{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:55:23Z","timestamp":1760144123821,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T00:00:00Z","timestamp":1709856000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Enhancing Offshore System Productivity, Integrity, and Survivability in Extreme Environments (ENSURE)","award":["A19F1a0104"],"award-info":[{"award-number":["A19F1a0104"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The Jones matrix and the Mueller matrix of the coherent Rayleigh backscattering (RB) in single-mode fibers (SMFs) have been derived recently. It has been shown that both matrices depict two polarization effects\u2014birefringence and polarization-dependent loss (PDL)\u2014although the SMF under investigation is purely birefringent, having no PDL. In this paper, we aim to perform a theoretical analysis of both matrices using polar decomposition. The derived sub-Jones\/Mueller matrices, representing birefringence and PDL, respectively, can be used to investigate the polarization properties of the coherent RB. As an application of the theoretical results, we use the derived formulas to investigate the polarization properties of the optical signals in phase-sensitive optical time-domain reflectometry (\u03c6-OTDR). For the first time, to our knowledge, by using the derived birefringence\u2013Jones matrix, the common optical phase of the optical signal in \u03c6-OTDR is obtained as the function of the forward phase and birefringence distributions. By using the derived PDL\u2013Mueller matrix, the optical intensity of the optical signal in \u03c6-OTDR is obtained as the function of the forward phase and birefringence distributions as well as the input state of polarization (SOP). Further theoretical predictions show that, in \u03c6-OTDR, the common optical phase depends on only the local birefringence in the first half of the fiber section, which is occupied by the sensing pulse, irrelevant of the input SOP. However, the intensity of the \u03c6-OTDR signal is not a local parameter, which depends on the input SOP and the birefringence distribution along the entire fiber section before the optical pulse. Moreover, the PDL measured in \u03c6-OTDR is theoretically proven to be a local parameter, which is determined by the local birefringence and local optical phase distributions.<\/jats:p>","DOI":"10.3390\/s24061760","type":"journal-article","created":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T10:10:52Z","timestamp":1709892652000},"page":"1760","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Polar Decomposition of Jones Matrix and Mueller Matrix of Coherent Rayleigh Backscattering in Single-Mode Fibers"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0820-3799","authenticated-orcid":false,"given":"Hui","family":"Dong","sequence":"first","affiliation":[{"name":"Institute for Infocomm Research (I2R), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #21-01, Connexis South Tower, Singapore 138632, Singapore"}]},{"given":"Hailiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Institute for Infocomm Research (I2R), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #21-01, Connexis South Tower, Singapore 138632, Singapore"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8822-3900","authenticated-orcid":false,"given":"Dora Juan Juan","family":"Hu","sequence":"additional","affiliation":[{"name":"Institute for Infocomm Research (I2R), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #21-01, Connexis South Tower, Singapore 138632, Singapore"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,8]]},"reference":[{"key":"ref_1","unstructured":"Taylor, H.F., and Lee, C.E. 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