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.

A planar all-dielectric metamaterial made of a double-periodic lattice whose unit cell consists of a single subwavelength dielectric particle having the form of a disk possessing a penetrating hole is considered. The resonant states in the transmitted spectra of the metamaterial are identified considering modes inherent to the individual cylindrical dielectric resonator. A correlation between the asymmetry in the particle's geometry, which arises from the off-centered displacement of the hole and the formation of the Mie-type and trapped modes, is established. The advantages of using a coaxial-sector notch instead of a round hole for the trapped mode excitation are explained.

helix (a solenoid) bent in a ring (a toroid). The current flowing through the helix cre ates a magnetic field trapped inside the toroid. The resulting moment of such a system is oriented along the axis of revo lution of the toroid, and it is defined as a toroidal moment. If the toroid is rigid, then no magnetic field produced by external sources can act on the toroid as a whole. In the nonideal case, an electro magnetic coupling with such a toroidal moment is possible, although one can expect that this effect should be very weak and hardly measurable. Despite this, the toroidal moment was found to exist in different problems of condensed matter physics, and it was studied in many papers. [2][3][4][5] Similar to the standard multipole expansion [6] related to the electromag netic potentials and sources, the toroidal multipoles originated from the decompo sition of the moment tensor have a dual nature. [7] It means that there appears a distinction between magnetic and electric toroidal multipoles manifested in different flow paths of their polarization cur rents. In particular, a magnetic (polar) toroidal dipole is created by the polarization currents flowing on a surface of a toroid along its meridian (the poloidal direction), whereas an electric (axial) toroidal dipole appears from a ring of polarization cur rents flowing along the toroid (the toroidal direction).The study of toroidal dipole modes has attracted a growing attention due to the specific properties of the toroidal electromagnetic response which differs from more familiar electric and magnetic dipole modes. Herein, toroidal dipole modes generated by metasurfaces composed of trimer clusters of high-index dielectric particles are observed. Both far-field transmission measurements and direct near-field mapping of the electromagnetic fields are performed in microwave experiments, and two distinct types of the toroidal dipole modes are observed in a single geometry of the metasurface design, where the toroidal modes are generated either inside of the three- particle clusters (the so-called intra-cluster toroidal modes) or between the neighboring particles in the clusters (inter-cluster toroidal modes). A transient response of the toroidal dipole modes excited by a pulse is studied in detail.Since the metasurface is composed of simple dielectric disks without the use of any metallic components, the proposed design can be feasibly scalable to both micro-and nanometer-size dielectric structures, and it can be employed in the flat-optics platform for realizing the beams shaping and efficient light-matter interaction for multiple hotspot energy localization, nonlinear frequency conversion, and highly efficient trapping of light. Toroidal Dipole ModesAppearance of a toroidal moment is an intriguing phenomenon in the physics of light-matter interaction, first predicted theo retically in the middle of the last century. It was introduced in the particle physics in the study of the interaction with parity violation for elementary particles and weak electromagnetic f...

for almost two centuries, the great part of the interest in chirality is determined by peculiar chiral optical phenomena that have been reported and analyzed [3,4] many decades before a rigorous definition of the very term by Lord Kelvin. [5] Although optically observable effects of chirality of natural materials are typically weak, the convenience and precision of light-based instruments determine the persistence in their improvement and innovation. [6] As metasurfaces have become a new paradigm for flat optics enabling flexible engineering of numerous electromagnetic functionalities, chiral metasurfaces, defined as planar arrays of subwavelength elements with broken mirror symmetry, have repeatedly demonstrated unprecedentedly large characteristics of optical chirality: circular dichroism, polarization rotation, as well as asymmetric conversion of circular polarizations in transmission and reflection. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Clear applied benefits of nanoscale chiral light manipulation and drastic improvement of chiral sensing efficiency have motivated numerous attempts to realize strong artificial chirality employing various concepts. [23,24] Thus, the spatial helicoidality of circularly polarized light inspired the design of chiral metasurfaces as subwavelength arrays of helices and springs fabricated by very different techniques. [8,10,11,16] It has been speculated already by Fresnel two centuries ago [3] that one can reasonably expect helical structures to interact selectively with light waves of different helicity. In practice, however, laboriously fabricated nanohelices exhibit moderate optical chirality, and are outperformed by simpler structures designed to break the mirror symmetry in a most vivid manner. [7,9,[13][14][15]17,19] The rapid progress in chiral nanophotonics poses the fundamental question about the limits of the optical chirality, and encourages the attempts to design and realize the structures approaching such limits. The extreme values of the optical chirality characteristics have been achieved, e.g., by complexshaped silver nanohole arrays, [14,15] where strong absorption by plasmon resonances determines the extreme chirality to occur in the range of low transparency. For applications, the irreversible loss of the most part of the energy and information is hardly acceptable, and it is desirable to realize the maximum chirality, i.e., to create metasurfaces transparent to one circular polarization and interacting extremely strongly with the opposite circular polarization. This obviously implicates Metasurfaces without a mirror symmetry may exhibit chiral electromagnetic response that differs substantially from any type of polarization transformation. A typical design of chiral metasurfaces is based on a complex arrangement of meta-atoms with chiral shapes assembled into rotationally symmetric arrays. Here it is demonstrated that, in a sharp contrast to our intuition, metasurfaces that break all point symmetries can outperform their rotationally symme...