  High quality factor optical nanostructures provide great opportunity to
enhance nonlinear optical processes such as third harmonic generation. However,
the field enhancement in these high quality factor structures is typically
accompanied by optical mode nonlocality. As a result, the enhancement of
nonlinear processes comes at the cost of their local control as needed for
nonlinear wavefront shaping, imaging and holography. Here we show simultaneous
strong enhancement and spatial control over third harmonic generation with a
local high-Q metasurface relying on higher-order Mie-resonant modes. Our
results demonstrate third harmonic generation at an efficiency of up to
$3.25\times10^{-5}$, high quality wavefront shaping as illustrated by a third
harmonic metalens, and a flatband, angle independent, third harmonic response
up to $\pm11^{\circ}$ incident angle. The demonstrated high level of local
control and efficient frequency conversion offer promising prospects for
realizing novel nonlinear optical devices.
