Nonlinear dielectric geometric-phase metasurface with simultaneous structure and lattice symmetry design

In this work, we utilize thin dielectric meta-atoms placed on a silver substrate to efficiently enhance and manipulate the third harmonic generation. We theoretically and experimentally reveal that when the structural symmetry of the meta-atom is incompatible with the lattice symmetry of an array, some generalized nonlinear geometric phases appear, which offers new possibilities for harmonic generation control beyond the accessible symmetries governed by the selection rule. The underlying mechanism is attributed to the modified rotation of the effective principal axis of a dense meta-atom array, where the strong coupling among the units gives rise to a generalized linear geometric phase modulation on the pump light. Therefore, nonlinear geometric phases carried by the third-harmonic emissions are the natural result of the wave-mixing process among the modes excited at the fundamental frequency. This mechanism further points out a new strategy to predict the nonlinear geometric phases delivered by the nanostructures according to their linear responses. Our design is simple and efficient, and offers alternatives for the nonlinear meta-devices that are capable of flexible photon generation and manipulation.