Topology optimization in nonlinear nanophotonics: from frequency conversion to exceptional points

We apply a large-scale inverse design strategy based on topology optimization (TO) toward the automatic discovery of complex nanophotonic structures-new kinds of micropillars, photonic-cyrstal slabs, and waveguides comprising complicated arrangements of subwavelength dielectrics-exhibiting unusual nonlinear and spectral properties. The structures support multiple, tightly confined resonances at far-away wavelengths and exhibit the largest nonlinear confinement factors predicted thus far (oders of magnitude larger than state-of-the-art ring resonators or PhC cavities), leading to highly efficient nonlinear frequency conversion (NFC). The same TO approach can be exploited to design PhCs supporting dual-polarization, dual-wavelength, or highly degenerate Dirac cones, with implications to zero-index metamaterials, topological photonics, and exceptional points (EP).