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 are essential for enhancement of the otherwise small harmonic generation efficiency through local field enhancement and are essential to circumvent the need of phase matching constraints. Until now, the metasurface-enhanced HHG was 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 show experimentally and theoretically that these unconventional nonlinearities arise from the high-Q resonances that generate local fields strong enough to substantially alter the contribution of higher order susceptibility tensors to the effective nonlinearities of the system. Our findings reveal how harmonic generation rooted in resonant field-driven modification of effective nonlinear susceptibilities can reshape our understanding of light-matter interaction at the nanoscale.