Thermal lensing in an cryogenic sapphire substrates

We report the reduction of thermal lensing in cryogenic sapphire mirrors, which are planned to be used in the large scale cryogenic gravitational wave telescope project. We measured three key parameters of sapphire substrate for thermal lensing at cryogenic temperature. They are the optical absorption coefficient, thermal conductivity and temperature coefficient of refractive index at cryogenic temperature. On the basis of these measurements, we estimated the shot noise sensitivity of the interferometer with thermal lensing by using a wavefront tracing simulation. We found that thermal lensing in cryogenic sapphire mirrors is negligible.