Intrinsic Defects in Amorphous Optical Coatings of TiO$_2$-doped GeO$_2$ for Gravitational-wave Detectors

Abstract

The increased laser power of future gravitational-wave detectors will require mirror coatings with optical absorption below 0.1 ppm per mirror. TiO$_2$-doped GeO$_2$, currently the best high-index material for reducing room-temperature coating thermal noise, still exhibits ppm-level absorption even after extrinsic contamination is minimized. Using ab-initio simulations and absorption measurements, we identify oxygen-deficient Ti-rich environments as the origin of this residual absorption. We find that ordinary structural disorder in the amorphous network can localize electronic states but does not produce defects capable of absorbing 1064-nm light. In contrast, oxygen vacancies in compact Ti-rich environments create localized Ti$^{3+}$--Ti$^{3+}$-like polaron-pair or mixed Ti-polaron states states with transitions near 1064 nm. Photothermal measurements show increased absorption after dry/inert annealing, supporting the formation of these reduction-sensitive defects. These results show that the residual absorption is not an intrinsic limitation of TiO$_2$-doped GeO$_2$, but a process-dependent defect that may be mitigated through control of oxygen stoichiometry during deposition and annealing.