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°. 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.