Optical Kerr nonlinearity enhancement in high-index metasurfaces via Mie void lattices

Recently, research in nanophotonics has turned toward Mie resonances in voids on the surface of high-refractive-index materials. The optical Kerr effect (OKE) in high-index membrane metasurfaces with Mie void lattices is investigated using three-dimensional finite-difference time-domain (FDTD) simulations, with gallium phosphide (GaP) as a model material. The effective nonlinear refractive index is extracted for empty spherical and truncated-cone (frustum) voids in a high-index slab. Metasurfaces with isolated Mie void resonances yield only modest effective OKE enhancement, up to a factor of ten relative to bulk GaP. Mie void resonances in GaP metasurfaces are observable when the separation between voids exceeds approximately 220 nm; otherwise, modes in the high-index material between the voids prevail. A much stronger response arises from the later modes developing in the high-index regions between closely spaced voids. While the nonlinear figure of merit of Mie-void metasurfaces is limited for applications relying solely on energy-density enhancement, the open-cavity geometry offers advantages for hybrid systems that require access to the confined field, such as quantum emitters or nonlinear materials infiltrated into the voids.