portugal"},{"name":"CTS-Centre of Technology and Systems and Associated Lab of Intelligent Systems (LASI), 2829-516 Caparica, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1063\/1.1652820","article-title":"Modes of propagating light waves in thin deposited semiconductor films","volume":"14","author":"Tien","year":"1969","journal-title":"Appl. Phys. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1080\/00150190701354927","article-title":"Optical Characterisation of a Three Layer Waveguide Structure by m-Lines Spectroscopy","volume":"352","author":"Schneider","year":"2007","journal-title":"Ferroelectrics"},{"key":"ref_3","unstructured":"Rosental, A. (2005). Application of multi-wavelength M-lines spectroscopy for optical analysis of sol-gel prepared waveguide thin films. Optical Materials and Applications, SPIE."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1325","DOI":"10.1364\/JOSA.60.001325","article-title":"Theory of Prism\u2013Film Coupler and Thin-Film Light Guides","volume":"60","author":"Tien","year":"1970","journal-title":"J. Opt. Soc. Am."},{"key":"ref_5","unstructured":"Hecht, E. (2016). Optics, Walter de Gruyter GmbH & Co KG. 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Determining Thin Film Characteristics by Prism Coupling Technique. Doctoral Conference on Computing, Electrical and Industrial Systems, Springer Nature.","DOI":"10.1007\/978-3-031-63851-0_24"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"00023","DOI":"10.1051\/epjconf\/202430500023","article-title":"Refractive index and thickness analysis of planar interfaces by prism coupling technique","volume":"305","author":"Vygranenko","year":"2024","journal-title":"EPJ Web Conf."},{"key":"ref_14","unstructured":"(2021, September 11). Refractiveindex.info. Refractive Index Database. Available online: https:\/\/refractiveindex.info\/."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"120434","DOI":"10.1016\/j.jnoncrysol.2020.120434","article-title":"Dependence of optical properties on composition of silicon carbonitride thin films deposited at low temperature by PECVD","volume":"551","author":"Lavareda","year":"2021","journal-title":"J. Non-Cryst. 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