  Thermal noise in high-reflectivity mirror coatings is a limiting factor in
ground-based gravitational wave detectors. Reducing this coating thermal noise
improves the sensitivity of detectors and enriches the scientific outcome of
observing runs. Crystalline gallium arsenide and aluminum-alloyed gallium
arsenide (referred to as AlGaAs) coatings are promising coating candidates for
future upgrades of gravitational wave detectors because of their low coating
thermal noise. However, AlGaAs-based crystalline coatings may be susceptible to
an electro-optic noise induced by fluctuations in an electric field. We
investigated the electro-optic effect in an AlGaAs coating by using a
Fabry-Perot cavity, and concluded that the noise level is well below the
sensitivity of current and planned gravitational-wave detectors.
