Robustness of the nanolaminate dissipation advantage beyond the single-loss-angle approximation

Determine whether the inequality W_NL/W_ISO < 1 remains valid for the benchmark SiO2/TiO2 system and the realistic isotropic effective-medium closures considered in the paper when the single-loss-angle approximation is relaxed by allowing independent bulk and shear loss angles, provided that all constituent bulk and shear loss angles remain in the low-loss regime.

Background

The analysis models each constituent with a complex Young’s modulus and a real Poisson ratio, thereby imposing a single mechanical loss angle for each phase. A more general viscoelastic description would allow independent bulk and shear loss angles, which would generally make the constituent Poisson ratios complex and require recomputation of the admissible effective-modulus regions and Brownian dissipation.

The authors conjecture that the nanolaminate’s lower dissipation remains valid under sufficiently small departures from this simplifying assumption. Establishing that conjecture requires a systematic parametric study of constituent optical and mechanical properties, together with reliable independent measurements of the bulk and shear loss angles for amorphous SiO2 and TiO2.

References

We conjecture that, for the benchmark $\mathrm{SiO_2/TiO_2}$ system and the realistic isotropic closures considered here, the inequality $W_{\rm NL}/W_{\rm ISO}<1$ remains valid under sufficiently small departures from the single-loss-angle approximation, provided that all constituent bulk and shear loss angles remain in the low-loss regime. A quantitative assessment of this conjecture and, more generally, of the robustness of the present conclusions requires a systematic parametric investigation of the constituent optical and mechanical properties, supported by reliable constituent-specific experimental data, particularly independent measurements of the bulk and shear loss angles.

— Thermal Noise in Optical Coatings: A Rigorous Opto-Mechanical Comparison of Nanolaminates and Isotropic Mixtures  (2609.03850 - Pierro et al., 3 Sep 2026) in Section 'Conclusions and Outlook'