A theoretical model for analyzing the combined effects of amplified
spontaneous emission (ASE) and intraband process on the propagation of
pulses through SOA is presented. An analysis for the differential
equations and the related parameters that describe the self phase
modulation SPM in SOA is presented. Moreover, the effects of these
variations on the pulse shape and spectrum is explained. A method for
driving the coupled propagation equations of the FWM process in SOA (for
the case of the pump-probe configuration) is proposed, which can be
extended to find the propagation equations of any number of signals. SOA
is divided theoretically into many segments in longitudinal z direction,
so that the pump power change in each segment can be considered very
small, this leads to solving the coupled propagation equations
analytically.