Accurate calculation of thermal noise in multilayer coating

TL;DR

This paper develops precise formulas for thermal noise in multilayer coatings by modeling light propagation and boundary displacements, enabling accurate noise spectral density calculations for interferometric applications.

Contribution

It introduces a transmission line model to accurately compute thermal fluctuations and reflected phase variations in multilayer coatings, advancing noise prediction methods.

Findings

Derived formulas for reflected wave phase as a function of boundary displacements.

Calculated spectral density of coating Brownian noise using the new approach.

Validated the model's accuracy in predicting thermal noise in multilayer coatings.

Abstract

We derive accurate formulas for thermal fluctuations in multilayer interferometric coating taking into account light propagation inside the coating. In particular, we calculate the reflected wave phase as a function of small displacements of the boundaries between the layers using transmission line model for interferometric coating and derive formula for spectral density of reflected phase in accordance with Fluctuation-Dissipation Theorem. We apply the developed approach for calculation of the spectral density of coating Brownian noise.