High-efficiency cascaded up and down conversion in nonlinear Kerr cavities.

In this work, we derive general conditions to achieve high efficiency cascaded third harmonic generation and three photon parametric down conversion in Kerr nonlinear resonant cavities. We employ the general yet rapid temporal coupled-mode method, previously shown to accurately predict electromagnetic conversion processes in the time domain. In our study, we find that high-efficiency cascaded third harmonic generation can be achieved in a triply resonant cavity. In contrast, high-efficiency cascaded three-photon parametric down conversion cannot be achieved directly in a triply resonant cavity, although a combination of two doubly resonant cavities and three waveguides is an effective alternative. The stabilities of the calculated steady-state solutions for both processes are revealed by applying Jacobian matrices. Finally, we find that the inclusion of self- and cross- phase modulation introduces multi-stable solutions. Further study is required to find a simple way to reliably achieve stable conversion at the highest possible efficiency.