  We demonstrate phase-matched second-harmonic generation (SHG) from
three-dimensional metamaterials consisting of stacked metasurfaces. To achieve
phase matching, we utilize a novel mechanism based on phase engineering of the
metasurfaces at the interacting wavelengths, facilitating phase-matched SHG in
the unconventional backward direction. By stacking up to five metasurfaces, we
obtain the expected factor of 25 enhancement in SHG efficiency. Our results
motivate further investigations to achieve higher conversion efficiencies also
with more complex wavefronts.
