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

Abstract

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 approximate 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 similar to 50 mW input powers in silicon micrometer-scale PhC nanobeam cavities.