Progress in the measurement and reduction of thermal noise in optical coatings for gravitational-wave detectors

Coating thermal noise is a fundamental limit for precision experiments based on optical and quantum transducers. In this review, after a brief overview of the techniques for coating thermal noise measurements, we present the latest world-wide research activity on low-noise coatings, with a focus on the results obtained at the Laboratoire des Mat\'{e}riaux Avanc\'{e}s. We report new updated values for the Ta$_2$O$_5$, Ta$_2$O$_5$-TiO$_2$ and SiO$_2$ coatings of the Advanced LIGO, Advanced Virgo and KAGRA detectors, and new results from sputtered Nb$_2$O$_5$, TiO$_2$-Nb$_2$O$_5$, Ta$_2$O$_5$-ZrO$_2$, MgF$_2$, AlF$_3$ and silicon nitride coatings. Amorphous silicon, crystalline coatings, high-temperature deposition, multi-material coatings and composite layers are also briefly discussed, together with the latest developments of structural analyses and models.