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

Using a combination of temporal coupled-mode theory and nonlinear finite-difference time-domain (FDTD) simulations, we study the nonlinear dynamics of all-resonant four-wave mixing processes and demonstrate the possibility of achieving high-efficiency limit cycles and steady states that lead to ≈100% depletion of the incident light at low input (critical) powers. Our analysis extends previous predictions to capture important effects associated with losses, self- and cross-phase modulation, and imperfect frequency matching (detuning) of the cavity frequencies. We find that maximum steady-state conversion is hypersensitive to frequency mismatch, resulting in high-efficiency limit cycles that arise from the presence of a homoclinic bifurcation in the solution phase space, but that a judicious choice of incident frequencies and input powers, in conjuction with self-phase and cross-phase modulation, can restore high-efficiency steady-state conversion even for large frequency mismatch. Assuming operation in the telecom range, we predict close to perfect quantum efficiencies at reasonably low ∼50mW input powers in silicon micrometer-scale PhC nanobeam cavities.