Meta-optics and bound states in the continuum

We discuss the recent advances in meta-optics and nanophotonics associated with the physics of bound states in the continuum (BICs). Such resonant states appear due to a strong coupling between leaky modes in optical guiding structures being supported by subwavelength high-index dielectric Mie-resonant nanoantennas or all-dielectric metasurfaces. First, we review briefly very recent developments in the BIC physics in application to isolated subwavelength particles. We pay a special attention to novel opportunities for nonlinear nanophotonics due to the large field enhancement inside the particle volume creating the resonant states with high-quality (high-$Q$) factors, the so-called quasi-BIC, that can be supported by the subwavelength particles. Second, we discuss novel applications of the BIC physics to all-dielectric optical metasurfaces with broken-symmetry meta-atoms when tuning to the BIC conditions allows to enhance substantially the $Q$ factor of the flat-optics dielectric structures. We also present the original results on nonlinear high-$Q$ metasurfaces and predict that the frequency conversion efficiency can be boosted dramatically by smart engineering of the asymmetry parameter of dielectric metasurfaces in the vicinity of the quasi-BIC regime.