A simple method has been proposed to use four-wave mixing to design and simulate the all-optical AND logic gate in a photonic crystal semiconductor optical amplifier (PC-SOA) that is integrated with an ideal optical bandpass filter. The preferred logical function could be carried out in the proposed scheme with no use of a continuous-wave signal. Nonlinearities including carrier depletion, carrier heating, and spectral hole burning have been considered in the presented simulations. Furthermore, for improvement of the AND logic gate performance, the impacts of the pattern effect of the signals propagating in the PC-SOA medium, the input signal bit rate effects, and gain recovery have been extensively investigated. The findings demonstrated that the optimal output signal featuring 3-fJ energy and 2-mA injection current could be achieved at a bit rate of 50 Gbps.