Approximate expressions for estimation of four-wave mixing efficiency in slow-light photonic crystal waveguides

摘要

We present approximate analytical expressions for the estimation of the degenerate four-wave mixing conversion efficiency in slow-light photonic crystal waveguides (PCWs). The derived formulas incorporate the different effective modal areas and the frequency-dependent linear and nonlinear parameters of the pump, signal, and idler waves. The influence of linear loss, two-photon absorption, and free-carrier generation is also accounted for. Numerical solution of the coupled propagation equations is used to verify the validity of the proposed expressions under different values of the linear and nonlinear parameters of the waveguide. It is shown that the derived expressions provide an accurate estimation of the conversion efficiency and are thus expected to be useful in the design of PCWs for nonlinear signal-processing applications.