Two-pump fiber optical parametric amplifiers: Beyond the 6-wave model

Two-pump (2-P) fiber optical parametric amplifiers (FOPAs) are a versatile class of FOPAs which can exhibit wide and flat gain spectra in arbitrary wavelength regions, when compared with one-pump (1-P) FOPAs. The 4-wave and the 6-wave models are commonly used to simulate 2-P FOPAs by considering four and six interacting waves, respectively. Although the 6-wave model provides more accurate results than the 4-wave model, it does not take into account higher-order four-wave mixing products (HFPs) especially when the FOPA saturates. The main goal of this paper is to accurately model the 2-P FOPA in which HFPs beyond six interacting waves are included. To this end, the nonlinear Schrödinger equation (NLSE) is solved using the split-step Fourier method and the results are compared with those of previous models such as the 4-wave and 6-wave models as well as an existing analytical solution. The results, which are compared with available experimental data, show that for high input signal levels where the FOPA operates in saturation, the 6-wave model fails to provide accurate simulation results and deviates from results obtained by the NLSE. Therefore, NLSE-based modeling, which includes arbitrary interacting waves beyond the 6-wave model is important for applications in the saturation regime such as signal processing, noise suppression and regeneration.