Gravitational waves were predicted by the theory of general relativity, they are created in the universe by extreme cosmic events. Their measurement on earth in large instruments such as VIRGO in Italy is a challenge in terms of measurement sensitivity. These instruments are large interferometers (several kilometers), and the entire optical chain must minimize noise to be sensitive to very small modifications in space-time. Mirrors are one of the key elements of the optical chain. In this thesis, we propose to create a new type of mirror making it possible to significantly improve the sensitivity of an interferometer. This mirror is based on a sequence of thin epitaxial layers with variations in optical index between each of them. These thin layers must be on a silica or sapphire base. Such a structure is not achievable by additive manufacturing (ie by depositing the layers on the sapphire or silica substrate), because the thin layers are monocrystalline, and the silica is amorphous when the sapphire has an unsuitable lattice parameter. Only thin layer transfer techniques allow the creation of such a stack. This thesis will study thin layer transfer technologies to study one or more options permitting the transfer of monocrystalline layers from the donor substrate to the receiver substrate. Each of the necessary steps will be studied, and mechanisms will be proposed to explain the experimental observations. Demonstrators will be produced and their optical performances evaluated to determine if they are in line with the required sensitivity.