Efficient frequency conversion with geometric phase control in optical metasurfaces

Metasurfaces have appeared as a versatile platform for miniaturized functional nonlinear optics due to their design freedom in tailoring wavefronts. The key factor that limits its application in functional devices is the low conversion efficiency. Recently, dielectric metasurfaces governed by either high-quality factor modes (quasi-bound states in the continuum) or Mie modes, enabling strong light-matter interaction, have become a prolific route to achieve high nonlinear efficiency. Here, we demonstrate both numerically and experimentally an effective way of spatial nonlinear phase control by using the Pancharatnam-Berry phase principle with a high third harmonic conversion efficiency of $10^{-4}$ $1/W^2$. We find that the magnetic Mie resonance appears to be the main contributor to the third harmonic response, while the contribution from the quasi-bound states in the continuum is negligible. This is confirmed by a phenomenological model based on coupled anharmonic oscillators. Besides, our metasurface provides experimentally a high diffraction efficiency (80-90%) in both polarization channels. We show a functional application of our approach by experimentally reconstructing an encoded polarization-multiplexed vortex beam array with different topological charges at the third harmonic frequency with high fidelity. Our approach has the potential viability for future on-chip nonlinear signal processing and wavefront control.