We theoretically study the nonlinear dynamics of silicon ring cavities with active carrier removal. In this system, linear dispersion, Kerr nonlinearity, two-photon absorption, and free-carrier dispersion / absorption play a key role in the dynamics and the steady-state behavior of the device. Placing the cavity inside a reverse-biased p-i-n junction allows one to reach a regime where both optical bistability and limit-cycle oscillations are accessible. Based on these phenomena, we propose and simulate a free-carrier based random number generator and an "Ising machine", consisting of interconnected ring cavities, which searches for the ground state of the NP-hard Ising XY problem.
In this paper, we analytically describe the parametric amplification in ring resonators using silicon and silicon nitride waveguides. Achievable gain and bandwidth of the ring-based amplifiers are studied taking into account the Kerr nonlinearity for silicon nitride and Kerr nonlinearity as well as two photon absorption and free carrier absorption for silicon waveguides. Both telecom and 2-μm wavelengths are investigated in case of silicon. An approach for obtaining the optimum amplifier design without initiating the comb generation has been introduced. It is shown that there is a trade-off between the input pump and amplifier bandwidth. It is estimated that using optimum designs an amplifier with a gain and bandwidth of 10 dB and 10 GHz could be feasible with silicon ring resonators in 2 μm.