The geometric phase in nonlinear frequency conversion

Abstract The geometric phase of light has been demonstrated in various platforms the linear optical regime, raising interest both for fundamental science as well applications, such flat elements. Recently, concept phases extended to nonlinear optics, following advances engineering bulk photonic crystals and metasurfaces. These new technologies offer a great promise applications manipulation light. In this review, we cover recent theoretical experimental field accompanying frequency conversion. We first consider case crystals, which interaction between propagating waves is quasi-phase-matched, with an engineerable accumulated by Nonlinear can efficient robust conversion linearized fully-nonlinear regimes interaction, allow several including adiabatic mode conversion, electromagnetic nonreciprocity novel topological effects then rapidly-growing Pancharatnam-Berry metasurfaces, simultaneous generation shaping using ultrathin elements subwavelength amplitude resolution. discuss macroscopic selection rules that depend on rotational symmetry constituent meta-atoms, order harmonic generations, change circular polarization. Continuous gradients steering beams their spatial modes. More complex designs perform imaging multiplex holograms, where functionality varied according generated Recent advancements fabrication three dimensional pursuit quantum sources based exciting possibilities phases.