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Thermal noise in optical coatings: A rigorous optomechanical comparison of nanolaminates and isotropic mixtures

Vincenzo Pierro1,2, Vincenzo Fiumara3,2, Veronica Granata4,2, and Guerino Avallone5,*

  • *Contact author: guavallone@unisa.it
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Phys. Rev. D 114, 082001 – Published 6 October, 2026

DOI: https://doi.org/10.1103/v9rw-b3pf

Abstract

We investigate whether a perfectly ordered periodic nanolaminate is intrinsically less mechanically dissipative than an isotropic cosputtered mixture designed to provide the exact same optical function. Focusing on a benchmark room-temperature SiO2/TiO2 material system, we compare coating Brownian dissipation under strict parity of optical thickness and effective refractive index. The constituent amorphous phases are modeled using complex Young’s moduli and purely real Poisson’s ratios, corresponding to a single-loss-angle approximation within each phase. A priori, the outcome of this comparison is highly nontrivial due to competing topological effects: while the nanolaminate is optically optimal, its structural anisotropy forces in-plane shear deformations to operate at the highly dissipative Voigt upper bound, mechanically penalizing the structure compared to a well-mixed isotropic medium. The nanolaminate is treated deterministically through the exact long-wavelength optical (Wiener) and mechanical (Backus) effective-medium relations. Conversely, the isotropic mixture is described by realistic optical closures (Lorentz-Lorenz and Bruggeman) coupled to a complex mechanical self-consistent scheme. To assess the residual uncertainty associated with the unknown cosputtered morphology, we explore the rigorous optical and mechanical admissible regions in the complex plane. We demonstrate that, owing to the small intrinsic optical and mechanical losses of the SiO2/TiO2 pair, these rigorous admissible regions collapse into extremely narrow lenses, drastically restricting the microstructural uncertainty. Moreover, across all realistic isotropic closures, the nanolaminate systematically exhibits lower mechanical dissipation than the corresponding cosputtered mixture. Crucially, even when evaluated against the absolute thermodynamic lower bound of the isotropic state, this topological advantage remains strictly valid in the high-effective refractive index regime. We prove that the ordered architecture exploits the optical upper bound to drastically minimize the required volume fraction of the highly dissipative high-index phase, an effect that overwhelmingly overcompensates for its intrinsic mechanical anisotropy penalty.

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Phys. Rev. D 114, 082001– Published 6 October, 2026
  • Received 11 July 2026
  • Accepted 2 September 2026
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