High-efficiency degenerate four wave-mixing in triply resonant nanobeam cavities

We demonstrate high-efficiency, degenerate four-wave mixing in triply resonant Kerr ${\chi }^{(}3)$ photonic crystal (PhC) nanobeam cavities. Using a combination of temporal coupled mode theory and nonlinear finite-difference time-domain (FDTD) simulations, we study the nonlinear dynamics of resonant four-wave mixing processes and demonstrate the possibility of observing high-efficiency limit cycles and steady-state conversion corresponding to $\approx 100$% depletion of the pump light at low powers, even including effects due to losses, self- and cross-phase modulation, and imperfect frequency matching. Assuming operation in the telecom range, we predict close to perfect quantum efficiencies at reasonably low $\sim$ 50 mW input powers in silicon micrometer-scale cavities.