Traveling-wave equation of the semiconductor optical amplifier is solved analytically in order to study the dynamical properties of the power output in terms of the input parameters that can influence its operation of semiconductor optical amplifier. Power output (number of photons) was calculated as a function of carrier density, input signal, and bias current. Material gain is found for the amplifier at different wavelengths of the input signal. The model investigated the population inversion along the waveguide of the amplifier. The model, which is used in this article, is one of many mathematical models that can be found in literature . The design of semiconductor amplifier in order to predict the operational characteristics can be obtained from its model. The simplicity of our model is in its ability to incorporate with any external stimulus on the amplifier directly in the wave equation.
Keywords: SOA, Traveling-wave equation , Numerical simulations.