Thermal lensing in cryogenic sapphire substrates

We report the reduction of the thermal lensing in cryogenic sapphire mirrors, which is planed to be used in the Large scale Cryogenic Gravitational wave Telescope (LCGT) project. We measured three key parameters of sapphire substrate for thermal lensing at cryogenic temperature. They are optical absorption coefficient, thermal conductivity and temperature coefficient of refractive index at cryogenic temperature. On basis of these measurements, we estimated the shot noise sensitivity of the interferometer with thermal lensing by using a wave-front tracing simulation. We found that thermal lensing in cryogenic sapphire mirrors is negligible.