Inverse Design of an All-Dielectric Nonlinear Polaritonic Metasurface

Nonlinear metasurfaces offer a new paradigm to realize optical nonlinear devices with new and unparalleled behavior compared to nonlinear crystals, due to the interplay between photonic resonances and materials properties. The complicated interdependency between efficiency and emission directionality of the nonlinear optical signal on the existence, localization, and lifetimes of photonic resonances, as well as on the nonlinear susceptibility, makes it extremely difficult to design optimal metasurfaces using conventional materials and geometries. Inverse design using topology optimization is a powerful design tool for photonic structures, but traditional approaches developed for linear photonics are not suitable for such high dimensional nonlinear problems. Here, we use a topology optimization approach to inverse-design a fabrication-robust nonlinear metasurface that includes quantum-engineered resonant nonlinearities in semiconductor heterostructures for efficient and directional second harmonic generation. Furthermore, we also demonstrate that under practical constraints, among all the parameters, the nonlinear modal overlap emerges as the dominant parameter that enhances conversion efficiency, a finding that contrasts with intuition-driven studies that often emphasize Purcell enhancement. Our results open new opportunities for optimizing nonlinear processes in nanophotonic structures for novel light sources, quantum information applications, and communication.