  The concept of optical bound states in the continuum (BICs) underpins the
existence of strongly localized waves embedded into the radiation spectrum that
can enhance the electromagnetic fields in subwavelength photonic structures.
Early studies of optical BICs in waveguides and photonic crystals uncovered
their topological properties, and the concept of quasi-BIC metasurfaces
facilitated applications of strong light-matter interactions to biosensing,
lasing, and low-order nonlinear processes. Here we employ BIC-empowered
dielectric metasurfaces to generate efficiently high optical harmonics up to
the 11th order. We optimize a BIC mode for the first few harmonics and observe
a transition between perturbative and nonperturbative nonlinear regimes. We
also suggest a general strategy for designing subwavelength structures with
strong resonances and nonperturbative nonlinearities. Our work bridges the
fields of perturbative and nonperturbative nonlinear optics on the
subwavelength scale.
