Polar Decomposition of Jones Matrix and Mueller Matrix of Coherent Rayleigh Backscattering in Single-Mode Fibers

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Polar Decomposition of Jones Matrix and Mueller Matrix of Coherent Rayleigh Backscattering in Single-Mode Fibers
Title:
Polar Decomposition of Jones Matrix and Mueller Matrix of Coherent Rayleigh Backscattering in Single-Mode Fibers
Journal Title:
Sensors
Publication Date:
08 March 2024
Citation:
Dong, H., Zhang, H., & Hu, D. J. J. (2024). Polar Decomposition of Jones Matrix and Mueller Matrix of Coherent Rayleigh Backscattering in Single-Mode Fibers. Sensors, 24(6), 1760. https://doi.org/10.3390/s24061760
Abstract:
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—birefringence and polarization-dependent loss (PDL)—although 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 (φ-OTDR). For the first time, to our knowledge, by using the derived birefringence–Jones matrix, the common optical phase of the optical signal in φ-OTDR is obtained as the function of the forward phase and birefringence distributions. By using the derived PDL–Mueller matrix, the optical intensity of the optical signal in φ-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 φ-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 φ-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 φ-OTDR is theoretically proven to be a local parameter, which is determined by the local birefringence and local optical phase distributions.
License type:
Attribution 4.0 International (CC BY 4.0)
Funding Info:
This research / project is supported by the A*STAR - Industry Alignment Fund
Grant Reference no. : A19F1a0104
Description:
ISSN:
1424-8220
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