Influence of nonuniformity in sapphire substrates for a gravitational wave telescope

The construction of a large-scale cryogenic gravitational wave telescope, KAGRA, has been completed, and four sapphire test masses have been installed in cryostat vacuum chambers. Recently, it was observed that a sapphire substrate used for one of the input test masses showed a characteristic structure in its transmission map due to nonuniformity of the crystal. We performed an interferometer simulation to observe the influence of the nonuniformity using measured transmission/reflection maps. Shot noise increased by 7% at low frequencies and by 16% at high frequencies. Laser frequency noise coupling increased by 1 order of magnitude. We also found deformation of an alignment control signal and higher tilt coupling in the output optics.