All-Optical control of linear and nonlinear energy transfer via Zeno effect

Microresonator-based nonlinear processes are fundamental to applications including microcomb generation, parametric frequency conversion, and harmonics generation. While nonlinear processes involving either second- ($\chi^{(2)}$) or third- $\chi^{(3)}$) order nonlinearity have been extensively studied, the interaction between these two basic nonlinear processes has seldom been reported. In this letter, we demonstrate a coherent interplay between second- and third- order nonlinear processes. The parametric ($\chi^{(2)})$ coupling to a lossy ancillary mode shortens the lifetime of the target photonic mode and suppresses its density of states, preventing the photon emissions into the target photonic mode via Zeno effect. Such effect is then used to control the stimulated four-wave mixing process and realize a suppression ratio of $34.5$.