Superiority of sapphire over silicon test masses regarding thermal noise and thermal lensing for laser interferometers with transmissive optics

A comparison between sapphire and silicon as test mass substrate regarding the sensitivity of advanced laser interferometers with transmissive optics has been performed. Our simulations include thermal noise magnitude and shot noise level from 5K to 300K. The thermal noise is dominated by thermoelastic noise from room to low temperature. At cryogenic temperature, the coating loss is the predominant source of noise. On the other hand, the shot noise level is strongly dependent on thermal lensing effect due to the substrate and coating optical absorption. Thermal lensing becomes negligible below 90 K for sapphire and below 50K for silicon. Even if silicon has a lower absorption than sapphire, this benefit is canceled due to its higher thermooptic coefficient. Both thermal noise and shot noise demonstrates the advantage of using sapphire test mass over silicon below 200K.