Interplay of χ$^{(2)}$ and χ$^{(3)}$ effects for microcomb generation

While frequency comb generation in passive nonlinear optical cavities has been demonstrated in purely quadratic and Kerr platforms, the interplay between χ(2) and χ(3) effects is yet to be fully understood. In this work, we propose a doubly resonant AlGaAs microring design for second-harmonic Kerr-comb generation. We compute the full dispersion profile of the guided modes to describe the resulting dynamics. The doubly resonant condition implies the use of a double envelope mean-field model, and the confined field owns spectral components around both the pump and second harmonic wavelengths. The fabrication of such devices is discussed, and preliminary experimental results are presented. Due to its record nonlinear performance, we address AlGaAs as a promising platform for the generation of such novel microcomb sources.