Ternary quarter wavelength coatings for gravitational wave detector mirrors: Design optimization via exhaustive search

Multimaterial optical coatings are a promising viable option to meet the challenging requirements (in terms of transmittance, absorbance, and thermal noise) of next-generation gravitational wave detector mirrors. In this paper we focus on ternary coatings consisting of quarter-wavelength-thick layers, where a third material (H^{′}) is added to the two presently in use, namely, silica (L) and titania-doped tantala (H), featuring higher dielectric contrast (against silica) and lower thermal noise (compared with titania-doped tantala), but higher optical losses. We seek the optimal material sequences, featuring minimal thermal (Brownian) noise under prescribed transmittance and absorbance constraints, by exhaustive simulation over all possible configurations, for different values of the optical density and extinction coefficient of the third material, including the case of amorphous silicon and silicon nitride operating at ambient and cryogenic temperatures. In all cases studied, the optimal designs consist of a stack of (H^{′}|L) doublets topped by a stack of (H|L) doublets, confirming previous heuristic assumptions, and the achievable coating noise power spectral density reduction factor ranges from ∼0.5 at 290 K down to ∼0.1 at 20 K. The robustness of the found optimal designs against layer thickness deposition errors and uncertainties and/or fluctuations in the optical losses of the third material is also investigated. Possible margins for further thermal noise reduction by layer thickness optimization, and strategies to implement it, are discussed.