  Resonant photonic nanostructures exhibiting enhanced nonlinear responses and
efficient frequency conversion are an emergent platform in nonlinear optics.
High-index semiconductor metasurfaces with rapidly tuned high-Q resonances
enable a novel class of time-variant metasurfaces, which expands the toolbox of
color management at the nanoscale. Here, we report on the dynamic control of
the nonlinear optical response in time-variant semiconductor metasurfaces
supporting high-quality factor resonances in the near-infrared spectral range.
Pump-probe measurements of germanium metasurfaces at negative pump-probe time
delays reveals frequency conversion in the fundamental beam and a blue-shift of
10~nm (3.05$\omega$) and 40% broadening in the third harmonic signal due to the
photoinduced time-variant refractive index. A time-dependent coupled-mode
theory, in excellent agreement with the experimental data, validated the
time-variant nature of the system. Our findings expand the scope of
time-variant metasurfaces and may serve as base for the next generation of
nanoscale pulse shapers, optical switches and light sources.
