Optical spectra of signals at the output of semiconductor optical amplifiers (SOA) provide useful insight into amplifier nonlinearities. In this work, we determine the parameters of an analytical SOA model with a pump-probe experiment by evaluating the measured spectra of the pump and probe pulses at the SOA output. The analytical lumped SOA model considers carrier depletion, carrier recovery, spectral hole burning, two-photon absorption, and we include an additional effect termed ‘two-photon induced free-carrier absorption’, that is responsible for creating an identifiable blue-shifted component in the spectra. We are able to relate the underlying physical nonlinear effects to the spectral peculiarities of the output pump and probe spectra, and give guidelines for the exploitation of these nonlinear effects for optical signal processing. In addition, with a much-simplified SOA model and by replacing the pump pulse with modulated data we show that the output spectrum is altered in a manner consistent with phase patterning effects.