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In this paper, we analyze and improve a modern structure optical design for an ultrafast all-optical half adder. This design is based on four wave mixing (FWM) in a semiconductor optical amplifier (SOA), with polarization-shift-keying (PolSK) modulation input signals. For analyzing the amplifier we use a finite-difference method based on solution of the traveling wave equations. In this study, we have shown that the output signal power of the device increases with the length of the SOA section and current injection.