Thermal Noise Reduction in Ternary Optical Coatings: From Ti::GeO${}_2$-Based Ternary Systems to High Index Materials

Abstract

Minimizing coating thermal noise is crucial for enhancing gravitational wave detector sensitivity, with a target Amplitude Spectral Density Reduction Factor (ASD RF) of $0.5$ relative to standard coatings. This study investigates the design of low-noise dielectric stacks using the 'Double Stack of Doublet' 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 material property uncertainties and absorption constraints. Optimization results show that this system, even with relaxed absorbance constraint (1 ppm), falls short of the target, achieving a best ASD RF of $\sim 0.69$. Consequently, we explore alternative ternary 'Double Stack of Doublet' 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.