Nonlinear Pancharatnam−Berry Phase Metasurfaces beyond the Dipole Approximation

Nanoscale optical antennas mediate frequency mixing processes via their optical modes. Within arrays, metasurfaces provide unique opportunities to control nonlinear processes. Macroscopic interpretations have so far prevailed, relying on arguments of underlying antenna symmetry. In this article, we show where such interpretations break down. We construct nonlinear gradient metasurfaces to produce diffraction orders of both second-harmonic and four-wave-mixing radiation. However, we find that higher order modes are required to explain the presence of diffraction orders not predicted by the generalized law of nonlinear refraction. A simple adaptation of the law to include higher order modes extends the interpretation of geometric phase nonlinear metasurfaces to include complex composite antennas and explains the observation of apparently symmetry disallowed nonlinear processes.