Mathematical model are required to aid in design of Semiconductor Optical Amplifier (SOA) and to predict their operational characteristics. SOAs is used to amplify signals at different wavelengths need a wideband SOA model. SOA models require accurate values for parameters such as material loss and recombination coefficients need parameter extraction using model predictions and experimental results. Mathematical model for Polarization dependent gain, noise, second and third order harmonic distortion, four waves mixing are simulated. This work is useful to the researchers who are working in research and development of optical network and Fiber Optic Communication Engineering.