Fluctuation Dissipation at work: Thermal noise in reflective optical coatings for GW detectors

In this paper we summarize the fundamentals of thermal noise in gravitational wave detectors as a metrological application. We repeat the evolution of noise calculation beginning at the classical process of Brownian motion via the Fluctuation-Dissipation theorem (FDT) of Callen and Welton and arriving at the direct formulation of the FDT. Using this direct approach we present the effect of anisotropic substrates on the Brownian coating noise using a finite element analysis. Previous investigations identified Brownian coating noise to dominate the thermal noise spectrum of current and future detectors. We summarize and discuss different existing ideas to reduce this kind of noise allowing for an increased sensitivity of future detectors.