Backward phase-matched second-harmonic generation from stacked metasurfaces

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.