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 a 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. In contrast to the previously suggested multilayer structures with zero permittivity, we reveal strong mode coupling and Fano resonances in homogeneous 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.

Metasurfaces based on resonant subwavelength photonic structures enable novel methods of wavefront control and light focusing, underpinning a new generation of flat-optics devices. Recently emerged all-dielectric metasurfaces exhibit high-quality resonances underpinned by the physics of bound states in the continuum that drives many interesting concepts in photonics. Here we suggest an approach to explain the physics of bound photonic states embedded in the radiation continuum. We study dielectric metasurfaces composed of planar periodic arrays of Mie-resonant nanoparticles (“meta-atoms”) which support both symmetry protected and accidental bound states in the continuum, and employ the multipole decomposition approach to reveal the physical mechanism of the formation of such nonradiating states in terms of multipolar modes generated by isolated meta-atoms. Based on the symmetry of the vector spherical harmonics, we identify the conditions for the existence of bound states in the continuum originating from the symmetries of both the lattice and the unit cell. Using this formalism we predict that metasurfaces with strongly suppressed spatial dispersion can support the bound states in the continuum with the wave vectors forming a line in the reciprocal space. Our results provide a method for designing high-quality resonant photonic systems based on the physics of bound states in the continuum.

Being motivated by recent achievements in the rapidly developing fields of optical bound states in the continuum (BICs) and excitons in monolayers of transition metal dichalcogenides, we analyze strong coupling between BICs in ${\mathrm{Ta}}_2{\mathrm{O}}_5$ periodic photonic structures and excitons in ${\mathrm{WSe}}_2$ monolayers. We demonstrate that the giant radiative lifetime of a BIC allows us to engineer the exciton-polariton lifetime, enhancing it by two orders of magnitude compared to a bare exciton. We show that the maximal lifetime of a hybrid light-matter state can be achieved at any point of $\mathbf{k}$ space by shaping the geometry of the photonic structure. Our findings open a different route for the realization of moving exciton-polariton condensates with a nonresonant pump and without Bragg mirrors, which is of paramount importance for polaritonic devices.

Being a general wave phenomenon, bound states in the continuum (BICs) appear in acoustic, hydrodynamic, and photonic systems of various dimensionalities. Here, we report the first experimental observation of an accidental electromagnetic BIC in a one-dimensional periodic chain of coaxial ceramic disks. We show that the accidental BIC manifests itself as a narrow peak in the transmission spectra of the chain placed between two loop antennas. We demonstrate a linear growth of the radiative quality factor of the BICs with the number of disks that is well described with the developed tight-binding model. We estimate the number of disks when the radiation losses become negligible in comparison to material absorption and, therefore, the chain can be considered as practically infinite. The presented analysis is supported by near-field measurements of the BIC profile. The obtained results provide useful guidelines for practical implementations of structures with BICs opening up horizons for the development of radio-frequency and optical metadevices.