Improving gravitational wave detectors sensitivity has been the main challenge to continue to dig deep in gravitational astronomy. One of the main limitation of the sensitivity of such detectors are the coatings thermal noise of the mirrors. The goal of this thesis research project is to understand thermal noises that occur in the Virgo detector mirrors and to explore new materials in order to reduce these thermal noises in the coatings. Focus has been made on new monocrystalline coatings to produce high reflectivity mirrors with low optical absorption and low mechanical dissipation. An excellent candidate is a crystalline III-V material: Gallium arsenide (GaAs). Such materials have both excellent optical specifications (low level of optical diffusion and absorption) and better mechanical properties (quality factor of 1e5), thus lower thermal noises. The conception of a crystalline Bragg mirror has been explored through the transfer of an AlGaAs/GaAs multilayer coating from a GaAs substrate to a SiO2 substrate.