Correlation between birefringence and absorption mapping in large-size Sapphire substrates for gravitational-wave interferometry

Abstract

In high-sensitive laser interferometers, such as the gravitational-wave detector KAGRA, ultra-high-quality mirrors are essential. In the case of KAGRA, where cavity mirrors are cooled down to 20 K, large-size Sapphire crystals are used as the substrate for the main mirrors to achieve both a good optical quality (i.e., low absorption and uniform refractive index) and optimized thermal behavior under cryogenic temperatures. To implement the very tight optical specifications required by this demanding application, it is mandatory to test the optical homogeneity of different substrates. In order to characterize refractive-index inhomogeneities of large-size uniaxial samples such as the KAGRA Sapphire test masses, we developed a dedicated setup, allowing to resolve birefringence changes with a sensitivity in the order of Δn≈2×10-10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta n\\approx 2 \ imes 10^{-10}$$\\end{document} and a spatial resolution of 1mm2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\,{{{\\hbox {mm}}}}^{2}$$\\end{document}. Moreover, the same setup allows us to simultaneously record residual absorption maps, thus allowing for a comparison between birefringence and absorption features. In this paper, we will present for the first time measurements on a KAGRA-sized Sapphire substrate which has been characterized in terms of absorption already in an earlier work. Both birefringence inhomogeneities and absorption distributions will be compared and correlations discussed.