Thermal noise reduction in ternary optical coatings: Some scenarios from Ti?GeO2-based ternary systems to high-index materials

Minimizing coating thermal noise is crucial for enhancing gravitational wave detector sensitivity, with a target amplitude spectral density reduction factor (henceforth ASD RF) of 0.5 relative to the coatings used currently. This study investigates the design of low-noise dielectric stacks using the double stack of doublets strategy, explored via ad hoc optimization heuristics specifically developed for efficient parametric analysis of coating performance. We analyze the performance limits of ternary coatings based on SiO ₂, Ti∷SiO ₂, and Ti∷GeO ₂, considering both their material and optical properties with respect to detector constraints. Optimization results suggest such coating configurations, even with a relaxed absorbance constraint (1 ppm), fall short of the target, achieving a best ASD RF of ∼0.69. Consequently, we explore alternative ternary double stack of doublets designs incorporating higher refractive index materials. Simulations demonstrate that incorporating alternative high-index materials offers a promising pathway, potentially enabling the achievement of the project target. We discuss the optimization strategies, performance trade-offs, design robustness, and implications of using high-index, potentially higher-loss materials for next-generation optical coatings.