Simulation of bulk-absorption thermal lensing in transmissive optics of gravitational waves detectors

Abstract

This paper presents finite-element modelling simulations of thermal lensing and thermal lens compensation in transmissive optics for gravitational wave detectors. We compare the current candidate test mass materials, fused silica and sapphire, in terms of sample geometry and time-dependent phenomena. For both materials, the thermal-lensing time constant is a few minutes, yet the core temperature needs several tens of minutes to stabilize. Thermal lens compensation using simple radiative heating is limited in temperature by absorption in the test mass. This effect limits the maximum allowed absorption for sapphire to ∼10–20 ppm/cm. For reasonable parameters, optical path length compensation within 1 nm can be achieved over a beam radius of 5 mm. If the optical absorption of the transmissive optics is too high, compensation can be achieved by means of a separate compensation plate.