Thermal Noise in Optical Coatings: A Rigorous Opto-Mechanical Comparison of Nanolaminates and Isotropic Mixtures

Abstract

We investigate whether a perfectly ordered periodic nanolaminate is intrinsically less mechanically dissipative than an isotropic co-sputtered mixture designed to provide the exact same optical function. Focusing on a room-temperature SiO2/TiO2 system, we compare coating Brownian dissipation under strict parity of optical thickness and effective refractive index. Amorphous phases are modeled using complex Young's moduli and real Poisson's ratios. The comparison is highly non-trivial: while the nanolaminate is optically optimal, its structural anisotropy forces in-plane shear to operate at the highly dissipative Voigt upper bound, mechanically penalizing it against an isotropic medium. The nanolaminate is treated via exact optical (Wiener) and mechanical (Backus) relations. The isotropic mixture is described by optical closures (Lorentz--Lorenz, Bruggeman) coupled to a complex mechanical self-consistent scheme. To assess uncertainty from the unknown co-sputtered morphology, we explore rigorous optical and mechanical admissible regions in the complex plane. Owing to the small intrinsic losses of SiO2/TiO2, these regions collapse into extremely narrow lenses, strictly limiting microstructural uncertainty. Across all realistic isotropic closures, the nanolaminate systematically exhibits lower mechanical dissipation than the co-sputtered mixture. Even against the thermodynamic lower bound of the isotropic state, this topological advantage remains valid for high effective refractive indices. We prove the ordered architecture exploits the optical upper bound to minimize the required volume fraction of the highly dissipative high-index phase, overwhelmingly overcompensating for its intrinsic mechanical anisotropy penalty.