Modified model for four-wave mixing-based wavelength conversion in silicon micro-ring resonators

A modified model for wavelength conversion based on the four-wave mixing (FWM) in a silicon micro-ring resonator is presented. Unlike previous contributions, the nonlinear phase shifts caused by self-phase modulation and cross-phase modulation are also taken into account in the present theoretical analysis besides the linear propagation loss and the nonlinear losses caused by two-photon absorption and free-carrier absorption. Analysis shows that the nonlinear phase shifts will cause different red shifts for the pump and signal (or converted) resonant wavelengths, and consequently an additional wavelength difference between the signal transmission dip and the efficiency peak, which will increase/decrease the conversion efficiency of the signal channel far from/near the pump. The conversion efficiency and the conversion peak width of each signal channel are both affected by the micro-ring radius and coupling coefficient. A broader conversion peak width can be obtained by using a micro-ring resonator with a smaller Q factor.