Progress in the measurement and reduction ofthermal noise in optical coatings forgravitational-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 worldwide research activity on low-noise coatings, with a focus on the results obtained at the Laboratoire des Materiaux Avances. We report new updated values for the $ {{\rm Ta}_2}{{\rm O}_5} $Ta2O5, $ {{\rm Ta}_2}{{\rm O}_5} {-} {{\rm TiO}_2} $Ta2O5−TiO2, and $ {{\rm SiO}_2} $SiO2 coatings of the Advanced LIGO, Advanced Virgo, and KAGRA detectors, and new results from sputtered $ {{\rm Nb}_2}{{\rm O}_5} $Nb2O5, $ {{\rm TiO}_2} {-} {{\rm Nb}_2}{{\rm O}_5} $TiO2−Nb2O5, $ {{\rm Ta}_2}{{\rm O}_5} {-} {{\rm ZrO}_2} $Ta2O5−ZrO2, $ {{\rm MgF}_2} $MgF2, $ {{\rm AlF}_3} $AlF3, 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 in structural analyses and models.