Calculation methods for thermo-optic noise and nonequilibrium noise in the coatings of space gravitational wave detection telescope

Coating noise is a consistently significant source of noise in high-precision gravitational wave measurements. In this paper, a model that quantifies the relationship between temperature noise and the optical path variation is proposed to analyze the thermo-optic noise of optical coating. There are two types of temperature-dependent noise-the traditional equilibrium thermal noise and the position noise introduced by the overall temperature fluctuation in the telescope load-that need to be considered for space gravitational wave detection satellites. In the current off-axis quad-mirror design, the incident angle of light from each mirror is very different, and the maximum incident angle reaches nearly 45 degrees. The optical path noise of all-dielectric reflective coating will be more significant under the large incident angle. Metal reflective coating can effectively suppress the optical path noise caused by low-frequency temperature fluctuation, making them a viable alternative for space gravitational wave detectors. This paper provides a valuable reference for the selection of reflective coatings in space-based gravitational wave telescopes from the perspective of coating noise.