In this paper, we present a theoretical analysis of four-wave mixing (FWM) between short optical pulses in a photonic crystal semiconductor optical amplifier (PC-SOA). The proposed model is based on a nonlinear propagation equation by taking into account self-phase modulation (SPM), carrier density pulsations (CDP), carrier heating (CH), and spectral-hole burning (SHB). To analyse the FWM in a PC-SOA, pulse evolution in a temporal and spectral domain are investigated. Also, the optical fluid method is used in the photonic structure for design and engineering an appropriate bandwidth with constant group index to analyse the FWM mechanism. The bandwidth is designed in the L-Band region of telecommunication optical networks. Based on calculated results, it is depicted that for low energy short pulses, the conversion efficiency (CE) of PC-SOA is higher than conventional SOA. Furthermore, it is shown that, by increasing the injection current the CE is increased.
