Unconventional high-harmonic generation in resonant membrane metasurfaces

High-harmonic generation (HHG) in solids has rapidly emerged as a promising platform for creating compact attosecond sources and probing ultrafast electron dynamics. Resonant metasurfaces provide essential features for harmonic generation, increasing its efficiency through local field enhancement and enabling to lift phase matching constraints in the process. Metasurface-enhanced HHG is believed to follow the conventional integer-power scaling laws that hold for non-resonant bulk HHG. Here, we discover that highly resonant metasurfaces driven by quasi-bound states in the continuum break this principle, manifesting non-integer intensity dependencies of the generated harmonic powers. We experimentally and theoretically show that these unconventional nonlinearities are enabled by the strong local fields arising from the high-Q resonances. The resonant local fields substantially alter the contribution of higher-order susceptibility tensors to the effective nonlinearities of the system. Our findings reveal how harmonic generation rooted in modification of effective nonlinear susceptibilities driven by resonant fields can reshape our understanding of light-matter interaction at the nanoscale.