Effect of temperature and wavelength on the refractive index of water: a fiber-optic sensor application

The refractive index n(λ,T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n(\lambda ,T$$\end{document}) is a basic optical property of materials. The refractive index and the thermo-optic coefficient (dn/dT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{d}}n/{\mathrm{d}}T$$\end{document}) are significant parameters of liquids for optically controlled systems, such as the direct measurement of liquid solution concentrations and optical paths. In this study, the variation in the refractive index of water in the liquid phase with temperature was measured with our self-designed fiber optic-based refractive index sensor and dn/dT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{d}}n/{\mathrm{d}}T$$\end{document} values were obtained with a full-width half-maximum method at wavelengths of 980, 1426, and 1550 nm, respectively. Water is the most abundant and life-critical substance in the world, and its optical properties pose challenging scientific problems that require knowledge of the refractive index to be resolved. The results indicate that the experimental refractive index values are compatible with both the theoretical and experimental data in the literature. We also tested the refraction index results with two theoretical models and obtained good agreement between the calculated and experimental values. The resolution of the fiber optic-based refractive index sensor was 10-5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-5}$$\end{document}. Our designed sensor could measure the refractive index of liquids with temperature with accuracy.