A novel scheme for carrying out all-optical intensity differentiation is proposed and demonstrated based on the cross-gain modulation (XGM) in a semiconductor optical amplifier (SOA). Because of the XGM, the mathematical definition of differentiation can be expressed by the combined power of the amplified pump pulse and the delayed modulated probe pulse at the output of the SOA. The final waveform and error evolution versus relative time delay between two pulses is investigated. Interestingly enough, it is shown that the acquisition of good differentiation is possible under zero time delay. A further study of zero time delay has been performed for various data rates and shows that the carrier recovery time of the SOA is a speed-limiting factor of the scheme.
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