Triply resonant coherent four-wave mixing in silicon nitride microresonators

Generation of multiple tones using four-wave mixing (FWM) has been exploited for many applications, ranging from wavelength conversion to frequency comb generation. FWM is a coherent process, meaning that its dynamics strongly depend on the relative phase among the waves involved. The coherent nature of FWM has been exploited for phase-sensitive processing in different waveguide structures, but it has never been studied in integrated microresonators. Waveguides arranged in a resonant way allow for an effective increase in the wavelength conversion efficiency (at the expense of a reduction in the operational bandwidth). In this Letter, we show that phase shaping of a three-wave pump provides an extra degree of freedom for controlling the FWM dynamics in microresonators. We present experimental results in single-mode, normal-dispersion high-Q silicon nitride resonators, and numerical calculations of systems operating in the anomalous dispersion regime. Our results indicate that the wavelength conversion efficiency and modulation instability gain in microcavities pumped by multiple waves can be significantly modified with the aid of simple lossless coherent control techniques.