A numerical model for the complex susceptibility of saturated erbium-doped amplifiers

A detailed model for the complex susceptibility behavior of erbium-doped amplifiers, which applies in the saturation regime of operation, is presented. The model takes into account the effective individual laser transitions between the upper and lower manifolds. The model is based on a curve fitting algorithm that fits the emission and absorption cross section with Voigt lineshapes, which correspond to the effects of both homogeneous and inhomogeneous line broadenings. Experimental measurements show that the model accurately predicts the susceptibility in the saturation regime. The sensitivity of the model susceptibility predictions to the Stark-split energy level data is shown to be minor, as long as the number of transition wavelengths used is high. Results show the full spectral behavior of the complex susceptibility of an integrated optical erbium-doped amplifier in the saturation regime and show that signal-induced changes in refractive index of up to around 1.6×10^-6 can be obtained with a few milliwatts of signal change by driving the amplifier into saturation