• bound states in the continuum
• membrane mechanical modes
• metamaterials
• metasurfaces
• optomechanics

In the last decades the possibility to realize nanoscale-sized features in dielectric and metallic layers has defined a new class of artificial materials, called metamaterials. When interacting with wave-like excitations, the macroscopic properties of metamaterials can be controlled by acting on their subwavelength structuration, not only mocking but even surpassing the properties of natural materials. This peculiar property makes them ideal systems for a tailorable interaction with excitations of different nature, enabling their use in diverse applications. For example, photonic metamaterials can be used to manipulate the scalar and vector properties of light, whereas phononic metamaterials can handle acoustic vibrations and deformations. A lower-dimensionality class of metamaterials is constituted by almost bidimensional patterned layers; the so-called metasurfaces show an easier integration with standard nanofabrication schemes and can additionally be embedded on fully suspended nanomembranes, paving the way to single optomechanical layers apt to the simultaneous control of light and vibrations.
In this Ph. D. thesis I report some progresses towards the realization of hybrid optomechanical metasurfaces. In a first experiment I investigated artificially induced mechanical anisotropy in phononic metasurfaces, showing the capabilities of arbitrarily controlling the mechanical material asymmetry and its impact in a finite-size structure such as a square membrane. In a second experiment I studied specific high-Q optical resonances (bound states in the continuum) within mechanically compliant metasurfaces, relying on their optomechanical modulation for enhanced optical spectroscopy. With the final goal of combining the control of photons and phonons within a single nanomembrane, the optomechanical metasurfaces I have investigated could represent a perspective bench for interesting systems, which can have an impact in sensor technology, dynamical modulation of light and creation of dynamical optical structured beams on demand.