Calculation method for light scattering caused by multilayer coated mirrors in gravitational wave detectors

Scattered light in inteferometric gravitational wave detectors needs to be reduced so that it will not harm the actual signals coming from a gravitational wave. In this paper, we report on the application of the theory of light scattering from mirrors in interferometric detectors having multilayer coatings on their surfaces and compared the results with single-surface scattering theories, which are traditionally used in the field of gravitational wave detectors. For the first time in this field, we have calculated the scattering distributions of the power-recycling, the signal-recycling, and the beam-splitter mirrors in KAGRA (a cryogenic interferometric gravitational wave detector currently under construction in the Kamioka mine in Japan) by using models of their multilayer coatings. Furthermore, we have performed simulations to show the differences between multilayer scattering and single-surface scattering models in the back-scattering of mechanical structures close to the mirrors and the impact on the sensitivity of the KAGRA detector. We show that the back-scattering by using those coatings can be larger by up to almost two orders of magnitude and they also give rise to additional scattering features that should be taken into account for all optical applications in gravitational wave detectors.