Nonlinear Wavefront Control by Geometric-Phase Dielectric Metasurfaces: Influence of Mode Field and Rotational Symmetry

Nonlinear Pancharatnam-Berry phase metasurfaces facilitate the nontrivial phase modulation for frequency conversion processes by leveraging photon-spin dependent nonlinear geometric-phases. However, plasmonic metasurfaces show some severe limitation for nonlinear frequency conversion due to the intrinsic high ohmic loss and low damage threshold of plasmonic nanostructures. Here, the nonlinear geometric-phases associated with the third-harmonic generation process occurring in all-dielectric metasurfaces is studied systematically, which are composed of silicon nanofins with different in-plane rotational symmetries. It is found that the wave coupling among different field components of the resonant fundamental field gives rise to the appearance of different nonlinear geometric-phases of the generated third-harmonic signals. The experimental observations of the nonlinear beam steering and nonlinear holography realized in this work by all-dielectric geometric-phase metasurfaces are well explained with the developed theory. This work offers a new physical picture to understand the nonlinear optical process occurring at nanoscale dielectric resonators and will help in the design of nonlinear metasurfaces with tailored phase properties.