Metasurface engineering through bound states in the continuum

Metasurfaces have attracted a lot of attention in recent years due to novel ways they provide for the efficient wavefront control and engineering of the resonant transmission. We discuss an approach allowing effectively control appearance of the sharp Fano resonances in metasurfaces associated with the {\it bound states in the continuum}. We demonstrate that by breaking the symmetry transversely, in the direction perpendicular to a metasurface with a complex unit cell, we can control the number, frequency, and type of high-$Q$ resonances originating from bound states in the continuum. As example, we demonstrate experimentally the metasurfaces with magnetic dipole and toroidal dipole responses governed by the physics of multipolar bound states.