  Generation of even-order optical harmonics requires noncentrosymmetric
structures being conventionally observed in crystals lacking the center of
inversion. In centrosymmetric systems, even-order harmonics may arise, e.g., at
surfaces but such effects are usually very weak. Here we observe optical
harmonics up to 4-th order generated under the normal incidence from
centrosymmetric dielectric metasurfaces empowered by resonances. We design
silicon metasurfaces supporting optical quasibound states in the continuum and
guided-mode resonances, and demonstrate the enhancement of second-harmonic
signals by over three orders of magnitude compared to nonresonant thin films.
Under the optimal conditions, the brightness of the second harmonic approaches
that of the third harmonic, and the 4th-order harmonic becomes detectable.
