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.
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