Four-Wave Mixing of Pulsed Signal in Dispersion-Shifted Fiber With Pump Depletion

The output signal and idler pulses generated by dispersion-shifted-fiber-based four-wave mixing (FWM) with pulsed signal input are analyzed. A set of analytical expressions for the amplitude and phase of the output pulses is derived. Analytical analysis shows that the generated idler pulse is far away from the phase conjugation of the input signal, and that the output signal is not an amplified replica of the input signal. These phenomena are due to both the phase distortion caused by self- and cross-phase modulation and the temporal envelope broadening resulting from pump depletion. Besides, in the frequency domain, the spectral inversion between signal/idler will be destroyed. The implications of the phase and shape distortions in all-optical signal processing by FWM are discussed. The induced phase distortions of idler pulses in dual pumps case are found to be much smaller than those of the single-pump case.