Theoretical model of gain-saturated semiconductor optical amplifiers in cross-phase modulation wavelength converters

In order to obtain high conversion speed and strong nonlinearity, semiconductor optical amplifiers (SOAs) in wavelength converters are operated with large bias currents and high optical powers. Therefore, the SOAs are strongly gain-saturated. For modeling wavelength converters based on cross-phase modulation (XPM) in SOAs, the effect of saturation on the optical phase needs to be considered. In this paper, we report a simple formula to calculate the optical phase for XPM in SOAs. The model is used to simulate a XPM wavelength converter using a Mach-Zehnder interferometer (MZI). The theoretical results are in good agreement with published experimental data.