  Nonlinear nanostructured surfaces provide a paradigm shift in nonlinear
optics with new ways to control and manipulate frequency conversion processes
at the nanoscale, also offering novel opportunities for applications in
photonics, chemistry, material science, and biosensing. Here, we develop a
general approach to employ sharp resonances in metasurfaces originated from the
physics of bound states in the continuum for both engineering and enhancing the
nonlinear response. We study experimentally the third-harmonic generation from
metasurfaces composed of symmetry-broken silicon meta-atoms and reveal that the
harmonic generation intensity depends critically on the asymmetry parameter. We
employ the concept of the critical coupling of light to the metasurface
resonances to uncover the effect of radiative and nonradiative losses on the
nonlinear conversion efficiency.
