Conditions for Parametric and Free-Carrier Oscillation in Silicon Ring Cavities

We model optical parametric oscillation in ring cavities with two-photon absorption, focusing on silicon at 1.55$\mu$m. Oscillation is possible if free-carrier absorption can be mitigated; this can be achieved using carrier sweep-out in a reverse-biased p-i-n junction to reduce the carrier lifetime. By varying the pump power, detuning, and reverse-bias voltage, it is possible to generate frequency combs in cavities with both normal and anomalous dispersion at a wide range of wavelengths including 1.55$\mu$m. Furthermore, a free-carrier self-pulsing instability leads to rich dynamics when the carrier lifetime is sufficiently long.