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 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.

We demonstrate how to create all-dielectric metasurfaces with a strong toroidal response by arranging two types of nanodisks into asymmetric quadrumer clusters.We demonstrate that a strong axial toroidal response of the metasurface is related to conditions of the trapped (dark) mode that is excited due the symmetry breaking in the cluster. We study the correlation between the toroidal response and asymmetry in the metasurface and nanocluster geometries, which appears from the different diameters of nanodisks or notches introduced into the nanodisks. 1 arXiv:1801.07131v1 [physics.optics] 22 Jan 2018Toroidal multipoles appear as fundamental electromagnetic excitations different from the familiar electric and magnetic multipoles. 1 It is known that electric multipoles result from positive and negative charges positioned over a distance, whereas magnetic multipoles are produced by electric currents circulating on a contour. In contrast, the simple member of the toroidal multipoles, a magnetic (polar ) toroidal dipole, is created by poloidal electric currents flowing on a surface of a torus along its meridians. Such a current flow can be represented as a set of magnetic dipoles arranged head-to-tail to form a closed ring. A dual counterpart of the polar toroidal dipole is an electric (axial ) toroidal dipole, which is composed by a ring of the electric dipolar configurations. 2,3 Mathematically speaking, both