Electro-optic metasurfaces.

We numerically study metasurfaces that incorporate electro-optic materials and show that they can achieve large amplitude and phase modulations across a distance that is a fraction of the operation wavelength. We show that the metasurfaces made of dielectric discs placed on a film of lithium niobate can exhibit three main types of resonances, associated with the Fabry-Perot modes in the structure, guided modes of the film and Mie modes of the disks. We compare metasurface performance in these different regimes for achieving largest electro-optic modulation and find that in the proposed geometry the strongest amplitude modulation can be achieved through excitation and re-emission of the guided modes in the substrate. We further show that to achieve larger 70 degrees phase modulation while maintaining high transmission, we need to utilise more complex metasurfaces that have at least two resonators per unit cell.