We reveal that metasurfaces created by seemingly different lattices of (dielectric or metallic) meta-atoms with broken in-plane symmetry can support sharp high-Q resonances that originate from the physics of bound states in the continuum. We prove rigorously a direct link between the bound states in the continuum and the Fano resonances, and develop a general theory of such metasurfaces, suggesting the way for smart engineering of resonances for many applications in nanophotonics and meta-optics.Metasurfaces have attracted a lot of attention in the recent years due to novel ways for wavefront control, advanced light focusing, and ultra-thin optical elements [1]. Recently, metasurfaces based on high-index resonant dielectric materials [2] have emerged as essential building blocks for various functional meta-optics devices [3] due to their low intrinsic loss, with unique capabilities for controlling the propagation and localization of light. A key concept underlying the specific functionalities of many metasurfaces is the use of constituent elements with spatially varying optical properties and optical response characterized by high quality factors (Q factors) of the resonances.Many interesting phenomena have been shown for metasurfaces composed of arrays of meta-atoms with broken inplane inversion symmetry (see Fig. 1), which all demonstrate the excitation of high-Q resonances for the normal incidence of light. The examples are the demonstration of imagingbased molecular barcoding with pixelated dielectric metasurfaces [4] and manifestation of polarization-induced chirality in metamaterials [5], which both are composed of asymmetric pairs of tilted bars [see Fig. 1(a)], observation of trapped modes in arrays of dielectric nanodisks with asymmetric holes [6] [see Fig. 1(b)], sharp trapped-mode resonances in plasmonic and dielectric split-ring structures [7,8] [see, e.g., Fig. 1(c)], broken-symmetry Fano metasurfaces for enhanced nonlinear effects [9, 10] [see Fig. 1(d)], tunable high-Q Fano resonances in plasmonic metasurfaces [11] [see Fig. 1(e)], trapped light and metamaterial-induced transparency in arrays of square split-ring resonators [12,13] presented in Fig. 1(f). Here, we demonstrate that all such seemingly different structures can be unified by a general concept of bound states in the continuum, and we prove rigorously their link to the Fano resonances.Bound states in the continuum (BICs) originated from quantum mechanics as a curiosity [14], but later they were rediscovered as an important physical concept of destructive interference [15] being then extended to other fields of wave physics, including acoustics [16] and optics [17,18]. A true BIC is a mathematical object with an infinite Q factor and vanishing resonance width, it can exist only in ideal lossless infinite structures or for extreme values of parameters [19][20][21]. In practice, BIC can be realized as a quasi-BIC in the form of a supercavity mode [22] when both Q factor and resonance width become finite at the BIC conditions due to ab-d c a...

Subwavelength optical resonators made of high-index dielectric materials provide efficient ways to manipulate light at the nanoscale through mode interferences and enhancement of both electric and magnetic fields. Such Mie-resonant dielectric structures have low absorption, and their functionalities are limited predominantly by radiative losses. We implement a new physical mechanism for suppressing radiative losses of individual nanoscale resonators to engineer special modes with high quality factors: optical bound states in the continuum (BICs). We demonstrate that an individual subwavelength dielectric resonator hosting a BIC mode can boost nonlinear effects increasing second-harmonic generation efficiency. Our work suggests a route to use subwavelength high-index dielectric resonators for a strong enhancement of light–matter interactions with applications to nonlinear optics, nanoscale lasers, quantum photonics, and sensors.

Recent progress in nanoscale optical physics is associated with the development of a new branch of nanophotonics exploring strong Mie resonances in dielectric nanoparticles with high refractive index. The high-index resonant dielectric nanostructures form building blocks for novel photonic metadevices with low losses and advanced functionalities. However, unlike extensively studied cavities in photonic crystals, such dielectric resonators demonstrate low quality factors (Q-factors). Here, we uncover a novel mechanism for achieving giant Q-factors of subwavelength nanoscale resonators by realizing the regime of bound states in the continuum. We reveal strong mode coupling and Fano resonances in high-index dielectric finite-length nanorods resulting in high-Q factors at the nanoscale. Thus, high-index dielectric resonators represent the simplest example of nanophotonic supercavities, expanding substantially the range of applications of all-dielectric resonant nanophotonics and meta-optics.Trapping of light in localized modes is extremely important for various applications in optics and photonics including lasing [1], sensing [2,3], harmonic generation [4,5], Raman scattering [6], and photovoltaics [7,8]. For many optical devices, it becomes critical to localize electromagnetic fields in small subwavelength volumes. Plasmonic structures based on metals allow subwavelength localization of light by means of surface plasmon polaritons [9]. However, metals impose inevitable losses and heating, which limit the device performance and efficiency. In contrast, dielectric nanoparticles with high refractive index offer a novel way for the subwavelength localization of light by employing the Mie resonances being limited only by the radiation damping [10]. Unlike metallic nanoscale structures, dielectric nanoparticles support both electric and magnetic Mie modes that expand substantially the applications of meta-optics [11]. Also, dielectric materials with high refractive index are available in a broad spectral range. At the same time, the standard Mie theory predicts relatively low values of the quality factor (Q ≈ 10) for nanoparticles made of conventional optical materials such as Si, Ge, and AlGaAs, both in the visible and near-infrared spectral ranges.However, for many applications of all-dielectric nanophotonics it is very desirable to achieve higher values of the Q factor. One way to enhance the Q factor is to increase the size of the resonator, for example by confining waves by cavities and defects in photonic crystals [12] or by exploiting modes with high angular momentum known as whispering gallery modes (WGM) [13]. Another way is to arrange several resonators in space and excite collective modes [14,15]. An alternative approach for enhancing the Q factors is to use the so-called anapole mode with the spectrally overlapped electric and toroidal dipole modes [16,17]. As a result, the Q factor of the anapole mode realized in a dielectric resonator may exceed 30 [18]. Here we suggest a novel approach based on bound stat...

Nonradiating sources of energy have traditionally been studied in quantum mechanics and astrophysics, while receiving a very little attention in the photonics community. This situation has changed recently due to a number of pioneering theoretical studies and remarkable experimental demonstrations of the exotic states of light in dielectric resonant photonic structures and metasurfaces, with the possibility to localize efficiently the electromagnetic fields of high intensities within small volumes of matter. These recent advances underpin novel concepts in nanophotonics, and provide a promising pathway to overcome the problem of losses usually associated with metals and plasmonic materials for the efficient control of the light-matter interaction at the nanoscale. This review paper provides the general background and several snapshots of the recent results in this young yet prominent research field, focusing on two types of nonradiating states of light that both have been recently at the center of many studies in all-dielectric resonant meta-optics and metasurfaces: optical anapoles and photonic bound states in the continuum. We discuss a brief history of these states in optics, their underlying physics and manifestations, and also emphasize their differences and similarities. We also review some applications of such novel photonic states in both linear and nonlinear optics for the nanoscale field enhancement, a design of novel dielectric structures with high-resonances, nonlinear wave mixing and enhanced harmonic generation, as well as advanced concepts for lasing and optical neural networks. arXiv:1903.04756v1 [physics.optics]